There are challenges and issues in teaching any subject. Math is no exception to the challenge of teaching. In this post, we will look at a brief history of math teaching in the United States and how math is taught in many parts of America today.
Brief History of Math Teaching
Talk to most students, and they while share how it is difficult to learn math. One of the biggest challenges may be how abstract it is. When studying math it is often more of a mixture of drilling with an expectation to solve problems that have no context or relevancy for the student. For example, solving 2x + 4 = 10 lacks a connection for many students.
Prior to the 1960s mathematics was taught in the United States with an emphasis on computation. Calculate over and over until you get was one of the main philosophies of this approach. During the 1960s, there was a change to an approach called “new math” which focused on the structure or the components/theories of mathematics. This made math even more abstract. In addition, at least with the focus on computation a student could memorize the steps to complete problems, with the “new math” approach the focus on theories without heavy computational practice made learning difficult.
Teaching Math Today
Today, whether to focus on computation or structure depends more on the level of math the students are studying. College bound students are still exposed more to structure while those who are not are often taught using more of a computational focus. The challenge with this is that everyone wants every child to be college bound which means essentially that most students are taught with a focus on the structure and theories of mathematics with a goal of understanding why certain steps are taken when calculating something.
Generally, it is common for math teachers at the high school level and above to focus on teaching conceptual understanding first before procedural steps (elementary is usually hands-on). In other words, explaining theory and the why of the steps before actually using the steps to solve problems. This can sometimes lead to the teaching of long complicated mathematical proofs for various concepts such as the quadratic formula. For a math expert, proofs are critical to knowing why a certain approach works, however, for the average person, proofs can be incredible confusing because they involve math that the learner is not total comfortable with in many situations with little practical application.
The downside of learning procedural steps first is that it becomes difficult to apply them in different situations or to transfer the knowledge to new contexts. For example, in my own experience, it was common for a math teacher to teach the steps of how to solve a problem but then when it was time to practice, the problems were always slightly different from what the teacher taught. I would need to square something that the teacher did not square or factor something that the teacher did not factor in order to have success. The focus on the steps made it impossible to bring in other tools or handle situations that called for other steps.
For the math teacher, who was a natural expert, seeing a problem and bringing in other tools and adding and taking away steps was easy because of their understanding of theory. However, for the rest of us, there is a need to drill and become comfortable before expanding the use of the concepts to unknown situations.
The goal is not to indicate that there is one particular way of teaching math. The challenge is really how to help non-math students have success at math. This involves using both concepts and drill in a combination that allows weaker students to survive or even succeed in a difficult academic situation for them.