Tuesday, February 28, 2012

The perils of asking English teachers to focus on texts

What would happen if English/language arts teachers revolutionized their instruction to focus intently—and exclusively—on the texts students are reading?

That’s what chief academic officers from 14 urban school districts discussed here last week. It’s a key shift in the Common Core State Standards that now guide teaching and learning in all but four states: Students are expected to engage in “close reading” of complex literary and informational texts.

In contrast to common practice, in which teachers explain reading passages and supply background information before students read, “close reading” confines initial study to the text itself. Students make sense of it by probing its words and structure for information and evidence. Through questions and class exercises, teachers guide students back through the reading in a hunt for answers and deeper understanding.

That scenario, however, requires profound shifts not only in how teachers teach, but how districts choose texts, how they test what students know, and how they evaluate teachers.
Were these paragraphs published anywhere other than Education Week, I would have assumed there were part of a parody: a series of "revelations" along these lines:
What would happen if chefs revolutionized their cooking to focus intently--and exclusively--on the ingredients and how they combine them together?
That scenario, however, requires profound shifts not only in how chefs cook, but in how restaurants choose recipes, how restaurant critics assess restaurant food, and how they evaluate chefs.
Here's a snippet of the new, revolutionary type of lesson that could occur under these standards, a discussion of Russell Freedman’s piece The Voice That Challenged a Nation, about Marian Anderson’s historic recital at the National Mall:
The CAO “students” [those 14 chief academic officers] were asked to read the passage silently, without any context or background knowledge supplied by their “teacher,” Mr. Pook, except brief word definitions listed in the margin. They explored “text dependent” questions that he had developed to help students understand the meaning and structure of the passage. The answers to such questions lie in the passage itself and help students make inferences and follow the arguments in it.

One of those questions was: “What words did Freedman use to characterize what happened next?” A key point of the presentation was that students could not expect their teacher to answer that for them. Instead, teachers would take what Mr. Pook called a “let’s find out” approach, guiding students back to the passage for answers.
Revoluationary ideas, naturally, have their detractors. First we have the concern (elaborated in an earlier Edweek article that I blogged about here) that the existence of biases brought by prior experiences mean we should focus less, not more, on the text. In the words of Richard M. Long, the director of government relations for the International Reading Association:
“The attempt is to make it just about the text. But it is never just about the text. Our concern is that this doesn’t take into account that prior experience exists and always affects the way the student interacts with the text.”
Another concern assumes that today's teachers are primarily providers of information and that group inquiry is something new:
How would teachers respond to a “sea change” that reframes their role from provider of information to facilitator of a group inquiry? And where would they get deep, focused lessons and units for such instruction?
Finally, there are concerns about what it will take to retrain today's English and literacy teachers to focus on the actual words in the text:
Moving teachers toward this way of working will require “some significant professional development” as they learn to refrain from providing quick answers, figure out instead how to formulate new kinds of questions that take them and their students back to the text repeatedly in their search for understanding.
“The percentage of my teachers who weren’t ever taught some of the skills you’re talking about here, like the ‘pivot point’ in a paragraph,” said one official, her voice trailing off in a sigh. “The teachers themselves don’t know many of those concepts.”
I'm a linguist and a writer, and I've never encountered the term "pivot point in a paragraph."  (Then again, I'm pretty sure I've also never enountered the term "let's find out approach."). But otherwise I share these concerns. If English teachers are so incapable of leading class discussions based on close readings that "significant professional development" is necessary, we indeed have a problem.

Sunday, February 26, 2012

Letter from Huck Finn: Navigating the Connections Between Algebra and Tomato Paste

Out in Left Field proudly presents the third in a series of letters by an aspiring math teacher formerly known as "John Dewey." All personal and place names have been changed to protect privacy.

