When I was in school, mathematics was the king of the education world. Few questioned its importance. Students who excelled at the subject were perceived to be “smart”, and were often praised for their work ethic as they practiced math problems from a textbook or worksheet on a daily basis . Even if many students did not fully understand why it was so highly regarded , they accepted the fact that math was THE academic subject.
Fast forward to 2016, math is now struggling to hang on to its identity of being one of the most important subjects we learn in school. These days many students seem to ask why we need mathematics. No longer do young people take it for granted that everyone has to learn the specific mathematics curriculum that is practiced with small variations all over the world. We don’t admire the diligent student who earns good grades in mathematics by spending many hours practicing math problems from a textbook or worksheets as much as we used to. The hero of our times is an extrovert who is vocal and assertive, with excellent communication skills and a love for interpersonal contact. School boards are attempting to reform mathematical education, hoping to make it more relevant and engaging for todays young people. For example The Peel District School Board in the Greater Toronto Area has started something called “Engage Math” which encourages their teachers to teach through problem solving and collaborative learning so that students can develop their understanding through active discussion. The question is are we changing mathematical education for the better?
Obviously no has the answer to my question, we can only hypothesize and wait for the answer to revel itself over time. From what I can observe the biggest obstacle in the way of making progress in mathematical education is the divide that seems to exist amongst educators. There appears to be two sides each believing there “approach” is right and the other wrong. On one side we have the educators who believe in the “old school approach” to teaching math. These educators see nothing wrong with the way we traditionally teach math (and the way they were taught math), they believe that practice, repetition, and intelligently designed rote learning allows students to gain hard won fluency with the material. On the other side we have the educators who believe in active understanding based teaching methods such as “problem based learning” or “investigative learning”. They tend to believe that understanding is what is most important, and that students need to be engaged and shown the relevance of what they are learning.
The problem isn’t that there are opposing view points. The problem is that often times members of the opposing camps don’t acknowledge the merits of each others points of view. I’ve been to many professional development workshops designed to show high school mathematics teachers how to teach math through active understanding based teaching methods where many teachers sat with their arms crossed disengaged from the presentation. These teachers believe that the movement towards understanding math through active discussion is a fad and does not allow students to develop a fluency with math because it does not force them to practice enough. On the other hand I’ve also encountered many resource teachers and administrators who strongly promote and support the reform in math education get upset when they walk by a math class room and see students sitting individually in rows working silently on math problems from a worksheet or textbook. To them repetition and memorization is demeaning and a waste of time for both students and teachers.
The reality is that both sides have merit. Traditional math has worked for some, Google, Apple, Facebook, and Microsoft gainfully employ many who have developed a fluency in mathematics being taught the “old fashioned” way. There can be no doubt that practice and repetition is necessary for students to gain a fluency with math. It is a subject that the brain needs time to get used to. Well designed rote learning scaffolds complex topics and guides students one step at a time. The new active understanding based approach to teaching math has generated many fresh new ideas that bring problems and conflicts that can be resolved using mathematics to life ( Google Dan Meyer’s three acts of a mathematical story for an example). This approach encourages students to think for themselves more and allows for more collaborative efforts to solve problems, An approach that is more friendly for those who enjoy interpersonal contact. Until we understand that a combination of the two approaches is ideal, progress in mathematical education is likely to be limited.