

Image: http://harvardeducation.tumblr.com/post/97884586499/today-hgse-proudly-launches-our-campaign-underLast spring, I completed my Master’s degree at the Harvard Graduate School of Education (HGSE). As the next batch of new students will be starting classes in a few weeks, I’ve been thinking back to the school’s slogan: “Learn to Change the World.”

Seperately, I’ve been listening to the soundtrack to Hamilton. At one point, Hamilton’s sister-in-law receives a letter from him. In response to the greeting line of the letter, she sings, in reply:

It says: “My dearest Angelica,” with a comma after “dearest.” You’ve written, “My dearest, Angelica.”

Image: http://cdn.thewritepractice.com/wp-content/uploads/2011/08/the-oxford-comma.jpgCommas are important, obviously. This is certainly true of the HGSE slogan. The meaning changes, subtly, when a comma is added: “Learn, to change the world.”

In general, I’m a strong advocate of learning how to change the world–the “non-comma” version. I once created and co-taught a course called “Be the Change(maker)” for undergrads which explored exactly this topic. I’m a firm advocate of the idea that such skills can, in fact, be taught.

However, I’m also intrigued by the deeper implications of including a comma. Instead of learning how to change the world, this elevates the learning, itself, to be a radical act of change.

Learn to change the world.

Learn, to change the world.

If we really believed that the act of learning, itself, could be transformative and, in fact, world changing, what would schools look like?


Education Cities’ “Education Equality Index” is a metric with problems

Education Cities has released a new report and interactive data on achievement gaps nationally. They have collected a large national data set and have created a new metric, which they are calling the Education Equality Index (EEI) in order to compare changes in achievement gaps in schools, cities, and states over time. Their calculations are based on pass-rates on state tests for students who are eligible for free or reduced lunch (FRL).

It is exciting that they are attempting to collect, organize, and interpret achievement gap data nationally, and the website provides great interactive graphics to dig into the data.

However, the EEI metric they have created is extremely problematic, to the extent of being nearly un-interpretable.


Strangely-triangular “normal” distribution from the methodology page

The methodology they released is a bit vague, but, essentially, to calculate a school’s EEI, they create a pseudo-school made up of just the school’s FRL students, calculate the performance of this pseudo-school as percentile compared to all of the other (real) schools in the state, and then do some adjustments. These school scores are combined to calculate city and state EEIs.



EEI doesn’t really measure equality or size of the achievement gap

Based on the information that has been released about their methodology, here are a few of the big concerns I have about the metric: things that are true about EEI, but that shouldn’t be true of any good measure of achievement gaps and academic equality.

  1. It is possible for two schools with identical EEI scores to have massively different internal achievement gaps.
    Assume that both schools enroll the same proportions of FRL students.Slide1
    At School A, the same percentage of FRL and non-FRL (say 70%) pass the state test–there is no gap.
    At School B, 70% of FRL students pass the test (just like School A), but, here, 100% of the non-FRL students pass–the gap is 30%. Slide2
    However, these two schools would have the same EEI score! EEI is publicized as a measure of equality (“Education Equality Index”), but a measure of equality is invalid if it gives the same rating to these two schools, which clearly have very different achievement gaps! 
  2. It is possible for the gap to be WIDENING in a school or small city, and yet that school or city shows improvement on the EEI. If a city’s non-FRL students increase by more than the FRL students, then the gap is widening, by definition. However, if the FRL students increased by more than other schools in the state, the EEI will improve. A metric publicized as being a measure of equality is not valid if it can improve when scores become less equal.
  3. A school or small city’s EEI (and the direction the EEI is moving–which supposedly indicates widening or shrinking achievement gaps) depends on arbitrary proficiency cut-scores.  Basing calculations on percentages of students who pass as opposed to students’ average scores has been well-documented to distort achievement gaps for several mathematical reasons. See this article, based on work by Andrew Ho, for more details.
    In addition to the problems described in that article, using such a metric as the raw data to construct the EEI leads to an unacceptable characteristic of EEI–that the EEI (and subsequent conclusions about existence of a gap, size of the gap, and change in the size of the gap) all depend not just on students’ actual test scores, but also depend on an arbitrarily chosen number, the cut-score. It is absurd that a school or city could be praised for closing an achievement gap (if the cut-score is set at 350), but that same school or city could be criticized for NOT closing the achievement gap (if the cut-score were to be set at 370)–even though the students’ actual test scores are identical in both situations. Whether or not an achievement gap exists is not dependant on an arbitrarily chosen number, so a metric that claims to quantify an achievement gap should not be, either. 

