Jo Boaler is (Half) Wrong — The Many Myths in Mathematical Mindsets

I recently finished reading Mathematical Mindsets by Jo Boaler, a professor of mathematics education at Stanford University (although she incorrectly represents herself as a “mathematics professor” on p. 38) I had previously read  only bits and pieces of Boaler’s work, until this book — which has been widely adopted by local school districts, and has become mandatory reading — showed up in my school mailbox over the summer.

I have to say that I find it somewhat troubling, the degree to which Boaler and her book/philosophies have been widely and almost universally accepted at face value around here. It’s not that I 100% disagree with Boaler, nor some of the activities and methodologies she claims are beneficial. Unlike the claims made by Boaler, it is not so black-and-white — there are some things of value in this book, and in some of the insights and potential learning activities that Boaler shares with us.

However, what I find troubling is:

(a) that there is an “all-or-nothing” approach (once again) to education, rather than recognizing that education is a delicate balancing act, and that any one-sided approach (such as the group-based-inquiry one espoused by Boaler) is not going to be highly effective, especially not when you consider that students and their learning styles are diverse;

(b) people are blindly accepting the claims and purported benefits at face value, without any sort of further research or critical analysis which reveals that there are actually numerous fallacies in the claims and conclusions Boaler makes, and that some of what she recommends is actually not only ineffective, but would actually be detrimental to students and their future prospects.

Indeed, it’s not so much that I disagree with Boaler’s statements; it’s that science and reality do not agree with many of Boaler’s claims. Problems include: misleading data manipulation; cherry-picked and insufficient research, much of which is actually antithetical to what the overall corpus of research has shown; and evident personal biases, in relation to personal/emotional anecdotes, as well as unsubstantiated opinions about what types/styles of math are “important” or “real.” As such, this book reads more like proselytizing instead of pedagogy; the conclusions made are more sales pitch than sound science.

Let me elaborate, fact-check style:

Many Problems & Falsehoods

Misleading Data Visualization

In numerous instances, Dr. Boaler uses figures known as “truncated bar graphs” in which the Y-axis has been truncated; ie. the scale does not start at zero. This is a textbook example of “misleading graphs” and, in fact, the curriculum I used last year specifically taught 6th grade students that such graphs are a misrepresentation of data generally intended not to enlighten but to obfuscate the facts. It must be noted that there are some occasions in which truncation is acceptable; this, however, is not one of them — these graphs would fall under the category of “how to lie with data visualization.” In fact, if these graphs were used in advertising, they would be labeled false advertising and would face consequences by the National Advertising Division of the Better Business Bureau. If misleading graphs are not allowed in advertising, then they certainly should not be allowed in the realm of research and academia, in books or reports that could have widespread consequences in education policy.

One of several misleading graphs in Mathematical Mindsets

Here, Dr. Boaler… I fixed it for you

NOTE: I generally agree with the statements Boaler makes with these graphs, that “fixed mindset” is highly detrimental, and that conceptualization is a more important skill/process for math than memorization is… but I don’t approve of misrepresenting data in order to try to prove these points. Surprisingly, the data above (when represented truthfully) actually tells a different narrative: “Memorization is almost as effective as understanding Big Ideas & Connections.”  What the data actually convinces me of is that memorization does have some value. Thus — as I stated earlier — a hybrid approach or partial adoption of conceptual activities like the ones in Mathematical Mindsets would be better than an all-out replacement of the “traditional” methods. Perhaps what needs to be memorized are not discreet “facts,” as Boaler claims math teachers try to enforce, but rather memorization of strategies, which is actually what most math curricula — even old-school ones — actually teach.)

Personal Anecdotes & confirmation bias

As passionate as I am about math, the English teacher in me continually cries “cite source?” as I read Mathematical Mindsets.

There is a surprising dearth of actual research being cited in this book (aside from the 22 references to Boaler’s own work.) Perhaps this is because many of the claims (aka personal beliefs/opinions) being made by Boaler simply aren’t supported by the research — in fact, many of them are antithetical to what the research actually shows! Perhaps that is why there is a high amount of unsupported opinions, assumptions, personal anecdotes, and “references” to things like blog posts (which are filled with even more anecdotes and opinions, rather than any sort of data or scientific research) in lieu of research studies.

There are at least 18 occurrences of Boaler sharing instances from her daughter and the ways her school/district were doing things “wrong.” Examples: “My own daughter was given very damaging  messages by teachers…” (p. 17); “When my own daughter started times table memorization and testing at age five, she started to come home and cry about math. This is not the emotion we want students to associate with mathematics…” (p. 38)

These types of stories are a persuasive tactic called an “emotional appeal.” It is an effective technique to try to convince people to agree with you — for example, the reader may commiserate: “Wow! I, too, have a child who doesn’t like homework! So it must be bad!”  What this really represents is a form of confirmation bias, and as such these anecdotes are not convincing in a scientific or research-based context.

False & Unsupported Claims

Claim: “Over the years, school mathematics has become more and more disconnected from the mathematics that mathematicians use and the mathematics of life. Students spend thousands of hours in classrooms learning sets of procedures and rules that they will never use, in their lives or in their work.” (p. 27)


Before addressing specific the specific minutiae and incorrect claims made in Mathematical Mindsets, we must first examine Boaler’s personal bias about what math actually is.  According to Boaler, schools do not teach “real mathematics” — yet never defines what “real mathematics” is. She states that “mathematics, real mathematics, is a subject full of uncertainty; it is about explorations, conjectures, and interpretations, not definitive answers.” (p. 21) Yet there are many, many professions in which we use math to solve problems and there are, in fact, “correct solutions” to those problems: carpenters need accurately-cut lengths of wood; bakers and chefs need precise proportion and scale of ingredients; mechanical engineers need precise gear ratios; etc.

“At its core, mathematics is about patterns. We can lay a mathematical lens upon the world, and when we do, we see patterns everywhere; and it is through our understanding of the patterns, developed through mathematical study, that new and powerful knowledge is created.” (p. 21)

True. The way I have explained it to people is this: “Language is the words we use to describe humankind; math is the language we use to describe the universe.”

However, we could also say “at its core, language is about symbols.” But, just because words are symbolic, doesn’t mean that’s the end goal… we don’t want to have students just identify symbols (or patterns)… we want them use them for some sort of practical purpose. The reductive definition of mathematics that Boaler uses defeats the entire purpose of why math was invented in the first place: math, like language, was invented to solve pragmatic problems. Math was never intended to be a form of navel-gazing or dreamy philosophy, as portrayed by Boaler; the earliest civilizations developed number systems, weights and measures, etc. to record transactions, make commerce more accurate and efficient, predict the weather and other agricultural phenomena, and myriad other practical purposes. In other words, I would argue that “real mathematics” has to do with solving problems in the real world. This is quite the opposite of what Boaler thinks is “real math.” What Boaler calls “real mathematics” is actually known as theoretical mathematics.

Thus, there is a serious disconnect between what is happening in schools and what Boaler thinks should happen in schools. Students learn sets of rules and procedures that they will use — when shopping, cooking, or in countless professions. Boaler talks a lot about “mathematicians,” but my goal as a teacher is not necessarily to create “mathematicians” like the names she mentions. My goal is to prepare students for the real world, including the applied math that goes into a whole variety of jobs, and required for everyday life.

According to the Bureau of Labor Statistics, there are only 3,500 mathematicians in the United States. Compare this to the number of occupations that require use of math skills — often including getting correct answers, and usually within a specific time limit: 24,500 actuaries; 30,000 statisticians; 72,400 aerospace engineers; 98,400 chemists; 316,000 electrical engineers; 328,600 computer programmers; and over 1 million other jobs that require constant calculations (which Boaler would argue could just as well be done with a calculator, but tell that to a baker with flour and dough all over his hands, or a carpenter already carrying various tools, and needing to perform cuts and measurements all day long.)

“(1) Joe can do a job in 6 hours and Charlie can do the same job in 5 hours. What part of the job can they finish by working together for 2 hours? (2) A restaurant charges $2.50 for 1/8 of a quiche. How much does a whole quiche cost? These questions all come from published textbooks and are typical of the questions students work with in math class. But they are all nonsensical. Everyone knows that people work at a different rate together than when alone, restaurants charge a different proportional price for food that is sold in bulk…” (p. 192)  [No, not “everyone” knows these things, and they are not even necessarily true. Cite source?]

Yes, math is important, but “real mathematics” is not just about creativity and beauty and patterns and making new discoveries. It’s about solving problems.


Claim: “research has consistently found homework to either negatively affect or not affect achievement” (p. 107)

Rating: FALSE

When it comes to talking about homework, Boaler is surprisingly regressive; for someone that preaches “innovation” and “reform” and “progress”, there is an overwhelming focus on “old-school” homework — worksheets, isolated lists of practice problems, etc. — without even acknowledging that newer forms of homework and tools that have been around for decades now (such as the personal computer) render those problems obsolete.

Once again, Boaler resorts to personal anecdotes / emotional appeals (“As a parent, I know that homework is the most common source of tears in our house, and the subject that is most stressful at home is math” p. 46), as well as citing a couple other sources… so let’s take a look at those scant few sources of “support” for Boaler’s clearly biased belief:

1) Boaler cites Alfie Kohn’s blog. For those of you who don’t know, Kohn has made a career out of being a sensationalist contrarian — an educational demagogue, if you will, who preys upon the things people “don’t like” (like testing and homework) and then constructs a false narrative to appease their confirmation bias. In other words, he tells people what they want to hear, without actually backing those claims up with facts and empirical evidence.

“Is it really possible to completely eliminate homework – or at least to assign it rarely, only when it’s truly needed – even in high school? We keep hearing from educators who say it’s not only possible but preferable to do so” the website boasts. And yet… despite all of the anecdotes, there is zero actual data or evidence on this blog page to say how it actually affected student learning, such as  would be measured by assessments. (oh, but Kohn doesn’t believe in the use of any sort of measuring tools… he thinks high test scores are actually bad: “This assessment is borne out by research finding a statistical association between high scores on standardized tests and relatively shallow thinking.” and that “Measurable outcomes may be the least significant results of learning.” How convenient!  How can you prove anything scientifically or make any sort of conclusions or data-driven decisions without measurement tools of some sort?)

Educators and policy-makers should run, not walk, from anything Alfie Kohn has to say. It is populist — yet almost entirely unscientific — garbage.

2) Boaler cites a white paper by “Challenge Success” (how convenient… yet another Stanford affiliation!), a group whose bias is evident up-front: “At Challenge Success, we believe that our society has become too focused on grades, test scores and performance.”

Ironically, though, despite the spin that they try to put on body of research, even their own white paper admits the same thing that I highlighted in my previous post, “The Million-Dollar Question: Is Homework Worth It?“:

“Harris Cooper (1989, 2001, & 2007) has reviewed hundreds of homework studies and is often thought to be the leading researcher on homework…there is almost no correlation for students in elementary school between the amount of time spent on homework and student achievement. In middle school, there is a moderate correlation, but, after 60-90 minutes spent on homework, this
association fades. The authors found a correlation in high school, but this also fades after two hours spent on homework.” (pp. 3-4)

This is quite different than Boaler’s assertion — what should actually be said is that there may be little to no academic effect in elementary school, but that large studies have shown moderate to significant correlation between homework and academic achievement in middle school and high school.  Yes, there is such a thing as “too much” homework, but the evidence is clear: zero practice (homework) — which is what Boaler promotes — would be detrimental to students’ academic success.  To state that “research has consistently found” that homework is negative or neutral is, quite frankly, wrong.

