Monday, July 28, 2014

Math, math, and more math

Last week was my own sort of math week. Seems like everything I read and posted about on was about math.

In February I read an opinion piece, "You Never Did Math in High School." The course that was the source of the author's ire? Calculus. Hang on to that.

Now why did this writer think students never did math in high school? Mr. Kun asserts "The problem is that American high school students are taught something named 'math' for four years which is not even close to math." Eyebrows raised. Say what??? After offering an insightful analogy using music, Mr. Kun quickly asserts that it is NOT the content. Math is very fine content. The issue is the way it is presented to students and the expectations most teachers seem to have for proof of student learning. He observes that most students who believe they are good at math are really saying, "I was very good at following obscure steps to manipulate mysterious symbols, without any real understanding of what I was doing." Let's go with that, shall we?

Then there was a series of article published in The New York Times.

July 23
"Why Do Americans Stink at Math?" asks Elizabeth Green. Well, maybe we don't stink at math. Maybe we stink at remembering which steps go with what. I remember scribbling formulas in the margins of a test and then seeing which one seemed to work out the best for each problem. I knew which formula to use for some problems, but for others I'd just try to plug in numbers and see if the answer seemed to make sense. Yea, I stunk at "math."

Ms. Green observes that Americans are constantly "reforming" education. Yes, we do re-form it. Various bureaucratic agencies become alarmed and then with typical hair-on-fire reaction, toss something on the educational flames and hope it doesn't explode into something worse. Without fail, teachers get frustrated because they aren't prepared and/or don't have enough PD and/or don't agree with the mandate so students get confused because the new shiny thing doesn't connect with last year's shiny thing. Because they are confused, they shut down and begin to hate math. Parents go beyond frustration because they don't see the correlations either, can't help their kids, and can't get an answer from teachers or administrators because there really isn't a good answer.

In all seriousness, Ms. Green reports on lesson study, an educational teaching and learning process that was and just might be in the process of becoming significant. Again. Lesson study is a very practical concept though difficult for most Americans to implement precisely as initially designed. However, with well-formed PLCs, lesson study is quite accessible and can make quite a difference across content areas. For more information on lesson study, you can explore the work of two of the godfathers of lesson study, Bill Saunders and Ron Gallimore. You can also explore the work of Brad Emerling, a protege, if you will, of both Dr. Saunders and Dr. Gallimore. Brad has another piece on lesson study here.

Just for kicks, you might want to read this piece by Ron on John Wooden.

July 24
"Don't Teach Math, Coach It" is published. Jordan Ellenberg equates learning and doing math to play, and uses his kids as great examples of math as a game.
What does it mean to coach math instead of teaching it? For C. J., it means I give him a “mystery number” to think about before bed. “I’m thinking of a mystery number, and when I multiply it by 2 and add 7, I get 29; what’s the mystery number?” And already you’re doing not just arithmetic but algebra.

For his little sister, who’s 4, that’s too formal. But say we’re at the grocery store and we need four cans of soup and she brings me two, and I say, “So we need three more, right?” and she says, “No, Daddy!” That’s really funny when you’re 4. It’s a game, and it’s math.
But Ellenberg also states that math is a skill that requires practice. He doesn't say that math is a content area that requires pages and pages of worksheets. While the example he gave for C.J. may not be sufficiently "real life" for some while the situation he presented to his 4-year-old daughter is. On the other hand, I'd say the mystery number that either put C.J. straight to sleep or kept him up for a while is an exercise in problem-solving. C.J. had to figure out how to figure out the mystery number, so he had to make sense of the data he had. He had to determine if he had enough information to solve the problem. Now that is real life.

July 28 (2012): "Is Algebra Necessary?" Yep, two years ago Andrew Hacker asked this question. And it is one that is asked all too frequently.

In Feb 2009, Arthur Benjamin asserted that students should be learning statistics before they learn calculus.

In 2012, the National Council of Teachers of Mathematics (NCTM) issued a position statement about calculus with the Mathematical Association of America. The general statement reads:
Although calculus can play an important role in secondary school, the ultimate goal of the K-12 mathematics curriculum should not be to get students into and through a course in calculus by twelfth grade but to have established the mathematical foundation that will enable students to pursue whatever course of study interests them when they get to college. The college curriculum should offer students an experience that is new and engaging, broadening their understanding of the world of mathematics while strengthening their mastery of tools that they will need if they choose to pursue a mathematically intensive discipline.
 The statement is a bit passive aggressive but suggests calculus is not the course in which all students must aspire to secure a passing grade. However, the background statement clarifies the position statement and makes it clearer that the MAA and NCTM understood the implications of the calculus situation.

