When I tell people I am a math teacher I tend to receive the same sentiment every time: “I am so glad I never have to take a math class again” and “I hate math”. I sympathize. Even engineers and other science professionals struggle with math. This will inevitably persist because math is a difficult and abstract subject, but the majority of the reaction people have to math is the way that it is taught.
Ever have to memorize the times tables? Do you remember around 4th or 5th grade when you had to take a timed test showing your proficiency in multiplication? The feeling of anxiety and fear are probably already creeping up. The bottom line is that standard pedagogical practices such as this teach students that math is to be memorized by rote, and it is to be done quickly, without thinking. I am a math teacher and I honestly do not have the times tables memorized. I know the threes, fives, tens, elevens, and the perfect squares. From this I can derive every multiple up to 13 times 13. Take 9*6, that is 9*5 +9, 54. It has been shown that the most high achieving math students minimize the amount that they memorize by using strategies such as this. Many books encourage students to believe that memorization and short problem solving is the way that math really is.
That is why this year NRA chose to overhaul it’s math curriculum. We chose a curriculum entitled cpm: College Preparatory Math. There are two fundamentally diametrically opposed approaches to teaching math. One is where the students are told math, and asked to repeat it. In the other students are given problems that require them to problem solve and in some way recreate math themselves. Each has it’s advantages, telling students math is very fast, and can lead students to be able to solve a variety of problems efficiently and accurately. Having students problem solve leads them to develop a general approach to solving problems, they are more self reliant and can be more critical of their own methods and strategies. CPM strikes a balance between these two extremes, students are asked to solve problems that are challenging and often wordy(much like real life problems). When the students get stuck the instructor can fill in gaps in knowledge to move them forward with their thinking and approach.
CPM has been shown to be effective through research and multiple studies. You can read the research and philosophical basis for the curriculum here. The main issues with this curriculum is that students have less procedural proficiency and they tend to cover fewer topics. This tends to happen because students cover each topic in further depth, giving students a better chance at retention. Does anyone remember what the law of sines is now? That is probably due to the fact that you were asked to learn it and then tested on it five days later, never to return to it. That is not the case with CPM. CPM has a review and preview section at the end of every lesson where students practice past and future concepts for homework.
So far this curriculum has been very successful with the students. We have done a number of group presentations, projects, and experiments. I wouldn’t set the goal of math to be for every student to love math, but a good gauge is how well people understand the math, and the effort that they are willing to put into solving a problem . Every student has shown improvement in there understanding of number relationships, functions, and graphs. They also tend to spend more time working independently to answer their own questions before asking the teacher(self-sufficiency will be key in later academic life). This I believe is math success, students who are willing to spend time solving problems, and change their strategies when they are not successful(pliability in problem solving), and are constantly evaluating their own processes to come up with better ones.
