Thoughts on Capsule Night--and a Wish

Capsule Night--not sure where the name came from--in some schools it is called Curriculum Night.

First of all, it's fabulous. Fabulous to see the teachers. (I kind of wish they did it each semester.) Fabulous to get a sense of my child's day, and at least create a mental map of where he is in each class. How many stairs does he climb every day?

Second of all, it's fun to see the parents--the ones I know, the ones I don't know. It made me realize I miss a lot of people whom I used to see regularly, back in elementary school. Next year, can we pair capsule night with some social time for parents at a coffee shop or bar? (Or in the school...)

Third of all, even though the classes are, like, 12 minutes each, I felt like I was sitting all too long! (Which is really funny, because mostly, I sit at a computer in my day job...)

Fourth of all--I was struck by how much access to computers teachers are requiring. And I wondered--if we didn't have more than one computer at our house--and/or if we had more than one child in high school now--that could potentially be a big problem. The technology divide seems to get bigger. And it's a lot more computer work than I remember from my two older kids. Which really makes me wonder--how much of that is necessary? Because exacerbating a technology divide is not a good thing.

Last, but not least, a wish:

Every year when I walk into the math class at Capsule Night, it reminds me that I wish the school district would offer a free evening class in every middle school and high school for parents, on how to use a graphing calculator. I'm sure it's not hard, but we didn't use them back when I took Algebra...or Geometry...or Trig....or Calculus. You know, back when the dinosaurs were alive.


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What is in the Smarter Balanced Pilot Test?

Read Part I:
Smarter Balanced Test: Try It Out Before Your Kids Take It

Read Part II:
Smarter Balanced Comes to Ann Arbor a Year Early. Why?


And here is Part III.

What is in the Smarter Balanced Pilot Test and How Will It Be Given?

The Smarter Balanced Test is a non-timed test (although there is a certain amount of time that they expect the test to take. It is given on a computer. The testing can be split up over several days. The test itself includes a variety of types of questions, including questions that are "drag and drop" (you drag objects into a location and "drop" them there); "click stick" (also known as click-stick-click-drop, and it requires less fine motor skills); multiple choice; and short answer questions. All of the answers, including the short answers, are graded by a computer. Smarter Balanced calls the computer program that delivers the test the "test delivery system." I'm not sure why I find that so humorous, but I do.

There are two parts to the Smarter Balanced Test. There is a "non-performance task" section--estimated to be two hours long for the English Language Arts section, and two hours long for the Math section. And there is a "performance task" section, which involves a half-hour classroom activity that is supposed to provide a "baseline" for a theme, and related to that there is an ELA section (estimated at two hours long) and a Math section (estimated at an hour and a half).

The idea of the performance-based task is that it allows testing of critical thinking and problem solving. The example I was given was that if you had a class task about teen driving restrictions, that there would be baseline information shared about those, and students would then be able to incorporate that information into their activities.

The classroom task itself is considered "non-secured," but at the same time, "Students may take notes during this time, but the notes must be collected before proceeding to the PT. Students may not use notes taken during the classroom activity for the PT." (Source.) Also, if students are absent the teachers are supposed to try to give the students who missed a similar experience.

The pilot tests are not "adaptive," they are "fixed." (In other words, they are the same for every student. Supposedly, the actual test will be made adaptive next year.)

Read lots more about the Smarter Balanced test here:

Classroom Task and Performance Task Administration Guidelines

Frequently Asked Questions for Spring 2014 Field Test

Here are the goals of the Smarter Balanced test, as taken from the Smarter Balanced Assessment web site:

• Accurately describe both student achievement and growth of student learning as part of program evaluation and school, district, and state accountability systems; 

• Provide valid, reliable, and fair measures of students’ progress toward, and attainment of the knowledge and skills required to be college- and career-ready; and 

• Capitalize on the strengths of computer adaptive testing—efficient and precise measurement across the full range of achievement and quick turnaround of results. (emphases added)

Just a comment about that "valid, reliable, and fair measures" piece. In case it's not obvious, if you don't read well, you are not going to do well on the math test, even if you are a math whiz.