Business Intelligence reported in 2013 that MBAs can't stop with calculus because of the high value of statistics in business. Noting the usual progression from algebra to calculus, Manyika and Chui, the article's writers, state that "This time-honored curriculum seems increasingly out of touch in a world that is flooded with noisy and voluminous data." Understanding of and capability with statistics is clearly more valuable.

Last but not least, an article in Forbes asked "Should We Stop Teaching Calculus in High School?" to make way for statistics and computer programming. In other words, encourage students to take math courses that are more relevant to them.

Provided, of course, the foundational courses are more than just drills for skills rather than actual learning to understand the beauty of the mathematics.

Tuesday, July 22, 2014

While we're talking about assessments: the absurdity of [standardized] tests

This just in: test scores are no sure guide to what students know. It has to be true because it's a headline in The Wall Street Journal.

The article is positioned about Common Core, sort of. That students in Kentucky and New York who took the tests did not do at all well. In fact, according to the article, the results were dismal.
The results alarmed parents, but the scores on these new tests—just like those on earlier forms of assessment—reveal less about what children know than about the way the test makers decide to measure that knowledge.
The article goes on to address cut scores and benchmarking, ways to identify the levels of proficiency. Well before Common Core, grading and test results has been an issue. What does an 82% on a test really mean? That the student got 82% of the questions right, which means. . . what?

In other words, tests rarely really indicate what students know. Test scores indicate how well students read and understand the questions, how well they are able to discern the correct answer on a multiple choice question or how well they guess, how well they are able interpret what the teacher might want to see in a short answer or essay question. If the questions require students to do something, such as a math or science question, they still need to be able to read and understand the question. And, significantly, while they are studying, they need to be able to discern, guess, and/or anticipate what the teacher might ask on the test and how the teacher might choose to measure what the students have studied and memorized.

In many cases, there is absolutely no proof of learning based on test results. That is, I believe, as much the fault of the test makers as it our expectations of what tests reveal.

So why do we give tests? Habit is my immediate facetious response. Testing is deeply ingrained in the fabric of our educational process.

I'm not saying there is no room for the kind of assessment that looks and feels like a test. But let's be realistic about our expectations of what any kind of test will reveal about student knowledge and learning. Written tests have to be supplemented by other forms of demonstrations of knowledge.

Those who are proponents of PBL, MakerSpace, genius hour, and hackschooling are well aware of the differences. Students demonstrate all kinds of knowledge and learning at a wide range of levels through and because of their experiences with any of these forms of learning and, yes, assessment.

The challenge is how to measure every US student so we can gauge their test-taking skills against those of every other student in the world. We seem to be so obsessed with uniformity and conformity of the assessments so we can be better than mediocre in the world that we've forgotten there are other measures of whatever we mean by student success.

Student success. What does that mean any more? Does it mean a student's ability to reach the highest benchmark of proficiency? And how do we know if that proficiency benchmark is consistent for every other student in every other state? We don't. What teachers in one state think is "well below proficiency" might be different from what teachers in any other state think is "well below proficiency." This could go on and on, and that's my point. Even if we had a national curriculum, we will never have an absolutely uniform and consistent measure of "student success."

I watch cooking competition shows: Chopped, Master Chef, Food Network Star. There are always three judges. Each competitor cooks based on whatever the challenge and each judge samples each competitor's food. Then they discuss the merits of each dish. Every dish is assessed on taste and presentation. It's a simple set of criteria though the nuances of each of those criterion are complex. The judges don't always agree but they come to agreement to determine who moves and who does not.

When I worked in the corporate world, I was assessed based on my performance. I gave an assessment of myself using the company standards and the goals my manager and I had set for me. My manager assessed my performance using those same criteria and his or her interpretation of how well I achieved my goals. It's not as though we talked only twice a year, so there were on-going conversations related to my work and our 1:1 meetings occasionally focused on my progress with my goals. At the end of the day, was I one of the best project managers in the company? in the state? in the country? in the world? Maybe in the company, but the rest? Meh. Who knows? Did I help the company achieve its goals? If I did, I was rewarded accordingly during my merit review.

