Adults can calculate with fractions

Posted on January 26, 2013 by Zachary_Goldman

Diane Ravitch’s blog recently posted a piece by a math teacher named Stephanie Sawyer who complains about the new Common Core math standards.

I certainly have my own concerns about the Common Core (probably a topic for a separate post), but I very much disagree with much of this teacher’s criticism that the Common Core doesn’t teach the standard math calculation algorithms early enough.

Actually, I think that some of the basic algorithms–long division, for example–probably should NEVER be taught, let alone in elementary school! (I’m somewhat less opposed to alternate algorithms like partial quotients.)

Despite disagreeing with the premise of this piece, she made one particularly thought-provoking point mid-way through:

I can ask adults over 35 how to add fractions and most can tell me. And do it. And I’m fairly certain they get the concept. There is something to be said for “traditional” methods and curriculum when looked at from this perspective.

First of all, she seems right: when interacting with adults, I assume that they have a basic number sense and a sufficient understanding of fractions. They know that \frac{1}{2} of something is more than \frac{1}{3}, they know that \frac{1}{3} of something plus another \frac{1}{3} is \frac{2}{3}.

Many, but probably a smaller number, might be able to determine that \frac{1}{2}+\frac{1}{3}=\frac{5}{6}.

Many adults can add and subtract large numbers by hand. Many can probably even explain the concepts of place value, carrying, regrouping, etc. (However, while these people do probably have some understanding of these concepts, I’m less certain that they understand deeply enough to be able to apply these in a new situation–maybe numerical bases besides base 10.)

Many people can probably also divide somewhat large numbers by hand (or at least divide a large number by a small number), but I am sure that a very small percent of adults understand why long division actually works.

Sawyer seems very concerned that her 4th grade son can’t divide by hand:

When asked to convert 568 inches to feet, he told me he needed to divide by 12, since he had to split the 568 into groups of 12. Yippee. He gets the concept. So I said to him, well, do it already! He explained that he couldn’t, since he only knew up to 12 times 12. But he did, after 7 agonizing minutes of developing his own iterated-subtraction-while-tallying system, tell me that 568 inches was 47 feet, 4 inches. Well, he got it right. But to be honest, I was mad; he could’ve done in a minute what ended up taking 7. And he already got the concept, since he knew he had to divide; he just needed to know how to actually do it.

Is her complaint really that “he could’ve done in a minute what ended up taking 7?” If this is really her concern, than just buy the kid a calculator! He can do it in 5 seconds then!

To me, this story illustrates a HUGE educational success. First, the student knew to DIVIDE by 12 to convert inches to feet. A very common misconception among students (even many quite a bit older than 4th grade) is to try to multiply by 12 in this situation since feet are bigger than inches.

Second, he realized that multiplication and division are opposite of each other, so that if he wanted to divide 568 by 12, he just needed to figure out what could be multiplied by 12 to give 568. He also had the self-awareness to realize that he didn’t currently have the information he needed, since he only knew multiples of 12 up to 12 x 12.

Third, he CREATED HIS OWN CORRECT METHOD FOR SOLVING THE PROBLEM! In my mind, this is the holy grail of math education (or, frankly, any kind of education). He understood the problem deeply enough to come up with a way (albeit a slow way) of getting the result he needed.

If he does eventually learn some manual division algorithm, that third point in particular puts him in an excellent position to be more successful at understanding why breaking a division problem into smaller division problems (which all division algorithms do) is actually helpful and valid.

Moreover, having done and understood “the long way” that he created, he is in a much better position to actually appreciate the thinking that goes into creating a better/faster way. Think of how this student’s experience later learning an efficient manual division algorithm will differ from that of a student whose teacher simply walks to the front of the classroom and says, “OK students, today we are dividing, here’s how you do it.”

So, Ms. Sawyer, if you want your son to be able to calculate things by hand without a calculator in the quickest possible way, then yes, his education is lacking. Alternatively, if you want your son to understand and appreciate the beautiful thinking that goes into mathematical algorithms, have a deep understanding of how and why they work, be able to apply them to new situations, and COME UP WITH HIS OWN ORIGINAL AND CORRECT SOLUTIONS TO PROBLEMS, then your son seems to currently be experiencing an excellent education!

Posted in Education, Math education | Tagged , , , , , , , , , | 3 Comments

The economics of a gun buyback counter-protest

Posted on January 22, 2013 by Zachary_Goldman

Gun buyback (and competing gun auction)

http://www.seattlepi.com/news/texas/article/Church-and-gun-enthusiasts-compete-for-weapons-4209609.php

Apparently, a church in Seattle organized a gun buy-back where they offered $50+ for people to turn in their guns.