As for "efficient and precise measurement," given that computers will be assessing students' writing, I'm not sure how precise it will be, although it certainly will be efficient!


But enough about the test.
I'm more interested in the testing.

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Missed Opportunities: Ann Arbor and the Washtenaw IB/WAY/ECA Consortium

I wasn't really paying attention to the big brouhaha as to whether the Ann Arbor schools should sign the contract to continue to participate in the International Baccalaureate program, the WAY (Washtenaw Alternatives for Youth) program, or the Early College Alliance. But now I am. And mostly what strikes me is that there have been several missed opportunities. Sure, I know that hindsight is perfect, but looking back and evaluating is also a good way to learn.

So here are five missed opportunities.

1. Missed Meetings: The Ann Arbor News reported that the Ann Arbor school representatives missed many of the consortium meetings. I don't know if Supt. Pat Green or Deputy Supt. Alesia Flye was to blame for that--maybe it was both of them. They're both gone now, so I'm not sure if it matters if we figure that out. Going forward though, if we have a seat at the table, we need to take it. It's pretty clear that we can have more influence if we are there early in the process.

2. Anti-union contract: Someone called me to say that he was worried that the contract the Ann Arbor school board was discussing was anti-union. Given that the contract (click on the link to see it) specifies that if a teacher is tenured in a district and goes to work for the IB, WAY, or ECA schools they are not operating under or accumulating tenure (among other things), you could describe it that way fairly, I think. But here's the thing--this same contract was already voted on by the Ann Arbor schools for this current year in August--and by the other school districts as well. Does the Ann Arbor Education Association or the Washtenaw Education Association not care, or did they just miss this? They probably could have influenced the terms and conditions...

3. Failure to Track: When the Ann Arbor school's Count Day numbers came out, and they were below expectations, much of the attention went to the number of AAPS high school students who were enrolled in the IB, WAY, and ECA programs. And the district seemed surprised by this. To my mind, either they weren't surprised, but wanted the public to feel that they were (which would be misleading), or they were surprised. And if they were surprised, then I have to ask why that is. You might remember that my son applied to the IB program at the Washtenaw International High School--and he found out that he was accepted sometime in late winter or early spring. Now surely, as consortium members, the district could find out how many Ann Arbor students had gotten in to--and later, decided to go to--these alternative programs. The question is, why didn't they take those numbers into consideration as they constructed this year's budget?

4. Transportation Thinking: I don't think the school board and administration really took into account the way that threatening to cut high school transportation could affect the way students looked at schools. I'll probably never be able to prove this, but to my mind, when the district said--at the same time that students were looking at high schools--that high school transportation might not be available, it changed the equation for many parents. I know for myself that I was intimidated by the idea of transporting my son to the IB school. On the other hand, if I lived far from my district high school, and would have to transport my child anyway, then I would not be comparing "drive my child to one school or have him take a bus to the other" but rather "drive my child to school A or school B?" So even the threat of the transportation being cut may have influenced the debate for students at the time when the choices were being made.

5. Going it alone: I believe the ECA, the IB program, and the WAY program are all very worthwhile. But Dexter--which decided to do its own IB program, and which decided not to join the WISD transportation consortium--may have done the best job in looking out for Dexter. I am glad to see the Ann Arbor school board now considering doing its own IB program, even if the consortium IB program continues.



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Math Lessons for Language People

One of the books I read over the summer was  When Languages Die: The Extinction of the World's Languages and the Erosion of Human Knowledge by K. David Harrison.  This book tackles the issue of languages with only a few speakers remaining, and asks--what do we lose when we lose these languages? Overall, I thought the book was interesting but uneven. At times the author tries too hard to prove that we lose a lot. (I sort of thought that was obvious, but maybe it's not.) There were two sections that I found very thought-provoking. One of those sections is very rich reading for math teachers.