    Here are some more details about how that could happen (optional): 
    As a thought experiment, imagine a state’s cut-score was 0 points–anyone who writes their name passes. In this case 100% of non-FRL students would pass and 100% of FRL students would pass: there is no achievement gap. Now, assume the highest possible test score on the state test is 500 points and imagine that the cut-score was 501–so high that no one can pass. Since 0% of FRL and 0% of non-FRL students pass,  there is also no achievement gap. Now, assume all of student tests have already been graded and each student has a particular score. Now, it just remains to determine if they passed. Imagine slowly sliding a hypothetical cut score from 0 points (where everyone passes) to above 500 points (where no one passes). As you slide, the percentage of students who pass decreases for FRL and non-FRL students in the school or city AND at the state level. As these numbers change, each school’s EEI will go up and down in a complex way that depends on the score distributions of each of these groups of students at all schools across the state, the proportions of FRL students at each school, and the total number of students at each school. In some cases, there can be particular values of the cut-score at which a school’s EEI may be higher than last year’s EEI (indicating a shrinking achievement gap) and at other particular values of the cut-score the EEI may be lower than last year’s (indicating a widening achievement gap). A state’s choice of a cut score shouldn’t be able to determine whether or not an achievement gap exists!
    In Education Cities’ defense, they were basing their analysis on these kinds of scores (reported as “% who exceeded a cutoff”) since that is what they had access to from states, as they apparently didn’t have student-level data. While this is understandable, it makes the analysis susceptible to these problems.

EEI is impossible to interpret (and designed that way)

It is hard to tell from just looking at EEI what each point on EEI actually represents. Moving from an EEI of a 32 to 33 means what exactly?

Unfortunately, although this metric is quite abstract, Education Cities has chosen to scale it onto a range of 0 to 100, making it very easy to misinterpret as some kind of percentage (which it is isn’t) or some kind of percentile, which it only kind-of is.

This 100-based scale also makes lay readers assume that 100 is a perfect score, but 100 may not actually be achievable, in most cases. Additionally, any EEI of 100 (or near 100) indicates that FRL students are doing substantially better than their non-FRL peers, which is actually a very non-equal situation and one that a valid measure of “equality” shouldn’t favor.

However, because EEI is designed to be on this 0-100 scale, it makes it very easy for people to misinterpret EEI data. For example,  Chalkbeat TN:

While Memphis’ gap is larger than 70 percent of major U.S. cities, it narrowed the gap by a whopping 19 percent between 2011 and 2014, one of the fastest rates in the nation, the study says.

Narrowing the achievement gap by 19% is NOT a valid interpretation of an EEI change from 23.7 in 2011 to 28.3 in 2014. Yes, the EEI has increased by 19%, but EEI isn’t directly a measure of points of achievement gap decline. It would be correct to, instead, say something like:

An abstract metric that can’t be directly interpreted due to its design but that is somewhat related to how Memphis’ FRL students performed relative to all students in the state has increased by 19%.


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This image has been going around online for the past few days:

A student was asked to use the “repeated addition strategy” to evaluate 5×3. The student wrote 5+5+5 and got 15 as a final answer. However, points were taken off since the student was apparently supposed to write 3+3+3+3+3. A point was also taken off of the second question for a similar reason (the student made 6 rows of 4 marks, instead of 4 rows of 6).

Some people use this as a critique of Common Core, saying that any set of standards that leads to this must be flawed.

Other people have defended the teacher for various reasons including that the teacher is being intentional about teaching the techniques/thinking that will be most useful later on when students deal with operations that aren’t commutative (subtraction, division, matrix multiplication, etc.) or that “if the teacher has not covered the commutative property, then it might be unwise to let a student continue with this line of thought.”

Both groups of people are wrong.

