Sunday, February 27, 2011

The attack on science is bipartisan

In a piece in this weekend's New York Time Magazine, Judith Warner discusses the bipartisan nature of the attack on science. In the late 1980s and 1990s, she notes, came an attach by the left: the sweeping postmodern relativist assault on scientific Truth. This assault, she claims, lost steam after it was parodied by the "progressive" physicist Alan Sokal in his "Transformative Hermeneutics of Quantum Gravity." At this point, she claims, the attack on science switched from left to right, now directed, in particular, at the science of global warming.


What Warner fails to realize is that the attack on science has been, and always will be, a bipartisan affair. It is renewed each time scientific findings challenge widespread cherished beliefs--whether about genetics and IQ; when fetuses become conscious and experience pain; the efficacy of alternative medicine; the role of vaccines in autism; the age of the earth; the tremendous complexity and uncertainty involved in climate change; the origin of species; the neurological wiring of religious belief; what the mastery of reading, math, and arithmetic entail; or what science is (highly analytical, with correct and incorrect answers) and isn't (postering and science appreciation).

Yes, we all love science... just so long as it doesn't make our brains buzz with cognitive dissonance, or our hearts burn with disappointment or anger.

Friday, February 25, 2011

Math problems of the week: 5th grade Investigations vs. Singapore Math

I. The third problem set in "Unit 4: What's that Potion?" in the 5th grade (TERC) Investigations Math Student Activity Book, Session 1.1:


Everyday Uses of Fractions, Decimals, and Percents

List in the spaces below the everyday uses you find for fractions, decimals, and percents. Cut out your examples from used magazines and newspapers, and attach them to this sheet.

Everyday Uses of Fractions

[space to attach]

Everyday Uses of Decimals

[space to attach]

Everyday Uses of Percents

[space to attach]

II. The third problem set in "Unit 3: Fractions" in the 5th grade Singapore Math Primary Mathematics Workbook 5A, pp. 53-54:

Add. Give each answer in its simplest form.

1.

(a) 7/8 + 3/4 = 7/8 + ?/8 =

(b) 2/3 + 4/9 = ?/9 + 4/9 =

(c) 4/5 + 3/10 =

(d) 3/4 + 7/12 = 

(e) 5/6 + 2/3 =

(f) 1/2 + 9/ 10 =

2.

(a) 1/6 + 3/4 = ?/12 + ?/12 =

(b) 5/9 + 1/2 = ?/18 + ?/18 =

(c) 1/2 + 3/5 =

(d) 2/5 + 3/4 =

(e) 9/10 + 1/6  =

(f) 3/10 + 5/6 =

III. Extra Credit

Speculate as to why supporters of Reform Math programs like Investigations say that Singapore Math is a good program but (i) refuse to consider using it and (ii) accuse anyone who even mentions Singapore Math of shilling for Singapore Math.

Wednesday, February 23, 2011

Barry Garelick's Open Letter to Deborah Ball

Out in Left Field is proud to publish a letter from Barry Garelick to Deborah Ball. Deborah Ball is Dean, University of Michigan School of Education. She is also listed as an advisor/consultant to the second edition of “Investigations in Number, Data, and Space.”

Dr. Ball:

We have never met but I write articles concerning math education and am committed to better math instruction and curricula in the U.S. You recently wrote an op-ed in the Huffington Post calling for effective teachers and better teacher training. You have given a brief description of what you feel constitutes effective teaching. In it you said:

We need to agree on a common core of the most essential capabilities for skilled teaching. Examples include being able to diagnose common student difficulties, explain core ideas and procedures understandably, lead a productive discussion, manage a classroom for learning, and work effectively with students with special needs. On this central core, we need to build assessments, using the best technology and tools available, that enable us to determine candidates' readiness for practice, and to monitor teachers' capability and continued development over time.

Given the importance you place on diagnosing student difficulties and explaining core ideas and procedures understandably I would like you to view the video that is posted here. You'll notice that the little girl is illustrating how to add two large numbers using a method from Investigations in Number, Data and Space, a program for which you are listed as an advisor/consultant for the second edition. Given your interest in better teaching and teachers, and your connection with this program, I would greatly appreciate it if you would answer the following questions:

What is your opinion of the method the girl has been taught for adding large numbers?