Sign Languages

Harrison does have a fascinating discussion at the end of the variety of sign languages that are being lost. As he writes:

So far, there are 121 identified and named sign languages used in deaf communities around the world, but potentially a great many more remain completely undocumented. Many sign languages are now rapidly vanishing. This is in part because many deaf communities possessing unique sign languages are small, indigenous, and rural. . . Signed communication systems arise spontaneously wherever deaf people live. . . as soon as there is a community of deaf people. . . these systems develop into full-fledged languages, rapidly becoming as complex as spoken languages (pp. 230-231).

Numbers and Language

The other chapter of the book that really got me thinking was the chapter on numbering systems. Here, I believe there is an opportunity for some really great math lessons (Chapter 6, pp. 167-200--I'm only going to talk about bases here, but for math teachers there is some really great food for thought in this chapter about all kinds of math concepts).

I was a very good math student, but a better "English and other languages" student. And one part of math that I never fully understood (I got it, but I never really "got" it) has to do with counting in other bases. Yes, we learned to count in base 2, and base 5, and base 12. . . but the truth is that my mind was really "converting" from base 10 to the other bases.

From reading this book, I started understanding that languages embody their math bases, and that not every language uses base 10. Chapter 6, Endangered Number Systems, is all about this. In the Pomo language of California (which now has fewer than 60 speakers), the counting system is in base twenty. The number 20 is "1 stick," and 400 is "1 big stick."

Some languages count with body parts. Fingers and toes seem obvious, but other counting systems rely on arms, elbows, and even nostrils and collarbones. The Kewa people of Papua New Guinea count in base 4, using the hand as the basic unit--but they omit the thumb!

It goes on--there are many languages in Papua New Guinea, and among them the Aiome employ a base-2 counting system; the Loboda use both base-5 and base-20 systems; the Huli use a base-15 system; and the Bukiyip use base 3 and base 4.

Harrison notes that non-base-10 languages may have a cumbersome way to say a number that we think is important, like 1,000, but on the other hand, "non-decimal bases make it easy to say other numbers. In base-15 Huli, 225 is expressed simply as ngui ngui (15 x 15). Compare this to the relatively complex English expression 'two-hundred and twenty-five (2 x 100) + (2 x 10) +5. (p. 191)."

As I read this, it occurred to me that developing lesson plans that teach the way some other languages think about counting would be a natural way to teach about various math bases. For instance, could students design their own (non-base 10) counting system using body parts or other things that we find around us? Which

And at the same time, it would achieve one of my ulterior motives--to keep U.S. students from thinking that what we do in our country, and in English, is the only or best way to do things.*

*Fueled by a recent conversation I had with a graduate of a local high school who told me she never took any foreign language because "I'm American, and I live here, and we use English, and I don't need it--it's not important." 

The Birthday Problem Revisited

Math people, history people, social science people, people people--this one's for you.

What follows in this New York Times article is a nice exposition of a classic puzzle.

Does anyone in your family share a birthday? Steven Strogatz writes. . .

By an amazing coincidence my sister, Cathy, and my Aunt Vere have the same birthday: April 4.

Read on.

Actually, this entire Steven Strogatz series about math in everyday life is excellent.

Time and Time Again

Lately my son has been getting a lot of bar and bat mitzvah invitations. A bar mitzvah or bat mitzvah (bar mitzvah for a boy, bat mitzvah for a girl) is a Jewish ritual rite of passage marking the transition from being a Jewish kid to a Jewish adult (ritually speaking). (My son has not had his bar mitzvah yet.)

As you might or might not know, generally when kids have a bar or bat mitzvah they get presents. And then they have to write thank you notes. When I had my bat mitzvah, the thank you notes seemed endless.

Which led me to the following recent conversation.

Me: "Joe got his thank you notes out really quickly! His bar mitzvah was just last week!"
Son: "Well, it takes less time if you do it quickly."
Me: "It doesn't take less time. Whether you do it quickly or slowly, it takes the same amount of time."
Son: "No, if you get them done in a week instead of two weeks, it takes less time."
Me: "But if every thank you note takes 5 minutes, and you have to write 20 notes, it takes 100 minutes altogether, whether you write 2 a day for 10 days, or do all 20 in 1 day!"

[We'll leave aside the fact that you might achieve efficiencies if you do a lot of them at once. Because you also might get writer's cramp.]