First, teachers should never take points off for this. If I were the student whose work lost points in the image above, I would probably never forgive this teacher, and not take him or her seriously for the remainder of the school year, which is no one’s best interest. I assume I would not be alone in having that reaction. Similarly, the above argument that this would only be acceptable if the commutative property had already been explicitly taught is absurd. Punishing students for having (correct) mathematical insights that have not yet been taught is counterproductive.

However, just because a teacher should not have taken points off here doesn’t mean the Common Core is flawed. It is a GOOD thing that the Common Core encourages teachers and students to think about math using various mental models (here, thinking of multiplication as repeated addition or as an array). If you haven’t thought about it before, it is actually not immediately obvious why 5+5+5 should be equal to 3+3+3+3+3.

For people fluent in math, we interchange 3×5 and 5×3 automatically in our minds without thinking about it (this called commutative property). For people already fluent in math, it is still valuable to think deeply about why it is actually the case that 3 groups of 5 is actually equivalent to 5 groups 3.

For people not (yet) fluent in math, it is valuable to think deeply about why this actually the case so that this can be integrated into their understanding of math as they develop math fluency. Looking at 3×5 and 5×3 both as repeated addition and as arrays helps students to more deeply understand what is really going on here. The Common Core, like every good math teacher, WANTS kids to realize that these are all different representations of the same thing.

Here’s what could have happened, consistent with both Common Core and common sense.

Teacher asks four questions:  

  1. Evaluate 5×3 by repeatedly adding 5 the proper number of times.
  2. Evaluate 3×5 by repeatedly adding 3 the proper number of times.
  3. Compare your answers in 1 and 2. Notice anything surprising? Explain.
  4. Evaluate 4×7 by repeated addition in two different ways.


  1. Evaluate 5×3 by making an array with 5 rows.
  2. Evaluate 3×5 by making an array with 3 rows
  4. Evaluate 4×7 by making an array in two different ways.

When the students later discuss division (or WAY later when they discuss matrix multiplication), there can then be separate deep conversations about why those operations are not commutative.

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The “challenge zone” and group norms

You may be familiar with the following model of task challenge and learning:

Comfort Zone, Challenge Zone, Panic Zone

Comfort Zone: Tasks are easy and comfortable and pleasant–little learning occurs.

Challenge Zone: Tasks are complex enough to push the boundaries of one’s thinking and skills and maintain active engagement–lots of learning and growth occurs.

Panic Zone: Tasks are far beyond current abilities, anxiety and fear take over and people become overwhelmed and shut down–little learning occurs.

Students of educational psychology may recognize some parallels to the Zone of Proximal Development.

I’ve seen several other names for each of the three levels:
Comfort Zone Boredom Zone
Challenge Zone Risk Zone, Stretch Zone, Learning Zone
Panic Zone Chaos Zone, Danger Zone

I’m a fan of this Comfort/Challenge/Panic model and frequently use it as an internal check on the things I’m doing. When I’m in my Comfort Zone too often, I seek tasks that push me more. When I’m in my Panic Zone, I seek support (and learn to avoid what got me there in the first place).

I was recently in a the first meeting of a yearlong conversation about race and diversity at my university. To start off, the facilitator led a necessary, but otherwise un-noteworthy chat about group norms (well within my Comfort Zone).

Then, she presented the comfort/challenge/panic model of learning (cool, but still not really pushing my thinking).

Then, she guided a jump into my Challenge Zone!

She linked the norms conversation with the comfort/challenge/panic model:  “these group norms are what will keep us in the challenge zone as a group.”

Whoa. Mind blown.

Stretch Zone and Performance

If you want, you can think of learning as an example of “performance,” here.

We didn’t get to dig into this as the group, unfortunately (do we need a norm for when/how to “parking lot” ideas?), so I’d like to explore a bit more here, and get your thoughts.

The underlying theory seems to be that a group functions better and more learning occurs when people are in their Challenge Zones and that well-designed and well-implemented norms enable people to spend more time in their Challenge Zones.

