Sunday, February 28, 2010

Artsy math; what about mathy art?

Here we go again. Yet another breathless report of a right-brain math class, this one out of North Penn, Pennsylvania. It begins with a typical math diss:

If you think geometry is a bit boring, well, you may be right.
Geometry was one of my favorite math classes--and my favorite class at the time. I especially loved the abstract proofs, and the elegant, infinite world you could construct out of a handful of axioms. This class took me places I'd never been before, and, I think, took my thinking to a whole new level. Writing about it makes me smile.

The article continues:
But for one Pennridge 10th-grade geometry class, a hands-on architecture project has made geometry exciting.

Geometry teacher JoAnn Rubin uses a creative architecture project that teaches her students to use the precision of geometry and architecture as well as the freedom of artistic expression to help all types of students succeed in her math course.

"Not everyone is good at math," Rubin said about the project. "Some kids are really artistic."

The project asks students to create a representation of a building that they think is interesting or original.

They can make a model or a poster or any kind of representation of the building using their geometry skills. There is really only one thing curtailing the student's creativity on the project.

"The only restriction was that the buildings couldn't be rectangular," Rubin said with a smile.
This one restriction led students in many different directions and had them recreating all different kinds of buildings, from architectural classics to the downright bizarre.
Rubin's assignment appears to have fulfilled her goals--with flying colors:
Although the project results were all over the spectrum, students of all mathematical abilities consistently succeeded.

"It's about recognizing that we all have our talents and interests," Rubin said about the project that allowed every student to explore their abilities beyond the chalkboard. "I wanted them to look at the geometry of the actual buildings."
Equality of outcome; celebration of multiple intelligences; real-life examples; it's all there.

But I can't help feeling concerned for one of Rubin's thriving students:
One of the more creative projects was built by Brett Saddington, who turned the parameters for the project completely upside-down.

"I just looked up the world's strangest buildings," Saddington said about the Google search that led him to an upside-down house built in Szymbark, Poland.

He said that he one day hopes to be an architect or an engineer, and he showed off his talent with his topsy-turvy creation.
His teacher is hopeful, too:
Most of Rubin's students will not become architects or engineers, but by giving her students a look at the practical and creative side of geometry, she has given them an appreciation that could take them anywhere.

"They really don't know what direction they may be heading," Rubin said. "But who knows? They may become architects or engineers."
But I'm worried that, in this topsy turvy world of math education, where art is math and appreciation is learning, Brett's high school teachers may never teach him the math he needs to pursue an architecture or engineering degree in college and beyond.

Unless, of course, the art teacher is having Brett and his classmates spend the same amount of time doing math problems about the geometry of perspective drawing and optical wave forms.

Friday, February 26, 2010

Math problems of the week: 1900's algebra vs. College Preparatory Mathematics

I. Two of the problems in the second chapter of Wentworth's New School Algebra, published in 1898 (written by G.A. Wentworth), p. 22:

Write in symbols:

A man has x dollars y dimes and z cents. If he spends a half-dollars and b quarters, how many cents has he left?

A rectangular floor is a feet long and b feet wide. In the middle of the floor there is a square carpet c feet on a side. How many square yards of the floor are bare?

II. Two of the problems in the final chapter of College Preparatory Mathematics Algebra Connections, Volume 1, (written by  Leslie Dietiker, Evra Baldinger, Carlos Cabana, John Cooper, Mark Cote, Joanne da Luz, David Gulick, Patricia King, Lara Lomac, Bob Petersen, Ward Qincey, Babara Shreve, and Michael Titelbaum) p. 266:

Using the variable x, write an equation that has no solution. Explain how you know it has no solution.

Given the hypothesis that 2x + 3y = 6 and x = 0, what can you conclude?  Justify your conclusion.

III. Extra Credit

The following is the final problem in CPM's Algebra Connections, Volume 1.  Discuss.