I mention the cooking competition shows and the corporate world for several reasons.
  • First, as I continue to contemplate how we assess our students and their learning, I'm reaching into other areas to think about how we figure out what our kids know and can do. 
  • Second, when Gordon Ramsey proclaims the next Master Chef, that will be the opinion of three expert judges. Does that mean that home cook is better than every other home cook in the world? Yes. For that moment. Based on the expert opinions of those particular three expert judges.
  • Third, as I think about how we measure "student success" and how we measure ourselves in the vastly diverse country as well as against the rest of the world, I wonder how far off kilter we've gotten in trying to determine educational supremacy.
  • Fourth, it seems to me our priorities for assessment are completely wrong. It is not about the percentage of students who pass the 8th grade assessment at a particular level, which probably tells us more about the days or weeks of test prep leading up to the assessment rather than what students really know.
When we assess student learning, we should be finding ways for students to demonstrate what they have learned and be able to explain how they've learned it. When we assess student learning, it seems to me we should be helping students determine their strengths, their weaknesses, their capabilities and competencies, their passions so they can be successful however they deem success in their lives. Sure, most of them will need some guidance and adult supervision. And many of them will have to be cajoled to do work in areas that seem less interesting to them because they don't yet understand its value. But the big question isn't if students can reach a high level of proficiency on a standardized test. The real question is whether or not students have truly learned anything that will enable them to lead lives as successful, productive citizens. . .however they ultimately choose to define "success."

In the WSJ article, Mr. Rockoff, an economist at Columbia Business School, said, "The deeper question parents ought to be asking themselves is 'Did I know what my kid was learning last year, and if I compare it to the new Common Core curriculum, am I happy or sad?'"

With all due respect Mr. Rockoff, I think that's the completely wrong question. The deeper questions parents should be asking themselves this is this: Did I know what my kid was learning last year? Do I know what my kids are learning this year? Do I understand why my kids are learning what they're learning? More importantly, do my kids understand why they are learning what they're learning and how do they know what they've learned?

More to come.

Wednesday, July 16, 2014

Where engineering and English majors end up

Pew Research. I do love their work because I am a research geek. As much as I like research, I find it compelling and comforting when real-life anecdotal experiences support, maybe enhance, the research.

According to the Pew Research folks, ". . .only about 26% of physical-sciences majors work in any STEM occupation at all; their biggest employment categories are health care (17%), non-STEM managerial jobs (14%) and education (12%)."

So maybe we're asking the wrong questions.

I'm not a STEM expert by any stretch of the imagination, but physical science majors working in health care doesn't seem to be a big surprise, nor does the move to education. I can only hope they got their teaching certificates and are encouraging students that science can be really cool and, perhaps, training the next generation of science mavens.

While the chart is interesting in its specifics, I think the story it tells is even more interesting. But let me back up to those real-life anecdotal experiences. I had a student who was an English major. She wasn't really sure what she was going to do with that degree, but we knew she had a lot of options and not just because English majors generally have excellent research and communication skills. Once she graduated she realized what she really wanted to do is teach, so she got her Master's degree with her teaching certification and has been a teacher since.

A friend of mine majored in computer science and operations management. While she had a long and steady career in the computer industry, she has become a life coach with a wide range of ministry. She's still organizing and helping others organize, but on a very different level than she once did.

Still another friend of mine majored in education. She taught for a period of time and then circumstances necessitated a change. She started working for a university and took a chance on a whole new opportunity, which led to work she's been doing ever since. And, for a period of time, she was able to be an assistant coach, which fed her passion.

One other friend of mine had aspirations to be an astronaut. He pursued computer science and engineering and he got to work on some projects that supported the space program. Eventually he left the computer industry to open a travel agency and pursue his lifelong passion of music, so he still DJs and he has a band.

Over and over again, whether through friends or former students or my own life experience, it's easy to see that a college major is often an incidental indicator. Everyone wants to do meaningful work, and that's not always possible. Sometimes the work is meaningful to someone, but it's not what feeds our souls.

Sure, my friends are boomers and my former students are not the current millennial generation. But time and time and time again, what I see and hear are people talking about passion. Those who end up doing work that is also their passion are blessed. Those who are able to do work that enables them to pursue their passions are also blessed. Those who pursued work to get stuff have found their lives a bit emptier, in spite of all of the stuff. That's what today's millennials see and why they are more interested in work that has meaning and work that enables them to pursue their passions.

We shouldn't be surprised when an English major ends up doing pretty much anything because English majors are well equipped to do many things. We shouldn't be surprised when an engineering major ends up as a manager for a non-STEM company because what led that student to become an engineer has something to do with the way he or she thinks and is. (Management can be a form of engineering, I think.) We shouldn't be surprised when folks find ways to intersect their interests with their work. Those who have been able to make those intersections have been doing so for generations.