A pro-gun advocate staged a counter-initiative across the street. Apparently, he organized an auction: people in line for the church buy-back could instead have their gun auctioned off to the highest bidder across the street.

Let’s think about that for a moment….

Upon first reading about this, I had several reactions:

1. Opposing a church gun buy-back??? Really?!?

2. The pro-gun people’s counter-initiative to auction-off guns is actually a pretty creative idea in this context. (I don’t approve of their motivation, but I have to give them props for having an interesting idea.)

3. It is actually not immediately obvious to me if the auction actually has the intended effect of reducing guns on the streets.

Let’s explore that third point a little more deeply….

For simplicity, I’ll refer to people giving up their guns as the “sellers,” people purchasing the guns at auction as the “buyers,” the people organizing the auction as “pro-gun” advocates, and the people at the church who organized the auction as the “anti-gun” advocates. Getting guns “off the streets” will refer to a reduction in the total number of guns held by private citizens in the community.

Sellers

By selling at auction as opposed to doing the buy-back, the sellers certainly come out ahead financially–the prices at the auction were apparently quite a bit higher than the reward being given by the church. However, the sellers lose the satisfaction of getting guns off the streets.

The sellers could, though, use their extra profit from selling at auction to fund additional violence-reduction or anti-gun initiatives in the future. They could also hand the money right over to the church to increase the reward they are able to give for turned-in guns.

This couldn’t increase the reward to match the auction cost, but it COULD increase the reward enough such that the (monetary) reward from the church PLUS the satisfaction of getting the guns off of the streets would indeed exceed the subjective benefit of the higher available profit from the auction (in the minds of at least some people standing later in line).

Buyers

People wanting to buy guns can possibly do so more cheaply than buying a new gun in the traditional way. It is not clear how the auction prices relate to prices for comparable guns for sale at stores. It is very possible that, in this situation, the buyers are actually willing to bid up the price above the retail price of a similar gun–they apparently get some value from convincing people to sell to them instead of sell to the church.

Any money the buyers spend on guns in the auction is money that CANNOT be spent to buy guns directly from a store.

What is not clear, however, is whether buying a gun in the auction prevented any of the buyers from making another gun purchase from a store. Was there another (store) gun they were planning to purchase either right now or in the future that they are no longer planning to purchase because they bought a gun at the auction?

This is the key point that determines the net effect of the auction on the number of guns on the streets.

Who wins: pro-gun or anti-gun?

If the buyer had been planning to buy a new gun from the store, but instead buys a gun from the auction, then the auction actually has NO net effect on the number of guns on the streets.

The total number of guns on the streets is the same in both of these scenarios:

  1. The seller gives 1 gun to church (in exchange for a small payment) and the buyer goes to the store and buys 1 gun.
  2. The seller auctions 1 gun to the seller (for some higher payment).

Either way, the seller ends up with one fewer gun and the buyer ends up with one additional gun.

Note that, in the long run, this still applies if the buyer, for example, had been planning to buy a gun a month in the future, but decides to buy one at the auction instead–the net effect is the same.

On the other hand, if a particular buyer’s likelihood of buying another gun at a store does NOT change as a result of buying a gun at the auction, then the number of guns on the streets is not reduced. (I suppose it is also possible that there could be a few people who are MORE likely to buy another gun at the store after buying one at the auction–this would increase the number of guns on the streets even more!)

The more of these people the auction can convince to come and buy guns, the more effective they will be at preventing the church from reducing the number of guns…. recruiting potential buyers from a crowd waiting in line at a gun store is probably has no net benefit to their cause.

Posted in Political thought | Tagged , , , , , , , , , | 2 Comments

Teacher effects on cognitive and non-cognitive skills

Posted on January 5, 2013 by Zachary_Goldman

There is a very interesting new paper out from C. Kirabo Jackson of Northwestern University: Non-Cognitive Ability, Test Scores, and Teacher Quality: Evidence from 9th Grade Teachers in North Carolina.

He looked at LOTS of data and isolated two factors–which he refers to as cognitive and non-cognitive skill–that each seem to explain much of the variation in particular stats for a given student: algebra I and English standardized test scores, attendance, discipline, GPA, on-time grade promotion, etc.

He was able to statistically isolate these two factors from other demographic factors and was able to track how these changed over time for particular students.

In particular, he looked at the effect that teachers had on both of these factors.

He built a very sophisticated model designed to separate out the effects strictly associated with particular teachers (as opposed to effects due to other courses students might be taking simultaneously, students/teachers not being randomly assigned to courses/levels, school-wide effects, etc.). Students were effectively only compared with other students who took the same classes and went to the same school. He worked through very detailed justifications for why this model is indeed valid (and better than alternatives).