Investigations teaches the standard algorithm for adding large numbers in the fourth grade. Do you agree that it is beneficial for the girl not to be allowed to use "stacking" until then?

Do you see any harm in the approach that the third grade Singapore "Primary Math" textbook uses to teach this same procedure? (See illustration)

Do you think the girl's mother has done the girl harm by teaching her the standard ("stacking") method?

Do you think the process the girl is using is more important than her getting the
right answer? If so, why?

If two teachers were to teach this method, and one used the Investigations method illustrated in the video and the other used the method in Singapore's textbook, how would you judge the effectiveness of each teacher?

Do you believe that a teacher who opposes the Investigations method and uses instead the method Singapore's textbook employs is an effective teacher? Do you believe such judgment on the teacher's part indicates a lack of "readiness for practice"?

Lastly, tell us where you stand on Investigations, Everyday Math, and Connected Math Program. Do you support them and believe they are effective? Why? Many of us await your answer.

Illustration of Singapore Math 3rd grade textbook lesson on adding large numbers:


Source: "Primary Mathematics 3A" (2003); Marshall Cavendish Education
--------------------------
***Update: Blogger is swallowing a large number of comments on this thread (even though these comments are unmoderated). To ensure your comment appears, feel free to email me a copy of what you post here at katharine [dot] p [dot] beals [at] gmail [dot] com.

Tuesday, February 22, 2011

Enough about math, already! Let's look at writing instead...

I'm a big fan of sentences. When I edit my work, I'm constantly combining and recombining them, altering the order of phrases, or their depth of embedding, to maximize clarity, flow, and efficiency.  Following this, almost in lockstep, is clarifying my message. This works in both directions: the more I play around with sentence syntax, the clearer my thoughts become; when I know exactly what I want to say, the ideal sentence structure comes along for the ride. 


None of my writing instructors ever focused on sentence-level syntax--except to tell us to "vary our sentence structures." But varying structure for the sake of variation alone does not enhance writing; when you structure each sentence for clarity, flow, and efficiency, you will, willy nilly, vary your sentence structures. My focus on syntax comes not from my English teachers, but from my own personal interest in sentence structure (one that ultimately culminated in a doctorate in linguistics).  From a young age, I'd constantly scrutinize the variety of structures that undergird effective prose and try to internalize them so they'd become part of my own syntactic repertoire.

So when Catherine Johnson recently sent me an article by Robert J Connors on The Erasure of the Sentence, I was astounded to realize that explicit instruction in sentence syntax had been a staple of composition classes (dating back to classical antiquity) until just a few decades ago. 

What happened? Here, in a nutshell, is Connors' thesis:
The usefulness of sentence-based rhetorics was never disproved, but a growing wave of anti-formalism, anti-behaviorism, and anti-empiricism within English-based composition studies after 1980 doomed them to a marginality under which they still exist today. The result of this erasure of sentence pedagogies is a culture of writing instruction that has very little to do with or say about the sentence outside of a purely grammatical discourse.
But first, what are these sentence-based rhetorics that have fallen out of favor?

Recent champions of sentence-based rhetorics include Francis Christensen, whose specialty was "sentence combining."  In Connors' words, "Sentence-combining in its simplest form is the process of joining two or more short, simple sentences to make one longer sentence, using embedding, deletion, subordination, and coordination." 
According to Christensen, you could be a good writer if you could learn to write a good sentence. His pedagogy consisted of short base-level sentences to which students were asked to attach increasingly sophisticated systems of initial and final modifying clauses and phrases-what he called "free modifiers." Effective use of free modifiers would result in effective "cumulative sentences," and Christensen's most famous observation about teaching the cumulative sentence was that he wanted to push his students "to level after level, not just two or there, but four, five, or six, even more, as far as the students' powers of observation will take them. I want them to become sentence acrobats, to dazzle by their syntactic dexterity."
Another "sentence-based rhetoric" was Edward Corbett's "imitation exercises," which involved the "the emulation of the syntax of good prose models." Students would begin by copying a model sentence word for word. Then came "pattern practice," in which students construct new sentences that parallel the grammatical type, number, and order of phrases and clauses of the model sentence, perhaps with the help of a syntactic description of the model sentence's structure. Students might also perform syntactic transformations (informed by Noam Chomsky's Universal Grammar) on the model sentence. In Corbett's words, the aim of such imitation exercises was to "achieve an awareness of the variety of sentence structure of which the English language is capable." Other advocates of imitation exercises noted that student writing "is often stylistically barren because of lack of familiarity with good models of prose style;" the remedy was explicit emulation of good models. 