I student taught for 15 weeks at Aragones Junior High. The school is located in an agricultural region known primarily for its strawberry fields. It is in a residential neighborhood surrounded by hilly farmland. Some of the farms have cows on them, but most grow strawberries. The make-up of the school is about 96% Hispanic students, many of whose parents work in the fields I would be passing on a daily basis. During my time there, the students sometimes appeared to me as adults, sometimes as kids, and other times as people caught in between.

The first weeks of my program I would be observing the three classes I would be teaching; by the fourth week I would begin to teach some classes. On my first day Tina, my supervising teacher, asked me to circulate among the students during the algebra class and answer questions or offer help as needed. The algebra class was a discovery-based class that used the CPM textbook (College Preparatory Math). The problems the students were working on in their groups of four were “guess and check” problems. The book spends more than half of the semester on these types of problems and even provides instruction in how to set up tables of values to maximize the efficiency of an inefficient process. Tina even gave instruction and pointers on how to do this during the class. She’s a good teacher and explains things well, which bolsters a point I’ve made in my previous incarnation as John Dewey: It’s possible to do something horrendous tremendously well.

A moment of full disclosure: I went to school at a time when math was taught in a traditional manner in K-12. Despite my average intelligence and despite claims from various quarters that such method was more destructive than typhoid fever except for very bright people, I managed to learn enough to allow me to major in the subject. The algebra book I used started almost immediately with how to express words as algebraic expressions, and to use that skill to set up and solve equations. The book briefly discussed the “guess and check” technique which at that time was called “trial and error”. It illustrated how a problem could be solved using trial and error, and then how the same problem could be done quickly and efficiently with algebra which then remained the focus of my algebra course.

A boy named Rudy asked me for some help with a problem. Rudy was fairly bright and his group mates seemed to rely on him to get through the problems. The problem was as follows: “In making a batch of soup, the number of cans of tomato paste was five more than twice the number of cans of noodles. A total of 44 cans were emptied into the soup. How many cans of each ingredient did the team use?”

I was mindful of the not-very-optimistic warning I got from the local university which placed me at the school: “You are a visitor/guest in the classroom. If there are any differences of opinion with the teacher, things have to be done as she wants them since it is her classroom.” Thus, I strived to adhere to the guess and check nature of the assignment. I knew from watching a pre-algebra class earlier that students learned how to translate English expressions into algebraic ones. I figured that these students knew how to do that at the very least. But while CPM touts itself as connecting knowledge, connecting to what they learned in pre-algebra was apparently not on the agenda.

“OK,” I said. “If you have twice the number of cans of noodles, how can we write that?”

They stared blankly at me

“How do we write ‘twice’?” I asked. “What number do we use?”

Rudy brightened and said “Two”.

“Yes, two; so if I have four cans of noodles what’s twice that amount?” Rudy thought a bit while the others in the group looked at him.


“Right! So if I call a can of noodles ‘x’, what’s twice that amount?”

Rudy thought again. “2x?”

Now we were getting somewhere. “OK, so if the number of cans of tomato paste is 5 more than twice the number of cans of noodles, how do we say that?”

Rudy thought for a moment. I expected to hear “2x + 5” but instead, he said: “Paste.”

I asked the others. They all said “Paste.” The others now started to giggle. What I didn’t know was that the students had been setting up guess and check problems with headings like “cans of noodles”, and “tomato paste = twice the number of cans of noodles + 5”. Rudy was stuck on “paste” as an answer and the more he said it, the more I tried to get them to use letters rather than words. The futile conversation with Rudy was making them all laugh. They tried not to, but that only made it worse. They all spoke English well, but for all practical purposes we were speaking different languages. For lack of experience and anything better to say I told them, “If you want to joke around, you’re wasting your time and mine,” and moved to the next group.

Tina told me later that the class wasn't ready yet to translate into expressions using “x”. “You don’t know what ‘guess and check’ is about yet,” she said. The motif of old school teacher meets the modern method then became the basis for her retelling the story to others in the teacher’s lounge. “Guess and check isn’t easy to teach,” she said consolingly. "The book eventually does connect guess and check with equations, and then the light bulbs come on when they put it all together."