Here are the results:

  •  These two statistically-meaningful measures (cognitive and non-cognitive skill) can indeed be identified for each student. The factor called cognitive skill is most-closely related to standardized test scores, while the factor called non-cognitive skill is most-closely related to the measures of attendance, behavior, GPA, etc. These factors are indeed distinct: students with high cognitive skill may or may not have high non-cognitive skill.
  • BOTH of these can be used to predict future outcomes (college attendance, arrest rates, future wages).
  • Individual teachers do indeed play a large role in changing student cognitive and non-cognitive skill.
  • The effect of teachers on cognitive skill is NOT correlated with those same teachers’ effect on non-cognitive skill. Thus, for teachers who are above average at improving cognitive skill, about half will be above average at improving non-cognitive skill while about half will be BELOW average at improving non-cognitive skill. (If teachers who are the best at improving non-cognitive skill are also the best at improving non-cognitive skill, we’d expect all teachers who are “above average” at for cognitive to also be “above average” for non-cognitive. However, this study, surprisingly, says that a teacher’s ability to improve cognitive skill IS NOT linked with their ability to improve non-cognitive skill.)

Thus, since test scores are most-closely associated statistically with the cognitive skill factor, not all teachers who are particularly good at raising test scores are particularly good at improving non-cognitive skills.

Yet, the non-cognitive skills are strong predictors of future outcomes (particularly for students closer to the lower end of the income spectrum, interestingly). Thus, test-scores themselves miss out on this important factor AND a teacher who is good at increasing test scores might fall in ANY percentile of teachers with regard to how well (s)he increases  non-cognitive skills.

While measuring teachers’ ability to increase test-scores seems to be a measure of the effect they have had on students’ cognitive skills, this entirely misses the (equally important) effect the teachers may or may not be having on non-cognitive skills:

Because unexplained variability in outcomes associated with individual teachers is not just noise, but is systematically associated with their ability to improve unmeasured noncognitive skills, classifying teachers based on their test score value-added will likely lead to large shares of excellent teachers being deemed poor and vice versa.

Jackson goes on to point out the possible frightening implications of incentivizing teachers JUST to raise scores:

[…] if teachers must expend less effort improving non-cognitive ability in order to improve cognitive ability, regimes that increase the external rewards for test scores (such as paying teachers for test score performance or test-based accountability) may undermine the creation of students’ non-cognitive skills.

I’m curious to see how this will change the debate about teacher assessment (let alone about STUDENT assessment)!

HT: Larry Ferlazzo

Posted in Education | Tagged , , , , , , , , , | 3 Comments

Annual Report

Posted on January 1, 2013 by Zachary_Goldman

Overall, 2012 was a pretty good year!

Here are some of the noteworthy things to report…

Professional:

I got a new job! City Year! I’m getting paid substantially less, but I am WAY less stressed out and I am actually making more of a difference in kids’ lives.

Also, for the first time I can ever remember, I have free time! I get home in the evening and there is nothing I have to be working on. As a student, I always had work that I should have been doing. Last year, I always had homework to grade, lesson plans to create, certification coursework to work on, etc. It is nice to have free time, now!

I am currently in the process of figuring out what to do next year–City Year is a one year program. Many options are listed here. I have posted this list previously, but I’d definitely still love to hear your thoughts. You can add things directly onto that spreadsheet or comment on this post.

Geographic:

I moved to Orlando! Orlando is pretty nice: lots of interesting thunderstorms. I do miss the snow, though.

Depending on options for next year, there is a good chance I’ll move somewhere else.

Educational:

I participated in several Coursera courses to varying extents (for most of them, I watched some subset of the videos, and didn’t do much of the coursework).

A quick list:

  • Human-Computer Interaction
  • Intro to Sociology
  • Health Policy and Affordable Care Act
  • Intro to Finance
  • Internet History/Technology/Security
  • Machine Learning
  • Model Thinking
  • Think Again: How to Reason and Argue

Overall, this has been an excellent experience for me. One of the things I miss most about college is having smart people discuss interesting things with me all day. The faculty and other students on Coursera provide an adequate substitute for this.

For this coming year, my goal is to be participating FULLY in at least one of these courses at any given time. That is, doing all of the work and engaging fully with other students in the forums (fora?). I’ll continue to lurk in as many additional courses as I feel like, but my goal is to currently be fully active in at least one course at all times.

One of the options for next year is grad school of some kind, so I may get some education that way, too!

Guitar:

Starting in September, I volunteered to co-facilitate an after-school guitar class for my students. Luckily, unlike me, my co-facilitators actually do have some experience playing the guitar. I bought a guitar and started teaching myself how to play.