Both Corbett's and  Christensen's methods were subject to empirical scrutiny, and studies showed that both methods not only increased the grammatical complexity of student writing, but also improved the overall writing quality (as compared with control groups and as rated by blind raters). In particular, internalizing syntactic structures, even by slavishly copying them, ultimately increased originality and creativity--presumably by giving students a wide repertoire of syntactic tools to choose from and handy ways to play around with them.

But as Connors notes, almost as soon as this sentence-syntax teaching methodology starting showing empirical success, it was shouted down into oblivion by critics who found it philosophically distasteful.  After all, these methods involved:

1. textbooks
2. mere exercises, devoid of content and real-world application, with (worse yet!) correct and incorrect answers
3. rote imitation
4. an inorganic, narrow, analytical, reductionist approach that stifles creativity 
5. a procedural focus at odds with the authentic writing process in which motivation and communicative intent and self-expression come first and everything else comes along for the ride (including, apparently, grammatically well-formed sentences).

The result of this backlash was that most writing instructors came to believe that "research has shown that sentence combining doesn't work."

Sound familiar? 

If not, try substituting "sentence combining" with "traditional math," syntactic transformations with "mere calculation," "imitation exercises" with "drill and kill," and "communicative competence" with "conceptual understanding."

Woops! I thought that by writing about writing I'd be taking a break from math.

Sunday, February 20, 2011

Investigations Math in action: crashing and burning with large numbers

A third grade girl attempts, unsuccessfully, to add several large numbers using an Investigations Math strategy. She then adds them successfully using traditional "stacking" (disallowed at school) in a fraction of the time the Investigations method took her:




Filmed and edited by a fellow concerned parent who is a specialist in math remediation.

Friday, February 18, 2011

Math problems of the week: 4th grade Trailblazers vs. Singapore Math

I. Final five word problems in the 4th grade Math Trailblazers Discovery Assignment Book (p. 215):

John's older brother is in college. His brother and his three roommates want to buy a new stereo that costs $764. If they split the cost of the stereo evenly, how much should each student pitch in?

Ming built a house of cards. Before the house came tumbling down, he used 2 full decks of cards. The house also contained all but 15 cards from a third deck. About how many cards were in Ming's house of cards? (A deck of cards has 52 cards).

On vacation, Shannon's family took 3 rolls of 24 pictures and 2 rolls of 36 pictures. How much pictures did the family take in all?

Roberto is driving with his family to visit his grandmother. After driving 144 miles from Chicago, the family stops for lunch. They drive 89 more miles and stop for gas. Then, they stop for a soft drink after driving 123 more miles. Roberto's grandma lives 375 miles form Chicago. About how many more miles must they drive before they reach their grandmother's house?

If one year is 365, how many days old will you be when you are 16 years old?


II. Final five word problems in the 4th grade Singapore Math Primary Mathematics 4B Workbook, (p. 215):

A tank can hold 30.1 gal of water. A bucket can hold 1/7 as much water as the tank. Find the capacity of the bucket.

The perimeter of a rectangle is 30 in. The width of the rectangle is half its length. Find the area of the rectangle.

Neil saved 15 quarters in January. He saved 35 nickels in February. He saved 21 dimes in March. How much money did he save in the three months?

How many quarters are there in $116.75?

Show all the possible outcomes for the gender (boy or girl) of three children in a family.

III.  Extra Credit

Estimate the ratio of verbiage to mathematical challenge in the Trailblazers vs. the Singapore Math problem sets.

Wednesday, February 16, 2011

Headlines, opening paragraphs, and confirmation bias

What lesson will most educators draw about schools and social skills after looking through last week's Education Week?


If they simply scan the headlines, they will see an article entitled "Study Finds Social-Skills Teaching Boosts Academics."

If they read the first two paragraphs of this article they will find what might look like solid evidence:
From role-playing games for students to parent seminars, teaching social and emotional learning requires a lot of moving parts, but when all the pieces come together such instruction can rival the effectiveness of purely academic interventions to boost student achievement, according to the largest analysis of such programs to date.