I was about to say it might be a lot easier just to teach them algebra. But I thought it probably would be best to keep my mouth shut, so that’s what I did.

Friday, February 24, 2012

Math problems of the week: introductory algebra in CPM vs. Singapore Math

I. The first 3 pages in College Preparatory Mathematics (CPM)'s Foundations for Algebra, Year 2 [click to enlarge]:

II. The first 3 pages in 6th grade Singapore Math, Primary Mathematics 6A [click to enlarge]:

III. Extra Credit

Is there any answer a student could give in response to "What kinds of activities do you find frustrating?" that would allow him or her to opt out of any aspect of CPM?

Wednesday, February 22, 2012

Constructivizing STEM

It's hard not to detect a certain worry among those who write STEM articles for Education Week that the drive to educate students for careers in Science, Technology, Engineering, and Mathematics might include a drive to increase core scientific and mathematical content at the expense of things that Constructivists hold dear. Things, for example, like "model building," "data analysis," and "communicating findings."

These are what Jean Moon and Susan Rundell Singer, in their backpage Edweek Commentary on Bringing STEM into Focus, want to be sure schools are focusing on:

Re-visioning school science around science and engineering practices, such as model-building, data analysis, and evidence-based reasoning, is a transformative step, a step found in the NRC report, which is critical to STEM learners and teachers, both K-12 and postsecondary. It puts forward the message that knowledge-building practices found under the STEM umbrella are practices frequently held in common by STEM professionals across the disciplines as they investigate, model, communicate, and explain the natural and designed world.
Not that this is all that Moon and Singer care about. They also care about big ideas, which they divide into two categories: "crosscutting concepts (major ideas that cut across disciplines)", and "disciplinary core ideas (ideas with major explanatory power across science and engineering disciplines." The former include "scale, proportion, and "quantity or the use of patterns;" the authors don't cite any examples of the latter.

Besides "practices" and "ideas," the authors mention "strategies" and "tools" (again, without specific examples). What they don't mention is underlying content, except to say:
Lest some believe this is setting up another false dichotomy in science or mathematics education between content and process, let us quickly add a strong evidentiary note: Epistemic practices and the learning and knowledge produced through such practices as building models, arguing from evidence, and communicating findings increase the likelihood that students will learn the ideas of science or engineering and mathematics at a deeper, more enduring level than otherwise would be the case. Research evidence consistently supports this assertion.
I'm curious what "research evidence" means, but I gather that it doesn't include the research evidence that cognitive scientist Dan Willingham cites in support of the idea that students aren't little scientists and need a foundation of years of core knowledge before being ready to function as actual scientists.

In promoting their ideas as "transformative," the authors are overlooking the fact that the kinds of Constructivist practices they desire are already standard in many schools (particularly those held up as models for others). If they want to promote something truly transformative for STEM, they should instead be advocating a reinstatement of the years of solid, content-based instruction in math and science that many of our K12 schools used to offer (and that one still finds in schools in most developed countries around the world).

Monday, February 20, 2012

The achievement gap, III: forgetting to hand things in

In J's case, this most recently made the difference between a B and a C in one class, and an A and a B in another. It has dogged him throughout his 9-odd years of homework assignments.

It's chronic, and it's widespread. Troll through the various autism/asperger listservs and you'll find discussion after discussion of AS students losing substantial points for failing to turn in completed assignements, with parents wracking their brains about how to get the schools to "accommodate" their kids. It's painful to imagine the total number of man hours consumed by parent-school meetings specifically devoted to this problem (checklists? graphic organizers? communication books? reward systems?)--not to mention the hours of befuddled brooding and stress.

J's teacher told me that she's aware of the problem, but that, what with 30 kids in the class, it's really hard for her to remember to make sure everyone has handed things in. I nodded and bit my tongue.

