kitchen table math, the sequel: 12/6/09 - 12/13/09

Saturday, December 12, 2009

meanwhile, in Britain

State schools admit they do not push gifted pupils because they don't want to promote 'elitism'

As many as three-quarters of state schools are failing to push their brightest pupils because teachers are reluctant to promote 'elitism', an Ofsted study says today. Many teachers are not convinced of the importance of providing more challenging tasks for their gifted and talented pupils. Bright youngsters told inspectors they were forced to ask for harder work. Others were resentful at being dragooned into 'mentoring' weaker pupils.

In nearly three-quarters of 26 schools studied, pupils designated as being academically gifted or talented in sport or the arts were 'not a priority', Ofsted found.Teachers feared that a focus on the brightest pupils would 'undermine the school's efforts to improve the attainment and progress of all other groups of pupils'.

Read more:

Everyone has won. All must have prizes. (fixed.)

Friday, December 11, 2009

From Russia with love: real wor[l]d problems

A friend of mine discovered this paper, Word Problems in Russia and America, by Andrei Toom. Quite a find. A long read, but worth it if you need any moral support in your personal fight against fuzzy math. Here is an excerpt:

The high-school part of [ed. American NCTM 1989, I think is being referred to]“standards” contains a list of topics to increase attention, where the first place is given to “the use of real-world problems to motivate and apply theory” (p. 126). What is a “real-world problem”?

Browsing through “standards”, I found quite a few statements about these mysterious critters. On p. 76 (middle-school part) it is said:

“The nonroutine problem situations envisioned in these standards are much broader in scope and substance than isolated puzzle problems. They are also very different from traditional word problems, which provide contexts for using particular formulas or algorithms but do not offer opportunities for true problem solving.”

What? What did they say about traditional word problems? What a nonsence! With their narrow experience the authors pretend to set standards! Are they aware of the rich resourses of excellent traditional word problems around the world? Let us read further:

“Real-world problems are not ready-made exercises with easily processed procedures and numbers. Situations that allow students to experience problems with “messy” numbers or too much or not enough informations or that have multiple solutions, each with different consequences, will better prepare them to solve problems they are likely to encounter in their daily lives”.

Pay attention that the author uses future tense. This means that he or she has never actually used such problems in teaching and never observed influence of this usage on his or her students’ daily lives. He or she has not even invented such problems because he or she does not present any of them. Nevertheless, he or she is quite sure that these hypothetized problems will benefit students. What a self-assurance!

After such a pompous promise it would be very appropriate to give several examples of these magic problems. Indeed, we find a problem on the same page, just below the quoted statement. Here it is:

Problem 48: Maria used her calculator to explore this problem: Select five digits to form a two-digit and a three-digit number so that their product is the largest possible. Then find the arrangement that gives the smallest product.

This is a good problem, although rather difficult for regular school because having guessed the answer, Maria needs to prove it. But the author never mentions the necessity of proof. What does the author expect of calculator’s usage here? It can help to do the multiplications, but it cannot help to prove. It seems that the author expects Maria to try several cases, to choose that one which provides the greatest product and to declare that it is the answer. But what if the right choice never happened to come to her mind? This is very bad pedagogics. Also let us notice that Maria is expected only to “explore” this problem rather than to solve it. According to my vision, exploration is the first stage towards a complete solution. Do the authors expect Maria ever to attain a complete solution? Do they want children to solve problems or just to tamper for a while?

But let us return to our main concern: so-called “real-world problems”. Notice that this problem has none of the qualities attributed to these mysterious critters on the same page: there is neither too much nor not enough information and there are no multiple solutions, each with different consequences.

One colleague noticed that the book still contains some problems described on page 76. Indeed, there are, but in another document. Here is one of them:

Problem 49: You have 10 items to purchase at a grocery store. Six people are waiting in the express lane (10 items or fewer). Lane 1 has one person waiting, and lane 3 has two people waiting. The other lanes are closed. What check-out line should you join?

I have never read any report about usage of this problem. Also I have never read any solution of this problem. Irresponsibility again!

What about problems with too much or not enough informations, they attract much attention in Europe lately, but European scolars want children to treat them critically and in many cases to refuse to solve them! Take for example that famous problem, after which Stella Baruk named her book [Baruk]. In the late seventies, the following problem was given to 97 second and third graders of primary school in France:

Problem 50: There are 26 sheep and 10 goats on a ship. How old is the captain? [Baruk], p. 25

76 children (out of 97) presented a numerical answer obtained by tampering with the given numbers. For instance, they might add the numbers and declare that the captain was 36 years old. Educators of several European countries (France, Germany, Switzerland, Poland) are very preoccupied by the fact that children “solve” unsolvable problems. The European educators would be very pleased if children refused to solve such problems with a comment like “It cannot be solved”. The European educators are quite right. But the same is true of what the “Standards” call “real-world problems”.

The most sound reaction to the problem 49 is “I don’t know”. But what a grade will an American student get after that?

Thursday, December 10, 2009

TIMSS Advanced 2008 International Release


The data were released yesterday in Norway:

Too bad the U.S. didn't participate.


Ideologically-motivated intellectual gatekeepers

What Climategate and Discovery/Constructivist math have in common.

Narrow intellectual gatekeeping is omnipresent in academia. Want to know why the government wastes hundreds of millions of dollars on math and science programs that never seem to improve the test scores of American students?[3] Part of the reason for this is that today’s K-12 educators—unlike educators in other high-scoring countries of the world—refuse to acknowledge evidence that memorization plays an important role in mastering mathematics. Any proposed program that supports memorization is deemed to be against “creativity” by today’s intellectual gatekeepers in K-12 education, including those behind the Math and Science Partnerships. As one NSF program director told me: “We hear about success stories with practice and repetition-based programs like Kumon Mathematics. But I’ll be frank with you—you’ll never get anything like that funded. We don’t believe in it.” Instead the intellectual leadership in education encourages enormously expensive pimping programs that put America even further behind the international learning curve.

I like it. This will be widely distributed to our local educators.

Perhaps I should picket like this Climategate picketer (I have no idea who he is) at the entrance to NCAR (National Center for Atmospheric Research) in Boulder.

Imagine, that could be me!
Change title to "Discovery Math Protest Longmont, Colorado Day 1

Wednesday, December 9, 2009

Testing Shows Improvement in Shoe Tying

Recent testing has shown improvement in shoe tying by fourth and eighth graders over the past two years, although the growth has been stagnant in some districts. Urban school activists, however, can be encouraged by the statistical improvement in areas with populations of 250,000 or more. This continues an upward trend that started 6 years ago when this testing began.

Urban districts still face enormous issues of poverty and large numbers of English language learners. Forty-eight percent of 4th graders tested nationwide were eligible for free or reduced-price lunches. In spite of the improvements, many still point to the problem of the large shoe tying gap and the lack of properly trained teachers in urban areas.

Still others claim that they are testing the wrong things. "Kids don't want to tie their shoes", said Sarah Sandala. "The other kids would make fun of them if they did." She said she knows that the skill is important to get ahead in the world, but many kids might just decide to wear loafers. However, those in charge of the testing emphasized that some districts are willing to be held to high standards. "I think we are now safely walking on the right path.", said Dan Foote, chairman of the testing board.

Tuesday, December 8, 2009

Late, but unique opportunity


I apologize for sending this message at such a late date. It is directed toward those flexible individuals in the DC area. ;->

There will be a workshop on fractions presented in DC by one of only two mathematics master teachers in Singapore on Friday, 11 December from 1 - 4:30pm. There are a few spaces available. If you are interested and able to participate, please email me:

Again, my apologies for the late notification.