This has been very rewarding so far, and is something I plan to continue with for the foreseeable future. I am pleased to report that a few of the students in the class have started to be better than me at guitar!

Personal:

It has been great getting to know the other City Year people! They are a great group of people. I look forward to our next few months together, and I look forward to maintaining my friendship with many of these people after our year together has ended!

I went on a few dates this year. I’ll keep working on that next year!

This blog:

This blog provides an excellent mechanism for helping me think through interesting things I want to explore in some depth. It is great to be able to flesh out some of my own thoughts and share the results.

I have been very pleased with the discussion that has started on facebook and elsewhere regarding things I have posted here. In the new year, I’m going to try to work to get more of that discussion to start happening more deeply in the comments on this website (instead of just on facebook) so that everyone who views the posts can participate in the discussion, and so the discussion stays linked with the post later on.

 

Posted in CIty Year, Online education, Personal Experiences | Tagged , , , , , , , , , | Leave a comment

A bad (article about a) study on success in math class

Posted on December 29, 2012 by Zachary_Goldman

Scientific American just published this article (apparently syndicated by a company called LiveScience) which includes some questionable conclusions drawn from a questionable study about math success in school.

The original study seems to be behind a paywall, so I haven’t been able to read it directly. Thus, everything I know about the study came from this article. I am trying to give the study authors the benefit of the doubt that the actual study was a little clearer than this article about the possible conclusions that can be drawn from the study’s results!

This study of 3500 German students seems to show that students who are more motivated to study math and use better “strategies” to study math improve more in math than do other students.

This is an extremely NOT surprising result: students who like learning math and are better at studying math improve more. OK.

What is presented as a more startling result (but still isn’t that startling) is that students’ IQ did NOT predict how much they would improve. On average, regardless of IQ, students scored at the same levels as they did before (if those levels were high to start with, they stayed high; if those levels were low, they stayed low).

This is not a surprise. No one would ever assume that if I told you a student’s IQ, you could predict whether her math scores would increase next year or decrease next year. You may assume that this student’s scores might be higher than her classmates, but you couldn’t know if this student’s scores were higher than her own scores last year. In fact, the article does even mention that at the beginning of the study, students with higher IQs had higher scores, on average.

These two results are combined into the following  (kind of technically correct) statement:

Motivation to work hard and good study techniques, not IQ, lead to better math skills, a new study shows.

…which is true–if by “better” they mean “more improved.”

However, in a quick reading, this statement is  easily confused with “motivation to work hard and good study techniques lead to higher math scores than people who just have high IQs,” which is NOT supported by this study, but which makes a much better headline. The article only mentioned that these students INCREASED their scores by more….for all we know, the scores may still be much lower than those of the students with the higher IQs.

That being said, there IS some good work being done on how things such as hard work, perseverance, etc. can be extremely beneficial academically for students. Paul Tough has a nice summary in his new book.

This is also a helpful reminder to all students that, whatever your current level of math achievement, it is possible to improve, if they (and their teachers) follow the guidance of this study.

That future success is not determined just by ability, but by working harder/better is a mindset that TFA teachers in particular (and others?) are encouraged to try to instill in kids. I think this is probably a good thing. My fear is that studies like this will be used as “evidence” that ONLY motivation/hard work/etc. matter.

A very positive outcome of this study is that there is now evidence that motivation to study math actually improves scores–just drilling students on random, boring procedures is probably less effective than actually getting them interested in what they are studying!

Again, when stated like this, that statement is perfectly obvious, but it is nice to have some data to back that up. My impression is that a too-extreme focus on data has been leading to an increase in the drill-them-on-random-stuff paradigm, so maybe some data showing that actually developing students’ interests in a subject leads to better test results will shift that a bit the other way!

Three minor additional (bonus!) concerns about the Scientific American article:

1.

The title of the piece is “Like math? Thank your motivation, not IQ.” However, the article mentions nothing about how enjoyment of math is linked more closely to motivation than IQ, so the title has nothing to do with the article. The only way this title could actually follow from this study is if people who like math are only those who are successful at it, which actually seems contrary to the spirit of this work.

2.

[…] people who were driven by their own interest improved the most. So rather than keeping Junior’s nose to the grindstone, it may be more helpful for parents or teachers to show him how math ties to real life (for instance, understanding that two $3 candy bars cost $6 rather than just memorizing times tables), [study author, Murayama] said.

It is excellent that he advocates for teaching students to understand math rather than just memorize. However, saying “you have to memorize that 2×3=6 since two $3-candy-bars cost $6” is only just barely superior to telling kids “memorize that 2×3=6.” Being presented with an intriguing question (thanks Dan Meyer!) is usually quite a bit more effective than trying to justify forced memorization.