Sympathetic though I feel towards overwhelmed teachers, I just don't get it. Back in ancient times when I attended K12 classrooms, forgetting to hand things in was a non-issue. Teachers explicitly asked for and collected our assignments at the beginning of class, and it was immediately apparent to all concerned when a student wasn't turning something in. No checklists, graphic organizers, or reward systems were necessary, and the entire process took a fraction of a percent of the time it would have taken to have a single meeting about it.

As for deducting a whole letter grade for chronic forgetfulness during class time? Well, let's just say that all this ancient history took place well before the diagnosis of Asperger's began its short-lived tenure in America's "inclusive" classrooms, and well before teachers started giving out grades for autism.

Saturday, February 18, 2012

The achievement gap, II: how our schools are working hard to make it go away

If you're concerned about achievement gaps of the sort recently reported on by the Times, you could either (re)instate rigorous, structured, direct instruction in line with the latest findings in cognitive science research, teaching each child in his or her Zone of Proximal Development, i.e., at his or her instructional level, with proper scaffolding, and furnishing each classroom with teachers who've mastered both their content areas and these best practices. Or you could:

I. Eliminate the ability of academically advanced students to get ahead in the classroom by:

1. implementing low level, one-size-fits-all instruction (for which there's no better model than Investigations math)
2. eliminating grade acceleration and individualized instruction
3. eliminating gifted programming or making it about time-consuming projects that supplement existing assignments rather about academic challenges that replace these assignments.

II. Reduce the ability of students to get ahead on their own time by:
1. assigning tons of homework of the low-ratio-of-learning-to-effort variety 
2. including massive summer projects and one-size-fits all reading lists.

III. Reduce the ability of grades to reflect achievement differences via"grade compression" and inflexible "rubrics" that:
1. employ subjective grading standards (elevating "creativity" and "engagement" over correct answers, clarity, articulateness, and solid analysis) 
2. take points off for unexplained answers, however correct 
3. give partial credit for "explained" incorrect answers 
4. keep the purely academic demands/expectations of assessments and assignments as low as possible 
4. minimize the opportunity for students to demonstrate work that exceeds those demands/expectations 
5. even if students find a way to demonstrably exceed expectations or go above and beyond academically, don't give them any extra points for it 
6. deploy "wild card" variables that partially randomize who gets what grade (e.g., trick questions; unclear directions; trivial requirements like including today's date on the title page of your report or using the word "I" in your science project abstract; rather than collecting homework, leaving it up to the students to turn it in and giving out zeroes for things not turned in on time) 
7. assign heterogeneous-ability group projects and give everyone in the group the same grade

IV. Reduce the ability of NCLB tests to reflect achievement differences, via:
1. low academic ceilings 
2. partial credit for explained incorrect answers; points off for unexplained correct answers (as above) 
3. wild card variables (as above)

V. Lobby colleges to pay less attention to high-ceiling standardized tests like the SATs and the Achievement Tests, and more attention to grades and "leadership" activities.

But then the next question becomes how to eliminate the growing achievement gap between U.S. students and those from other developed countries.

Thursday, February 16, 2012

Math problems of the week: 2nd grade 1920's math vs. Investigations

I. From the middle of the 2nd grade section of Hamilton's Essentials of Arithmetic (published in 1919), p. 50 [click to enlarge]:

II. From the middle of the 2nd grade (TERC) Investigations curriculum, assigned in early February [click to enlarge]:

III. Extra Credit:
Which involves higher-level thinking: doing nine word problems mixing up the four basic operations of arithmetic, or "making a representation"?

Tuesday, February 14, 2012

How today's schools are widening the achievement gap

A recent, much-discussed New York Times article on the achievement gap between rich and poor students is just as noteworthy for what it omits. As Barry Garelick comments on this past week's problem of the week:

The article just leaves it as a big puzzle as to why there is disparity in educational achievement based on income levels. There is not even a hint that education practices in the US do not serve students well, and that those who can afford it, get the education they need through parents, tutors, and learning centers (Sylvan, Kumon and the like). Low income families are not able to afford the external education.
The effects of the achievement gap are profoundly worrying, the more so as it won't go away until the Powers that Be start looking at how schools themselves are complicit.