The math on this--which my son did understand--goes like this:
5 minutes/note x 20 notes = 100 minutes
2 notes/day x 10 days = 20 notes/day x 1 day
And yet, my son insisted: "No, it takes less time, because it's a shorter amount of time."
And here, my son is referring to the difference between 10 days, and 1 day. In other words, he was thinking of time as a spatial entity, and I was thinking of time as a quantity. [Mathematicians might have different words for that, by the way.]

I know, you're thinking, "That's a cute story, Ruth, but what does that have to do with schools?"

When I was in elementary, middle, and high school, we had to go to school a minimum of 180 days/year. So school was scheduled for 183 days/year, in order to account for snow days and other unforeseen events.

But now, school is scheduled with a minimum number of minutes as a requirement. A few years ago, when the legislature increased the number of minutes that students had to go to school, most districts just distributed those minutes over the school days, rather than add days to the school year. Typically, just a few minutes a day really added up.  All of which led to the following exchange that I thought was very funny with an elementary school teacher.

That year, we were chronically late to school with our oldest son, and the teacher commented on it.
Me: "I guess I had the time school starts wrong. What time is the bell?"
Teacher: "Well, the first bell is at 8:08."
Me: "OK, what time is the second bell?"
Teacher: "It used to be at 8:14, but now we don't have a second bell any more."

Does it make a difference, minutes or days? Is time a quantity or a spatial entity? You be the judge.

Update 12/13/11: Honestly, I did not know when I wrote this that annarbor.com had just published an article on the idea of using a balanced calendar at Scarlett and Mitchell. Nothing has been decided yet, and you can read the article here. As I've written about before, I myself am not interested in a balanced calendar for my kids. I know that other people are. I think the balanced calendar would be fine if people can opt in or out of it. So if Scarlett/Mitchell becomes a K-8 magnet with a balanced calendar, I'm sure some people will want it. Others won't, and they should be able to go elsewhere.

Racial Disparities in Special Education

If you are a parent in the Ann Arbor Public Schools, last week you got a letter that was nearly unintelligible.

You might have wondered what that meant--I know I did, and I know that others asked me what it meant.

Let's start with the basics. School districts are supposed to track and explain whether, or if, some racial/ethnic groups are disproportionately enrolled in special education program. There's a really nice explanation of how this gets calculated in this document, but if you don't want to read the whole thing, here is a thumbnail sketch. (If you understand risk ratios, skip the part that is in red.)

The whole point of using these statistics is to describe and understand sub-groups in the school environment. Don't be scared that math is involved.

Composition: Let's say that 10% of the district population is Hispanic/Latino, but 20% of the students who are identified as having a disability are Hispanic/Latino. Then we know that there is a disparity, because twice as many Hispanic/Latino students are enrolled in special education compared to the Hispanic/Latino population. (This is a good basic number, but it may be less accurate when we are talking about groups that make up a small percentage of a district's population.)

Risk Ratio: A Risk Ratio compares one population (say, African American students diagnosed with autism) to a comparison group. According to what I read, generally the risk comparison that is preferred is to compare one population group to the risk for all other students combined, because that way you can use a consistent comparison group for all calculations.

So. . . the equation for the risk ratio would be:

Risk ratio = Risk for racial/ethnic group for disability category / Risk for comparison group for disability category

Let's say that the autism risk for Black students is 4%, but for all other students is 2%. Then the Risk Ratio is 2.0. In other words, in this example, Black students are two times more likely than all other students to receive services for autism. A risk ratio of 1.0 means there is no difference between the two groups. (Risk ratio >1 equals increased risk for the identified sub-group; risk ratio <1 equals decreased risk for the identified sub-group.)

Weighted Risk Ratios allow you to compare data across school districts, where (as we know) the racial/ethnic composition varies greatly. Read about the math of the weighted risk ratios in the link I gave you earlier--but they are similar to Risk Ratios in the way that they work: weighted risk ratio >1 equals increased risk for the identified sub-group; weighted risk ratio <1 equals decreased risk for the identified sub-group.

So--now that we've taken a statistical detour, what exactly did that letter that we got mean?

