For an overview of the situation regarding math instruction and math achievement in Canada, readers are advised to read the policy report
The State of Math Education in Western Canada
The purpose of this initiative is to form a coalition among concerned parents, citizens, teachers, employers, scientists, mathematicians, and post-secondary instructors with the purpose of rallying together to improve K-12 mathematics education. This is a non-partisan initiative that was founded by math professors in Manitoba and Saskatchewan who feel that math education has reached a state of crisis in schools and are prepared to lobby for changes.
If you are frustrated, as we are, by the state of math education in Canadian schools, we encourage you to join our initiative by signing your name here. We welcome individual support and also more comprehensive types of support, such as support from companies, school divisions, or departments within a university or faculty. There is strength in numbers and, by signing your name, you will help give us a stronger voice in advocating for improved math education for children.
We began this initiative because we are experts in mathematics and we care deeply about the education of Canadian children. Children who do not receive the strong education in math that they deserve may ultimately be excluded from many careers in trades, technology, science, engineering, business, and economics, to name a few. Our ultimate goal is to ensure that all children have the opportunity to achieve their potential in math so that they may enjoy lives free of innumeracy, may experience the beauty in math, and so that they may have a wide range of career opportunities.
Many parents are frustrated by the math instruction that their children are receiving in schools. Many parents, who can afford to do so, have hired tutors to help their children with math and many parents spend large amounts of time tutoring their own children outside of school hours. Many parents in Canada are unable to do either of these things due to financial constraints or gaps in their own math education. It is extremely important that children receive effective instruction in math, guided by strong math curricula, during school hours.
Teachers, employers and post-secondary instructors
Many teachers are frustrated by pendulum swings in math curricula based on the latest fads in math education. Many employers are frustrated by new graduates who may have very weak math skills and poor problem-solving skills which interfere with their ability to perform well on the job. Post-secondary instructors are also frustrated by the weak math skills of many new graduates and are troubled by the fact that many math teachers are not receiving adequate training in math before entering classrooms in Canada.
In order for positive change to occur, several areas need to be addressed. The two issues that this initiative will primarily focus upon are math teacher preparation and inadequate math curricula. The western Canadian provinces and territories share a common math curriculum on which this initiative shall focus. (See this website for details on the Western and Northern Canadian Protocol (WNCP) math curriculum.) Some specific objectives can be viewed on a separate page, while a description of some of the issues is outlined below.
The math curriculum needs improvement
There are serious problems with the WNCP math curriculum.
We support a balanced approach between understanding and skills. Unfortunately, in the shift towards ensuring that children understand math concepts, which we support, several important elements of mathematics have been neglected, or completely eliminated, from curricula and math classrooms. A few of the most obvious, and potentially damaging, flaws are discussed below.
Fluency with standard algorithms for arithmetic:
Recent versions of the WNCP math curriculum downplay standard algorithms for addition, subtraction, multiplication and division and encourage multiple strategies for arithmetic. (The standard algorithms for addition, subtraction and multiplication are the vertical carrying or borrowing algorithms that most parents learned in school. The standard algorithm for division is usually referred to as “long division”.) Thus, students are left with insufficient and cumbersome methods for solving arithmetic problems which are often confusing for both parents and children. Furthermore, standard algorithms, which should be mastered in elementary school, have theoretical significance which is important for learning later mathematics. Standard algorithms must be taught to children early in elementary school, and they must be taught properly with the meaning behind the algorithms explained by knowledgeable teachers.
We support including standard algorithms for arithmetic early in math curricula and ensuring that children become fluent with them through plenty of practice. While we do not oppose teaching children alternative algorithms, standard algorithms should be the primary methods arithmetic methods taught in school and students must become fluent with these algorithms.
For further information regarding the importance of learning standard algorithms, see this article and this letter which was signed by over 200 eminent mathematicians/scientists in the US, where this unfortunate situation has already unfolded.
Basic math skills and automaticity of number facts:
Parents may also have noticed that their children are not required to memorize times tables or practice math facts regularly. There is also deliberate de-emphasis on practice of procedural math skills in many schools. The notion that practice of basic skills interferes with understanding of math concepts is illogical and misguided and denigrating terms like “drill and kill” do not serve students or teachers well. Indeed, understanding and practice of basic skills go hand-in-hand.
In order to become a competent piano player, a child must practice regularly and memorize piano scales. We also know that children can only become good in sports by rigorous and regular practice. The same is true of mathematics – children must practice regularly to become good at math. They must also develop automaticity of basic number facts in order to free up working memory so that more difficult concepts may be learned. We are not, by any means, advocating for the inclusion of pages of endless rote. Rather, we are advocating for the inclusion of incremental practice and a reasonable balance between understanding, novel problem-solving situations and practice of basic skills.
Fluency with fraction arithmetic is extremely important for success in high school mathematics, yet fraction arithmetic is not introduced in the WNCP curriculum until Grades 7 and 8. Fraction arithmetic must be introduced much earlier (Grades 4 and 5), coupled with plenty of student practice so that students become fluent with fraction arithmetic.
Early knowledge of fractions and long division predicts long-term math success.
More specific objectives that will be lobbied for in regards to math curricula are listed here.
Math teacher training needs improvement
There are many excellent math teachers in Canada. There are also many teachers in Canada who have not received sufficient training in math and may be uncomfortable with math but are still charged with the task of teaching math to children. This is a very unfortunate situation, which creates a perpetual negative cycle for teachers and children. We certainly do not blame teachers who may find themselves in this latter category but we do blame the system under which they were educated and certified, and we feel that this system is in need of a serious overhaul.
We have chosen to concentrate initially on the math preparation of K-8 teachers since this is where the foundation for math learning is laid and because most K-8 teachers are required to teach math. As a baseline step, teachers who may be called upon to teach math must have taken an academic stream of math from high school.
Teachers who may ultimately teach math should also have taken math courses at the university level. Teachers in the K-8 stream need to be able to explain to children why algorithms work, why one inverts and multiplies when dividing by a fraction, why a negative number multiplied by a positive number produces a negative number, why certain numbers are irrational, and many other things. In addition to ensuring that teachers themselves have a high level of math proficiency, math content courses need to be available at the university level, as part of K-8 math teacher training, that delve deeply into the concepts taught by K-8 teachers.
Some specific objectives we intend to pursue with respect to teacher training are described here.
Articles that argue for the objectives on which we have initially chosen to focus can be found here.