The more I think about this gap, the more it occurs to me that it marks a division not just between those who do and don't have resources for external education, but also between those who do and don't assume they can entrust their kids' education entirely to their schools. Wealthier parents tend to have the time and resources to find out about how schools (even many of the wealthier public schools and the more exclusive private and magnet schools) have changed since they themselves were in school. Not too long after their kids enroll, they start learning about the myriad problems with Reform Math and about how penmanship, phonics-based reading instruction, and sentence-based writing instruction are no longer in vogue. Their tigerish parental interventions are swift and effective.

I'm guessing that poorer parents, especially if they happen to be recent immigrants from countries whose schools still practice direct, structured instruction, are less likely to suspect the reality of today's American classrooms--and more likely to make the should-be natural assumption that the schools will properly educate their kids. I see this close to home, in West Philadelphia's African immigrant communities.

Of course, if you're a parent in the first category--one who's providing your kids with extracurricular educational opportunities--it helps if your kids are some combination of compliant, academically motivated, and voracious in their reading habits. Then you can rest assured that they will achieve, no matter how Constructivist their classrooms are.

Which leads me to a third set of parents, a subset of the generally wealthy ones (wealthy and resourceful enough to keep their homes stocked with a wide variety of good fiction and nonfiction at appropriate reading levels) whose kids are on the high side America's achievement gap. I'm thinking of parents with kids whose reading habits are especially voracious and omnivorous, and whose writing is prolific (and legible). I'm thinking of humanities types who tend not to care that much about math and science education. These parents, seeing their kids learning plenty of history and literature, and producing plenty of decent writing, and making their teachers happy at school, don't see what their parental peers are so worked up about. Why worry about what's not happening in school: surely, assuming you're a good enough parent, your kids will be curious enough to learn what matters on their own!

What these people--and many others--don't realize is that not all kids are, by nature, voracious and omnivorous enough readers (or prolific enough writers) to make up on their own for deficiencies in K12 literacy and social studies. They thereby overlook two secondary achievement gaps (besides the big one between rich and poor) that our schools are failing to narrow: a gap in general knowledge between kids who read a lot on their own and those who don't, and a similar gap in writing ability.

Sunday, February 12, 2012

Letter from Huck Finn: Drifting Down the Great Divide, and the Sunrise in the South

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

For those who don’t know me, I am on a second career, having retired last summer. I completed my student teaching in December. My real name is not Huck Finn. I’m the same person who wrote a series of letters under the name of John Dewey some years ago, chronicling some of my experiences in ed school.

After my last missive, some readers were downright angry so I’ll just say that with respect to the professor who bore a resemblance to Meg Ryan, I got a lot out of her class, and have nothing against someone lying on a bed of nails while someone smashes a rock on her stomach with a sledge hammer on back to school night or any other night. It’s a lot better than most of the back to school nights I’ve attended. My daughter’s 7th grade speech/drama teacher’s greeting was that she just got back from Bahrain and would rather still be living there than teaching here. I don’t know what was more remarkable: the fact that she said that, or the fact that the parents in the audience nodded their heads in appreciation.

I have chosen the name Huck Finn since it seemed to fit better than John Dewey for someone drifting along the pedagogical, political and cultural river that crosses the battles over how best to teach math. The battles over math teaching remind me of something that happened years ago. I am a creature of habit, and throughout high school I walked to school every day, which meant walking eastward every morning. When I started at college, I consequently assumed without thinking about it that my walk to my first class was eastward. I was surprised therefore one day to see the sun rising in the south. For a moment I considered what could have caused this, before I realized that I was walking northward. My experiences in education are similar. I meet people who see a sun rising in the south, are able to explain it, and will not entertain any suggestion of where true north is.

