We include here an excellent article that appeared in the most recent Notes of the Canadian Mathematical Society, the Society’s official newsletter.
The article, titled PIMS and Mathematics Education in BC (See Pg. 10 – 12), is adapted from a paper written by Dr. Malgorzata Dubiel, a Senior Lecturer in the Department of Mathematics at Simon Fraser University. Dr. Dubiel discusses flaws in the WNCP curriculum, errors in the popular textbook Math Makes Sense and the need for better preparation in mathematics for teachers. The original article was a discussion paper that Dr. Dubiel prepared to send to the BC Ministry of Eduction to represent the concerns of the Pacific Institute for Mathematical Sciences.
Here are some relevant quotes from the article:
What we need to realize here is that earlier grades teach – or ought to teach – concepts that are essential to understanding mathematics at university level, and that building strong foundations in elementary grades is at least as important as the last two years of high school.
…removal of mathematical algorithms from elementary school will affect those who need to understand the nature and use of algorithms in computer science and computer programming; also, not teaching the long division algorithm makes it difficult for students to understand how to divide polynomials in precalculus and calculus. The algorithms, which have been used for hundreds of years, were removed supposedly because children had difficulties in understanding them. But – was the problem with the algorithms, or the way they were taught?
While manipulatives [blocks, strips of paper, algebra tiles] can help students understand new concepts, their use in the new curriculum (and the textbooks based on the curriculum) is misguided…manipulatives are treated as something one is required to master and then to demonstrate that mastery on provincial exams, rather than simply as an aid in understanding certain concepts and techniques.
…the Suggested Achievement Indicators, which “translate” the curriculum for the teachers, are written in a way that suggest a lack of understanding of the relative importance of facts and concepts, of differences between definitions and conclusions, and what details need to be included in teaching materials used by students.
[Regarding the textbook series Math Makes Sense]…there are so many problems with the content including: mathematical errors; incorrect terminology; word problems that are an insult to the students’ intelligence and common sense; lack of coherence and focus throughout the series; and investigations of patterns and sequences and an introduction to algebraic thinking that reinforce the perception that mathematics is a set of rules that only a teacher knows rather than a result of creative thought.
Note that many of those problems could have been corrected easily, given the opportunity, and many mathematicians would be happy to assist with this. Subject specialists (mathematicians and scientists from BC post secondary institutions) have not been involved sufficiently in discussions about, or design of, the school curriculum in mathematics. Discussions have been limited, restricted to grades 11 and 12 only using a poorly designed and cumbersome questionnaire based on the previous curriculum.
We agree wholeheartedly with most of the article, though we take some issue with the claim that the text Math Makes Sense is based on “sound pedagogy” since we believe that, in fact, it is the pedagogical ideology upon which the text is based that has led to elimination of algorithms, over-dependence on manipulatives and other harmful changes in the classroom. We also beg to differ with Dr. Dubiel’s statement that the current curriculum is an improvement over the previous ones. But aside from quibbles about a couple of casual, generalized statements in the article, we concur with its analysis, which is excellent, and we thank Dr. Margolzata Dubiel for writing it.