1. We know that it was written because it was state-mandated.
1. We know that it was based on data from 2009-2010.
2. The issues raised center on suspensions, expulsions, and the category of students labeled as "cognitively-impaired."
3. The first few times I read the letter, I assumed that the problem with suspensions and expulsions was specific to African American students, but let's note that the letter doesn't say that. I therefore believe that this is a problem for more than one group. The letter also doesn't state the weighted risk ratio for suspensions and expulsions.
4. In the cognitive impairment group, African Americans are more than 3 times more likely than the statewide comparison group (of all other students, I believe--although it is not stated in the letter!) to be identified as cognitively impaired.

To put it baldly, the letter is terribly-written, and it was clearly written just to meet the letter of the law and not the spirit.  I'd say that the district missed an important chance to really explain (not just in vague platitudes) what it is doing to improve things.

The district writes:
"Ann Arbor Public Schools was also determined to have significant disproportionality because..."

The English teacher in me notes the passive tense here--who exactly is responsible for the problem?


The letter doesn't explain this at all, but I dug up an old Ann Arbor News article which says that in 2007-2008, 47% of the students who were identified as cognitively impaired were African American.  The article (David Jesse, 3/12/2009) says, "the district was not complying with federal and state law in the way it determined which students were cognitively impaired." So was misdiagnosis involved? The letter doesn't say. If kids were misdiagnosed, were they moved out of the "cognitive impairment" group and is that responsible for the slight improvement in numbers?

Based on the ratios disclosed in the letter, I believe that while things may have improved somewhat, I am not sure they have improved at all significantly. And in using the word "significantly," here, I'm talking about statistical significance. Is it just a fluke the numbers have dropped slightly or are the results related to something specific?

Further, the letter only addresses the areas of disparity which reached a state-mandated benchmark. There are other areas of disparity--many other areas of disparity--in special education, that fall short of the benchmark.

But any time there is a big disparity, we need to ask why the disparity exists:


1. Is it because different races/ethnicities are differentially diagnosed? In other words, is the bar for "cognitive impairment" set equally for everbody?

Translation: This could be due to obvious or subtle racism. Historically, kids who had trouble switching from Black English to Standard English were sometimes labeled cognitively impaired or placed in other special education categories.

2. Does the disparity represent a real difference? In other words, using the same exact standards, are more African Americans in the Ann Arbor schools cognitively impaired than other kids in the Ann Arbor schools?

Translation: The numbers could be describing real differences. For instance--more African American babies are born prematurely than White or Hispanic/Latino babies, and premature babies are more likely to grow up to have cognitive impairments.

3. Does the racial disparity mask a different disparity?

Translation: Is this problem really about poverty, and because proportionally more African American kids live in poverty, a disparity based on class shows up as a disparity based on race? For instance--do poor housing conditions lead to increased exposure to lead paint and thereby to cognitive impairments?

You can read an earlier post I wrote on disparities here, but to cut to the chase: racial disparities have been with the district for over 30 years. There are no easy solutions, or we would have solved the problem.

On the other hand, I think the conversations about how to solve the problems need to take place with more parental and taxpayer involvement than has been the case previously. This letter is a weak start.

Miss USA: Should math and evolution be taught in schools??

One is the original, the other is farce. Can you tell which is which?

What Else is Math Good For?

Yup--art.

Check out the work of Sol LeWitt, on display at MassMoCA, the Massachusetts Museum of Contemporary Art, until 2033--so you've got plenty of time to get there. It is beautiful art, but also mathematical masterpieces.

View this, or this, or this, or this.

About LeWitt's work:

"LeWitt—who stressed the idea behind his work over its execution—is widely regarded as one of the leading exponents of Minimalism and Conceptual art, and is known primarily for his deceptively simple geometric structures and architecturally scaled wall drawings. His experiments with the latter commenced in 1968 and were considered radical, in part because this new form of drawing was purposely temporal and often executed not just by LeWitt but also by other artists and students whom he invited to assist him in the installation of his artworks.
Each wall drawing begins as a set of instructions or simple diagram to be followed in executing the work. . . " From About the Artist, MassMoCA. Emphasis added.