This course focuses on five different Ways of Thinking: reverse thinking, justifying, generalizing, making connections, and applying and extending understanding These are some of the ways in which you think while trying to make sense of a concept of to solve a problem (even outside of math class). During the chapter, you have probably used each Way of Thinking multiple times without realizing it!

Review each of the Ways of Thinking that are described in the closure sections of Chapters 1 through 5. Then choose three of these Ways of Thinking that you remember using while working in this chapter. For each Way of Thinking that you choose, show and exlain where yo used it and how you used it. Describe why thinking in this way helped you solve a particular problem or understand something new. (For instance, explain why you wanted to generalize in this particular case or why it was useful to see these particular connections). Be sure to include examples to demonstrate your thinking.

Wednesday, February 24, 2010

Artsy science; what about sciency art? II

I just learned that my 10th grader's chemistry teacher gave students the assignment of constructing a mole.

No, not a mole as in a unit of chemical substance, but a mole as in the furry creature that tunnels under yards and eats earthworms.

The idea, apparently, was to find an "entry point" to learning about the mammal's eponymous homonym (i.e., the chemical mole) for the more artsy, less scientifically inclined students. What actually happened was the many students rebelled against the assignment, calling it stupid and patronizing.

The teacher compromised by making the assignment optional--for extra credit. My son said "No, thanks." Shortly before the assignment was due, however, one of his more ambitious, industrious friends went down to the lost and found, retrieved an old T-shirt, stuffed it with scrap paper, stapled it up, drew dots for eyes, and turned it in.

I'm now waiting for the art teacher to allow the more sciency students to do an optical analysis in lieu of a painting.

Monday, February 22, 2010

Enlightened Exchanges Over Math Education, V

This time my critic is an anonymous commenter on the thread for last week's problem of the week.

Anonymous begins by taking issue with the idea of comparing specific problems. The several comments he/she makes--in reaction to several other commenters as well as to my original post--inspire me with a new thought. Besides comparing Reform Math with other curricula, it would be interesting to compare the different tones used by those on each side of the debate. 

With this in mind, I present my point by point reaction to various of Anonymous' remarks:
Anonymous: Your superficial analysis above (comparing one page of TERC with Singapore Math) is what parents should expect from a blog like this.
KB: "Superficial" is the wrong word. "Narrow" is better here. This blog has presented one narrowly-focused math problem comparison per week for over two years. Comparison of specific problems must absolutely be part of the debate over math curricula.
Anonymous: Maybe you should look up the last word in the Singaporean dictionary and compare it to zyzzyva.
KB: Dictionary entries are another source that come in handy, depending on what you are analyzing. If one's goal were to compare the English and Malay lexicons (there's no language called "Singaporean"), it's useful to compare specific entries in the English and Malay dictionaries. On the other hand, if one wants to make a more shallow comparison, one could compare the last two entries, as you suggest.
Anonymous: So according to bky and JC, 2nd grade should be only about teaching simple computation with number.
[bky wrote "Kids learning Singapore math are going to have a firmer concept of number, place value, and what operations mean"; and JC wrote "The focus should be on numbers. They are what math is about."]
KB: Here another comparison is in order: what bky and JC actually said about what aspects of number should be taught, with what Anonymous says they said.
Anonymous: Oh and by the way, Singaporean math pedagogy is much more about inquiry than direct instruction.
KB: I've often pointed this out on this very blog. There's a lot of Inquiry, in the best sense of term, built into the Singapore Math curriculum.
Anonymous: But you shouldn't let the facts get in the way of your rhetoric.
KB: Indeed.
Anonymous: The amazing paradox is that you support Singapore Math (which is fine with me) but you only want traditional drill with this text.
KB: Again, it's interesting to compare this characterization of bky, JC, and anonymous 2's comments with what they actually wrote.
[Anonymous 2 wrote: "I do Singapore math with my kids. It is largely direct instruction, at least in the early grades." JC added " Students from countries where direct instruction is used significantly outperform us. This is especially true on the PISA test, which tests the ability to apply knowledge." JC also cites Mayer on evidence that "unguided instruction" does not work.]
Anonymous: The majority of Asian students do their computational drills at home or afterschool but NOT in school.
KB: The book "The Learning Gap" argues otherwise.
Anonymous: School hours are for inquiry, problem solving, and critical thinking.
KB: As seen in this blog's weekly comparisons, inquiry, problem solving, and critical thinking are very present in the Singapore Math curriculum, and very different from the "inquiry," "problem solving," "critical thinking" seen in Reform Math.
Here ends this extended meta-comment, to which Anonymous did not reply. But either he or she or another Anonymous poster, in reaction to a subsequent comment by Barry Garelick on how "Discovery or inquiry based learning can be done well or poorly" begins with the following:
Anonymous (Anonymous 3?): Thanks for Garelick for admitting that discovery/inquiry learning can be done well. That it is not the cause of all America's woes as you read in the attack traditionalist blogs.
Which led me to the following question:
KB: Does anyone out there know which "attack traditionalist blogs" Anonymous is referring to? I.e., blogs that say that math should consist only of rote drills and that inquiry can't be done well?
Surely there there are more rational, less angry voices out there with criticisms of the various criticisms of Reform Math who are capable of reading and accurately characterizing those criticisms before they critique them.  