Also, this was a study of 5th-10th graders. Multiplication may be extrapolating a little too far….

3.

The article twice referred to Tiger Moms, once saying that the study showed they were “half-right” and once saying that Tiger Moms have been “vindicated” by the study. My understanding of Tiger Mom philosophy is that they assume that future success is not predetermined, so working ultra-hard on academics and extra-curriculars will lead to greater future success. Apparently, the “half-right” and “vindication” for Tiger Moms is that success is not predetermined.

However, this article (THANK YOU!) also points out very clearly that simply forcing students to do extreme studying of topics they aren’t interested in is NOT what the study found to be most predictive of improved math scores, rather being MOTIVATED and interested in the topic turned out to be particularly important. The study certainly agrees that success is not predetermined, but draws the OPPOSITE conclusion–that the Tiger Moms are doing exactly the wrong thing by forcing their kids to spend more time studying. Because they share the premise that success is not predetermined, but draw opposite conclusions about how to actually increase success, I think saying the Tiger Moms are “half-right” is a bit of an overstatement.

Posted in Math education, TFA | Tagged , , , , , , , , , , , , , , , | Leave a comment

What can we infer about City Year and TFA based on their different ad strategies?

Posted on December 27, 2012 by Zachary_Goldman

During my recent journey home for winter break, I encountered advertisements for both City Year and Teach For America. I currently work with City Year and I had worked with TFA last year.

Share this photo if you believe that City Year corps members #makebetterhappen

On the public bus from my apartment to the airport, there was a City Year ad similar to this one (different person and tweet, but same idea).

The tweet says, “Want to see what it’s like to change a student’s life? Follow me. #makebetterhappen.”

At the airport, in the bottom of the bins people put their stuff in while going through security, this is the TFA ad.

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The words say, “What do our nation’s leaders look like?” with a “YOU” inside the silhouette and a TFA logo at the bottom.

Full disclosure: I actually took this picture of the airport bin on my way out of town for Thanksgiving, but the ads were still there when I went through the airport again last week.

Certainly, this is a very small sample of all of the advertising these two organizations do nationally. However, I was struck by the fact that City Year was advertising on a public bus, while TFA was advertising in an airport.

I don’t have any data in front of me, but I think it is fair to assume that the demographics of air-travelers differ pretty significantly from the demographics of city bus riders.  I wonder about the degree to which the recruitment strategies of these two organizations purposely focus on these particular demographics.

I think is also interesting to note that the City Year ad (more so than the TFA ad) is not just about recruitment, but also builds wider awareness of the organization’s work–and support for that work–which I think City Year does a SUBSTANTIALLY better job of than TFA.

Having worked within both, the community support of City Year is dramatically more actively positive than it is for TFA. By “community support,” I mean the support of teachers and administrators in the schools, parents/students/etc., local companies and foundations, local media, and local elected officials. Ads like this play an important role in simply increasing community awareness of City Year.

That being said, some of my City Year colleagues are sometimes concerned about the extreme degree to which City Year focuses on its branding and on attracting (positive) attention to itself at the expense of spending time on actually supporting kids–a position I sometimes do agree with. However, in the long run, I do think much of this stuff–the bus ad included–probably does increase our image in the community to such an extent that it is possible to serve more students more effectively by getting new sponsorships, approval to expand to additional schools, etc.

While the City Year ad tries to recruit people while also building recognition and support in the community, the TFA ad may actually have a secondary purpose beyond just recruitment, as well.

Many people find travel to be pretty stressful and airport security to be the peak of this stress. Since successful TFA corps members must be able to effectively handle an extreme amount of stress, I wonder if positioning ads at airport security is a strategic plan to select out people who are able to focus on the ad while going through the stress of airport security

Maybe TFA thinks that being able to pay attention to the ad deeply enough to follow up later means that the person handles stress exceptionally well and can still think about the big picture while in a stressful situation.

Certainly, I have no way of knowing if any of this actually matches the thinking of the marketing people in both organizations, but I certainly do find it interesting to compare these small signals about the organizations’ deeper philosophies.

I am curious to hear if you notice any other interesting comparisons between these ads (or other TFA or CY ads)….

Posted in CIty Year, Personal Experiences, TFA | Tagged , , , , , , , | Leave a comment

Healing

Posted on December 15, 2012 by Zachary_Goldman

On Friday, when asked about the policy ramifications of that day’s elementary school shootings in Connecticut, White House spokesperson Jay Carney mentioned there would be “a day for discussion of the usual Washington policy debates, but I do not think today is that day.”