In the report, published Feb. 4 in the peer-reviewed journal Child Development, researchers led by Joseph A. Durlak, a professor emeritus of psychology at the University of Chicago, found that students who took part in social and emotional learning, or SEL, programs improved in grades and standardized-test scores by 11 percentile points compared with nonparticipating students. That difference, the authors say, was significant—equivalent to moving a student in the middle of the class academically to the top 40 percent of students during the course of the intervention. Such improvement fell within the range of effectiveness for recent analyses of interventions focused on academics.
Only if they read as far as the ninth paragraph will they encounter the idea that academic gains may result simply from better behaved students being easier to teach, and not from some broader, fuzzier connection between social skills and academic achievement:
Corinne Gregory, the president and founder of the Seattle-based schoolwide SEL program SocialSmarts, suggested the improvement ...[occurred] in part because educators could teach more efficiently with calmer, more cooperative students.
And only if they reach the twelfth paragraph will they learn that:
One finding ran counter to both the researchers’ expectations and prior research: Simple teacher-led programs vastly outperformed multifaceted programs involving schoolwide activities and parent involvement. While classroom-based programs showed significant improvements across all five social measures and academics, comprehensive [school and home based] programs showed no significant effect on students’ social-emotional skills or positive social behavior, and were less effective at improving academic performance.
Any guesses as to whether this article will result in fewer cooperative-group -centered classrooms and comprehensive social skills programs--including in schools in which student behavior is not a major distraction from academics--or even more?

Monday, February 14, 2011

More fallacies in the media about cooperative groups

With the release of Edward Glaeser's book Triumph of the City, and with a new University of Michigan study on group cooperation, the supposed virtues of cooperative groups are once again the talk of the media—as seen, for example, in a recent New York Times Op-Ed by David Brooks on "The Splendor of Cities" and a recent article in last weekend's Wall Street Journal on the "Sunset of the Solo Scientist". 

You can be sure that anyone in the education establishment who reads these articles will find just what he or she is looking for: more reasons to make students spend significant time working in groups. Confirmation bias blinds most people to the underlying fallacies:

1. Cooperation does not equal collaboration.
I’ve made this point many times over: Many (and I’m guessing most) group collaborations, while they include collective brainstorming, ongoing conversation, and, ultimately, some sort of collective wrapping up, have people spending the majority of the time working on their own. Construction sites and film sets aside, how often is the bulk of the work, and of the time spent on it, accomplished by people occupying the same open (cubicle-free) space and constantly interacting and doing things together?

2. Carefully chosen cooperative games aren’t representative of most collaborations.
A corollary to 1: The specially-designed cooperative games of the University of Michigan's recent psychological experiments aren’t representative of most human endeavors. The fact that highly cooperative groups (those with higher social or “group intelligence”) outperform less cooperative ones on certain highly cooperation-dependent games says nothing about collaborations in general. Were the same experiments performed on real-world collaborations in STEM or business, would “group intelligence” still be the most important factor?

4. Even ostensibly “cooperative” groups can be arenas for competition and bullying.
(Another point I’ve made many times over and won’t belabor here).

3. Density and frequent contact do not equal cooperation.
I haven't read Glaeser's book, but some of the reviews of it I've seen suggest that brainstorming and competition, and not necessarily group cooperation, are key ingredients in how cities advance civilizations via increased human interaction.

5. The rarity of solitary geniuses does not equal their demise.
As one WSJ letter notes in response to the WSJ’s recent article on the “Sunset of the Solo Scientist”:

Minds like Einstein’s or Newton’s come infrequently, and the gap in time between theirs and the next true greats may be now. Or maybe not. What about Stephen Hawking? He may yet eclipse Einstein.

Maybe you just don’t know who today’s greats are. Some may not be recognized until well after they’re dead. Ideas are still the realm of individuals.

Great ideas typically spring from a single mind. Teams of researches may trudge through mountains of data but not have the “Aha!” moment… ever.

I think that encouraging individual, critical and creative thought is the only way to create true greats.

Saturday, February 12, 2011

Autism and abstract thinking, II: concrete vs. figurative language

Several months ago, I wrote a post about how frequently people assume that autism involves deficits in abstract thinking, and proposed several reasons for this widespread misconception:

1. For many people, abstraction is synonymous with fuzziness, flexibility, and open-endedness. Because autistic people tend to be rigid, ritualistic, precise, pendantic, and/or detail-focused, and because many of them don't do well when faced with open-ended questions or open-ended tasks assigned to them by other people, they do not look like abstract thinkers according to this misconception of "abstract." All too often, for example, people forget that the concept of "polygon" is no less abstract than the concept of "love."