It's just that I haven't had the privilege of having an enlightened exchange with such people on this blog (hint).

Saturday, February 20, 2010

The therapeutic childhood

Consider a quirky, unsocial child who grew up a generation or so ago.  At home, his parents worry about friends and bullies; at school, his teachers comment that he's always alone at recess, but praise him for his independence and intelligence, and for how quickly he's moving through the advanced math and reading books they've given him to work on on his own.

After school, he plays outside in the dirt and sand among the other kids on the block, rides his bike around the neighborhood and swings on the playground swing sets.  He gets good grades in school despite his sloppy handwriting.

But his handwriting is improving, thanks, perhaps, to all that in-class penmanship instruction and practice.  More importantly, he's gradually opening up and becoming more sociable; perhaps he's just following his own quirky developmental time table.

Consider his contemporary counterpart.  At home, his parents agonize over those notes and phone calls from the teacher and school psychologist; at school, he refuses to cooperate in group activities, refuses to complete his class assignments, and either fidgets uncontrollably or zones out during Circle Time.  He never hands in his homework on time, and his projects are sloppy and show minimal effort. Get him evaluated, they keep saying.

Once he's evaluated and duly diagnosed, an IEP meeting is scheduled, and his parents secure accommodations that allow him to spend a portion of class time working independently on more challenging material than what the rest of the class is doing in groups or discussing during Circle Time.

He spends his late afternoons at Social Skills Class, Play Therapy, and Occupational Therapy: working his pencil grip and letter formation, playing with shaving cream and sand, peddling therapeutic riding toys, and swinging on therapeutic swings.  All this is completely covered by insurance, and is tightly scheduled between his many hours of weekly homework.  Even if he had time for outdoor activities, in this day and age no one dares send their kids out unattended.

His grades improve, and, gradually, he opens up and becomes more sociable.  The experts rave about how well the system is working:  the therapies, the IEP, and the involvement of experts.

Is it?

Thursday, February 18, 2010

Math problems of the week: 2nd grade Investigations vs. Singapore Math

1. Two of the last addition problems in the 2nd grade Investigations (TERC) workbook, p. 61 of Unit 8 (Partners, Teams and Paper Clips):

Solve each problem. Show your work.

Kira has trouble with 7 + 9.  Write a clue that will help Kira remember 7 + 9.

9 + 7 =
7 + 9 =

Clue: _______________________

Franco has trouble with 8 + 6. Write a clue that will help Franco remember 8 + 6.

6 + 8 = 
8 + 6 =

Clue: _______________________

2. The last addition problems in the 2nd grade Singapore Math Primary Mathematics Workbook 2B, p. 17:

(a) 183 + 99 =
(b) 246 + 98 =
(c) 199 + 99 =
(d) 206 + 98 =
(e) 99 + 556 =
(f) 98 + 235 =
(g) 99 + 408 =
(h) 98 + 399 =

3. Extra Credit:

What do you think is the best way to help Kira and Franco?

