Battle Ground Schools

Battleground Schools written by Gerofsky summarizes three "battles" concerning mathematics in the 20th century that occurred in North America. In particular, there was the Progressive movement, the New Math Reform movement, and the "Math Wars". In general, all three of the debates concern different stances in mathematical education and how we should approach teaching students the subject.

The first period, the Progressivist Movement, emphasized and criticized school mathematics as "meaningless memorized procedures". The crux of the argument was that though the students studied and knew the algorithms to arrive at a solution, there was no flexibility because the students would not know any alternative methods to achieve the answer and did not understand the concept (the WHY) of why one would use the procedure to solve the answer. With this line of thinking, Dewey (one of the leading figures of the Progressivist Movement) revolutionalized the idea of the Montessori classroom. The focus of this classroom was not to memorize and implement, but rather to experiment, inquire, and interpret by having students actively engage in activities. Though many teachers stuck with the tradition of lectures and homework exercises, some classrooms had put Dewey's inspirations into practice.

Over time, the New Math movement began. The trigger for this was the space race between Americans and the USSR. The main fear was that Americans were losing in the space race due to the fact that "school mathematics was not keeping pace with ... research level mathematics". With the goal of creating a generation of "elite rocket scientists", mathematics in education began to change once again. The whole curriculum from grades K-12 was changed and the goal was to "create a unified, logical, highly abstract algebraic structure based on set theory". In order to help the students become familiar with mathematical notations and concepts used in the sciences, many topics from university were taught in from grades K-12. However, there were major problems with the New Math movement. Many teachers had little knowledge of the new material and would have had trouble teaching children. For homework, parents would not be able to aid their children with their homework even in elementary grades. It was difficult to justify why students were taught this material as not every child planned or wanted to become a rocket scientist. In the end, New Math was scrapped as a misguided experiment.

Finally, we come to discuss the Math Wars over the NCTM Standards. This is a "battle" that has started in the 1990's and is still occurring. The focus of the Math Wars once again is, "How do we best educate our young in mathematics?". Should we focus on using a progressive approach or using a traditional method of teaching? With the NCTM Standards in 1980's, there was a focus to have "flexible problem solving skills", using mathematical relationships in different forms, and to use technology as an aid to solve math problems. It was a progressive step to help students appreciate the "beauty of mathematics". However, by 1990's, a "backlash" occured and there was protests against the NCTM Standards. There were people who prefered the traditional and conservative style of teaching.

Hence, over the years, though there has been drastic changes and movements in education and mathematical pedagogy, the question still remains, is it better to have instrumental or relational understanding of mathematics? Is it better to lean on one side or to have a balance of both? I believe that there are both positives and negatives behind conservative and progressive stances in mathematics educaion and a balance should be struck between the two. However, without trying and without experimentation, one can not achieve this goal and "perfect" this way of instruction. When the general public is concerned, change is not always welcomed with open arms, and I believe that is why "battles" over mathematics education is always brought up. One thing that I had not considered much before but am much more aware of now is that the STANCE of which form of teaching is "better" depends much on what goes on with the world around us and the goals of the nation. Do we want to create a generation of rocket scientists? Do we want our children to be "practical" and robots? Would we like them to be philosophical and inquisitive? The culture around us will dictate what the public requires and desires. And what the public desires will inevitably end up effect the way math education is taught.