Here’s another interesting finding from Boaler’s own cited source (Challenge Success) which contradicts Boaler’s message that, if homework is given, it should not be graded: “In one study of low income ninth and tenth graders, the authors found that when students were given homework but had few consequences for not completing it, students showed an increase in disengagement from school. (Bempechat et al., 2011).” This research actually shows the negative results of Boaler’s stance of not grading homework (if it “has to be” given.)

My own experiences in the classroom have shown homework to be very valuable, when it was meaningful, relevant, given value, and enforced. My homeroom students who completed the assigned homework last year did well when tested; those who did not do homework suffered academically, as shown by the assessments. Note: Yes,  I did grade the homework (but only at 10% weight of grade; this assigns the homework “value” as Bempechat et al. study suggests, but allows overall grades to be based on more relevant assessments.)

Correlation between homework and mean test scores for my students last year

Claim: “teachers should abandon testing and grading” (p. 17)

Rating: FALSE

Boaler’s reasoning behind doing away with both tests and grading basically boils down to one thing: they induce stress or anxiety. Boaler makes references to “stress” 16 times in this book, and “anxiety” 18 times. The underlying premise for most of her recommendations — that homework, tests, and grading should be eliminated — could be summarized as this: These things are stressful, and stress impairs learning and induces negative associations, so we should eliminate all of the sources of stress.

I think most people could agree that stress and anxiety are no fun. Raise your hand if you like stress. I sure don’t. But that doesn’t mean (a) that it is beneficial to entirely eliminate these scenarios; nor (b) that the situations described by Boaler have to be “stressful” or “anxiety-inducing”.

“When students are stressed, such as when they are taking math questions under time pressure, the working memory becomes blocked, and students cannot access math facts they know (Beilock, 2011).” (p. 38) This is true — it has been found that stress impairs cognitive functioning. The part that is unsupported, however, is the claim that timed tests are automatically stressful. (Whom does Boaler cite to support this claim? Herself.)

Likewise, Boaler claims “Grading reduces the achievement of students.” (p. 142), citing a few studies relating grading vs. formative feedback and the effect on motivation and performance. Most of these studies are from the 1980s, two of them being seminal works by Ruth Butler, as well as a more recent one by Pulfrey, Buchs, and Butera (2011.) That study replicated findings of Butler’s 1988 study, which essentially says this: “being graded can cause anxiety.”  Yes, it has been shown that the mere awareness that you are being evaluated can cause stress or anxiety. And, as noted above, anxiety causes decreased cognitive performance, so it is not a surprise that — especially if they receive low marks — students become demotivated and that graded assessment would thus impair learning. (Boaler doesn’t mention that the findings actually showed that, if students scored high marks, it had a motivational and positive effect on further learning and perseverance.)

However, to propose complete elimination of an assessment or evaluation system is unrealistic, and — even if such a paradigm shift were to be made in public schools — students would find themselves ill-prepared to face the realities beyond the classroom. The fact of the matter is that students will be evaluated, rated, and ranked in life. It is inevitable, and I would argue that performance evaluations and ranking systems are actually necessary in society, to ensure that we have the “best person for the job” in many different situations. Whether it is at a job interview, obtaining a driver’s license, passing a bar exam, or a performance evaluation at work… they will be evaluated and, in most cases, rated (not just given feedback), even if it is as simple as “pass/fail” or “hired/not hired.” So, the premise that we can simply “do away with” grades or evaluation is an unrealistic one, and to do so in schools would be damaging, as it would not prepare students for the realities outside of the classroom.

It is ironic that Carol Dweck (author of Mindset: The New Psychology of Success) wrote the foreword to Boaler’s book, because Boaler completely exhibits a fixed mindsetnot a growth mindset when she claims that we should simply avoid doing anything that could induce stress or anxiety. In a fixed mindset, you avoid challenging situations because they might lead to difficulty — and this is exactly what Boaler proposes we should do!

Tests have actually been found to be a powerful learning tool. At a “Learning and the Brain” conference in San Francisco a few years ago, I watched Dr. Robert Bjork present his findings on learning and memory gleaned through many years of research as a cognitive psychologist at UCLA. A few important elements from the cognitive science research refute Boaler’s claim that (a) tests should be eliminated, and (b) that anything stressful should be eliminated. First of all, studies have shown that testing can be a very powerful learning tool — that’s right, not just an assessment tool, but one that results in formation of long-term memory (ie. learning):

Dr. Bjork has also extensively researched “desirable difficulties” — these are interventions that cause difficulty, and thus can induce some level of stress and slow down learning… but they actually result in better long-term retention.  [To be fair, Boaler agrees with some of these strategies, or similar ones, such as noting the problem that “most practice examples give the most simplified and disconnected version of the method to be practiced” (p. 42); ie. not presenting things with more open-ended complexity and diversity to more fully represent a concept.]

To try to simply eliminate any source of stress is actually quite detrimental to the student, because the fact of the matter is that they will, at some point, encounter those situations, whether it is tests or it is having to perform accurately in a time-limited situation. As much as we may not like the anxiety that it can induce, the reality is that such stressful situations are part of life, and it is better to prepare students to deal with them, than to simply pretend like they will never exist. Examples: standardized tests such as ACT and SAT are currently required for college entrance; after college, job interview processes often involve performance tests — especially for STEM careers. (In the many interviews I had for software engineering positions, I was tested in all of them. In order to get the job, I had to prove that I had the knowledge to perform a task… and, yes, there was a time limit! And, yes, there were “right and wrong” answers!)

In essence, Boaler says that, because timed tests induce fear/anxiety (and, thus, reduced cognitive function), we should eliminate them. This is actually harmful to a student’s future, because that future will involve being tested, assessed, or evaluated! Boaler’s approach is the exact opposite of what cognitive behavioral psychology tells us we should do to overcome phobias. 

It is not “stressful” situations that are the problem; it is how we react to those situations. In other words, the only thing that defines a situation as “stressful” is whether or not it induces a stress response in us. What if we were able to reduce or eliminate that stress response, instead of trying to reduce or eliminate the stimulus/trigger?

One of the most recommended methods for overcoming phobia is called “exposure therapy” and it involves: “Gradual, repeated exposure to the source of your specific phobia and the related thoughts, feelings and sensations may help you learn to manage your anxiety.” (Mayo Clinic) In other words, when something is scary, the way to overcome that anxiety is to be repeatedly exposed to that fear-inducing stimulus, but in small, non-threatening ways to show that nothing bad actually happens.

I have found this does work to reduce test anxiety and the cognitive impairment that can result, as well. Instead of eliminating tests, I simply changed the way they are given, in a way that makes them less scary and, indeed, more of what Boaler called an “assessment for learning” (A4L), rather than just an “assessment of learning” (although, in reality, it serves as both!):

  1. I gave tests far more frequently, rather than less frequently. The more tests you give, the less of an overall impact each one has on your grade, so there is less fear that doing poorly on one could ruin your entire grade.
  2. More importantly, I gave the same assessment multiple times  (but with different questions; concepts remained the same, but numbers and details changed) — ie. each test was both an assessment for learning (formative), as well as an assessment of learning (summative.) How did this work?
    1. At the culmination of learning a topic (including, yes, plenty of practice via “homework”, although many students were able to do that work at school due to morning and after-school opportunities we provided — there goes Boaler’s argument of “inequity”), I would assign the topic test.
    2. The topic test was called a “practice test” — the message was “Let’s see how much we have learned, and how much we still need to learn.”  There was an incentive to try their best — if they liked the score they received, they could keep it (but, unless they received 100%, there was still room for improvement so they would get a chance to try again.)
    3. An item-analysis of errors from the test would allow us to examine the most common mistakes, misconceptions, or learning gaps, as a group in the classroom. We would analyze our weaknesses or confusions, do some more teaching and practicing, and then try again.
    4. A second test was given — sometimes this was yet another independent “practice” test to see how much we had grown after reviewing the things we had difficulty yet.
    5. When the final test was given, anxiety had been reduced, because (a) it was not a surprise what types of skills were going to be assessed; (b) their grades could not go down — they could only go up!  They had already taken the test before, and if they did worse on this one… it wouldn’t count (so why not try and see if we can do better? It was a zero-risk proposition); (c) the message was not a high-stakes one. The message was “Our goal is not scoring 100%. Our goal is to learn. If you score any better than you did on the last test… you are learning! If you score worse? Then you are still learning, it just shows there is more learning to be done!”

That last piece — the messages that are used and the priorities that are communicated — are an essential part of building growth mindset (as shown by Carol Dweck, but similar messages are also outlined in Mathematical Mindsets), but what Boaler doesn’t seem to acknowledge is that it is possible to reduce stress and anxiety and build growth mindset while still keeping the valuable benefits of homework, testing, and grades.


Claim: “if (teachers) do continue to test and grade, they should give the same grade, or higher, for mistakes” (p. 17)

Rating: FALSE

I understand the rationale behind this idea: the purpose is to build perseverance and motivation, by not making students fearful of mistakes, since mistakes and “failures” are a natural and necessary part of the learning process. While it is true that such a policy would definitely eliminate that fear of “being wrong,” Boaler’s recommendation would actually be harmful to students.

The tenets of behavioral psychology have been around for a long time, but they are completely ignored by Boaler in her recommendation. Operant conditioning, as shown by B.F. Skinner 80 years ago, has shown that, when people (or animals) are given a reward for a behavior, it provides positive reinforcement and encourages the behavior to continue or be repeated in the future.

In other words, if we reward making mistakes, that actually encourages students to make mistakes. In fact, if you give students a higher grade for mistakes than for correct answers, as Boaler ludicrously suggests, then this is actually a motivation to purposefully get the wrong answer.

The delusion here has to do with the value of mistakes. It’s not that mistakes are good — it’s that they are expected or acceptable, in certain situations… such as when learning.  The only reason we want to celebrate mistakes is not because mistakes are inherently good, but because they show that a student put in effort and took a risk, when they could have otherwise simply quit or used avoidance tactics.

It is not the mistake, then, that is actually what we should be happy about — the mistake is just a byproduct of the actions we should be celebrating: ie. “giving it a try” and refusal to be afraid of failure.

So, Boaler has it wrong: it’s not the mistakes that we should be celebrating and rewarding (of course, nor should they be punished!) They should be acknowledged for what they are: not the desired goal, but a possible indicator that progress is being made toward the desired goal — that goal being a useful discovery or a successful solution to a problem.

What we should be rewarding is: effort; perseverance; modeling and communication. These are the actions that can lead to mistakes, so it’s good to communicate to students that making mistakes is normal and expected and okay as part of the process. But to reward mistakes sends the message that mistakes are the desired goal … and that is blatantly false. If you teach students this, they are going to have serious problems when they enter the workforce. NASA is not going to reward you for making mistakes when engineering a rocket; Apple and Google are not going to reward you for making mistakes when coding security features of their platforms.

So, it is best to keep things real and honest with students: mistakes are not “good”, but they are a natural indicator that good things are happening (effort & learning.) So, there are times when mistakes are “okay” (ie. when we are learning), and other times when they are not (ie. when we are actually performing.) In any case, mistakes are something to be accepted, but not rewarded.

Unconvincing Results from “Exemplary” Schools and Programs

Despite all of the anecdotes and stories presented in Mathematical Mindsets, what a lot of readers are looking for, really, is the answer to: “How can we fix this?”  As in, how can we do better at teaching math to our students? Currently, the #1 metric (and perhaps the only “universal” one for the United States) to measure and compare learning from one school or a program to another is: standardized CCSS testing.