2. Many people, especially in education, conflate logical inferencing with the sorts of inferencing that good readers engage in when making sense of a text. As I've discussed in previous posts (here and here), many of today's assigned texts require the sorts of social inferences and and bridging inferences (integration of background knowledge) with which autistic children tend to struggle. These are not the same as inferring the contrapositive or doing a reductio ad absurdum.

3. Many people, as I discussed in a recent post, confuse labels with concepts and assume that a child who doesn't know the label for a given concept also doesn't understand the concept. Many labels for abstract concepts and logical processes are difficult for autistic children to pick up on their own: they often require explicit vocabulary instruction that other children don't need. Unless and until they receive such instruction, many people will assume that they don't understand the underlying abstractions--e.g., that if he doesn't know the word "because," he doesn't understand causality.


I'm once again teaching a class on language difficulties in autism, and yet another reason for linking autism to limited, concrete thinking has emerged:

4. People conflate concrete vs. figurative language with concrete vs. abstract concepts.  While it's true that individuals with autism tend to interpret language concretely, this entails nothing about their ability to form abstract concepts.  

Moreover, as I discuss in a chapter in this forthcoming book, the tendency by autistic children to interpret language concretely isn't a conceptual difficulty with nonliteral language per se, but the result of a combination of deficits in social reasoning and deficits in vocabulary and idioms. For example, a child who assumes that "stuck" always means physically "stuck" has probably simply never learned the more metaphorical meaning of stuck.  

J, for his part, loves metaphorical extensions and uses of language, and is quite inventive about making up new ones.

Thursday, February 10, 2011

Math problems of the week: 6th grade Connected Math vs. Singapore Math


Initial 6th grade fractions problems:

I. The second fractions problem set in 6th Grade Connected Math (Bits and Pieces I, p. 7):

A. 
1. Use strips of paper that are 8 1/2 inches long. Fold the strips to show halves, thirds, fourths, fifths, sixths, eighths, ninths, tenths, and twelfths. Mark the folds so you can see them better.

2. What strategies did you use to fold your strips?

B.
1. How could you use the halves strip to fold eighths?
2. How could you use the halves strip to fold twelfths?

C. What fractions strips can you make if you start with a thirds strip?

D. Which of the fraction strips you folded have at least one mark with the arks on the twelfths strip?

E.
1. Sketch a picture of a fifths strip and mark 1/5/, 2/5, 3/5, 3/5, and 5/5 on the strip.
2. Show 1/10, 2/10, 3/10, 4/10, 5/10, 6/10, 7/10, 8/10, 9/10, and 10/10 on the fifths strip that you sketched.

F. What do the numerator and the denominator of a fraction tell you?


II. The second fractions problems set in 6th Grade Singapore Math (Primary Mathematics 6B, p. 7):

1. Divide

(a) 1/3 ÷ 3 = 1/3 × 1/3 =

(b) 1/6 ÷ 6 = 1/2 × ___ =

(c) 1/6 ÷ 4 =

(d) 4/5 ÷ 2 =

(e) 2/5 ÷ 4 =

(f) 8/9 ÷ 4 =

(g) 3/4 ÷ 2 =

(h) 2/3 ÷ 6 =

III. Extra Credit:

What is your preferred way of discovering things about fractions: fraction strips or repeated calculation of carefully contrived fractions problems?

Wednesday, February 9, 2011

Floors vs. ceilings: or U.S. math vs. Russian Math

A dear old friend recently wrote me about her impressions of her son's 1st grade math class and of the Russian Math class they are sending him to after hours.
I hate doing my son's public school homework with him. It takes him about 10 minutes and is so idiotic. I can't keep from hiding my disgust. What a waste of time.
I was just going over his work (1st grade). They began with worksheets he could have completed when he was 3. After 2 months, they began addition with equations in sequential order. (1+1, 1+2, 1+3...) Now, they color in pieces of pie to introduce fractions. It has improved through the year, but the progress is excruciatingly slow and many of the problems give you the answer in the diagram which means they really aren't figuring anything out.
We are enjoying a private program from a Russian Math school. I think it is similar to Singapore Math in that it addresses Math problems from many perspectives and builds very quickly while continuing to introduce new concepts. Much more challenging and fun too.
Russian Math began the first day by teaching them symbols (>, <, = and more). They then used these to compare two equations at a time. This taught him to add while at the same time compare numbers to get a sense of how they relate. They were also shown geometric shapes that fit into each other. They had to either combine two shapes or break apart two shapes. By the second class, they were comparing diagrams that demonstrated weights on a scale and comparing subtraction equations. 