He was right.

But, now, it is tomorrow.

Gun Control

Many people and news sources have quickly brought up the debate about gun control laws as a means of preventing future crimes like this.  Most of the actual data I have seen being used as evidence for BOTH sides of this debate have been of the form “in this particular subset of cities that I am choosing to mention, during this particular period, right after a gun law was [enacted/repealed] , the [rate/number] of [murders/crimes] with guns went [up/down].” Pick your favorite word inside the brackets.

Among all such arguments I have seen recently on both sides of the debate, these arguments do not include data about ALL relevant cities (some conveniently unmentioned cities that implemented similar laws had the opposite trend?!??!) and never account for other confounding factors that may simultaneously have been affecting gun violence rates (or for that matter, may be affected BY gun violence rates).

There does, indeed, seem to be conflicting evidence. However, I’ve never heard a good reason why assault weapons–whose only purpose that I’m aware of is killing people quickly–should be legal. For other types of weapons, my thinking is less cut and dry, but my instinct is still pretty strong that fewer is better.

Mental Health

Watching the conversation both personally and in the national media after this and other major violent crimes, after people beat to death all of the arguments for and against stricter gun control laws (sorry for that sadly ironic figure of speech), the conversation  shifts towards a discussion of mental health.

People rightly argue for more mental health support so mentally ill people can get the help they need and don’t resort to acts of violence. People also rightly beseech others not to stigmatize mentally ill people as violent criminals, since this stigma is false, cruel, and actually counterproductive since it prevents people from personally seeking mental health support.

Broadening people’s personal definition of mental illness can achieve both of these goals simultaneously. First of all, if someone goes out and shoots a bunch of people, something is psychologically wrong. I don’t know if it is congenital or not (maybe some of both); I don’t know whether it is a short term issue or a long term issue (maybe an underlying longer term issue with a short term spark); I don’t know whether the person technically falls in a particular DSM diagnosis; I don’t know whether psychiatric or psychological treatment might be helpful.

I DO know that if someone goes out and shoots people, something is wrong, and that this person (like all people) should have been given more  support to have prevented his problems from getting this far and should have had easy access to psychological support once things started going poorly.  In fact, I think that whenever someone purposely harms another person,  something is psychologically wrong (an only exception possibly being in the attempted defense of one’s self, community, or country–although, admittedly, lots of people who commit unnecessary acts of violence think they are doing it for one of these reasons). Hopefully, reducing all real or perceived threats to safety will reduce these acts of violence as well.

If we as a country are willing to make a concerted effort to help people develop, from a young age, skills of introspection, empathy, stress management, anger management, and positive relationship development, then less violence will happen at all levels. This applies to fights at school, domestic violence, shootings, terrorist attacks, etc.

In addition to helping people develop the tools, mindsets, and experience necessary to deescalate short- or long-term situations that could turn violent, we need to make acute support more readily available and easily accessible when people perceive that a situation is escalating towards violence (two people who are mad at each other, a depressed loner with no friends, etc.).

Finally, in addition to helping people develop more robust ways of dealing with stress and anger, and providing more/better/more-accessible acute support in situations where stress and anger are boiling over anyway, it is also important to do what we can to reduce the sources of stress and anger in the first place. Underlying financial issues, medical issues, family issues, interpersonal conflicts, work issues, etc. all make it significantly harder to deal with new stress and, when in place for extended periods of time, can sometimes push people to lash out at others.

All work that is done to help people improve their lives in these areas, in addition to obviously being valid for its own sake, also reduces everyone’s levels of extreme stress and anger, bringing situations back in the range where people are better able to deal with issues themselves (due to their prior strong emotional education!) or at least which can be supported by a professional in when necessary.

Healing and moving forward

However, taking all of these steps to prevent future crimes is only one step towards healing in this situation. Mr. Rogers had some wonderful insights about how to communicate with kids abut scary situations.

“What children probably need to hear most from us adults is that they can talk with us about anything, and that we will do all that we can to keep them safe in any scary time.”

“When I was a boy and I would see scary things in the news, my mother would say to me, ‘Look for the helpers. You will always find people who are helping.’ To this day, especially in times of “disaster,” I remember my mother’s words and I am always comforted by realizing that there are still so many helpers – so many caring people in this world.”

What is not mentioned in all of the links that are going around about Mr. Rogers is that this is good advice for EVERYONE, not just kids…

(The fictional) President Bartlett eloquently honors the helpers who ran INTO the fire.

State Senator Mike Johnston of Colorado (who will be President of the United States in a few years) wrote beautifully about the myriad “helpers” who sprang to action after the Aurora theater shootings and about the triumph of love over hate.