So, as I read Mathematical Mindsets, whenever Boaler would mention teachers, or schools, or districts who were doing great and innovative things, I had to admit that it all “sounded good” on paper and in theory, but the nagging question was always: “So… how well did it work? Did learning improve?”  I wanted empirical evidence… data. Not just quotes from kids about how much they “liked it”  (Which is a very common piece of support Boaler likes to use — cherry-picked personal narratives and qualitative anecdotes. Which is all well and good, but enjoyment level is irrelevant in a classroom if learning is not occurring…) I wanted to know: how well did they learn?

So, I tried to find unbiased, quantitative data the best that I could and… it turns out that test scores show the achievement levels are not so impressive as Dr. Boaler paints it to be.

Boaler begins Chapter 6: “I am passionate about equity” (p. 92) and asserts that “When mathematics is taught as a connected, inquiry-based subject, inequities disappear and achievement is increased overall.” (p. 103) Let’s see how true that is…

1) Life Academy

Boaler explains that she takes her undergraduate class each year “on a field trip to the incredible Life Academy, a public school in Oakland that is committed to disrupting patterns of inequity on a daily basis.” She states that “The accomplishments of Life Academy are many; the school has the highest college acceptance rate of any high school in Oakland, and the proportion of students who leave ‘college ready’ with California’s required classes is an impressive 87%, higher than at the suburban schools in wealthy areas close to Stanford.” (p. 99)

Okay… but… those look like cherry-picked stats… those are the types of numbers that can be manipulated, simply by giving students easy grades, or graduating them when they haven’t earned it. How much do they actually learn? Let’s see what has to say, based on actual performance:

Here are the “incredible” college eligibility rates of Life Academy (note: “incredible” literally means “not believable”, so I agree…)

Yet… here’s what the standardized tests show:

How do 85% of students have a C or higher on A-G classes, when only 14% of them passed standardized testing?? This should be a red flag.

And how does equity rate at this school? Not good, either… the only “equitable” thing at this school is that they perform equally poorly:What does this highlight?  It actually highlights a serious problem: schools can “fudge” success very simply through grade inflation. While this might help students get into college, it sets them up for failure once they arrive, and in the years beyond, because they have not been given an honest evaluation of what they know and what they still need to learn… it also creates an “uneven playing field,” giving an unfair advantage when colleges are comparing these students — whose grades appear to show that the students are proficient, when the test scores show that is not the case at all. You want equity? This is the opposite of equity.

2) “Railside”
Boaler’s previous seminal works have centered around: (a) “inequity” (based on race/ethnicity and socioeconomic status or, more often, gender); (b) traditional vs “reform” open inquiry-based instruction; (c) tracking vs de-tracked, heterogeneous groups.

While others on the internet have noted Boaler’s clear biases and unsupported conclusions in some of those studies, the one that stands out as being an influential work is her “Railside” study, which is referenced on various pages of Mathematical Mindsets, but mainly with regard to heterogeneous grouping on pages 119-120.

The data and conclusions have been called into question by others, including expert mathematicians — You can click here to read the report two university professors and a statisticians wrote when they dug deeper and found evidence that the conclusions Boaler drew were not accurate, based on the data, and that the methodology was essentially flawed.  You can also click here to read Boaler’s rebuttal, calling the revealing of her data “harassment and persecution.” (I can only presume she would have the same response to me and the facts I am revealing in this blog post. However, I hope if she were to respond to the points I am making here, she would do so with logical and research-supported defenses, instead of resorting to the ad hominem diatribe she made in retaliation to Milgram et al.) She also has some of her facts wrong, stating “Milgram and Bishop’s ‘paper’ contravenes federal law that protects the human subjects of research as it identifies schools, teachers and students. Its identification of individual students breaches the Family Educational Rights and Privacy Act (FERPA).”  I did not see any identification of individual students in their paper — they only identified cohorts. This is no different than the type of data reporting done on state standardized testing sites. In other words, it is legal. But the fact that she tried to use it as a defense says a lot.

The reason the (influential) results of the (questionable) Railside study are so concerning, is that several districts and schools have bought into the “inquiry-based” math curricula used, such as CPM (College Preparatory Math)… and the results have not been pretty. For one, Boaler claims (and provides lots of cherry-picked anecdotal quotes, of course) that enjoyment and motivation are increased… but when I searched for reviews and opinions about CPM online, the response is quite different than what Boaler suggests. Many parents, teachers, and students have complained about the program — about its avoidance of direct instruction, about its insistence on group work for all aspects, and about its (apparent) lack of efficacy. One group of parents was so concerned that they created a “Fairfield Math Advocates” group to combat the adoption of CPM, and has a whole lot of data to highlight problems with it, as well as a list of myriad other advocacy groups that have arisen to rail against it. (They also highlight how it caused fewer and fewer students — a disproportionate number of boys, especially — to complete the math program as years went on. So much for equity!)  In fact, I tried to find positive reviews of CPM, and the only positive messages I could find were by Boaler and her colleagues, or people who had direct professional connections to CPM (but, if you don’t believe me, check it out for yourself)

The comments of these disheartened teachers, parents, and students also reveal a major flaw in the logic of “student-centered” / inquiry / constructivist philosophies: the premise is that people only really “learn” when they discover things for themselves. The problem is… people do not easily do this. It takes time. A lot of time.

Evidence indicates that modern Homo sapiens first appeared over 200,000 years ago. So, consider the following:

The concept of “zero” was not discovered until sometime between 300 B.C. and 458 A.D.  Yes, left to our own devices to “figure things out”, it took humankind about 200,000 years to learn how to use zero as a symbol and a placeholder.
But, through the power of direct instruction, we can ensure that students know and use the number zero by the time they are 5 years old.

The above is an example that demonstrates what is true, ad infinitum, for everything we know about mathematics: Pythagorean theorem… algebra… etc. The fact is that all of these mathematical discoveries have some things in common:

  • Conceptual understanding takes time (often a lot of time), and…
  • They come about by first learning and understanding other, prerequisite concepts. Discoveries are sequential, they are not “Eureka!” moments (not even for Archimedes, who already had background knowledge and concepts that would be prerequisite to making new discoveries.)

Doesn’t it make sense, then, that we should accelerate discovery by first actually imparting the knowledge that it took humankind hundreds of thousands of years to discover? Rather than expecting students to “discover” 200,000 years worth of knowledge within a few short years of their lives, we can ensure that they learn those skills in a swift and efficient manner, and then they will be properly prepared to move forward into the realm of the unknown — the realm of theoretical mathematics.

A Few Good Things

Despite all of the shortcomings above, there are valuable nuggets of insight, new things to try, and ways to enrich/supplement existing mathematics programs. I think that is the crux of the message here: everything in moderation. So, what are some of these valuable tenets that can be used, at least partially, to improve learning?

Growth Mindset

Despite the lack of growth mindset when it comes to dealing with “stressful” realities like practice, assessment, and grades, this book does have a lot of good examples of tools and effective communications that can be use to bolster confidence and motivation and a “non-defeatist attitude” through growth mindset messages to students. It is worthwhile to take a look at the various verbal cues and responses, reflection questions, and more that do seem like they will bolster growth mindset in students (although you can also get these exact same ideas from Carol Dweck’s Mindset book.)

Pragmatic Suggestions for Group Work

There does not seem to be consensus on whether group work is superior to independent work (indeed, studies show that it is often beneficial, but detrimental for some students, and sometimes detrimental to the learning process in general), but at least Boaler admits that group work is fraught with challenges and obstacles to overcome.  The problem lies when curricula like CPM (the much-touted program used in the Railside study) insist on group work for everything (even assessment), all the time. One beneficial/practical feature in Mathematical Mindsets could be the examples and recommendations for structuring and managing groups, including specific roles and methods for handling communication, reflection, and power/social dynamics (which are often the greatest hurdle in grouping.)  Although there does not seem to be any actual empirical data regarding the efficacy of these group strategies, I am curious to give them a try…

Support FOR Common Core

Since the above skills — modeling, critical analysis, and communication — are now essential parts of the CCSS standards, it is not surprising that Boaler supports CCSS. She even admits that the standardized tests are better assessments of mathematical abilities than the older ones (it is surprising then, that she never seems to use CCSS standardized test data as a data point in the research or school examples…):

“One critical principle of good testing is that it should assess what is important. For many decades in the United States, tests have assessed what is easy to test instead of important and valuable mathematics. This has meant that mathematics teachers have had to focus their teaching on narrow procedural mathematics, not the broad, creative, and growth mathematics that is so important. The new common core assessments promise something different, with few multiple-choice questions and more assessments of problem solving, but they are being met with considerable opposition from parents.” (p. 141)

I have experienced this firsthand, and it is unfortunate. But, just like some people are too quick to jump on board something because it is new (like, ahem, those who uncritically accept the entirety of messages in Mathematical Mindsets), there are also those who think the status quo should never change, that it’s “good enough” despite the harsh truth that evidence is to the contrary.  Hopefully, growth mindset training / interventions can extend beyond students and the classroom, to also be able to reach (and undo fixed mindsets) in parents and households everywhere.

The Importance of Modeling, Communication, & Critical analysis

“One of the most important contributions of the Common Core State Standards (CCSS), in my view, is their inclusion of mathematical practices—the actions that are important to mathematics, in which students need to engage as they learn mathematics knowledge. ‘Modeling with Mathematics’ is one of the 8 Mathematics Practices Standards…

The act of modeling can be thought of as the simplification of any real-world problem into a pure mathematical form that can help to solve the problem. Modeling happens all through mathematics, but students have not typically been aware that they are modeling or asked to think about the process.” (p. 194)

I agree with this, and — in my personal (anecdotal) experience — it is true that it is a major mind shift for students, who have not really been asked to discuss, analyze, model, or critically analyze the work they are doing. Thankfully, the CCSS curriculum is addressing that problem… but, in my experience, the quality of those experiences and skills in the current curricula varies widely. As such, it could be beneficial to supplement (not replace) it with some of the open-ended, puzzle/pattern-style activities Boaler highlights in Mathematical Mindsets.

CAASPP Results: The Middle-School Math Mindset

After a rather lengthy delay, CAASPP results were finally released today… and our 6th grade math results are consistent with the past 3 years: highest percentage of “met/exceeded standard” students in the school district, and higher than expected performance for an at-risk demographic (82% Hispanic, and 74% free or reduced lunch.)

Here are the district-wide results:

At first glance, you might be thinking: “Hmmm… what’s to be so proud of? That doesn’t look so great. Less than half of the students passed! Only 47% proficiency?”


  1. I take particular ownership and pride in these results, because this year I was the sole math teacher for 6th grade.  In previous years, results were a combination of all 6th grade classes, since we had self-contained classes of all subjects. This year, we did “middle-school style” subject period rotations, and I was in charge of math (which is not to say some other people didn’t also have an impact: other 6th grade teachers and volunteers who helped, for example, at our after-school homework center, or with before-school tutoring.) This is also why I’m focusing on Math scores in this post, as it is something I can speak directly about, regarding strategies that may have contributed (for better or worse) to the results seen here…
  2. The great (fun? I hesitate to call it that, but it can be) part of math is that it allows us to use the numbers to dig deeper, to solve a mystery…
    In short, numbers can be used to lie, but they can also be used to discover truths that are not apparent on the surface… and that is the case here….

