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Heschel Online Auction

Posted On ו׳ בניסן ה׳תשע״ב (March 29, 2012) by Morah Naomi

Going, going, gone…

The 2^nd Annual Heschel Online Auction closes Wednesday, April 4 at 2pm. Don’t miss out on the fabulous items up for bid this year! Tickets to a Canada’s Got Talent taping, Centre Camp and Camp Northland B’nai Brith sessions, Babysitting, Leafs tickets and much more. Check out the auction at www.heschelonlineauction.org and please forward to your family and friends.

Why Margaret Wente is a Few Decimal Points off Base

Posted On כ״ג בכסלו ה׳תשע״ב (December 19, 2011) by Moreh Greg

Read the article here.

My response:

In her recent Globe and Mail article, Margaret Wente derides teaching mathematics for understanding and advocates a return to standard algorithms we learned as children.   Wente argues that ‘standard algorithms’ are foolproof and efficient.  In fact, for many computations, they are anything but.  To give one example, there is nothing efficient about using the standard algorithm we learned as kids to compute a problem like 399 x 4.  Carefully lining up the four under the first nine, being sure to carry the 3 (are you still with me?) over to the next column (why am I doing that again?), repeating this process (how many times?) and remembering to put a zero there (one or two?), is time consuming and very likely to produce errors.  Students are far better off looking at this kind of problem and realizing that a better strategy –yes, strategy — to solve this problem might be 400 x 4 – 4 .    This way of solving the problem involves far fewer steps than the ‘standard algorithm’, so there is far less chance of error.   More importantly, a student who uses this strategy demonstrates a far better number sense than one who slavishly applies a cumbersome algorithm learned by rote.

In an age before calculators, computers, and spreadsheets, it was perhaps important to create a ‘fool-proof’ way for those of us who didn’t understand mathematics to be able to produce the correct answer.   In economies which include a sector of low-paid number-crunchers, such a method may continue to serve some purpose.  But as technology and our economy evolve, it is far more important for all our children – not just those who are already mathematically inclined – to actually understand what mathematics is all about.  One of the best ways for students to develop strong a sense of numeracy is to regard computations from a problem solving perspective.  Just as not every problem can be solved using the same solution, so not every addition, multiplication, or division problem should be solved using the same method.

Teaching students to understand math and to choose appropriate, truly efficient, and logical strategies does not have to come at the cost of proficiency.  Just as the old algorithms had to be practiced, so do good strategies.  It would be wrong to equate a strategy based approach to teaching math with an elimination of worksheets, tests, and high standards; and I would whole-heartedly agree that schools are deficient if they implement a strategy based approach without a means for practicing and assessing proficiency.   Rather, worksheets and tests must be thoughtfully designed to train students to think logically and strategically about the math they are doing.   Standards must in fact be higher:  as students must not only get the right answer, but also be able to demonstrate understanding.

Wente leads us astray when she says that “U.S. heavy weights” are against teaching math for understanding.  The NCTM – the National Council of Teachers of Mathematics, one of the most significant math education think tanks based in the U.S., continues to strongly advocate the importance of understanding in mathematics.   Their most up-to-date statement on standards for numeracy reads as follows:

Central to the Number and Operations Standard is the development of number sense. Students with number sense naturally decompose numbers, use particular numbers as referents, solve problems using the relationships among operations and knowledge about the base-ten system, estimate a reasonable result for a problem, and have a disposition to make sense of numbers, problems, and results. For example, children in the lower elementary grades can learn that numbers can be decomposed and thought about in many different ways–that 24 is 2 tens and 4 ones and also two sets of 12.

The NCTM statement adds that “computational fluency should develop in tandem with understanding.”

It is understandable that some people might find a strategy-based approach to numeracy unfamiliar, even intimidating.  It isn’t how we learned.  My recommendation is to try out the strategies your children are learning.  Parents I know, who have given these methods a try, usually have one of two reactions.  Those who are successful at math, and who are natural mathematical thinkers say:  “Wow, this is exactly how I do math all the time.”  And those who struggled with the old algorithms we were taught say, “Wow, I wished I had learned this way.  I might actually understand math now.”

Greg Beiles

Director, The Lola Stein Institute for Leadership in Education

Curriculum Consultant, The Toronto Heschel School