Since then, he has learned how to measure the perimeter of different shapes and solve for X in equations. He can add and subtract multiple numbers in one equation, do simple multiplication, and measure objects in centimeters and inches. He can distinguish multiple shapes within a complex form and solve simple algebraic problems. In his free time, he began to add very large numbers (fifteen digits long or more) because of an exercise he did in his Russian Math class (around the 7th or 8th class).

I understand the public schools are teaching to the struggling student. But, I can't imagine how a dumbed down curriculum helps anyone. I could see using the current curriculum as a supplement for a student who is struggling. But, I don't really see how it is helping the majority of kids. The irony is, they have taken all other subjects out of the curriculum except English and Math. And, this is the Math they are teaching?
Precisely: it might seem from a distance as if the removal of all but English and Math means school days full of relentless academic pressure. Look a little closer and you see that the pressure is actually that of a relentlessly descending ceiling.

As for lifting the ceiling and raising the floor, getting my hands on the Russian Math series is high on my to-do list.

Monday, February 7, 2011

Science fairs and Sputnik moments

A front-page report in Saturday's New York Times laments the decline of the science fair and the resultant threat to our nation's "competitive edge":
As science fair season kicks into high gear, participation among high school students appears to be declining...

“To say that we need engineers and ‘this is our Sputnik moment’ is meaningless if we have no time to teach students how to do science,” said Dean Gilbert, the president of the Los Angeles County Science Fair, referring to a line in President Obama’s State of the Union address last week. 
The article makes clear, however, that science fairs are still alive and well in middle schools--along with at least one of their many potential downsides:
In middle school, science fair projects are typically still required — and, teachers lament, all too often completed by parents.
And many high schools are still encouraging their scientifically minded students to participate:
Some high schools funnel their best students into elite science competitions that require years of work and lengthy research papers: a few thousand students enter such contests each year.
But the Times claims that other students, by not participating in science fairs, aren't getting exposed to the scientific process (as if science fairs are the only--or best--way to learn scientific thinking):
What has been lost, proponents of local science fairs say, is the potential to expose a much broader swath of American teenagers to the scientific process: to test an idea, evaluate evidence, ask a question about how the world works — and perhaps discover how difficult it can be to find an answer.
The article also cites science fair projects as especially demanding of "creative, independent exploration."

But does requiring broad-scale participation in science fairs really increase the overall scientific skills and scientific creativity of American students? Much of what passes for science skills in the science fair world, after all, amounts to skills in public speaking, verbal expression, and graphic design (or having parents with such skills). Much of what passes for scientific creativity is the showy visual creativity of the props and poster.  

Furthermore, as even some of the science fair advocates suggest, science fairs don't necessarily have nurturing scientists as their primary agenda:
“Science fairs develop skills that reach down to everybody’s lives, whether you want to be a scientist or not,” said Michele Glidden, a director at Society for Science & the Public... “The point is to breed science-minded citizens.”
The Times cites just two reasons for the decline of the science fair: competition from other extracurricular activities, and the pressure of state-mandated testing in math and reading:
One obvious reason for flagging interest in science fairs is competing demands for high school students’ extracurricular attention. But many educators said they wished the projects were deemed important enough to devote class time to them, which is difficult for schools whose federal funding hinges on improving math and reading test scores. Under the main federal education law, schools must achieve proficiency in math and reading by 2014, or risk sanctions.

[snip]

Many science teachers say the problem is not a lack of celebration, but the Obama administration’s own education policy, which holds schools accountable for math and reading scores at the expense of the kind of creative, independent exploration that science fair projects require.
The science behind scientific creativity, as cognitive scientists like Dan Willingham have pointed out, paints somewhat a different picture. Creativity in any field depends on deep, rich, domain-specific knowledge. The ability to acquire deep, rich, domain-specific knowledge in science depends on a solid foundation in mathematics. For most kids, rigorous training in k12 math is a far better preparation for the acquisition and development of scientific skills and creativity than the typical k12 science fair is.