Tuesday, February 16, 2010

A plea for cool, analytical, logical, and (yes!) left-brained conversation

I've been meaning for some time to blog about an article in one of last year's final editions of the Economist Magazine on Socrates and Socratic dialog.  Inspired by growing frustrations with the level of political discourse I see everywhere around me, I do so now.

First, heat trumps light:
Visiting America today, Socrates might have dropped in on last summer’s “town hall” meetings, in which members of the public allegedly came to debate the reform of health care with their elected representatives. Socrates would have beheld hysterical firebrands shouting that America’s president and senators were Marxists, Nazis or both.
Second, winning trumps truth seeking:
Socrates considered the debate in such settings unedifying, pointless and unworthy—in a word, “eristic”. Eris was the Greek goddess of strife (the Roman Discordia). It was Eris who cunningly dropped a golden apple with the inscription “to the fairest” into a feast, inciting three goddesses—Hera, Athena and Aphrodite—to bicker over who deserved it and thus launching the ten-year Trojan War. Eris is present in presidential debates, in court rooms and wherever people are talking not to discover truth but to win.
Third and fourth, opinion trumps argument, and expression trumps listening:
In 1968 Stringfellow Barr, an historian and president of St John’s College in Maryland, wrote a Socratic critique of American discourse: “There is a pathos in television dialogue: the rapid exchange of monologues that fail to find the issue, like ships passing in the night; the reiterated preface, ‘I think that…,’ as if it mattered who held which opinion rather than which opinion is worth holding; the impressive personal vanity that prevents each ‘discussant’ from really listening to another speaker”.
Wouldn't it be nice if...
Socrates’s alternative was “good” conversation or dialectic. To converse originally meant to turn towards one another, in order to find a common humanity and to move closer to the truth of something. Dialectic, in other words, is decidedly not about winning or losing, because all the conversants are ennobled by it. It is a joint search. Unfortunately, as Mr Barr put it, it is also “the most difficult” kind of conversation “especially for Americans to achieve”.

On a good day, Socrates’s conversations bore all the marks of dialectic. There was little long-winded monologue and much pithy back-and-forth. The conversation often meandered and sometimes Socrates contradicted himself.
Here in America, we  prefer to use conversation to further cement prejudices, bond with the "right people", and deflect opposing arguments.  Here are some well-worn strategies:

1. Rather than using a conversation with someone who disagrees with you to test out your ideas and modify them in light of what the other person says, use the conversation as a means to proclaim your opinions and catch the other guy whenever he or she slips up or appears to contradict him or herself.  ("But earlier you said that...")

2. Rather than listening to the most intelligent, thoughtful members of the opposing side in order better to understand their arguments, harp on the least intelligent, least thoughtful members of the opposition.  

3. Rather than focusing on the substance of the arguments on the other side, focus on the personal character flaws of the least savory members of the opposition; other, more disturbing opinions that they hold (however irrelevant); the most troubling aspects of their personal and professional associates; and the bias you perceive in the venues that publish or air their views--and use each one of these factors to further impugn every other factor.

4. Assume that everyone in the opposition is ipso facto stupid, reckless, heartless, or advancing a sinister agenda, and view everything they say through this prism.

Finally, as has worked so well for all other prejudices (from ethnicity to race to sexual preference), minimize personal contact with those who disagree with you by ensuring that your friends and neighbors are all "good," "intelligent," "open minded" people--regardless of what those terms might actually mean.