The problem with taking a quick glance at a data visualization like the column chart above is that it is missing important information; it is data “in a vacuum,” but the real world (and especially the world of education) does not work that way. As much as people want to believe that test scores are the sole result and responsibility of the teacher, and a pure indicator of quality of education given, that is not true. Research has shown that all of the following factors can create an “at-risk” population of students:

  • Race/ethnicity
  • Primary language spoken in home (ie. English as a second language)
  • Socioeconomic status
  • Level of proficiency / prior knowledge students have at the beginning of the year

I would like to place a particular emphasis on that final one. It seems like a no-brainer, but many people seem to assume that the level of proficiency a student has when entering a grade level has no bearing or affect on what a teacher can achieve with that student. It is true (as I will prove through the data), that deficits in knowledge can be overcome through effective strategies and interventions… but it does have an impact, and it does limit success, and it isn’t easy. I would also say that there are limits to what can actually be done; a student starting out the year one grade level behind has a significantly better chance of being rehabilitated than one entering 3 or 4 (or even more) grade levels behind in the prerequisite skills they are expected to have. But GROWTH MINDSET is something I believe in, and something that is important; what it tells us is that deficits can be overcome (it’s just, in many cases, a matter of effort… and time.)

So, if we are talking growth mindset, we should be looking at the data not as a snapshot, but from a growth perspective.  For example, when you glance at the results, it appears that both the 4th grade and 6th grade teams found success… and this is true. We work under the same conditions, at the same school, with the same demographic. So, an achievement of close to 50% proficiency, given the circumstances, is a feat.

However, where I am particularly pleased with the 6th grade results is due to the sheer growth that occurred.  If, for example, you look at the 4th grade math scores from a growth model, it looks like this:

As you can see, there was great growth in some ways (for example, a significant increase in “standard exceeded” as well as a significant reduction in “standard not met”), but it must also be noted that the students actually also entered the year with a good deal of preparation from 3rd grade: 51% of students met or exceeded standard. At the end of 4th grade, 45% met or exceeded standard.

On the other hand, the 5th grade test scores do not look great, with only 23% of students meeting or exceeding standard. If you look at growth, however,  you will see that this is actually an improvement from last year (only 21% met/exceeded standard at the end of 4th grade)! In fact, 5th graders were the only ones in the district (aside from my 6th graders) to show positive growth in the number of students who met/exceeded standard compared to the previous year…

This all just goes to show why boiling things down to a single metric or visual can be misleading, and is insufficient for drawing conclusions. You need more than a simple number to tell a whole story.

Which brings me to why I am proud of my (and my students’, and my 6th grade team’s) hard work last year: Although we fell short of my initial goal of 50% proficiency… the results still came close to that, and are significantly higher than would be expected: not only was the statewide proficiency rate for socioeconomically disadvantaged Hispanic students only 20%, but this particular cohort of students also entered my classes with very low proficiency: only 28% of students had passed the CAASPP test. More challenging was the fact that a large number of them (41%!) were not only slightly below (standard nearly met), but significantly below grade level proficiency upon entering 6th grade: 

To visualize this another way, this would be the chart that shows how much this particular cohort of students actually grew during my 2016-2017 school year:

These were statistical “non-movers” for multiple years, some showing small gains in proficiency in 5th grade, but others falling even further behind in math abilities.

  • 96% of these students had an increase in raw test scores
  • 79% increased at least one full proficiency level (several of the students jumped two proficiency levels!)
  • Overall, there was an 85% growth in number of students who met/exceeded standard compared to the previous year!

To put it another way… this is the chart that shows how much students actually grew/improved in proficiency (met/exceeded standard) at each grade level, compared to previous year CAASPP results:

This level of growth is why I am proud of these results, and why I feel like… well, I feel like I actually have figured out some of the secrets of success for teaching math (and, I hate to tell all you Jo Boaler fans out there… if you want to achieve similar results, I suggest that you ignore about half of what she recommends, much of which is actually antithetical to what the cognitive and education research actually shows. I elaborate on that in the next post... )

Putting an Educational Spin on Fidget Spinners

"fidget spinner"

If you haven’t seen one of these lately, you are:

  1. Not a parent
  2. Not a teacher
  3. Probably living under a rock, and even from there you can probably hear the whirring siren’s song of these Weapons of Mass Distraction

The above device is called a “fidget spinner” — a bit of a misnomer, if you ask me, because these toys are marketed as tools for reducing anxiety and improving attention — ie. as helpful devices to combat challenges imposed by ADHD, autism, and more, due to the fact that there is some research showing that fidgeting (and sensory stimuli) can be beneficial for some people. (In fact, I myself fidget, and had to learn productive ways to do so, starting in middle school when my teachers would say “Can you stop tapping the pen on the table?” Since then, my go-to is silently bouncing my knee/leg under the table. It gets the blood flowing — in fact, I do it more when I am either thinking hard or under a little bit of duress — and I think it helps! I have actually taught this method to my students as an effective “non-disruptive” form of fidgeting!)

But the reality is… there is no proof that “fidget spinners” actually meet the above need. They are a toy. “Some experts do believe that so-called ‘fidgets’ — silent, unimposing toys like squeezey balls or textured items like puddy — can provide some children with an outlet for brain stimulation to counteract hyperactivity in the classroom. But, says Anderson, ‘the distinction between those interventions and [fidget spinners] is that those interventions allow the child to move, but this particular intervention isn’t necessarily letting the child get their wiggles out, but rather play with a toy.'”

So, long story short: fidget spinners aren’t eliminating distractions and increasing focus on learning — they are doing the opposite.  When my students say to me “You know what tricks I can do with a spinner?” my response is “My trick beats all of those… I can make it disappear!”

A Positive Spin…

Middle School Fads of 2016-2017However, I know a good craze when I see one (and nowhere are trends more pervasive and addictive than they are during the adolescent / middle-school years!  This year started with Pokémon, progressed to “bottle-flipping,” transmogrified into DIY “slime” being brought into the classroom, and has now spun out of control in a new direction…), and I know that it’s wiser to redirect excitement than to quell it entirely!

As such, I came up with a plan (above and beyond simply confiscating spinners in my classroom — which I also do): I was already going to make my end-of-year classes fun, PBL-style projects involving learning CAD modeling and 3D printing; why not inform the kids that one of the things they would be able to print would be a “fidget spinner”??

Now, that got their attention!  Of course, there were a few caveats (the key is to make something that you really want them to do anyway seem like it’s a special privilege or reward — which, of course, is what gaining knowledge really is, but it’s not always viewed that way by students…):

  • In order to participate in our 3D modeling/printing activity, they would have to have all of their math homework done for the end of the year.
  • They would have to provide some of their own parts/money (in particular, the key component of spinners — ball bearings, such as those used in skateboards and in-line skates — can add up in price. Especially if you have 75+ students like I do.)

Especially fitting was when one of my many “spun” students asked “Can we really design and print our own spinners?” and I replied “Yes… but you’ll probably need to provide your own bearings… not sure I can afford them for everybody, or purchase them in time.”  His response? “That’s okay… they’re cheap. Only $5.”
“For how many?” I asked.
His response: “Does it matter?”

Uh oh. Time for a math review!  (Unit price is a 6th grade CCSS standard!)

Ways to give Spinners an Educational Spin!

Spinner Design in TinkerCAD

Here are some creative ideas I came up with to bring spinners into the classroom and incorporate the excitement, rather than crush it:

  • Perform an experiment to see how long spinners stay spinning on a single flick. (Science and math, including hypothesis, scientific method, dependent and independent variables, mean and median.)
  • Create your own DIY spinners: CAD modeling/3D printing, or even out of other materials (For ours, we will be creating CAD designs with TinkerCAD, and then 3D printing the models — you can learn more about 3D printers on my Maker Tools For Schools website)
  • Spinner science:
    • What makes the spinner spin?
    • Does it matter if all of the sides or “spokes” are balanced?
    • Why are they weighted?
    • What happens if you move the weights further out from the center?
    • Does the type of bearing in the middle matter?
    • What about the bearings on the outer edges?
  • Spinner math:
    • How much will materials cost to make one?
    • How can we find the best deal on parts? (Example: I will be having students compare unit price of different offerings for bearings on
    • Performance Task: Determine the “best” components to purchase to create a fidget spinner (hint: this is not a single, simple answer! It involves unit price, as well as evaluating and weighing user reviews, as well as recognition that the purpose of center bearings and outside bearings are not the same…)

Happy spinning!


6 Keys to #CommonCore / #CCSS Standardized Test Success

In my last post, I shared the surprisingly good test results achieved with our group of underprivileged, at-risk 6th grade students.

Since the things below are what actually drive me to make the choices I do in education, and to teach the way I do (and, while there were some differences in the pedagogy between the three 6th grade teachers on our team, many of these things were shared in common), I figured I would share them in the hopes that others can find the same successes we have:

1. Cognitive Science

After attending a “Learning and the Brain” cognitive science conference in San Francisco a little over a year ago, I was reaffirmed that many of my teaching strategies and beliefs are sound, and are backed by years of science research. I also came away with new understandings, and ideas for how to incorporate the scientific research into sound pedagogy that works to build long-term memory (long-term memory is what it’s all about; if you merely focus on short-term or “working” memory, you cannot recall that information in the future when you may need it… and it’s also a big reason why students fail on tests at the end of the year, after some time has passed since they were taught a skill or concept.)

I took copious notes and collected a variety of presentations and research articles from this conference, which I then synthesized into a simple presentation, but I will sum up a few of the 14 big takeaways here:

  • Repetition is crucial. Repetition is a key factor in transferring information from short-term/working memory into long-term storage. However, it can’t just be a sudden “drill and kill” span of repeating the same type of problem/information over and over in a short time span. It needs to be (a) varied, and (b) spaced out over time. The ideas of “spiral review” or “mixed review” apply here. (This is also why homework, at least in some areas, is so beneficial.)
  • Exercise and sleep are super important. There may not be a whole lot a teacher can control in this department… but there are ways you can get a little exercise and get the blood flowing. (As for sleep — it literally saves and repairs brain cells, and flushes toxic metabolites from your brain. It’s like an oil-change for the gears in your head.)
  • Brain breaks are useful. Similar to the above, and even more applicable to the classroom, it can be useful to take breaks from “focused” thinking and switch over to a more “diffuse” thinking state. Whereas focused cognition allows following and strengthening existing pathways of thought, diffuse thinking and brain breaks allow the brain to form new, more tenuous connections.
  • “Testing” can be even more effective than “teaching”! A lot of people are so “anti-testing” that they will find this concept onerous or even contemptible… but the science is convincing. The idea is not merely “high-stakes” or even “summative” testing, but rather that, when you are being “quizzed” in some way, your brain goes into a more focused mode that does a better job of organizing and storing information. Therefore, even if it’s just quick checks or formative “testing” built into a lesson, the learning gets vastly improved over a “lecture” model of direct instruction.
  • Music and noise are bad. A note to all you teachers who think it’s cool to let the students listen to pop music while they work: it’s not. Study after study have shown that listening to music while reading, studying, testing, or learning hinders comprehension, cognition,  and the formation of both short-term and long-term memories.  Likewise, talking/chatter are bad for learning. Now, let’s be clear, the cognitive science says that on-task talking can actually be a great thing: both peer discussions (such as Think-Pair-Share) and peer teaching. But, when it comes to off-task talking… that’s never a good thing.
    In short: unless there is a reason for productive discussion, silence has been shown to be the best condition for learning.
  • Time limits are good. “If you give yourself a month to get something done, it will take a month. If you give yourself a week, it will take a week.” (Sandra Bond Chapman, Ph.D.)  Unfortunately, there is a big push to give kids “as much time as they need” and not hold them accountable for time limits, especially when it comes to testing. The thinking behind this is that it induces anxiety; the reality is that, in the real world, everything has a time limit, so it’s something students need to get used to.

2. Homework

As I outlined in a previous blog post, homework is valuable. How valuable? Well, homework could end up earning a student an extra $1 million over the course his/her lifetime. Bottom line: without (some) homework, our students simply wouldn’t have had the success that they did. I wish I had access to the individual CAASPP scores… once I am able to access those, I will be able to crunch the numbers and accurately show you that there is nearly a 100% correlation between test scores and the amount of effort / work (such as homework) each student did.