Finally, The Atlantic Wire is collecting stories of the heroes of the Connecticut tragedy.

I take comfort that there are helpers all around, always. When I walk into a movie theater, mall, or airplane, I feel safe knowing that 100% of the people in the crowds around me are on my side. On the unlucky day when there is one person in the crowd who wishes me harm, I am satisfied to know that there are hundreds of others whose thoughts and actions counteract that.

I am proud to live in a society where I know this is the case.

More broadly, I take further comfort in the knowledge that so many people do so many things each day to support others (in an organized/ongoing way, or in the spur of the moment). I am proud to live in a world full of nice people who work to support our common humanity!

Beyond State Senator Johnston’s suggestion to acknowledge all of the love out there and work to increase it in our daily lives, it may seem hard to personally have an effect on violent crime (let alone gun control or mental health policy).

I’d encourage you to explore (or donate to!) some of the following initiatives designed help people get along better:

Roots of Empathy

The Sustained Dialogue Campus Network

The Arbinger Institute (authors of The Anatomy of Peace, among other things)

PACER’s National Bullying Prevention Center

Finally, in this time of sorrow, music can provide some healing and catharsis: The Prayer of the Children.

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A glaring example of misplaced priorities….

Posted on December 8, 2012 by Zachary_Goldman

For two days next week, a teacher I work with has been assigned to proctor a test in the media center, so a sub has been scheduled to be in her classroom.

The state of Florida seems to think it is more important for a certified teacher to be proctoring this test than it is for this certified teacher to be in her classroom teaching her students.

This doesn’t seem like a very effective way of educating children.

I’ll give the state the benefit of the doubt and assume that the desire to have tests proctored by certified teachers was well-intentioned. However, this leads to the comically embarrassing outcome of pulling teachers out of class to watch students take standardized tests, creating their own real-life satire of contemporary K-12 education.

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City Year (internally) published an essay of mine!

Posted on December 3, 2012 by Zachary_Goldman

City Year’s national office has published an essay of mine! It is posted on CYconnect, City Year’s internal communication system.

Unfortunately, it does not seem to be accessible by non-City Year people. If you do have a CYconnect login, the original essay is available here.

For everyone else, the essay is duplicated below.   The Idealist’s Journey is City Year’s (cornily named, but actually quite strong) model for personal development.

The Anatomy of Peace is an excellent book (click the link for its amazon page–currently quite cheap in kindle or physical form).

Striving to embody The Anatomy of Peace in our service

As my Idealist’s Journey proceeds, I continue to appreciate and reflect back upon a session from summer training about The Anatomy of Peace. Treating people as people with valid emotions and valid experiences as opposed to treating people as objects who simply do various helpful or not helpful things is a broadly applicable perspective on the world, continuously helpful when dealing with students, teachers, and fellow corps members.

The related principle of avoiding collusion in conflicts is just as profound: when a student is acting in a counterproductive way, I always need to do a better job of reflecting on how MY actions may subtly be encouraging this unhelpful behavior. My awareness of this principle has made instances of collusion apparent throughout my service. For example, my school encourages teachers to have students self-assess their own understanding periodically throughout a lesson by giving a thumbs-up, thumbs-to-the-side, or thumbs-down to indicate how well they understand the current topic. Many of my students weren’t doing these signals at all or weren’t answering honestly. For students who had been answering with a thumbs-down or thumbs-to-the-side, my teacher and I had been requiring them to explain their confusion or to ask a clarifying question. It turns out that putting them on the spot like this during class actually made it less likely for them to use their thumb signals in a valid way—they’d give a thumbs-up just so they wouldn’t have to talk about their own confusion. By probing them in this way, we were colluding in the problem of causing invalid responses!

In addition to my continuous efforts to reduce my collusion in conflicts, there is a second, deeper, insight I still frequently consider when interacting with my students and others. During the summer training, we had an excellent conversation about the challenge of being kind and respectful with people who have wronged us. This is extremely important in being able to effectively resolve a conflict in the long term. However, for most people, myself included, this is also very difficult to do successfully (particularly in response to others’ actions that are particularly cruel). It was good to have an opportunity to explicitly sit down and consider this in the context of our work this year.

Something I always struggle with when students have done or said cruel things to other students or to me is to move beyond that and still have a constructive relationship with the student. There are situations in which a student has severely disrupted a carefully planned activity or when a student has simply been mean to other students, or CMs, or school staff. It is often difficult to move past that and regain trust and respect for that student (or for that matter, a fellow CM, a family member, etc. in a similar situation). When stated explicitly, it seems obvious that moving past a negative situation in a constructive way is clearly the best outcome, but actually doing this can be quite difficult in practice.