Sunday, February 14, 2010

Gifted children and organizational skills

In an online Teacher Magazine article this past week, Tamara Fisher reports on a 2006 National Institutes of Mental Health study whose results showed (via MRI) that children with IQs in the 121-145 range had cortex layers that:

started out much thinner at age 7 (compared to the cortex thickness of the average and above average kids) and reached peak thickness much later (age 12 in gifted kids compared to about age 8 or 9 for average and above average children).
To Fisher, these findings are suggestive:
Well, given that the pre-frontal cortex controls organization, this might help explain why some of our brainy middle-schoolers can do algebra but can't find the homework they know they did the night before!
Fisher's words so aptly describe many of the mathematically gifted kids whose families I interviewed for my book that I posted the following comment in response:

One more reason *not* to require organizationally demanding assignments of young children! And one more reason *to* assign academically challenging work to gifted children.

Unfortunately, organizationally-demanding projects have become increasingly common in elementary school. Meanwhile, thanks to Reform Math, mathematically challenging assignments are in decline. One consequence of this for gifted kids, beyond sheer boredom and lack of learning, is that they often earn *lower grades* than their peers. (I discuss this upside-down state of affairs in "Raising a Left-Brain Child in a Right-Brain World.")

Making matters worse for gifted kids, gifted programming increasingly focuses on organizationally-demanding projects rather than on conceptually challenging assignments.

Meanwhile, in response to my last post on gifted children, Robert Chametzky of the University of Iowa writes the following:

No doubt many OILF readers already aware of the University of Iowa's Belin-Blank International Center for Gifted Education and Talent Development, its Institute for Research and Policy on Acceleration (IRPA), and their publication "A Nation Deceived: How Schools Hold Back America's Brightest Students". For those who are not, here are the URLs:

Friday, February 12, 2010

Math problems of the week: 3rd grade Trailblazers vs. Singapore Math

I. The final multiplication and division problems in the 3rd grade Math Trailblazers Student Guide, p. 323:

1. 2 × 8 = ?
2. 9/3 = ?
3. 6 × 7 = ?
4. 30 ÷ 5 = ?
5. 28/4 = ?
6. 7 × 9 = ?
7. 45 ÷ 5 = ?
8. 24/6 = ?
9. 64/8 = ?
10. 13/1 = ?
11. 10/2 = ?
12. 3 × 7 = ?
13. Write a story problem to go with one of the multiplication problems in Questions 1-12.
14. Write a story problem to go with one of the division problems in Questions 1-12.

II. The final multiplication and division problems in the 3rd grade Singapore Math Primary Mathematics Workbook 3B, p. 156 and p. 183:

Find the value of each of the following.
(a) 894 × 7
(b) 1294 ÷ 4
(c) $1.25 × 6
(d) $4.95 ÷ 9

A pen costs $4.30. A book costs 8 times as much as the pen. What is the cost of the book?

There are 8 sugar cookies and 6 coconut cookies in one box. How many cookies are there in 5 boxes?

III. Extra Credit:
1. Compare the skill sets in multiplication and division assumed at the end of 3rd grade in each curriculum.
2. Weigh the costs and benefits of making up word problems vs. doing them.

Tuesday, February 9, 2010

How "text-to-self" connections might backfire--big time

Text-to-self connections are highly personal connections that a reader makes between a piece of reading material and the reader’s own experiences or life. An example of a text-to-self connection might be, "This story reminds me of a vacation we took to my grandfather’s farm."
So explains the Florida Online Reading Professional Development site, a site dedicated "to providing quality professional development services and support to Florida educators in effective reading instruction through its online course, expert staff, quality resources, and other professional development services."

The ability to make text-to-self connections, FORPD states, is part of what distinguishes good readers from poor ones (emphasis mine):
Good readers draw on prior knowledge and experience to help them understand what they are reading and are thus able to use that knowledge to make connections. Struggling readers often move directly through a text without stopping to consider whether the text makes sense based on their own background knowledge, or whether their knowledge can be used to help them understand confusing or challenging materials. By teaching students how to connect to text they are able to better understand what they are reading (Harvey & Goudvis, 2000). Accessing prior knowledge and experiences is a good starting place when teaching strategies because every student has experiences, knowledge, opinions, and emotions that they can draw upon.
The cognitive science literature, however, suggests that text-to-self advocates may have it exactly backwards. 