If you read his instructions in the piece below (taken from here), you can see how math can be used to create art. 

 

It's Art! It's Math!

I doodled my way through high school, so I found this fascinating, even had no idea who Hilbert is. (Find out who he is here.)




[So this is what math is good for! Doodling! I never doodled so symmetrically.]

Technology and (Lots) More

OK, I know you've been wondering where I've been...hey, it's summer!

I have been working on some longer posts, but in the meantime, here are some updates.

1. Tuesday, if you're like me you'll be keeping an eye on the recall elections going on in Wisconsin. At their core, they are all about how public employees are treated. On twitter I think you can search #wivotes or #wiunion for up to the minute information. I blogged about my experiences back in February at the rallies in Madison.

2. Also Tuesday, the Ann Arbor school board will be discussing the possibility of putting a technology millage on the ballot. It's a special meeting to discuss this--I'd encourage you to share your opinion, either by going to the board meeting (Balas, 7 p.m.) or by emailing the board at boe@aaps.k12.mi.us. I wrote about my concerns about whether this is a good way to pay for technology, in the post How should schools pay for technology? I also haven't heard much enthusiasm for the idea from anyone except school board members, so I wonder--why pursue something and spend so much time and energy on something that is going to be voted down anyway? And if I were in the teachers' union, I might consider opposing this. Why? Well, it was only a couple of years ago that the Saline superintendent threatened to eliminate the high school math department and move completely to on-line learning. (Yes, it was a dumb idea--and likely mostly a bargaining tool--but still--why support that kind of thinking?)

3. And this article, Michigan teachers continue to leave for other states,  has really gotten a lot of play. It's not a big surprise to anyone that there are very few teaching jobs in Michigan, and that we are training too many teachers. I wrote about that a short while ago. It would be nice if teacher training institutions consciously chose to reduce their class sizes and upgrade the quality of their incoming classes. Will they? I bet not nearly enough, because teacher education is their bread and butter...

4. The Ann Arbor district did a nice job sharing information with Ann Arbor Open parents when the fire happened in the building (it was an electrical problem). 

5. I'm quite sure Governor Rick Snyder isn't interested, but nonetheless I'm going to put out here, for my gazillion readers, two thoughts about how the state could raise more money. First, let's turn I-94 into a toll road, and dedicate those funds to improving the roads. (I grew up on the east coast. Most of the roads are tolled. People who use them, pay for them.) Second, let's look at what mobile home owners pay in lieu of "property taxes." The last time I checked, it was something like $15/year and was set in the 1950s. Maybe it's time to raise them.

6. Ypsilanti Schools have unveiled a new design for their website at www.ypsd.org. Let them know what you think!

7. I was a little sorry to see that Stone School got renamed Ann Arbor Technical High School. It reminded me of a line from a Grace Paley poem, "I gave away that kid like he was an old button." I admit, it's not exactly "giving away the kid," but did we have to lose the name? And if we did, couldn't we think of something less...boring...trendy...I mean, we've already got New Tech High School, and Washtenaw Technical Middle College...and is the name really going to change the reputation?

In case you are wondering, the original Stone School is now a cooperative preschool, at the corner of Packard and Stone School roads, and the building is 100 years old, this year.

8. About Ypsilanti's New Tech High School--A couple of weeks ago, I was checking out of a store, and because I was buying a backpack, I started talking about schools with the cashier. Her child has been going to New Tech. She thinks it is fabulous, that it has rekindled his interest in learning. Now, she said to me, he's thinking about college. She said, "Well, he was behind in school, and he's still behind, but now he's interested in catching up." I thought that was very high praise for a brand new program. And apparently they were just named a national demonstration site, too, so that is promising. (Now, I would link to the New Tech web site, but I guess ypsd.org still has some work to do, because the link is broken...if it gets fixed I will update it.)

Asking the Right Questions

Rick Garlikov describes the Socratic Method as "Teaching by Asking Instead of Telling."