When I advised my incoming freshmen, and tried to assuage the concerns of their parents, I asked those kids what they wanted to do if time and money were of no concern. Keep in mind these kids were college freshmen, so only a few months out of high school with their whole lives in front of them. They were more honest when their parents weren't in the room, especially those who had parents who wanted to answer for them, projecting parental dreams and aspirations on their kids. And we'd talk through the hopes, dreams, and passions of the kids to try to find a major, perhaps along with a minor, that would help propel them.

But I would often tell kids and parents alike that a college major isn't a guarantee nor is it a life sentence. At most, it is a doorway to a lifetime of opportunities. I had a student who got to the end of his junior year and just knew he was in the wrong major and going after the wrong things, so he changed his major and I helped him explain why he was going to be on the 5-year plan for graduation. He worked hard to catch up and finish only a year late, and was so much happier for it. Pursuing a college major is often a way of discovering what one might be as much as it is learning what one is not.

By all means encourage students to pursue science, technology, engineering, art, mathematics, music, biology, graphic design, culinary arts, and English. But don't pay any attention to the trumpeting headlines that suggest some degrees are worth less than others because a college degree is only part of anyone's story. And a college degree is not the end of learning, not by a long shot.

Where any student with any degree ends up depends on years of choices, including what should be years of pursuing more and other learning, most of which rarely takes place in a classroom.

Monday, July 7, 2014

Getting ready for college/career: Smash the damn box

I like to daydream about the future. Ross Dawson is one of many futurists who make a living thinking about the future: studying global trends, examining growing technologies, and then helping organizations prepare for the world in which their current customers will eventually be living and working.

Dawson's "The Future of Work" framework released in September 2012 offers some of his insights into what the world of work might look like in 2025 and refers to the key drivers that will drive that change.

There have been and will be many articles on what work will look like and how technology is changing it. TIME did a whole spread on the new work order. Forbes has published several articles including "The Future of Work (and Life) is Conscientiousness," "10 Ways Millennials Are Creating the Future of Work," and "Defining the Future of Work."

Two key things are consistent: technology and collaboration. What also seems to be consistent is that work will increasingly focus on what you do, not where you do it. In other words, in our increasingly global society and with a wide range of technological offerings that make it easier to connect, the work place is less important than the work. On the other hand, even millennials are mindful of the need to balance the power of technology with the importance of all other soft skills.

So I thought more about these articles and the insights of futurists as I considered the infographic on the 10 most important work skills for 2020: sense making, social intelligence, novel and adaptive thinking, cross cultural competency, computational thinking, new media literacy, transdisciplinary, design mindset, cognitive load management, and virtual collaboration.

Many of these are somewhat self-explanatory; the infographic does a good job of providing some context and additional information. I don't think, though, that too many of these are really new.

A lot of forward-thinking companies already expect these skills from their employees even if they don't use these terms. What might be different is that the expectations are coming from across work place disciplines. It used to be that certain skills existed only in some work place disciplines; that is, some skills required in the financial domain might not be required in manufacturing. Because of technology, things can change with some degree of rapidity in the work place. Because of globalization and technology, things can change fairly dramatically and quickly.

I think a skill that's missing is the ability to determine what is real change and what is going to flame out after it's gotten it's 15 minutes of fame in social media. Because there is so much potential for change and because social media enables the ridiculous and the sublime to go viral, organizations could exhaust themselves chasing after whatever might be the Next Big Thing. So knowing how to use those important work skills intelligently and with a clear understanding of the vision of the organization may be even more important.

Ayelet Baron is another futurist. Her ideas about the future of work can be found here. She reminds us to think about the work force and who will make up the preponderance of the work force in a decade or so. She reminds us of the importance of those in leadership to be thinking now, and I mean RIGHT NOW, about their organization's core competencies and how the organization needs to prepare to adapt over the next few years to be ready not only for the customer expectations of work, but the work force's expectations of work.

My dissertation chair, Dr. Dwight Allen, is a futurist. People would say of Dwight that he didn't think outside of the box because he didn't know there was a box.

It is my considered opinion that high school and college/university educators need to use some of these resources as they reflect on the design of their syllabi and lesson plans for the upcoming school year. In fact, elementary and middle school teachers should be aware of these resources. In fact, superintendents and principals should ensure there are periodic meetings of K-12 teachers to discuss implications of the future of work trends (not fads) and how those implications might inform their students' learning.

And then when teachers discover ways to integrate problem-based learning, action research, maker/tinkerer/inventor learning, competency-based learning, and passion-based learning, they will quickly see how easy it can be to enable their students to begin to develop or to refine the very skills they may need for their futures.