Consider, for example, a paper by Courtnay Norbury and Dorothy Bishop entitled "Inferential processing and story recall in children with communication problems: a comparison of specific language impairment, pragmatic language impairment, and high functioning autism." This paper finds inferencing difficulties characterizing all poor readers with the above conditions. What Norbury and Bishop find, however, isn't that these readers weren't able to make inferences, but that they made the wrong ones.  For example, when asked, in reference to a scene at the seashore with a clock on a pier,  "Where is the clock?", many children replied "In her bedroom."

Norbury and Bishop propose that these errors may arise when the child fails to suppress stereotypical information about clock locations based on his/her own experience.  In support of this hypothesis, they cite Morton Gernsbacher's book Language Comprehension in Sentence Building, which provides evidence that adults with poor reading difficulties are less able to suppress irrelevant information. As Norbury and Bishop explain it (emphasis mine):
As we listen to a story, we are constantly making associations beween what we hear and our experiences in the world. When we hear "clock," representations of different clocks may be activated, including alarm clocks.  If the irrelevant representation is not quickly suppressed, individuals may not take in the information presented in the story about the clock being on the pier. They would therefore not update the mental representation of the story to include references to the seaside which would in turn lead to further comprehension errors.
Text-to-self connections, in other words, may be the default reading mode, and not something that needs to be taught. What needs to be taught instead, at least where poor readers are concerned, is how not to make text-to-self connections.

I'm neither a reading specialist nor a cognitive scientist, but my gut feeling is that, while accessing general background knowledge helps with reading comprehension, accessing personal background knowledge does indeed lead you astray. Text-to-world, OK, fine; but not text-to-self.

Especially, I imagine, for those most entrenched in the self, for example, children on the autistic spectrum.

Monday, February 8, 2010

Further thoughts on Susan Engel... and on others who think that today's schools are overly academic

How can so many people, without visiting actual classrooms, so confidently and so wrong-headedly conclude that today's schools are so overly-focused on drill & kill and cramming for high school?

It occurs to me that, from the outside, all you might see is this:

1. More and more cuts to arts and music programs and recess time.
2. All that No Child Left Behind testing
3. All that early literacy, which now begins in pre-K or kindergarten.
4. All that homework, which also begins in pre-K or kindergarten.

But what too many outsiders don't realize is this:

1. Kindergarten is more like first grade in yet another way: with December cut-offs moved up to September 1st, kindergartners are often 25% to 33% older than they used to be.
2. No Child Left Behind tests set a very low bar (that’s how states maximize school "success" and minimize the need for costly sanctions), which keeps classroom instruction, and homework, at a very low academic level.
3. Grade-school literacy means lots of "read-alouds," "100-book challenges," and "writer's workshops," journaling, and "personal reflections"; not lots of actual instruction in phonics, penmanship, and academic writing.
4. While math instruction begins earlier than ever, NCLB testing, together with Reform Math's watered down curriculum, has reduced the level of instruction, and of mathematical challenge, to record low levels.
5. Art--albeit uninstructed art--is alive and well in all those math, science, and social studies projects. Indeed, if you don't produce colorful "creative" art in these projects, you won't earn a top grade--no matter how strong your academic output.

I agree that there’s too much homework and too much writing and too little recess. But my objection about the homework isn't that it's academically oppressive, but rather that it's a waste of time that deprives young children of precious free hours--for actual creativity (as opposed to "be creative"), for actual art (as opposed to "project art"), for actual games (as opposed to "close to 100" and "fractions war"), for actual reflection (as opposed to "text-to-self"), and for all those academically challenging things they might do at home in spite of school.

And I wonder why so many of those who make accurate observations about early literacy pay no attention to what’s happening in math. Might that have something to do with our broader culture, in which “I hate reading” raises eyebrows, but not “I hate math”?