I do believe — as the research shows — that there is such a thing as too much homework. However, the fact of the matter is that, at some point, this has to happen: independent practice of skills that are in the process of being learned. It’s one of the prerequisites for moving information from short-term memory into long-term memory (ie. true learning; see the cognitive science studies above.)

Every year that I have been teaching 6th grade, I have been slowly whittling away and whittling away at the homework — cutting it back more and more so that we can get by with just the bare minimum of the practice that is required. But, make no mistake, some practice is required, and our regular 7-hour school day simply doesn’t give enough time for that practice to occur in class, in addition to the instruction and lessons that are already happening. Hence, the necessity for homework.

Last year, we narrowed it down to just nightly math homework (30-40 min) and attempts to get students to read books (20-30 minutes per night); of these two, the math homework was a lot easier to manage and ensure, so it may prove to be the more valuable of the two.  Social studies and science work was reserved for classroom time, and the only reason it would ever become “homework” was if students were not working on it or managing their time well enough to complete the work in class.

Having said all of this, we have to keep in mind that not all homework is created equal. There is a real difference between the following: assessment of knowledge (probably best saved for in class); busywork (useless); and true homework (ie. independent practice.)  We must also recognize that homework is not what it used to be.  So, when I say homework, if “worksheet” is what immediately comes to mind… then you are living in the past, and don’t yet understand what homework can — and should — look like. (this is not to say that worksheets are always necessarily a bad thing… but they can be. See Technology section below for more details…)

3. Data-Driven Teaching

What is “Data-Driven Teaching”? Any reference to “data-driven decision-making” basically means that you take the time to collect and analyze data in order to help guide the choices you make. Teaching is no different, and most teachers have been doing some form of “data-driven teaching” for a long time now… every time you do a “quick check” for understanding — whether it’s a thumbs-up, a show of hands, a whiteboard, or walking around the room checking answers on a paper — that’s data-driven decision-making (as long as you actually use the feedback/data to guide your next course of action!)

And using such formative data to guide teaching decisions is absolutely critical. As the cognitive science studies have shown (see above), you can’t just “Teach, Test, and Move On.” This has been a standard model for many years, both because we feel a time crunch to fit in all of the standards and topics, but also because it is easy to simply “pass the buck” when learning doesn’t happen, and say “Well, I did my part, I taught the lesson.”

If learning didn’t occur, it’s true that this may be the fault of the learner — perhaps they didn’t pay attention, or put in zero effort. Or perhaps they simply need more practice. Or they need things explained a different way. This is where data comes in — it can tell us exactly how effective our teaching has been, and it can do so immediately, while we still have time to modify or reteach the material…

The flexibility and ability to adjust instruction “on the fly” can be greatly improved through the use of modern technology tools…

4. Sensible, Purposeful Technology Integration

So, here comes the crux of my list. So… why did I save it until 4th place? Because technology is not a solution, in and of itself. Technology is a tool. In the same way that you cannot just hand somebody a hammer and say “now you’re a carpenter!”, you cannot hand a teacher (or students) a computer device and say “now learning will happen!”

Having said that, modern technology tools can facilitate and improve the efficiency of just about every single thing I have listed above. It’s just that the technology tools have to be used (a) sensibly, and (b) purposefully. What do I mean by this?

  • Sensible: you don’t use technology just because it is there. Or just because it is new / novelty. And you don’t use it for everything because, like most tools, it’s not the best tool for every job. (See my previous post: 100% paperless != 100% digital) Examples: even though I am mostly paperless, and even though our math curriculum is 100% digital, I have students write down their homework on plain lined notebook paper. Why? Because (a) students do not have active digitizer stylus tablets at home, and (b) 6th grade math mostly requires “working out” problems to solve them — bye bye mental math, hello work. It would be irresponsible for me to allow them to “guess and check” on the digital homework, or to try to find solutions without writing down work for things like: order of operations; solving one-step equations; factor trees; surface area; etc.Similarly, there are tasks that are simply better if you can do them hands-on. Science experiments, for one (virtual labs are great; real labs are better); we have students mummify chickens. No virtual lab or textbook is going to be as cool or meaningful as that!
  • Purposeful: There has to be planning and a purpose behind how and why you are integrating technology. It can’t just be haphazard. It can’t be lazy. It can’t be something you force the technology to do just because you have it. And it can’t be the digital equivalent of busywork.

So, in which purposeful ways do we use technology? Basically, to address all of the above cognitive and pedagogical needs!  Here are some of the many ways that we have implemented technology tools, not as a gimmick or on a whim, but very purposefully to meet goals that were more difficult without the tech:

  1. Homework / Independent Practice and Repetition:
    1. Using technology tools allows students to get immediate checking/feedback/grading, useful for…
      1. Metacognition / reflection about what they are doing (and why it may not be resulting in success.)
      2. Immediate correction of those behaviors, instead of repetition of incorrect work that will only reinforce erroneous methods.
    2. Built-in supports to give instruction, reminders, or hints: whereas “old-school” homework without assistance just leads to frustration or giving up, technology supports can sometimes work as well as (or possibly even better than) having a human helper (parent or tutor) to provide assistance. Examples:
      1. Videos students can watch in Khan Academy to learn (or remind, or reteach) a skill.
      2. Audio narration for e-books/e-texts to help struggling readers.
    3. Mixed Review / Spiral Review — Students need repetition of skills over time; “teach, test, and move on” doesn’t work well.  Fortunately, we have Mixed Review components built into our Digits math curriculum, but even without a curriculum like this, you can use tools like Khan Academy to assign practice and review of subjects you have covered previously in the year.
  2. Data Collection and Analysis. Because the computer can instantly check/correct/grade many types of work, this can have a powerful effect:
    1. Less class time spent on checking/reviewing homework = more time learning. With our pencil-and-paper math curriculum, we would spent up to 20 minutes per day checking and reviewing the homework. Those 20 minutes per day can now be spent on teaching new skills, reteaching areas of confusion, extra practice, or fun and exciting enrichment activities
    2. Instant item analysis allows for immediate reteaching opportunities! For example, whenever we finish a topic in our Pearson Digits math curriculum, I assign the test as a practice test first (the technology makes this easily feasible — I can give the same test multiple times, because the numbers and details of the problems are randomly generated, and thus vary each time, and from student to student.)  By doing this, it (a) gives the students a chance to see what they know without it being a high-stakes scenario; (b) lowers test anxiety when we do the “real test”; and (c) provides formative feedback for the teacher so I can see, at the click of a button, which skills I need to reteach and have them practice before the real test!
    3. No more “taking home papers”, or worrying about losing them, or where to store them, or how to keep a record while making sure students and parents also get the paper back! Using digital work tools like Google Classroom, the cumbersome days of paper are gone. You can access the work from anywhere, on any device (as long as you have an internet connection); you can provide feedback right on the work, and return that work to the student — while still having a copy for yourself for future reference, and never have to worry about using a copying machine or filing cabinet!
  3. Behavior Management, Brain Breaks, and Exercise: These 3 things have been clumped together, because they are somewhat related; when students don’t get enough chances to give their brains a rest and/or to move their bodies, it affects both cognitive ability and behaviors.  Likewise, teachers have long used tools to track behaviors, report them to parents, have reward systems, etc. Technology tools make both of the above more efficient:
    1. GoNoodle provides an assortment of free “whole group” brain break and exercise (often dance routine) videos to get the students relaxing, or get them moving.
    2. ClassDojo is a free behavior management app that allows you to log positive behaviors and “needs work” behaviors as soon as they happen, as simple as touching a button on your phone (or computer.) Parents can get reports about student behaviors, and can also use the app to communicate with the teacher via messages. (There are also other behavior management tech tools, such as ClassCraft, which attempts to gamify the behavior-management experience)
  4. Increased Interaction and Engagement:  Lessons can be made simply more interesting — and knowledge more accessible — through multimedia tools like:
    1. Educational videos, animations, and songs (Discovery Education, YouTube, BrainPop, Flocabulary, etc.)
    2. Educational Games — too many to list! But some favorites for math in my class are SumDog and Prodigy; they also enjoy practicing vocab words using Quizlet
    3. Virtual science labs and field trips (not as good as the real thing… but the next best thing!)
    4. “Just right” practice that levels, individualizes, and sometimes gives student choice in the equation, such as reading practice using kid-friendly news articles at Newsela
  5. Authentic 21st Century STEM & PBL Tasks: students are entering a globally-competitive world in which problem-solving and product creation are more valuable tools than ever. Technology makes even the following cutting-edge skills accessible to even the youngest of learners!
    1. Computer-Aided Design (3d modeling) and 3D printing
    2. Coding, programming, robotics, and electronics
    3. The “Maker Movement” of creating homegrown inventions and solutions when you have a problem!
    4. For more resources and information about the above, you can visit my Maker Tools for Schools website.

5. Test Preparation

I would be remiss if I did not admit that one activity which almost certainly guarantees higher test success is test preparation. What do I mean by this? Although we teach to the standards throughout the year, and this should be enough for success on the CCSS test, it is important that students get exposed to the actual format and layout, interaction, and expectations of the CAASPP test (or whichever test you are using.)

It would be a real shame if students actually knew how to answer the questions or solve the tasks being demanded by the test, yet failed due to a lack of understanding of what was being asked, or how they should enter the information.  We discovered this was actually happening, when we observed students while they were taking the CAASPP the first year it was administered.


  • Knowing that there are often MULTIPLE checkboxes for correct answers (not a single multiple-choice answer, as students may expect), and that the test sometimes explicitly tells you how many to mark.
  • What level of depth/detail do “short response” written answers require?
  • What is expected during a “performance task”? What does a sufficient response look like? (especially for writing tasks)

So, periodically throughout the year — and especially right before the official testing window — I have students practice the above skills using tools like the CAASPP Interim assessments (these are formative assessments that can be used without “counting” for an actual score) and the CAASPP Practice Test.  Last year we were unable to actually see scoring for Interim assessments, so it was hard to use data from those; meanwhile, the Practice test does not record or grade student responses at all. However, we did these activities as “guided practice”, wherein students would answer each question (projected on the front screen in the classroom), and then I would tell them the correct answers and they would grade their own work (using a “digital/virtual whiteboard” approach; I simply made one cell per question on the test, and each student would fill their cell with green if they got it correct, yellow if partially correct, and red if incorrect. They enjoyed this task a lot more than I expected!)

Does this mean we are “teaching to the test”? Yes and no… we are teaching what the test is, what it looks like, what is expected, user interface and input, and other ways to be prepared for it, but it is not the be-all, end-all of all of our lessons and activities. It is a little extra thing we do in addition to (not instead of) our regular classroom lessons and activities…

6. Reasonable Class Sizes

It has to be said: CLASS SIZE MATTERS. In this past year that we attained the highest CAASPP (CCSS/SBAC) scores to date for our district, there were 20 students per class.

Teachers don’t really have much of a say over their class sizes, so I don’t want this final item to make readers feel like the other ones above are invalidated, or that they can’t reach success if they don’t have reasonable class sizes. After all, studies have shown teacher quality/effectiveness to be the number one determinant of student success — it can (somewhat) overcome demographic challenges and “at-risk” factors, and it can (somewhat) overcome large class sizes. However, all else being equal, smaller classes have been shown to be beneficial. (So, for those who do have the ability to control this — administrators, districts, and states — it is important to consider, and to devote the resources to give those highly-effective teachers the best conditions in which to excel…)

I have taught classes from Kindergarten to high school, with sizes ranging anywhere from 15 students to 35 students. In some ways, the impact of size depends on a variety of factors, such as the age/grade of the students, their demographic or home life, etc. I would argue that the following groups of students really benefit from smaller classes:

  • primary grades (especially K-1);
  • middle school grades (6-8; for some reason, nobody seems to think these grade levels need class size caps like the primary grades do, and then everybody seems to shrug their shoulders and wonder why problems such as behavior issues — and, thus, distractions that impact learning — arise);
  • English language learners (they simply need a lot more one-on-one guidance, reteaching, verbal support, and more in-depth feedback for tasks like writing.)