I will reveal that I live in California, but had completed my ed school course work at a school back east that allowed me to do my student teaching in California. My effort was coordinated with a local university here who said they would place me in a school to do my student teaching. By mid-August, I still hadn’t heard about where my placement as a student teacher would be. I told them that the school back east requires me to put in 15 weeks of student teaching and the schools where they wanted to place me would start next week. There was a flurry of activity suddenly—I was told to write a bio which they would circulate. I wrote a bio in which I mentioned that I had majored in math and had been in the Michigan Marching Band—not that these two things are related but I wanted to show that I was a team player.

The next week, I was told to report for an interview at a junior high school about an hour's drive from my house. The school’s website listed the textbooks they used. I was disconcerted to see that for algebra, they were using College Preparatory Math (CPM): Algebra Connections. It is a discovery-based program and one that caused a significant uproar when it was used in Palo Alto in the early 90’s.

I met with Tina who would be my supervising teacher and had taught for 10 years. She mentioned she had a son in high school who was in the marching band and she herself played in the band at the community college. I thought perhaps my mention of the Michigan Marching Band had caused her to select me. “I guess you know from my bio that I was in the Michigan Marching Band,” I said.

“What bio?” she asked. The world of education is seldom as organized as one might believe.

In the course of our conversation she revealed that she liked the standards of the National Council of Teachers of Mathematics (NCTM and was also happy that California had just adopted the Common Core standards for math. “Do you know those?” she asked. My feeling about Common Core is very similar to that of NCTM’s but I left it at: “I am familiar with both.”

“So they placed you in a middle school,” my teacher said as if confirming that I had a disease that had no cure and was both fatal and painful. “Are you OK with that?”

“Actually, I requested middle school,” I said.


“I’m out of my mind,” I replied. She thought this was pretty funny and I was tempted to leave things at that, but I added that middle school was often the last chance students had to get proficient with fractions, decimals, percents and other concepts that they may be weak on before the onslaught of algebra.

“Exactly!” Tina said. “I taught high school for a year and was so heartbroken when I saw seniors who were still taking algebra 1 and not passing because they didn’t know their basic math. I decided that middle school was where I should be.”

This was beginning to show some promise. She said I would eventually be teaching three periods. Two periods were pre-algebra which used a standard, traditional-style textbook. The other period was algebra which used the text known as College Preparatory Math (CPM): Algebra Connections. “It’s discovery-based,” she said with some excitement and perhaps an expectation that I would rejoice in this. I looked around the room at the desks pushed together in groups of four, and tried to believe that somehow we would all know and agree where true north is, and that the sun rises in the east.

Friday, February 10, 2012

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

I. A 4th  grade (TERC) Investigations assignment, assigned in mid January [click to enlarge]:

II. From the beginning of the 4th grade Singapore Math Primary Mathematics 4A workbook (p. 40) [click to enlarge]:

III. Extra Credit:

Relate the educational opportunities presented by the Investigations assignment to this article in today's New York Times on the widening achievement gap between America's rich and poor. To what extent do Reform Math programs like Investigations serve as "great equalizers"?

Wednesday, February 8, 2012

What Philadelphia 5th graders should know how to do

I recently came into possession of one the Philadelphia School District Parent Teacher Brochures, which breaks down the goals that each Philadelphia School District student should be able to meet by the end of each grade level.  Since I'm homeschooling my 5th grade daughter, I was particularly interested in the goals for fifth grade. And I was shocked, shocked, to find myself more baffled than enlightened after reading through these goals.

The language arts goals are all about process, purposes, and genres, with a developmentally inappropriate assignment thrown in in the form of a research project:

•Continue to build a reading, writing and speaking vocabulary
•Read to learn new information
•Read a wide range of stories, books and magazines for enjoyment
•Understand a problem or conflict in stories or books and talk or write about an appropriate solution
•Make connections between stories and texts that they have read and the world around them
•Tell and/ or write a summary that gives the main idea of what they read and the most important details or events
•Complete a research project including a written report
•Write stories with several paragraphs
•Write poems, plays, and reports
Not a word about specific reading skills (vocabulary level, sentence complexity, making deductions and bridging inferences within the context of the text) or writing skills (grammar and punctuation, sentence construction, paragraph construction).