He has an extremely interesting experiment teaching third graders binary numbers* and writes,  

This was to be the Socratic method in what I consider its purest form, where questions (and only questions) are used to arouse curiosity and at the same time serve as a logical, incremental, step-wise guide that enables students to figure out about a complex topic or issue with their own thinking and insights. 

You will find the experiment here. (Read it! It is fascinating.) 


*By the way, it's okay if you don't know what a binary number is. First of all, if you read about the experiment, you will understand what they are by the end of the article. Second of all, the experiment is not about binary numbers, but it is about asking questions and using the Socratic method.


Memory: When I was in high school, I had a biology teacher who wrote many outlines on the board. Phylum, Class, Order, Family, Genus, Species. . . all nicely outlined in copperplate handwriting. (Yes, she had been raised in Catholic schools and like so many of my public school teachers, I believe she had been a nun.) All of that outlining explained the "what," which we dutifully copied. But it didn't explain the "why." I was always asking "why," and one day, my teacher asked me if there was trouble at my home. (No! Why was she asking? Clearly the line between having an inquisitive mind and being trouble for her was a fine one.) I realize now that she probably did not have a strong biology background, and she knew the basics--but she found questions that she did not know the answer to, to be threatening.

Of course, the great irony of this is that good scientists are not driven by answers--they are driven by questions, and their favorite kinds of questions are the ones that cannot be immediately answered.

Tiger: The Lighter Side

TIGER, tiger, burning bright
In the forests of the night,
What immortal hand or eye
Could frame thy fearful symmetry?
(William Blake, The Tiger)

Headlining a chapter in my daughter's math book is a picture of Tiger Woods. You know, it's the attempt to introduce relevance. As if Tiger sits down with his calculator to analyze the best angles for hitting balls on the golf course.

"Mom," she said. "Look at this picture. I'll bet they wouldn't include that picture if they were writing this textbook now."

I'll bet they wouldn't. Math teachers are just not as interested in angles of repose. (Sorry, I couldn't resist.)

Trimesters and Algebra

New state standards have pushed many districts into a trimester system. (The majority of Washtenaw County districts have switched over. In Ann Arbor, only Skyline has switched.) A key section of the new standards focuses on ensuring that all kids have more math.
According to the new curriculum law:

Students must complete at least Algebra I, Geometry, and Algebra II, or an integrated sequence of this course content that consists of 3 credits, and an additional mathematics credit, such as Trigonometry, Statistics, Pre-calculus, Calculus, Applied Math, Accounting, Business Math, or a retake of Algebra II. Each pupil must successfully complete at least 1 mathematics course during his or her final year of high school enrollment. (Emphasis added.)

Math, you might say, is frequently privileged in schools. It is the driving force in Ann Arbor in middle school scheduling (your math class often determines most of your other classes). Want to see the achievement gap in action? See who is placed in which math classes in eighth grade.

And now it is the driving force in high school as well. Since math is often the subject that students have trouble with, one idea was that you could teach a standard year of math in two trimesters, and if a student was having trouble, they could repeat a class in a third trimester. And--since with trimesters there are 15 classes in the year (3 trimesters x 5 classes) instead of 14 with the semester system (2x7), this wouldn't disadvantage kids who were having trouble with math. At the same time, kids who didn't have trouble with math would get an extra elective. Prior to these standards, many (many!) kids did not take Algebra II.

At least at Skyline, that experiment has been less than successful. So many kids were having difficulty learning the math in two trimesters, in the school's second year they changed the "standard" math option to a three trimester option.

Today in my inbox, I got a link from Education Week that says that the Algebra-For-All Push Is Yielding Poor Results.

This is really a very interesting article, with a summary of a lot of different research studies, and I encourage you to read it (you might need to register at the site).  Some of the salient points:
*Misclassification of kids matters (who goes in which class)
*When you eliminate tracking, the top students don't learn as much
*However, the bottom students seem to learn more
*Simply taking algebra doesn't seem to affect the likelihood of attending college (and that is a very complicated issue--I'm sure there are lots of confounding factors there).

Side note: Is college the desired outcome here? Or learning math?

Obviously, learning math is important, but it's often not clear why, as I discuss here.
It's not just about math, though. I think we also need to ask whether the trimester system works.