This principle of moving beyond a major wrong without resorting to vengeance or ongoing hard feelings actually turns out to be more broadly relevant throughout history and literature in situations much larger and more severe than a student’s classroom misbehavior. In fact, this idea forms the basis of all non-violent resistance: MLK, Ghandi, Mandela, and others who represented groups of people who were SEVERELY wronged by those in power and still encouraged their followers to resist in a peaceful way. Even though angry retaliation against the oppressors may indeed have been justified and fair, they chose another alternative. This is hard.

The entire field of restorative justice is also based in these ideas. The Truth and Reconciliation Commission in South Africa after apartheid is an excellent example of this.

Finally, the best fictional account of this principle appears in Victor Hugo’s Les Miserables (the book, the musical, and the upcoming major motion picture). A man named Jean Valjean steals some bread, goes to jail for a long time, and eventually gets released–but he can’t find a good job since he is a convict.

He encounters a bishop who provides him some food and a place to sleep. The next morning, Valjean steals some silver from the Bishop, but Valjean is quickly caught and returned to the bishop. Instead of identifying Valjean as the thief (which he was), the bishop instead makes up a story about how the silver–and even an additional pair of candle sticks–were a gift to Valjean from him. The bishop and Valjean discuss the second chance Valjean has been given. Even though Valjean had severely wronged the bishop (by stealing from him), the bishop did NOT help the police make a case against him, but rather took the opposite course: forgiving Valjean for his crime and setting him up with the resources and inspiration necessary to turn his life around.

This is the turning point in Valjean’s life. He emerges as an extremely noble man, enriching the lives of many people around him. Meanwhile, his arch-enemy, Javert, a police inspector, has been continuously hunting Valjean since Valjean broke his parole years before. A bunch of revolutionary students eventually capture Javert and plan to execute him. Valjean saves Javert and frees him even though Javert had been pursuing Valjean for years.

Valjean was able to spare Javert from punishment (a punishment which may indeed have been deserved) only after the bishop had done the same for Valjean, decades earlier. Quite a ripple! As it turns out, the story still does not end well for Javert, who is utterly unable to comprehend how Valjean would have chosen to spare his life.

The bishop’s actions serve as a good reminder to keep in mind the humanity of those who have wronged you (a student, colleague, roommate, relative, etc.). Even though losing respect for another person or making the assumption that they are a bad person (or a bad student, or a bad teacher, or a bad friend) may indeed be fair and justified, it might not be productive. I need to continuously work on making sure I live up to this standard, instead of forming opinions and judgments that collude to make a problem worse.

As we all continue in our Idealists’ Journeys, this is certainly a perspective I will strive to strengthen in my own mind. The Les Miserables movie comes out in late December. That will provide a good opportunity to reflect on how much our interactions large and small resemble the actions of the bishop and Valjean! Even when we have been wronged, are we still willing to take positive action to support the wrongdoer? Is this reflected in our interactions with students? (…and are we doing enough to help our students achieve this in their own relationships with other people?)

Posted in CIty Year, Education, Leadership, Personal Experiences | Tagged , , , , , , , , , | 2 Comments

Just mimic the example in the book! That’s learning…right?

Posted on November 29, 2012 by Zachary_Goldman

This is a picture of a page of the alegbra 1 textbook my school uses. The students are learning about linear equations.

The book provides lots of worked out sample problems. What is frustrating about this book is that it references the sample problems right next to the actual problems students are supposed to do for practice (“See example 2, p. 356”). The sample problems are identical in structure to the practice problems, with different numbers.

For many of my students, when they see a problem that isn’t structurally identical to a previously-worked-out question, they tend to get very upset and are unable to make any progress on the question without some additional prodding. For many of the students I tutor, they rarely (if ever) encounter “un-taught” questions in their math class.

This plug-and-chug model of teaching math makes absolutely no sense: why would we possibly care if students are able to mimic an example problem and plug in different numbers? This textbook is explicitly encouraging students to just regurgitate a meaningless procedure they have practiced a bunch of times.

In most other books where there are worked out examples (but not a box next to every problem pointing to an analogous worked-out problem), students at least have to look through multiple example questions. If nothing else, they gain some exposure to all of the techniques in the section and (just as importantly) they practice being able to discern enough about an in-progress problem to decide which sample problem(s) provide the relevant information.

All of the push for higher standards and for more rigorous curricula is utterly meaningless if math is taught in this way. If math students aren’t learning how to THINK deeply, rigorously, and originally, I really don’t know what the point is of making them sit in math class every day….

We can do better than to teach our students from books/curricula like this.

Posted in Education, Math education | Tagged , , , , , , | 1 Comment