As for the math goals, most are vague ("compute" and "find the relationships"), easy (locating numbers on a number line; comparing numbers; sorting shapes), and emphasize verbal explanations over mathematical performance. Four out of the 13 goals are about data and probability. Here the developmentally inappropriate goal (especially given what isn't covered here) involves algebra:
• Compute and find the relationships using whole numbers, fractions, and decimals
• Locate positive and negative numbers on a number line (integers)
• Explain to you what prime numbers, factors, multiples and compositie numbers mean
• Compare numbers (equal to, greater than, and less than)
• Collect, organize, display, and analyze data in a variety of ways
• Find mean (average), median (middle number), mode (most frequent) and range (difference between largest and smallest) of data
• Predict or determine all possible combinations and outcomes, such as, "How many outfits can be created with six shirts and eight pants?"
• Calculate the chance of a simple event happening
• Use a variety of methods to solve for unknown quantities in simple one-step algebra equations (solve for x)
• Sort polygons according to their properties and angles, such as triangles, rhombi, and parallelograms
• Define and compare perimeter (distance around) and area (amount covered inside) of shapes
• Understand properties of a circle
• Explain how they solved a math problem in their own words.
Not a word about which computation skills the child should develop, what sorts of numbers, fractions, and decimals the child should be able to do computations on (perhaps only the "friendly" fractions and decimals), and what level of computational fluency the child should have. Not a word about multiplication tables, long division, repeating decimals, ratios and percents, and multi-step word problems.

Turning to science, only one substantive topic is mentioned (solar energy) and goals pertaining to it remain vague ("build an understanding;" "recognize"). Most the goals pertain to process rather than achievement, many of them involving developmentally inappropriate activities that wrongly assume that children can function as little scientists:
• Develop skills that will emphasize the five senses while doing science
• Use prior knowledge when making observations
• Make predictions and hypotheses based on observations
• Design investigations with a control and one or two variables
• Gather, organize and display data independently
• Build an understanding of how solar energy is transferred
• Recognize that the sun is the main source of energy for people and they use it in various ways
• Design and conduct experiments with variables. Students should be able to explain cause and effect
• Study the relationship in an ecosystem that shows the relationship of an organism to its environment
• Conduct hands-on investigations to discover and understand their world
• Record observations in science notebooks
It would seem that, "goals" aside, the Philadelphia Schools are avoiding any commitment to help your 5th grader increase his or her vocabulary, reading level, sentence construction skills, or computational fluency with "unfriendly" numbers; or learn any scientific content other than a few vague propositions about solar energy.

Monday, February 6, 2012

Artsy math vs. mathy art, II

Most attempts to connect math and art strike me as superficial at best, mostly spotlighting those aspects of math that already get too much attention under America's new Reform Math: shape sorting, visual patterns, rotations, and symmetry, with a dash of area and perimeter thrown in. Here, for example, is the 5th grade lesson from the 2003 Math in Art festival (thanks to Barry Garelick for alerting me to this), held at a math and technology magnet school in Grand Rapids:

Project--Mondrian Squares:

Students used squares of bright color in certain proportions to create their own geometric abstract compositions.
Spirals, Fibonacci and the Golden Ratio: Students used a rectangular spiral to find connections to similarity, the Fibonacci Sequence (1, 1, 2, 3, 5, ?) and the Golden Ratio, an abstract mathematical number important to ancient civilizations.
Piet Mondrian and the Jazz Age: Students experienced swing music, and found the connection to Mondrian's work, especially the piece Broadway Boogie Woogie. They made their pieces thinking about proportion, rhythm and movement.
Especially when it comes to Fibonacci, there are interesting possibilities out there. One is this video (thanks to Nancy Bea Miller for this link) that provides the best explanation I've seen of the connections between the Fibonacci series and natural phenomena (Part 1 of 3):

