Part One: Mathematics in Education

Mathematics has had many forms over the years in schools. Some vividly remember the "new math" in the 1960s, whose focus on abstract theories spurred a back-to-basics movement, emphasizing rote learning and drills. After that came “reform math,” whose focus on problem solving and conceptual understanding has been derided by critics as the “new new math.”

What is happening in schools today? Truly, there is no one formula. Some schools are still teaching the rote learning and drills of the 60's; Some are embracing trends that come from other countries, such as Singapore, and there is everything in between. The question educators are asking is: what works best, faster, and yields higher test scores?

The National Council of Teachers of Mathematics (NCTM) urges a problem solving approach utilizing multiple representations whenever applicable. The thought is that if students see the problem in multiple ways and form, it will hold more meaning than looking at only one representation. This creates the bridge between the concrete and the abstract, which is sometimes a huge leap for students. This approach is similar to the Singapore Math in that the Singapore approach involves students moving through a three-step learning process: concrete, pictorial, abstract. American math programs, have typically skipped the middle step and students get lost when making the jump from concrete to abstract.

Another shift, or focus, seen in the NCTM standards is the focus on Curriculum Focal Points. These are defined as important mathematical topics essential in grades preK-8. These focal points are core structures that lay a conceptual foundation. NCTM has published them to be used as a guide for organizing content and bringing coherence to multiple concepts that are taught across grade levels. There are three tests for each item before it can be called a Focal Point. Those tests are:

• Is it mathematically important, both for further study in mathematics and for use in applications in and outside of school?
• Does it “fit” with what is known about learning mathematics?
• Does it connect logically with the mathematics in earlier and later grade levels?

The decision to organize instruction around focal points assumes that the learning of mathematics is cumulative, with work in the later grades building on and deepening what students have learned in the earlier grades, without repetitious and inefficient reteaching.

This is good for the future of mathematics. Allowing students to build bridges between the concrete and abstract, and providing a curriculum structure that supports mathematical thinking will undoubtedly help students in the future.

For high school students, NCTM is recommending a series on Reasoning and Sense Making across the curriculum. This is very different from simply memorizing formulas and copying what the teacher does at the board. The problems they propose take entire class periods to solve and require analysis of patterns and making predictions. Students are being asked to think rather than mimic.

So why hasn't the shift to thinking happened in all classrooms? The information is readily available. I think this is a good question for us to look at together. Maybe it's high stakes standardized tests, untrained teachers, unmotivated students, absent parents...

Please leave your thoughts.

Why haven't we made the shift from rote learning and drills to thinking and making connections in the math classroom?

Sources:

"Making Math Lessons as easy as 1, pause, 2, pause..." Winnie Hu, 9/30/10 New York Times

National Council of Teachers of Mathematics Standards and Focal Points, www.nctm.org