Given this, the Times, ironically, is actually correct in implying that holding schools accountable for math scores is part of the problem. But the reason why math score accountability is problematic isn't that it takes time away from science fairs. Rather, such accountability has resulted, not only in teachers spending lots of time teaching to the test, but in math tests that are substantially watered down relative to what most other developed countries expect of their students (after all, watering down a test is the best way to make sure no child is left behind). The ultimate consequence is a dumbed down math curriculum that doesn't prepare anyone for true scientific reasoning and creativity.

Saturday, February 5, 2011

Autism diaries XXIV: Death

J first learned about death when he was 4. He'd discovered his first computer game, Bugdom, and whenever his bug was smashed by a foot or consumed by a giant slug, or died any of the other deaths that the different levels that Bugdom has to offer, he'd restart the game with a new bug and stoically carry on.


"What happens if the bug falls into a lava pool again?" I asked him once.

"Get new bug!" he cried out, grinning ear to ear.

"But what happens when you fall into a lava pool?"

"Get new J!" he answered with equal glee.

"But there is no new J!" I blurted out, struck by the consequences of J apparently thinking he'd live forever no matter how careless he was. Even more stricken than I was, J burst into tears.

Our first Dialog about Death began, and I reassured him that most people live into their 70's or 80's. I pointed to Granddaddy, his 90 year old great grandfather. Soon he was scouring the obituary pages to verify my claims. He asked me what happened to dead bodies, and I told him the various options. Shortly thereafter he found a phone and called up a grownup friend of ours. "When you die, do you want to be burned, buried, or given to science," he yelled into the receiver as soon as she said "Hello." ("Burned," she answered, not missing a beat). He asked me repeatedly what's the longest people live, and I gave him a nice round number.

Living to one hundred became his personal goal. And, like every other drive of his, I tried to milk it to its fullest. "Don't put too much salt on that--salt is bad for your heart;" "Don't use too much butter;" "You need to eat the skin of the apple, too. Apple skins are very good for you. Granddaddy always eats apple skins." The effects of this last admonition were particularly striking. Ever since he was 1 1/2, J, apple-fiend though he was, had refused to eat apple skins, leaving a yucky trail of chewed up skins wherever he went. As soon as he heard about Granddaddy's habits, he started eating them again--religiously.

Granddaddy intrigued him. Every time we visited him, J would ask how old he was. Once when he answered 96, J seemed particularly impressed, perhaps realizing that Granddaddy was now over halfway through his presumably final decade. He turned from Granddaddy to the rest of us and announced, loudly, that "Granddaddy is almost dead." (Granddaddy laughed heartily, along with the rest of us.) When Granddaddy turned 97, he asked him "How much longer do you think you will live?" ("I think I will live two or three more years," Granddaddy answered, not missing a beat).

This past November we celebrated Granddaddy's 100th birthday. J was very excited about the festivities, and asked about them repeatedly in the weeks leading up. After briefly checking in with Granddaddy on the day thereof, however, he was quickly distracted by even more pressing things: the many, many ceiling fans at Granddaddy's retirement home--a frequent subject of conversation and reminiscence.

Granddaddy died this past Tuesday evening (peacefully, in his sleep). When I told J, he looked stricken. But like so many other things, his true feelings remain a mystery. Was he upset that he'd lost his only remaining great grandparent? That he'd never see those fans again? Or that 100 really is the outer limit, no matter how little salt, how little butter, and how many apple skins you eat?

Thursday, February 3, 2011

Math problems of the week: 5th grade Everyday Math vs. Singapore Math

ESTIMATION PROBLEMS

I. From the 5th grade Everyday Math Student Math Journal Volume 2, p. 290:

[click on picture to enlarge]



II. From the 5th grade Singapore Math Primary Mathematics Workbook 5A (volume 1), p. 17:

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III. Extra Credit
Estimate the percentage of 5th social studies class time that is devoted to topics in 5th grade math.

Tuesday, February 1, 2011

Letter from Huck Finn

Out in Left Field proudly presents the first in a series of letters by an aspiring math teacher formerly known as "John Dewey":



For those few of you who know me, you probably know me by John Dewey, a nom de plume that I used to write a series of letters about education school on a blog called Edspresso mostly in 2007. I am a working stiff who will be retiring this year after which I will pursue an apr├Ęs retirement career of teaching math in middle or high school. I have finished all my courses and only have to complete my student teaching in order to get my certificate.