Saline, Math, and the Retweet

Ten days ago I wrote up a summary of the rumors that were going on about Saline eliminating the high school math department.
I said at the time that I didn't know what was true. In fact, I retweeted the Saline superintendent's tweet that "no decisions had been made."

It turns out that, in fact, the rumors were true, as explained in this annarbor.com article by David Jesse.

In fact, the superintendent had met with the leaders of the teachers union and presented them with a list of potential layoffs--including the entire high school math department. Backpedalling, Scot Graden then tells annarbor.com that "the notice of intent was just part of a budget-cutting process he’s promised would leave nothing off the table."  And then--after the teachers' union rightfully raises a hue and cry, he says that he will not recommend eliminating the math department.

Oh, come on. Mr. Graden, you were being disingenuous at best. The honest thing to have done would have been to make public to the community that you had shared with the teachers' union a list of potential layoffs, including the entire math department, and that a notice of intent was required to give the district the maximum wiggle room. And while you were at it, why not make the notice of intent for possible layoffs apply to every single teacher in the district? THAT would give you wiggle room.

Funnily (but I don't mean that in a ha-ha way), just before Christmas, Scot Graden had blogged about the budget process in a post called Judgment. And in it, he writes,

The saying goes, with good judgment, little else matters and without good judgment, nothing else matters. Judgment is the essence of leadership.  In the face of instability, uncertainty and conflicting demands, the quality of a leader’s judgment determines the fate of the entire organization.

 He also questions the importance of process, writing "while the process is important, ultimately we are judged on the results."

Umm, yes. The process is important. Of course you are judged on the results, that is a GIVEN.
But when you use poor process, and (in this case) show poor judgment, what you end up doing is setting yourself up as less trustworthy. If you don't tell someone the truth, and they find out, the next time they are a lot less likely to believe you.

Leaving aside the issue of trust, I believe that with good process, you will get some better budget-cutting ideas than putting the entire math department online. And maybe this was just a maneuver to get the union to take a wage cut and enter into negotiations--union-busting seems to be popular these days--but an honest, open process would have shared the information with people, in a publicly accessible manner.

As for me--I am new to the twitter world--I retweeted Scot Graden's twitter that was essentially denying the rumors. In this way, I feel I made myself an accessory to the poor decision-making. Next time, I am going to be a lot more careful when I decide what to retweet.

I believe that process matters. And I would feel a whole lot better about the whole thing if Mr. Graden would write a note to the community apologizing for his poor judgment this time, and explaining how he will improve the process next time. Everyone makes mistakes, but (as my ninth grade math teacher used to say), it is best to make a different one every time.

Quote of the Day

"The harder the math homework is, the more useless the math is."
--High school student

For more background reading, see this post.

Square Root Day

It turns out that today, March 3, 2009 (or 3/3/09, as you might prefer) is Square Root Day. Why? Because 3 x 3=9, and so we say that 3 squared equals 9.

Math educators have been pushing the idea that you need to understand the concepts behind math, and I have to admit that I haven't fully bought into the idea. It's not that I'm pro-rote learning...it's really more that I think sometimes you can learn the concepts after you learn how to do the problems. But in any case I hate to be dogmatic and I am sure learning the concepts first works better for some kids.

The importance of understanding the concepts in math got a boost the other day, as far as I'm concerned, after a conversation with one of my children (one who is in elementary school).

Child (out of the blue, while sitting in traffic): I finally understand the idea of why a squared number is called a square.

Me: Really? Why?

Child: Well, because each side of the square is the same, and when you want to get the area you have to do the width times the height and in a square those lengths are the same.

Me: (To my internal alter ego) Wow! I've been squaring things all these years and I know how to do it, but I never knew why it was called a square.

Me: (To my child) That is exactly right! And do you know why the next power up is called a cube? (Discussion followed.)

Seriously. I use math very frequently at work, and I think I'm pretty good at math concepts, but I never put together the idea that squares and cubes are not just representing a multiplication fact, but also a geometric concept...until this week.

Which adds a whole new dimension to Square Root Day. Have a happy one!