>Wednesday, June 11, 2008BY ALFRED POSAMENTIERThe approach taken by the reformists is a nice form of enrichment, but it does not replace the need to teach children basic arithmetic skills.
FOR THE PAST FEW YEARS, parents and educators in this country seemed to be obsessed with the conflict about the best way to teach mathematics – particularly in the elementary grades.
This conflict, known nationally as “the math wars,” has recently flared up again in Wayne and Ridgewood, where the school system has been using a “reform program,” one that stresses arithmetic-concept understanding over algorithm skills.
The educational ideas that form the basis for this approach to teaching elementary mathematics are good and have their place on the instructional stage. Most math-savvy adults would agree that children should be exposed to these ideas, largely because they give students some useful quantitative insights.
However, when we adults look at this approach, we do so with a well-established arsenal of arithmetic skills; that is, we are thoroughly familiar with algorithms for the basic arithmetic operations, and we have many “number facts” solidly memorized.
Surely, from this vantage point, the approach taken by the reformists is a nice form of enrichment. But it does not replace the need to teach children basic arithmetic skills.
It is incumbent upon towns such as Wayne and Ridgewood to look at mathematics education from the vantage point of the learner who must get facility with arithmetic tools before, or while, being exposed to discovering quantitative patterns.
Familiarity with numbers
For example, if asked to multiply 25 x 28, some adults would say that this is equivalent to (25 x 4) x 7 = 100 x 7 = 700, or they might say 25 x 28 = (25 x 30) – (25 x 2) = 750 – 50 = 700, or other such combinations. However, we already know how to use an algorithm to multiply 28 x 25 directly. This sort of number facility might be less useful when multiplying 63 x 27, where the algorithm would be more desirable.
There is a school of thought among reformers that with today’s technology, arithmetic skills are less important. Yet, this position is taken by those who take their own arithmetic skills for granted.
As students gradually increase their quantitative talents – something we always enhance throughout our lives – they rely increasingly on the calculator, discounting their reliance on their now-well-ingrained arithmetic skill. They look at nifty number patterns and relationships and marvel at alternative ways of doing simple calculations based on these relationships.
Educators who discount their own arithmetic facility in making recommendations to others run the risk of providing inappropriate suggestions.
We constantly denigrate our own educational system – particularly when it comes to learning mathematics. We look overseas to other countries that seem to show better results on standardized testing. All too often, these tests are run on different types of populations and under different circumstances in different cultures, all of which clearly affect the outcome and render it inappropriate as a comparison.
Interestingly, many of these countries to whom we draw comparisons look to the United States as the educational paradigm to follow. This history of mathematics education of the past 50 years has been one of alternating fads, where we tend to go from one extreme to another, each time retaining some small particles from each extreme.
Aiming for the middle ground
We are once again at a point where the middle ground should be the goal.
Students must master arithmetic algorithms and as many number facts as they can, and then investigate number relationships and patterns, many of which they should be guided to discover on their own for a more genuine understanding.
The towns of Wayne and Ridgewood, which seem to have brought this issue to the surface through parental discontent, could serve to model these alternative forms of arithmetic calculation as mathematical enrichment, but only after students have attained a solid command of arithmetic, even if that is a somewhat traditional approach.
There is nothing wrong with a somewhat traditional approach. Quite the contrary, it is surely time-tested.
Alfred Posamentier of River Vale is dean of the School of Education at City College of New York and co-author of “Progress in Mathematics.”
