In this special blog series, I will be interviewing Barry Garelick and J.R. Wilson about their new book, Traditional Math: An Effective Strategy that Teachers Feel Guilty Using. You can catch the whole saga, here.

Let’s dive right in, shall we?  

Q1: Can you tell me what you mean by “Traditional Math”? 

J.R./Barry: First, let’s look at how traditional math has been defined by others: 

  • The teacher stands at the front of the room and lectures nonstop for the duration of the class, students learn all procedures and problem-solving methods by rote, and no background on the conceptual underpinnings of the same are presented.  
  • Students are viewed as “doing math” but not “knowing math” and have no conceptual understanding of what they are doing.  
  • Topics are presented in isolated fashion with no connections to other topics. Word problems are dull and uninteresting, and students do not feel any desire to try to solve them.  

These mischaracterizations actually can help define what we mean by traditional math. In general, traditional math is the teaching of math using explicit instruction and worked examples to teach a logical sequence of skills and concepts. The method engages students as they develop fact and procedural mastery, algorithms and problem-solving procedures along with reasoning and understanding. 

In a traditional math classroom the teacher leads the students by providing explicit instruction; that is, by explaining how to solve specific types of problems. The teacher also provides worked examples which provide students with the opportunity for practice. This entails using what’s known as the “I do, we do, you do” technique. For the most part, the teacher does this by standing at the front of the room, and the seating arrangement would be the teacher’s preference whether students are seated in rows, pairs, clusters of four, or some other way. 

The teacher, however, is not “lecturing nonstop” for the duration of the class. The explicit instruction entails the teacher asking questions along the way, including but not limited to “Why did we do this?” and “What should we do next? And why?”  Also, as students work at their desks (independently rather than in groups), the teacher circulates around the room to make sure students are on track, and answers questions and/or provides hints as necessary. 

In teaching a procedure, the teacher will connect the concept behind the procedure to the procedure itself. In doing so, however, we want to keep the momentum going. While some students may follow along with the explanation of the concepts and how they link to a particular formula or procedure, most students want to know where it’s going, what it’s leading to, and how it will be used. Taking up time to make sure students understand every step and nuance of a derivation of a formula or procedure is often extraneous, distracting and contributes to overload. What is important is that in traditional teaching, topics are not taught in isolation. Rather, connections to other topics are indeed made as a means to lead to new procedures and concepts. In so doing, we teach for understanding, recognizing when students are ready to move on with new information. 

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