I decided to resurrect my letters but the name John Dewey seemed to belong to a different era and didn’t feel quite right. I’m now in an in-between mode, reflecting on all that has come before, and what will come after, floating down a river on a raft, having a vague idea of where I’ll end up. I’ve decided therefore to call myself Huck Finn. I welcome any of you to either listen to my tales of woe or tell me of your own. For those of you who choose to climb aboard the raft to talk of your enslavement by the education establishment, I will call you by a name designed to not in any way invoke the ongoing controversy surrounding the famous novel by Mark Twain, nor to make my kind hostess Miss Katharine nervous. I will call you James.

As followers of the John Dewey letters know, this river goes through territory that is decidedly divided between conflicting theories of education. The divisiveness has not subsided any since I stopped writing the first round of letters and it doesn’t look like it will end any time soon. School districts, school boards and the administrations in their grasp remain smitten by the lure of the promise that math (or any subject for that matter) need not be taught in any kind of logical sequence, and that whatever mastery of facts or procedures is needed can be learned on an as-needed basis because process is more important than content.

Some say that the divisiveness in education has been around for quite a while but I have to say that free form pondering and group discussions were the exception and not the rule back in the 50’s and 60’s when I was in school. When open-ended discussions did occur they were short lived—like the time in my 8th grade science class when the teacher, Mrs. Cohen got off on a tangent of what came before the universe was created. I don’t recall how we got off on that particular tack. I think she sensed that a full exploration of the topic might take more time than she had, so she brought the discussion to a memorable close by announcing that such things were beyond the capability of the human mind and that there had so far been only one human being capable of understanding these origins. We all thought she was referring to Albert Einstein and were therefore surprised when she announced that this person was (wait for it): Rod Serling.

Being that it was 1963 and Twilight Zone was at the height of its success, we had no problem accepting that. With that business done, Mrs. Cohen got back on track and we didn’t have to write any essays comparing Einstein to Serling, or work in groups to construct shoebox dioramas of the creation of the universe. But now we are in an age of education by collaboration, by small groups, by a student-led and teacher-facilitated inquiry-based approach. My educational psychology professor at ed school was the personification of this practice. She bore an uncanny resemblance to Meg Ryan and had taught middle school science for 15 years. Her classes were chock full of group activities, designed to help us learn the material as well as to become conversant with the various group activity techniques. I never learned her stance on Rod Serling versus Albert Einstein (or even Stephen Hawking) but she was big on student engagement and “hands on” learning. The extent to which her “hands on” or inquiry-based or student-centered approach to learning was grounded in specific content that was explicitly taught remained a mystery. She left clues throughout the semester, however, that she leaned toward the ed school thoughtworld that students should construct their own knowledge.

She definitely believed in student engagement as a key to motivation. I found this out when she told us about a particular “back to school” night for parents on which she demonstrated how she taught her students about the difference between force and pressure: She lay on a bed of nails with a rock balanced on her stomach and had a fellow teacher smash it with a sledge hammer. All of us were suitably impressed. Yes, she built the bed of nails herself. And no, she didn’t demonstrate it during our class.

I don’t expect that I will use the bed of nails technique with my future students. Nor do I expect to do half of the engaging engagement activities that I learned about. For those who are curious, I got an A+ in the class. I think it was because I used the term “Piagetian disequilibrium” in one of the papers I had to write. I also learned that if you have to make it look like you believe in students constructing their own knowledge, you can talk about Vygotsky, and the Zone of Proximal Development, and scaffolding, and people will see what they want to see. I thank Meg Ryan for teaching me the art of camouflage.

Well, it’s getting late, and Miss Katharine is looking like she’s nervous so I’ll wrap this up. My application to student teach is due in a week and I have to write a goals statement that sounds like I won’t tell my students what they need to know. It has to sound like I mean it. This might take me a while.

Talk to you soon, James.

Your pal,
Huck

Links to the former letters of the former John Dewey are: Letter # 1, Letter # 2, Letter # 3, Letter # 4, Letter # 5, Letter # 6, Letter # 7, Letter # 8, Letter # 9, Letter # 10