[DataDoxy]

I appreciate your query. This is currently a big issue in Alberta as math performance of students is slipping in the ranks according to international standardized test scores (PISA, 2012). As such, many people are questioning whether we should go “Back to the Basics” or continue to embrace the “New Math”. This is a pervasive problem and it can be confusing as both sides of these Math Wars continue to point fingers at each other.

I have been a math teacher for ten years and a mathematics education researcher for the past seven years. During this time, I have seen first-hand how many students are falling behind in math and it concerns me greatly. This is precisely why I completed my doctorate in this area as I am determined to change the equation so to speak. During my years of research, I have come to the conclusion that the problem is not just what math is best, it is also about how we, in Canada, train our teachers. I will address both points.

The Basics vs. The New Math

There is no question that students should learn their math facts as these are the foundational building blocks of math. When student do not know their facts they have difficulty advancing in mathematics as they struggle with the attainment of the higher level concepts which are built upon these foundational concepts. Additionally, many students that do not “know” their facts struggle significantly when solving complex or multi-step problems. This is because they are experiencing what we call cognitive overload as their working memory becomes over-taxed. In other words, these students end up using much of their mental energy finding the unknown math “fact” which they need to solve the larger problem which leaves insufficient mental energy to attend to the larger problem itself. Sadly, many of these students develop gaps in their learning and thus continue to struggle with math over the course of their lifetime. For example, I routinely hear many adults, parents and even teachers say, “I am just not a math person”. This belief is nothing more than a myth!

According to the latest neuroscience on learning, we now know that there is no such thing as “a math person” (Boaler, 2008; 2012). In fact, research states that everyone can become proficient at math (National Council of Teachers of Mathematics, 2000).

So… why the disconnect between neuroscience and students’ performance in math? The answer is simply that we are not teaching math optimally for the vast majority of learners. This is true whether we are embracing the Back to the Basics mentality or the New Math principles, but for different reasons.

Traditional Math & Back-to-the-Basics

Traditionally, the majority of classrooms have focused on learning the basics first through rote memorization first and attach meaning afterwards. Research tells us this process is backwards. Consider when we are learning to read, we understand what a cat is before we can read the word c-a-t. When we do acquire the ability to decode, we learn that c-a-t is in fact a “cat” which we have a mental picture of in our head and therefore, can attach the word “cat” to. We need to do this for learning math too! For example, it is more effective to understand what a group of two added to a group of three is conceptually before we learn the symbolic representation 2 + 3. Then, once we understand the concept of addition (and the concept of base ten) we can then apply this to higher level questions like 22 + 3 or 127 + 3.

Further complicating learning of math in schools is the weight placed on the speed and accuracy of math facts. Unfortunately, many traditional teachers tend to focus speed and accuracy long before students have made the necessary cognitive connections that we know need to come first. This can result in misconceptions that kids can carry with them for their entire math careers which can lead to further complications and misunderstandings.

In addition, when kids focus on the rote memorization of facts, they lack “number sense”. This is highly problematic as number sense is the foundation for all higher-level mathematics (Feikes & Schwingendorf, 2008). For example, research tell us that students who fail algebra (which is the gatekeeper to higher level math like calculus) often lack number sense (Boaler, 2012). Additional research stated that when looking at the difference between "high achievers" and “low achievers”, students categorized as low achievers were considered so because they lacked number sense (Gray & Tall, 1994). How is number sense attained? Number sense is developed when kids learn math conceptually first which is the principle idea behind the New Math movement.

The New Math

The optimistic ideals of the New Math movement lie in stark contrast to the traditional Back-to the-Basics movement. Personally, I see the concept of New Math as valiant and necessary, but misunderstood and poorly operationalized. I firmly believe in the goals of New Math as I think that kids need to understand math deeply so they can rationalize, problem solve, and be proficient in math at higher levels. These are the skills students will need to meet the emergent demands of our rapidly-changing, technologically-driven, 21st century world. Thus, the main problem with New Math in my opinion is not the idea behind it; instead the problem lies with how it has been implemented in our classrooms. This is because teaching the New Math as it is intended is complex and time consuming. Sadly, many teachers have not been privy to the kind of support and education, in both mathematics and in the neuroscience of learning math developmentally, that the New Math demands. Furthermore, there has not been sufficient time for many teachers to become proficient with it. Consequently, New Math has fallen short of its targets but again, this is not because its curriculum is bad for kids.

The Basics + New Math = Successful Learners

In sum, I believe the solution is that students must learn their math facts but the way they learn these facts needs to change! This is because the rote memorization of facts, which is still the most common practice in North American schools, inhibits the development of number sense. Furthermore, when the New Math is not implemented as intended the fluency of math facts is often missing. This sometimes occurs in addition to a lack of number sense, which is ironic as this is what the New Math curriculum was intended to cultivate.

So... when I am asked what I think of the Math Wars, my response is always that I think we need the both the Basics and the New Math! More specifically, I believe in the strategic combination of the New Math and the Basics coupled with highly supported, well-trained, teachers who can help students developmentally understand mathematics by teaching concepts conceptually first, attaching symbols second, and focusing on the efficient learning of math facts only after the appropriate level of abstraction has been attained. This is what I consider to be the successful formula for helping all kids learn math optimally!