In other ways, there are universal benefits to all students from smaller classes… perhaps some of these benefits contributed to the relative success seen in the test scores above?

  1. More time for personal interactions and assistance during class. It’s very simple: some percentage of students will need extra help and assistance grasping concepts or understanding a lesson. Even if that percentage stays consistent (let’s say 25% are gifted and need no assistance most of the time; 50% are average and need help here and there; and 25% need extra support), the actual number of students in each of those three categories increases. Meanwhile, the minutes allotted in an instructional period or day do not. The result? Students either have to have their personal assistance time cut short, or some students end up not getting helped at all (or, in a worst-case scenario, both things occur.)
  2. Better, more valuable feedback on assignments. This is a no-brainer: I have limited time to be able to grade and provide feedback on assignments. As it is, my school district gives us one hour of prep time during the week, during which I can grade assignments (or plan lessons, or both.) As any teacher knows, this is insufficient; even if I were to grade a single writing assignment, this means for a class of 20 students, I would only have 3 minutes to read, mark, and respond to each student’s written work.  Impossible when we’re talking about 6th-grade level writing (multi-paragraph essays.)
    So, like most teachers, I work extra hours outside of my contracted time. Having said this, there is still a limit on what can be done. If I take 10 minutes per paper to read, make corrections, and provide constructive feedback for each student, then this means a single assignment takes 200 minutes for a class of 20 kids. When that class size is raised to 26, grading that assignment requires an extra hour of time.  Something’s gotta give…
  3. Fewer distractions / behavioral issues in class.  Cognitive science (see above) shows us that feeling safe, feeling comfortable, and working in a low-noise environment all promote learning. However, these basic needs are impeded when even the best of behavior managers find it more challenging to run a classroom when proven management techniques are made more difficult:
    1. proximity (an simple but effective management technique) becomes more difficult when a larger class means farther to walk to reach students, and more students who are left unattended when you do;
    2. even small sounds and noises get amplified much more quickly when there are more people in the room;
    3. sometimes students need to be separated from each other, or moved to a different seating location to be successful. The more students there are in the room, the less likely you will be able to find a successful, trouble-free location for all of them.

#Paperless Classroom Success is not a Fluke!

It has been two years since the state of California has been releasing data from the standardized end-of year CCSS assessment, CAASPP (California’s version of the SBAC test: the California Assessment of Student Performance & Progress)

Last year, I posted the data from the first publicized CAASPP results, and they showed very promising results for our (almost completely) paperless 6th grade team!

However, I have to admit that I was anxious to see this following year’s results, partly because there were some questions raised about whether the first year’s results could have been merely due to having an especially-proficient group of students (it is true that, coincidentally, our 2014-2015 cohort of students had a lower number of English Learners and higher number of GATE students than average for our school.) Since we had no standardized data of performance from previous years, there was no way of knowing (for certain) whether the success levels we saw were due to our pedagogy (and skillful technology integration), or due merely to the confounding variable of simply getting “a good class.”

Well, the newest test scores have been reported, and the results are pretty astounding: our “low performing”, “high EL” group of students had even higher percentages of students who “met or exceeded standard” than the previous year’s “strong” students!

Even though I was awaiting the test scores because I just knew we would be more successful than people had imagined, I was still fairly blown away when I saw just how successful we were:

2016 ELA Highlighted2016 Math HighlightedNot only did our tech-based grade level have the highest levels of proficiency in the district, but we can also conclusively say that the results were not because it was a group of innately-superior group of kids. In fact, this cohort of students made huge gains in proficiency compared to the previous year:

ELA (English Language Arts) Success

In 5th grade, 39% met or exceeded standard; in paperless 6th grade, that number jumped to 63% of students. That’s nearly a 60% year-over-year increase in the number of proficient students!






math Success

In 5th grade, 31% of these students met or exceeded standard. After joining our all-digital 6th grade math curriculum, 55% of students met or exceeded standard! (That is a WHOPPING 77% INCREASE in the number of proficient students!)

5thGradeMath 6thGradeMath






The Keys to Success

Considering the circumstances and the data, it seems we are doing something right! And that’s a great feeling, because sometimes it’s hard to tell, and it’s easy to feel lost or unsuccessful at times…

So, if it’s not the demographic that is the cause of success — and, with about 80% free-and-reduced lunches, 80% EL students, and an even higher percentage of Hispanic students… it’s certainly not a privileged group of students; this is actually an “at-risk” demographic we are talking about — what, then, is leading to these fairly successful numbers?

I have a few sound theories, but it’s going to take a whole other post to delve into what, exactly, makes our technology-integrated classrooms so successful (and the technology itself is only one piece of that puzzle.)

In an upcoming post, I will outline 6 key things our 6th grade team is doing to try to ensure academic success year after year.

“But what about access?” – 5 Ways to Defeat the Digital Divide

“Today high speed broadband is not a luxury, it’s a necessity.”
– President Obama, January 14, 2015

A lot of people have read this blog, or my posts elsewhere, or attended my conference presentations (at CUE or EdTechTeam conferences) and, inevitably, this question comes up:

“Well, paperless sounds great and all… and these are wonderful digital resources, but… how can we do this if the kids don’t have access to computer devices or the internet?” 

It’s a completely important question and, around here, an extremely relevant one. The fact of the matter is that there is still, even with how ubiquitous technology has become, a “digital divide” and, unfortunately, it poses challenges for education (but I don’t believe they are insurmountable!)

What is “The digital Divide?”

dig·it·al di·vide
noun: digital divide; plural noun: digital divides
  1. the gulf between those who have ready access to computers and the Internet, and those who do not.
    a worrying “digital divide” based on race, gender, educational attainment, and income

In short, the “Digital Divide” is a term to describe the fact that, even though computer and internet usage/adoption has grown significantly over the past several years, it has not grown equitably among all social groups, and there still exists a big difference between the percentage of affluent, White, and/or Asian users in the United States, and the percentage of Black, Hispanic, Native American, and/or low-income members of society (White House Council of Economic Advisors). The digital divide can be seen along racial lines, along socioeconomic lines, and along geographical boundaries (for example, students in rural locations report lower levels of accessibility than those in urban locations.)

The Digital Divide is a real problem for many reasons. It has been cited as a major factor not only for education, but ultimately for economic equality, social mobility, democracy, and economic (business) growth. (Internet World Stats)  In short, being at a disadvantage when it comes to access to — and knowledge/interest in using — technology simply puts you at a disadvantage in life. Having, knowing, and using computers is no longer an optional luxury, it is absolutely imperative to survival.

Considering all of the research and data I have cited in previous posts on this blog (including the last one about the advantages of digital practice/homework), the following facts can pose a real obstacle to seeing the benefits of technology-enhanced education (and many schools are experiencing this):

  • Whereas ~87% of Asian and 77% of White households have internet access, those numbers drop to 67%, 61%, and 58% for Hispanic, Black, and Native American households. (White House Council of Economic Advisors)
  • Level of education for the head of household is an even more stark contrast: college-educated households (bachelor’s or higher) have 90% access, which tapers off significantly as the level of attained education decreases; where the head of household did not graduate from high school, less than 44% have access. (White House Council of Economic Advisors)
  • Likewise, income plays a factor: only 62% of households making less than $56k per year have access, compared to 86% of those making >$85k/year. (White House Council of Economic Advisors)
  • In a Pew survey of teachers, teachers of low income students tended to report more obstacles to using educational technology effectively than their peers in more affluent schools. (
  • Among teachers in the highest income areas, 70% said their school gave them good support for incorporating technology into their teaching. Among teachers in the lowest income areas, that number was just 50%. (
  • Fifty-six percent of teachers in low income schools say that their students’ inadequate access to technology is a “major challenge” for using technology as a teaching aid. (
  • Rural communities are also at a disadvantage. While high-speed (25mbps) internet bandwidth is accessible to 88% of people in urban environments, only 41% of those in rural environments have access. (White House Broadband Report)

5 Ways to Defeat the Digital Divide

While this problem is a real one, the solution is not to simply give up, nor to provide a sub-par education lacking technology and lacking 21st-century skills simply due to these constraints! To do so will only ensure that the digital divide — and the wealth/success gap — will continue.

I can tell you that it IS possible to overcome these obstacles because the student population I work with is about 80% Hispanic, 80% socioeconomically disadvantaged, and located in a rural/agricultural community!  Yet, slowly but surely, we are making 1:1 (and sometimes even paperless) edtech work! (Note: My school is in a Basic Aid / Excess Funding district, so is not as budget-crunched as some… but, as you will see, many solutions are cost-effective.)

  1. E-Rate. The government (FCC) created this program starting in the 1990s to make it easier and more affordable for schools to improve their infrastructure so that they can provide sufficient computer and internet access for students. If internet access or school network are the bottleneck, these discounts need to be used to ensure a sufficient infrastructure. Projects to upgrade local networks and high-speed broadband access are discounted at 20-90 percent off, or even better for disadvantaged schools.
  2. 1:1 devices provided by school budgets… or grant funding. Multiple studies have shown that sharing devices, such as at “workstations” or in a computer lab, is not nearly as beneficial and effective as having 1:1 computing (one device — tablet or computer, not smartphone — per student.)  A lot of schools and districts cite budget constraints for being unable to do so. Some might try to push for a “BYOD” (Bring Your Own Device”) model, which inherently has many problems (one of which is outlined above: disadvantaged students may not have a device at all!)  If schools avoid trying to buy the more expensive devices (such as Macbooks or iPads), it is possible to obtain more devices and increase the rate of becoming truly 1:1.  For example, low-cost, easy-to-manage Chromebook laptops can be obtained for less than $170 each. If you are really looking to save money (or prefer tablet usage), inexpensive Amazon Kindle Fire tablets cost <$50.  If even these relatively paltry prices are somehow too much for the school to swing, there are funding possibilities via grants, such as, or the $500 Gasser Grant  (this would buy 10 Kindle Fire tablets!)   NOTE: I would advocate that, if these devices are to be used in the classroom, they should remain at school instead of being sent home with the students. This prevents loss and damage.  However, a possibility for increasing home access could be to sell or give away the old models when it is time to upgrade and replace them with new ones. (Our school sold phased-out Chromebooks and iPads to students and families for about $20 each!)
  3. Computer lab access.  If providing 1:1 devices is not possible — especially for home/after-school use — why not make a computer lab available? A computer lab is something most schools have had — often for decades now. As long as it is located somewhere easy to monitor/manage (such as a media center), teachers or other supervisors could supervise the room and devices that can be made open even after school hours to enable online practice, research, and homework.  We do this at our school, providing a “Power Hour” of homework time (in the computer lab) that teachers take turns supervising (this is done via Boys & Girls Club and, although the teachers get paid for that hour of work, it costs less than our normal hourly rate of pay, and is funded through Boys & Girls Club instead of the school district budget.)
  4. Public libraries. Public libraries, too, generally have computers available for public use. The hours may be limited — and there may be a time limit — but anybody who has the transportation to get to the nearest library can generally have free computer/internet access.
  5. Discounted low-income broadband Internet services. Many families are hesitant to get Internet service at home because it is perceived as expensive and not a priority. Except for some truly remote locations where broadband simply isn’t available, this can be fixed! Parents and families need to be taught the educational and economic values of having an Internet connection, and there are various heavily-discounted broadband services that are available for low-income families!
    1. Click here to learn about Lifeline, the FCC subsidy for phone and internet access for low-income households
    2. Click here for another list of low-income broadband services that cost less than $10 per month (including AT&T, Cox, and other providers)

Based on my experiences, technology is so valuable for education that, personally, I would actually buy devices with money out of my own pocket (since they can be used for multiple years, a class set of Chromebooks comes out to a cost of about $1000 per year — less than the cost of a field trip! A class set of Kindle Fire tablets would cost about $250 per year… a one-night stay at most of the hotels in nearby San Francisco will cost you about this much!), sooner than allow students to go without any access at all.  That’s how crucial I have seen the role of educational technology to be.