This certainly seems plausible, but I have some more questions:

  1. Are well-designed and well-implemented norms necessary and sufficient to keep the group in its Challenge Zone?
  2. Is it necessary and sufficient for a group to be in its collective Challenge Zone in order to have optimal dialogue and optimal learning?
  3. How do personal Challenge Zones relate to group Challenge Zones? (Can a group be in its Challenge Zone while only some members are in their Challenge Zone? Is it possible for each of the group members to be in their own individual Challenge Zones, but the group as a whole is not?)

I’m curious to hear your thoughts on Q #1-3 above!

As an added twist, what happens if we replace “group” and “learning” with “team” and “performance?”

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My Philosophy of Education

For one of my courses, students were asked to bring a quick summary of their philosophies of education. Here is (a slightly modified version of) what I wrote.

I have lots of opinions about education. I think most emerge from what is written below. This is a work in progress and I’d love be to able to tighten or focus this, as well as explore any aspects of my thinking about education that aren’t captured here. Please share your thoughts!

“Your curiosity is valid. Your frustration is valid.”

Education is what has happened when you can see the world more clearly and/or connect more deeply with a person, idea, or work of natural or human-created beauty. “You” can be an individual (of any age), or a collection of individuals, or an institution of any kind. Education usually happens informally (often entirely by chance) and can sometimes happen by design.

Education is most likely to be deep and lasting (and occur at all) when you, your peers, your authority figures, and the institutions you are attached to agree with the following two statements both explicitly, in frequently reinforced words and actions, and implicitly, in structures and values:

1: Your curiosity is valid.

image from https://i1.wp.com/web.stemiliescps.wa.edu.au/wp-content/uploads/2014/07/156799-o.jpgWhen it is perfectly obvious to you that you are capable of, permitted to, and encouraged to pursue the little or big things that intrigue you, you learn. When you are surrounded by (and coached by, and coach of) lots of other people who are empowered to pursue their curiosity, these people model deep engagement for you AND you learn about and can build off of all of things they are curious about.

2: Your frustration is valid.

It is normal to be frustrated by a wide variety of you-specific and general things, big and small. When you know that this is normal and that, in fact, you may even have frustrations in common with those around you, it is possible to stay engaged with those frustrations to explore ways to image from https://i0.wp.com/sparkimurs.com/images%202009/Quote%20Frustration%20M%20Scott%20Peck.jpgproductively address and work through those frustrations, and maybe even innovate a new solution to alleviate the frustrations of lots of other people!

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The chair rotates 360 degrees!

My 88-year-old grandmother recently got a new desk chair. It is a pretty typical chair.

After putting it together for her, I walked her through getting the back adjusted to the right level. We discussed how to use the lever on the side to move the seat up or down and how to push the lever inward to lock the back and prevent it from rocking.

There are wheels on the chair, but it was physically difficult for her to roll the chair while sitting in it, so we got it set up so that, when she wanted to sit down, she could turn the seat a quarter turn to the side, sit down, and rotate back towards the desk so her legs went under the desk. She practiced all of these skills (actually, we went through a pretty solid “I do–We do–You do”) and she got the hang of this new-chair technology pretty quickly.


My grandmother reads and underlines the direction manual for every item that she owns, regardless of how simple or straightforward I think the item actually is and regardless of the extent to which she already knows how to get the desired functionality from the item. True to form, she read the direction manual for the chair.

I got a call the next day:

“I was reading the directions…”

“Yes, grandma.”

“It says the chair rotates 360 degrees–all the way around! I tried it and it works! Did you know it did that?!”

“Uh, yes.”


Since then, she has mentioned to me at least one additional time how excited she is that the chair goes all the way around (“360 degrees!”).

Until she shared her excitement (repeatedly), it never crossed my mind that:

  1. It wasn’t perfectly obvious that the chair went all the way around. (Particularly since we had even practiced doing a quarter-turn).
  2. The fact that it went all the way around was exciting!


This provides a useful reminder for anyone seeking to “educate” someone else on a particular topic: a detail you may not even consider discussing since (you think) it is so obvious could lead to an insight that will bring great joy to one of your students!

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How I think about conflicts

When thinking about most conflicts, large or small, I find myself mentally organizing people’s responses to the conflict into particular rungs within this ladder (a personal model adapted from the work of the Arbinger conflict ladderInstitute, Sustained Dialogue, and other sources)….