The Fibonacci Series strikes me as one of the most under-appreciated mysteries of the universe. Why does a series that describes an optimal growth pattern in nature have consecutive members that converge to the Golden Ratio--an idealized (possibly psychologically based) ratio of rectangular length to width in art, architecture, and design? Does this convergence of mathematical elegance, real-world practicality and aesthetics happen in all possible universes, or only, coincidentally, in ours?

Saturday, February 4, 2012

Miraculous recoveries from Asperger's Syndrome

For a brief, heady period in the history of autism spectrum diagnosis, in the late ’90s, I had Asperger syndrome.
Thus opens Benjamin Nugent's Op-Ed piece in yesterday's New York Times.  So certain was his psychologist/Asperger's specialist mother that Nugent had Asperger's Syndrome that she featured him at the age of 20 in an educational video. "It presents me as a young man living a full, meaningful life, despite his mental abnormality," Nugent notes.

At the time, Nugent did indeed meet the diagnostic criteria for autism:
I exhibited a “qualified impairment in social interaction,” specifically “failure to develop peer relationships appropriate to developmental level” (I had few friends) and a “lack of spontaneous seeking to share enjoyment, interests, or achievements with other people” (I spent a lot of time by myself in my room reading novels and listening to music, and when I did hang out with other kids I often tried to speak like an E. M. Forster narrator, annoying them). I exhibited an “encompassing preoccupation with one or more stereotyped and restricted patterns of interest that is abnormal either in intensity or focus” (I memorized poems and spent a lot of time playing the guitar and writing terrible poems and novels).
But all it took was to "ditch the Forsterian narrator thing," move to a big city, and meet people who shared his obsession, and, lo and behold, no longer did Nugent meet the criteria. Given that these describe Asperger's as “a continuous and lifelong disorder,” Nugent's recovery was nothing short of miraculous.

Possibly, as Nugent suggests, these soon-to-be revised criteria for autism are flawed:
You can be highly perceptive with regard to social interaction, as a child or adolescent, and still be a spectacular social failure. This is particularly true if you’re bad at sports or nervous or weird-looking.
It's interesting how the "heady period" of Asperger's diagnoses has coincided with certain trends in education. I'm thinking, of course, of those classroom environments and expectations that marginalize and pathologize awkward, nervous, or weird-looking children. Combine today's heightened expectations for social interaction (group work, cooperative learning, participation in class disucssions, sharing personal feelings) with the inherent subjectivity of the official criteria ("impairment in social interaction"; lack of peer relations "appropriate to developmental level") and we have yet another reason for the autistic spectrum epidemic.

Back when schools let kids work mostly on their own and viewed independent learning, intense academic interests, encyclopedic knowledge, and strong computation skills as good things, how many of today's Aspies would have ever been deemed "impaired"? However ostracized they might always have been on the playground, how many of them would have found respect for their academic skills, at least from their teachers, in the classroom? How differently might they have felt about themselves; how different might the whole psychological feedback loop have been between them and the adults they interact with?

Were schools to lower their social demands and raise their appreciation of academic skills, perhaps some of today's Aspies would, just like Nugent in New York, undergo spontaneous recoveries from their "lifelong" disabilities.

Thursday, February 2, 2012

Math problems of the week: tasks for families in Investigations vs. Singapore Math

I. The explanations and tasks that (TERC) Investigations explicitly gives to parents as part of its 3rd grade measurement unit [click to enlarge]:

II. The explanations and tasks that Singapore Math explicitly gives to parents as part of its 3rd grade measurement unit [no clicking necessary]:

III. Extra Credit:
Which curriculum shows more respect for parents: the one that explicitly involves them in teaching, or the one that doesn't.