Saturday, February 6, 2010

Please visit an actual classroom before you make recommendations, V

In her New York Times Op-Ed piece this past week, Susan Engel, a senior lecturer in psychology and the director of the teaching program at Williams college, notes that:

"Our current educational approach, and the testing that is driving it, is completely at odds with what scientists understand about how children develop during the elementary school years and has led to a curriculum that is strangling children and teachers alike."

So far I'm with her.

"In order to design a curriculum that teaches what truly matters, educators should remember a basic precept of modern developmental science: developmental precursors don’t always resemble the skill to which they are leading."

Agreed. As Dan Willingham notes, novices and experts learn in different ways. Children grow into good scientists not by acting like little scientists, but by learning scientific knowledge. But Engel's example is different:

"For example, saying the alphabet does not particularly help children learn to read."

Perhaps. It's probably far more productive to learn the sounds that the different letters stand for than to simply "say the alphabet."

But here's where I started to wonder about Engel's familiarity with actual classrooms. Are there many teachers out there who teach according to the premise that simply saying the alphabet helps children learn to read?

As I continued to read, my doubts about this education expert's classroom experiences continued to grow:

"Simply put, what children need to do in elementary school is not to cram for high school or college."

"What they shouldn’t do is spend tedious hours learning isolated mathematical formulas or memorizing sheets of science facts that are unlikely to matter much in the long run."

If Engel were to look around at what is actually happening in today's classrooms, she would find very little cramming for high school, and very few hours--tedious or not--spent on formulas and fact sheets.

In the more affluent, model schools, what she would find instead is everything she--and by extension the New York Times--is promoting as bold new "research-based" proposals:

Classrooms in which students write "stories, newspaper articles, captions for cartoons, letters to one another."

Classrooms that have students "building contraptions," "enacting stories," and "inventing games."

Classrooms that devote "lots of time for children to learn to collaborate with one another"

"A curriculum focused on... pattern detection, conversation and collaboration."

It is because so many "model" classrooms devote so much time to such activities, and because so few classrooms in general devote much time to to phonics, penmanship, and the fundamentals of arithmetic, science, and prose writing, that American education is in such trouble.

Then we have the plight of children on the autistic spectrum and other left-brainers, who flounder in "collaborative learning" environments, are especially ill-suited to learning how to read by "having conversations," and who especially crave conceptually challenging math and science--tedious formulas and all.

Thursday, February 4, 2010

Math problems of the week: 5th grade 1920s math vs. Everyday Math

I. From Hamilton's Essentials of Arithmetic, Volume I (published in 1919), final fractions word problems in the year 5 fractions and decimals section, p. 361-2:

Which is cheaper and how much, 3 1/2 lb of sugar for .35 or 5 lb for $.40?

Philip had $2.80, which was 2/3 of what he needed for a tennis racket. Find the price of the racket.

Edwin's father raises 120 lambs which average 78 1/2 lb. The cost of keeping the lambs is $200; they are sold at 12 cents a pound live white. Find his profits.

II. From the 5th grade Everyday Math Student Math Journal, Volume 2, final fractions word problems in the fractions and ratios chapter, p. 293-5:

Regina is cutting lanyard to make bracelets. She has 15 feet of lanyard and needs 1 1/2 feet for each bracelet. How many bracelets can she make? ____ bracelets.

Eric is planning a pizza party. He has 3 large pizzas. He figures each person will eat 3/8 of a pizza. How many people can attend the party, including himself? ___ people.

Explain why you think it is important to know how to find equivalent fractions with common denominators.

III. Extra Credit

The final problem in the 5th grade Everyday Math Student Math Journal fractions and ratios section is the following:

Look back through your journal pages for this unit. What do you think is the most important skill or concept you learned in this unit? Explain why.

Discuss the revolution in meta-cognitive awareness that underlies questions such as these, which are egregiously absent from 1920's math.

Tuesday, February 2, 2010

That's why they call it "social studies"

People who are familiar with autism diagnostics should be forgiven if they confuse this social studies assignment with a diagnostic test for autism.

Then again, I, too, was baffled by the picture, and I don't consider myself particularly far out on the autistic spectrum.