0. Anger.

My side is good, righteous, brave, wise, noble, thoughtful, moral, rational, etc.

The other side is cruel, evil, inhuman, immoral, irrational, ignorant, etc. and may be terrorists bent on the destruction of something I hold dear (literally in some situations, figuratively in others).

1. Acknowledgement.

I acknowledge that the other side may feel just as firmly about its beliefs on this issue as I do about my beliefs.

I don’t agree with the other side’s view, but I realize that this view exists and that the other side disagrees with me for reasons that IT thinks are valid (even if I don’t think those reasons are valid).

2. Respect.

I acknowledge that while they and I may have some fundamental disagreements on the issue at hand, I do, in fact, have some things in common with the people on the other side and may even agree with them on some (possibly small) aspects of the issue.

I believe that (at least most of) the people on the other side are good people, though I may disagree strongly with them.

3. Empathy.

While I firmly maintain my own identity and my beliefs that my own views on the issue are correct, I acknowledge that people on the other side may have different views that may also be correct, even if those views seem to be in conflict.

That there are legitimately pros to my side and cons to my opponents’ side does NOT imply that there are no pros to my opponents’ side nor does it imply that there are no cons to my side–my opponents may indeed be CORRECT about the pros to their side and the cons to my side.

It is always valuable to be intentional about exploring for the good on the other side.


4. Ubuntu/Heart at Peace.

This ladder rung is best defined by MLK, Nelson Mandela, and Anne Frank:

“When you rise to the level of love, of its great beauty and power, you seek only to defeat evil systems. Individuals who happen to be caught up in that system, you love, but you seek to defeat the system.” — MLK, Jr. (11/17/57).

“Darkness cannot drive out darkness, only light can do that. Hate cannot drive out hate, only love can do that.” — MLK, Jr.



Some observations:

  • This ladder applies to conflicts on a wide spectrum of sizes: from small interpersonal disputes (with a neighbor, boss, family member, etc.) to major international conflicts and everything in between.
  • Moving up this ladder is much easier said than done; moving up this ladder is much easier for conflicts you can see from afar. Regardless, it is important to move up this ladder.
  • It may sometimes appear that gains can be made by your side by moving to lower levels of the ladder. It may indeed be correct that you can score short-term gains. However, every time you do this, you make it harder for yourself, others on your side, and (particularly) people on the other side to move up the ladder in the future.
  • Personally moving up the ladder does not require others on your side to also move to higher levels of the ladder and does not require others on the other side to also move to higher levels of the ladder. In the short-term, it may be unlikely for anyone else to do so, but in the long run, the higher you move on the ladder, the more possible it is for others on all sides to also move up the ladder.
  • Regardless of whether you initially care about the interests or lives of people on the other side, it is always in your own side’s (long term) self-interest to move higher up this ladder.
  • The longer aconflicthas been happening and the angrier the participants, the more likely the following:
    • Many people are at low levels on the ladder.
    • The conflict may only be resolvable in the long-term by moving towards the top of the ladder.
  • Most propaganda exists at level 0. In fact, a good test of whether you are sharing propaganda (on Facebook, for example), is if the item you are posting fits nicely at this level.
    • Sharing level 0 propaganda may indeed be helpful in the short-term (see the bullet above about short-term gains). However, it is not in your side’s best interest in the long-term (let alone the best interest of everyone else) as it puts downward pressure on everyone– pushing them towards low rungs of the ladder.
  • Adaptive Leadership is a powerful framework for thinking about how to empower people to move to levels 3 and 4 and how to push them to productively work to resolve the conflict once they are there.
  • Rungs 0 and 1 refer to the other side as “it.” Rungs 2, 3, 4 refer to people on the other side as “they.” This is intentional.
  • Most of this is written in terms of “my side” and “the other side.” In reality, in many conflicts there may be lots of sides (not just two). Moving higher up the ladder may help you see more of those sides.


Think of some conflicts you are currently involved in or aware of. Think of some small scale interpersonal conflicts and think of some large scale political or international conflicts.

For each conflict you thought of, at what level of the ladder is your current thinking? Do you want to move to a different level? Why or why not?



Posted in Convopointer, Leadership, Political thought | Tagged , , , , , , , | 8 Comments