The Million-Dollar Question: “Is Homework Worth It?”

“is homework worth it?”

That’s the million-dollar question (quite literally, as I will outline below)… but to answer it, we first have to define “worth what?” What does one have to “pay” or give up in order to do homework?

Well, lately I’ve seen a lot of buzz about parents, schools, even teachers simply “calling it quits” on homework. Why? Here are some of the given reasons (aside from the more egregiously ridiculous ones), along with responses outlining how these stated challenges do not necessarily need to be problems:

  • “Kids don’t get enough time for play, and they need up to 10 hours of sleep per night.”  School is about 7 hours long. Even if a student gets 60 minutes of homework, this leaves 16 hours of the day remaining. If you advocate for 10 hours of sleep for a growing student, this still leaves them a whole 6 hours for meals, exercise, relaxation, hobbies, and fun. That’s a lot of time! (and, on weekends, it becomes 34 hours of free time, even if the kids are assigned homework on Friday and sleep for 10 hours each night)
  • “Homework is frustrating/stressful for students and/or parents.”  This can sometimes be true, so we have to address the source of frustrations, and then homework will no longer be stressful for students nor their families. Homework is generally meant to serve one of a couple of purposes:
    • (a) Independent practice. Cognitive science studies show us that repetition (ie. practice) transfer short-term/working memory into long-term memory, ie. true learning. The stressor (and real problem) here is that successful independent practice isn’t possible if a student doesn’t know the material well enough and doesn’t have support/guidance to help or check along the process. In this scenario, a student will, at best, complete all work — but do most of it wrong, thus reinforcing erroneous skills or behaviors (this is the opposite of what we want homework to do!) At worst, they will simply give up and not finish the homework at all.
      The solution, for a long time, has been to ensure that the student has a mentor/helper — such as a parent, older sibling, tutor, etc. But this is where the “stress/frustration” comes in for them, too. They not only have to give up their own time to help with the process, but also may not even be capable or comfortable enough with the material to provide sufficient assistance. All of these used to be very valid concerns… but they can be alleviated (or removed altogether) if we use 21st century tools! (see below)
    • (b) Sufficient time to work on larger projects (products such as research reports, models, etc. could take more time than is necessarily available during the school day.) The main cause of stress here usually has to do with time management or constraints — ie. getting the work done in time. If the teacher sufficiently “chunks” the work into smaller checkpoints or benchmarks that are due within shorter timespans, this can be alleviated.
  • “There’s no telling if the student is the one responsible for the work turned in. It could have been copied from a friend, done by a parent/sibling, or had their hand held through the whole process.”  This is (or, at least, has been) true, and it has been one of my major gripes about homework (especially paper-based, worksheet-style), for a long time. However, this is an “old school” way of thinking about homework, assuming it is all “pencil and paper” work. With modern technology, some of these problems can be alleviated (however, keep in mind: you can never really monitor who is completing the work. It is for that reason that I firmly believe homework should be used solely as independent practice — not as a summative assessment tool — and that it should, accordingly, make up a small portion of a student’s grade.)

the value of homework:
$1 million
($422 per hour!)

Despite the complaints and frustrations that some people feel, the overwhelming body of research-based evidence shows that homework is beneficial!

Why would teachers go through all of the effort to assign, grade, and otherwise deal with homework (especially given all of the challenges above), if there weren’t research-based proof that it was good for students?  Here are some of the facts:



    ‘With only rare exception, the relationship between the amount of homework students do and their achievement outcomes was found to be positive and statistically significant,’ the researchers report in a paper that appears in the spring 2006 edition of ‘Review of Educational Research.'” (Duke University)

  • Homework helps your child do better in school when the assignments are meaningful, are completed successfully and are returned to her with constructive comments from the teacher. An assignment should have a specific purpose, come with clear instructions, be fairly well matched to a child’s abilities and help to develop a child’s knowledge and skills.In the early grades, homework can help children to develop the good study habits and positive attitudes described earlier. From third through sixth grades, small amounts of homework, gradually increased each year, may support improved school achievement. In seventh grade and beyond, students who complete more homework score better on standardized tests and earn better grades, on the average, than do students who do less homework. The difference in test scores and grades between students who do more homework and those who do less increases as students move up through the grades.” (US Dept. of Education)
  • College graduates earn $1 million dollars more over their lifetime than high school graduates. This gap is widened even further if you consider that STEM (Science Technology Engineering and Mathematics) majors earn $3.4 million more than the lowest-paying majors. (Georgetown University, reported via Marketwatch)

What does this mean?  It means, in short, that doing homework is worth it, because doing homework increases the chances for better grades and higher test scores, which in turn increases the chances for college admissions, which increases your lifetime income by an average of $1 million.

Since my main subject of focus this year is math, I will use some math to show you exactly how much it is worth, using this formula:

$1,000,000 /
[180 days of homework per year — assuming homework every school night!)
* (the recommended homework minutes per grade level: 10 in K up to 120 in 12th)
/ 60 minutes per hour ]
= earnings per hour of homework

1,000,000/[180*(10+10+20+30+40+50+60+70+80+90+100+110+120)/60] =
$421.94 per hour

That’s how much homework is worth. Still think it’s “not worth it” to spend maybe 20 minutes, maybe an hour, maybe even 2 hours (in high school), doing some reading, writing, and arithmetic each night for a few years?

How going digital can help

Maybe not all, but many of the “problems” people have attributed to homework can simply be attributed to using the inefficient, outdated homework methods of the past!

Pencil-and-paper worksheets to practice and show what you know have many, many drawbacks:

  1. Students get no feedback about whether they are doing things correctly or not! Thus they could be practicing a skill incorrectly over and over again. Cognitive and behavioral psychology tells us that this will only reinforce the wrong way of doing things!
  2. There is very little (often zero) built-in guidance/scaffolding/support to provide help if you do need it. So, if you do need assistance, it all comes down to: (a) how well the textbook explains things (if you have access to one); (b) notes you have taken in class or have been given to you; (c) support/help you can get from someone like a parent or tutor.
  3. Students can simply copy the answers from each other. Most of the time, the same worksheet is given to each student. Because of this, students can simply copy the answers if they want to…

But this is a centuries-old way of doing homework that doesn’t take advantage of modern tools and technology! There are many, many educational technology tools that will provide the following benefits:

  1. Instantaneous feedback to students. Students will instantly know if they are doing things correctly or not, and can immediately correct their practice instead of reinforcing bad habits.
  2. Built-in support / help tools. Many programs include built-in supports to provide instruction or guidance (via tutorials, videos, etc.) when students need help. Thus, there is no longer the need for an additional person to provide tutoring and assistance…
  3. Students work independently. In many programs, such as our digital math curriculum (Pearson Digits), the problems given to students are dynamically generated. In other words, they change from student to student — the concept/skill may be the same, for example, but the numbers or details change. This provides an opportunity to practice the same problem again if they get it wrong, as well as preventing the ability to copy answers from another student.
  4. Studies show that the above factors do provide benefits over traditional pencil-and-paper work! “…given the large effect size, it may be worth the cost and effort to give Web-based homework when students have access to the needed equipment, such as in schools that have implemented one-to-one computing programs.” (studies like this one can be found at

There are many digital tools that allow for the above, and many of them are free. Some of the ones I use are: Newsela, Quizlet,, Khan Academy, Prodigy, SumDog, iXL, and there are many more…

Some people might say “That’s all well and good, but what if my students don’t have access to technology and internet to make the digital tools possible?” The answer is: in many cases, access can be made possible! Schools can provide inexpensive devices (and there are grant/donation systems such as Gasser Grants and DonorsChoose that can help pay for these), internet service, or even just an open computer lab after school, or a homework help club/session that provides the 1:1 technology. Public libraries offer computer access, and broadband providers currently offer discounted internet service for low income families, which range in cost from $0-$15 per month. (I will write more details about accessibility and closing the digital divide in my next post!)

When I give your child homework, I am literally giving them the opportunity to obtain a million dollars!

As you can see, there are ways to give independent practice/homework and have it be a successful, low-stress experience. Considering the very real long-term and financial benefits, why would any parent, teacher, or administrator in their right mind want to do away with that?

[NOTE: When I refer to “homework” herein, what I am actually referring to is “independent practice” — it’s not work that has to be done at home, but it generally requires additional time on top of the regular instructional schedule. This work time could be at home, could be in an after-school homework club or tutoring session, or could be minutes that schools decide to add onto the end of the existing school day.]



PokéMath – The Adventure Begins! … and PokéMath Duels!

MrGAshThe first day of school was Thursday, and we officially started PokéMath on Friday (for which I dressed all day in the costume shown here: Ash Ketchum!)

I have decorated the room with Pokémon decals, and have printed the PokéMath sticker awards for every student (see my previous PokéMath introduction and setup post to learn more about getting started and set up), and I have created a Pokémon-themed class website.  The students were introduced to how the PokéMath “game” will work in class, and it succeeded in generating a lot of excitement! About 40% of the students said they play Pokémon Go, so they were obviously excited… but several others also seemed interested in the idea of collecting monsters as they master math skills!

Some students asked “Can we work on these Khan Academy skills and try to catch them at home or on the weekends?” (YES!)

One student said “I didn’t think I was going to like math this year, but this changes everything!” (YES!)

Another student was so into it, he started brainstorming ways to improve it and make it more fun (and improve his chances to “Catch ’em all”): “Could you make it so the one for Band can also be caught if you spend, like, a lot of points?” (apparently, he is not in band, but still wants to have a chance to get them all. I don’t want to exclude anybody from that opportunity, so I’m changing it, due to his suggestion! Band participation or 500 ClassDojo points…)

He also asked “Is there a way we could challenge our friends?” (to a duel, like in the actual game)
“No, not right now…” I replied. “I know that would be fun, but I haven’t thought of a good way to do it yet. For now, it will just be collecting them, but if we come up with a good way to play with them, that could be fun…”
“Maybe students could, like, answer questions, and then get bonuses based on the type of Pokémon” (hey, that’s not a bad idea, I thought)
“Yeah, we’ll keep brainstorming, and if I can figure out a way to make it work, we’ll do it.”

Well, based on that kid’s insightful proposals, I may have figured out a good system for “battles” to take the interactivity, gamification (and motivation) to the next level!

Introducing… PokéMath Duels!

This is something I plan to try at some point… maybe once a week (on Fridays, for example), or just one question/duel each day.  Students will be able to actually use the monsters in their pokédex to win “battles” or challenges vs their table partners!

These duels will be a simplified version of how the game actually works:

  1. Each student in the pair will (secretly) choose a monster in his/her pokédex to use for the duel. They will write the monster name on their whiteboard.
  2. A question/problem will be shown on the projector for students to answer. Each student will write their answer on the whiteboard within a certain time limit (depending on the problem.)
  3.  If the student gets the answer right, their chosen pokémon scores a hit! The hit will have a strength that is modified by: (a) rarity (power) of the pokémon, and (b) the opponent’s pokémon type (each type has strengths and weaknesses against other types.)
  4. If both pokémon score a hit (both students get correct answer), the one with the stronger hit wins the duel!  The winning student is rewarded with ClassDojo points (in my class, I have a “Superstar” behavior that is worth 3 points.)

Updated resources including the Duel Instructions and Modifier Table as well as desk labels for Gyms/Teams will be found in the PokéMath Google Drive folder!

Class Bank – Google Sheets Add-On to Bank, Spend, or Raffle with ClassDojo!

ClassDojo Class Bank


I have been a big fan of behavior-management app ClassDojo for several years now… basically, ever since its inception. I started by using it in my computer classes with students in grades K-6, and it allowed me to easily send behavior reports to their homeroom teachers.

Often, those teachers would have a system of rewards based on performance. I, too, have used ClassDojo for this purpose in my class (and this year I plan to use it as a currency system integrated with my PokéMath classroom game!) Unfortunately, the app lacks built-in tools to help facilitate any sort of rewards or currency system in the classroom. Some teachers like to use the points as currency that can be spent, in a classroom store or auction. Some teachers like to use points as “raffle tickets” to win prizes.  Doing any of the above has been a fairly difficult process to manage… until now!

I programmed Class Bank & Raffle to help streamline and facilitate the process of doing any or all of the above in your classroom!  It still takes a few steps, but is much simpler than manually managing the processes… so let’s get started!

class bank setup / import

  1. To set up Class Bank, create any blank Google Spreadsheet that you would like to use. You can name this file anything you want, and store it in any folder.
  2. Next, install the Class Bank & Raffle add-on. This can be done under Add-Ons–>Get add-ons…
  3. Upon install, your Add-Ons menu will now have a Class Bank sub-menu. This is where you will go to: Update or Reset your students’ points in the bank; Spend student points; or do a Raffle drawing.
  4. To get set up — and every time you want to update the balances in the bank to reflect current totals in ClassDojo — you will need to download a ClassDojo Report csv file and make sure it goes into Google Drive (as a Google Sheet).  Here’s how to do this:

a) Log into ClassDojo and open your class. Click on the “View Reports” button:
ClassDojo ViewReports

b) Click on “View Spreadsheet” to download the CSV file:
ClassDojo View Spreadsheet

c) Upload the CSV file into a location of your choice in Google Drive. You may want to make a special folder for these. You may also want to either delete them after each use, or rename them to make it easier to find the correct one you are looking for. Note: The file doesn’t automatically get uploaded as a Google Sheet unless you first go into the Settings (gear icon) of Google Drive and make sure the “Convert Uploads” checkbox is checked.

Once you have a ClassDojo file ready to use as a Sheet in Google Drive, Class Bank will work! First, you just need to Import Points  (from the Add-Ons–>Class Bank menu.)  The first time you do this, be sure to select the “Reset” option, which imports all points and resets all “Spent Points” back to zero! Note: The Import Points feature defaults to “Add to existing points” because, if you prefer Total Points, it is easy to re-do the import with the correct setting… but if you chose Total and you really wanted to Add to existing points, you can not later recover your old point balance! (You could always use the Google Sheet’s File/Changes history to recover an older version, though)


spend points

Class Bank will automatically keep track of how many points your students have spent and keep a running balance for easy reference.  If a student tries to spend points, you don’t need to worry about manually checking whether they have enough to spend in their balance — Class Bank will check to see if they have enough points and, if there are insufficient funds in the Balance, it will not deduct the points and it will let you know which students had insufficient funds!

To spend points, simply enter a specified point value in the box, and check the boxes of all students who will be spending that many points.. This amount of points will be deducted from all selected students (as long as they have enough!)



The raffle drawing can be run at any time and does not alter the points in any way — it simply chooses “winners” based on how many points they have! Each point a student has is one entry/ticket in the raffle.

First, you must specify whether you want to use Total Points or the points in the Balance (this works well if you want to use both currency and raffles in your classroom.)   You can also set how many drawings to do in a row, and whether to limit to one prize per student — using this feature means students with more points will still have a better chance of winning a “top prize” or first pick, but will not be selected more than once.


privacy / coppa / FERPA compliance

Class Bank is a Google Sheets add-on that does not collect nor share any of the information contained within your files with any third parties. The only people who can see or access your spreadsheets (including data downloaded from ClassDojo) are those who have permissions set for the file/folder in your Google Drive.  Be sure to follow your school’s policies/guidelines regarding ClassDojo and Google Drive & Google Apps for Education, and the best practice is to keep the Class Bank file and ClassDojo reports in a folder that is visible only to yourself.

bug reports & suggestions

If you have any suggestions or need to report any bugs, please contact me at:


PokéMath – Gotta Solve ‘Em All!

Ash and Pikachu celebrate 20 years together...Introducing… PokéMath! “Gotta solve ’em all!”

I decided I wanted to do something thematic in my classroom this year, and was originally considering a Minecraft theme, because I know that there are a lot of Minecraft-fanatics in my incoming class of students… (and it lends itself well to things we study: geology, various math concepts including area and volume, etc)

HOWEVER, with this sudden Pokémon Go tidal wave, I changed my mind. I just know that many students are going to show up to school Pokémon-obsessed, so why not ride the wave of enthusiasm instead of fighting it?? [To be honest, I had thought of doing PokéMath for several years now, but there had never been such a fervent Pokémon interest in recent years, until now]

How does PokéMath work?

In essence, PokéMath is just a thematic rebranding of a sticker/badge rewards system. In this case, students are awarded badges (pokémon) for each specific skill they master in Khan Academy! The pokémon are based on the wildly popular new Pokémon Go game (151 slated pokémon at this date, though not all are readily available), and the goal — of course — is to “catch ’em all!”

Students “catch” a pokémon by reaching mastery level of a specific skill in Khan Academy, as listed in the table below. At the end of each week (ie. usually on Friday), I will collect the student math folders (a plastic pocket folder with metal tabs for holding notebook paper.) After school (Friday evening or over the weekend), I will check the Student Progress and/or Skills Progress section of the Khan Academy coach dashboard to see which skills have been mastered. For any skills that have been mastered, I will locate the corresponding monster sticker on that student’s sheet, and will affix it to their folder!

In this way, students can maintain a “pokédex” of their collection as trophies to be proud of, to show off to their friends, and to remind them (every time they take it out for homework) that they probably still have many more to catch!

Materials & resources


As the teacher, I have set up my PokéMath table of creatures based on the following procedure:

  1. Set up a class in Khan Academy for your grade level (mine is 6th grade, so I assigned “6th Grade Mission”)
  2. In the Khan Academy Coach Report, go to “Skill Progress” to see the required strands/skills. Copy & paste the name of each individual skill within the strands. For each skill, right-click (CTRL-click on Mac) on the “Open skill in a new tab” link and and choose to copy the address (URL).I then pasted one skill per pokémon, based on the following algorithm:
    1. I put related concepts together in a pokémon “family”
    2. The more evolved the pokémon, the more challenging/advanced the concept I assigned (the last level is often “word problems”)
    3. I generally structured it in chronological order synced to our actual math curriculum (Pearson Digits — it is a different order/sequence than Khan Academy, but I use Khan in addition to it)… the more “rare” the pokémon, the later in the year we will learn the concept.


Students will obtain pokémon by mastering the requisite skill. The dashboard for Coaches in Khan Academy shows the level of mastery for each subject. There are various levels:

  • Struggling
  • Needs Practice
  • Practiced
  • Level One
  • Level Two
  • Mastered

When students go directly to the chosen skill and “pass” the practice activities for the first time, it counts as “Practiced”… in order to master the skills, they must then be passed in the Khan Academy mastery challenges.

Evolution & Spending Points

Pokémon are arranged into “families” — ie. there is a “base” pokémon, as well as later “evolutions” or iterations based upon that original base. To obtain the evolutions, students must start by obtaining the base by mastering the required task. However, after obtaining the base pokémon, there are two routes to evolution:

  1. Master the required skill listed for that evolution
  2. or Spend a certain amount of points (listed in table) to achieve the evolution

In this way, students have an alternate route to obtain evolved pokémon if some of the more advanced math tasks prove too challenging.

Where do these points come from?

That is up to you. In my class, they will be ClassDojo points.  Every day, when students come to class, they will have multiple opportunities to earn points simply by paying attention, putting in effort, being well-behaved, and exhibiting Growth Mindset. If they do these things, they earn ClassDojo points, which can be spent (in lieu of mastering the math skill) to evolve a pokémon!

Notes on Evolution:

  • Evolutions cannot be skipped. To get to the third level (2nd evolution), you must evolve twice. (ie. master two skills or spend the points for the first evolution, plus the points for the second evolution. Or a combination of the above.)
  • When students obtain an evolution, they still get to keep the lower-level pokémon of the same family. They simply add the new one in addition to the others.


Not a lot is required to do this!

  1. Set up a table — like the one below — and assign within it the skills you want mastered for each pokémon.
  2. Determine how/when you will check mastery. I will be checking every Monday, and it will be student responsibility to let me know they have obtained one (or more) for the week, which they will do by lining up at my desk and waiting for me to confirm in the Khan Academy records. To help facilitate this, the full PokéMath Pokédex (the table below) will be distributed to all students in Google Classroom, with an additional column labeled “Caught?” Students can monitor their progress in Khan Academy and, as soon as they reach mastery for a skill, should place an “X” in the caught column.
  3. Hand the student a sticker of the pokémon! I will be custom-printing them (templates in Google Drive folder linked below) on 3/4″ round labels, which will then be stuck onto the student math folder as a badge of progress.

More fun stuff: thematic groupings

I decided I wanted to go all out with the Pokémon theme this year (just for fun — I’m even going to show up to school dressed as Ash Ketchum!), so I thought about ways I could incorporate that into the classroom (other than thematic decorations and features, such as Pokémon wall decals and miniature Pokémon figurines.)

I use friendly competition a lot in my classes (middle schoolers love it!); in addition to the individual aspects, students are assigned to small groups (ideally 4 students), both for competition purposes but also for group-based activities. In the past, these groups would often have very uninspired names (A, B, C, D, etc), but sometimes I would make it a little more interesting by bringing an education theme into it. For example, when we did our Ancient Greek unit, each team became a city-state, and we had “Olympic games” competitions during PE (sometimes actual games, like teaching them how to throw a discus; sometimes more silly stuff, like “chariot races” aka wheel-barrow race.)

This year, the small groups could be organized as Gyms! To keep it simple and easy to remember, I will just use the old-school Kanto gyms from the original Pokémon games: Pewter City, Cerulean City, Vermilion City, Celadon City, Fuchsia City, Saffron City, Cinnabar Island, and Viridian City (easy to do, they are basically just colors. You can click here to find the colors.)

Sometimes I need to separate the class into larger groups… for example, when we do Jeopardy-style quiz-show review games. In the past, I would simply split the class in half down the middle… but perhaps this year I should split them into three Teams: Valor, Mystic, and Instinct?  (the numbers this year mean I will have 6 Gyms per class, so it would amount to 2 gyms for each Team)

In the past, I would just tally points on the whiteboard (this year I was even considering buying some printable magnetic sheets to slap up on the magnetic whiteboard, showing the team colors or insignia), but with 3 different classes coming to me for math this year, that could be a challenge.

Instead, I will probably just log all group points in ClassDojo (they have had a Groups feature for about a year now)… only one set of groups can be created, but they can be named such that the larger Team is indicated, such as “Pewter (Valor)”

Note: This still poses challenges for one-on-one competitions. Those will either have to be round-robin turn-taking events, where one team spectates while the other two compete… or the Teams will have to be “broken” into two equal number of groups.