# Developing Flexible Thinkers May Require a Less Flexible Approach

*November 19, 2018*

### Over the past decade, emphasizing multiple solving strategies has permeated elementary mathematics instruction - a significant departure from the rote, procedural learning that previously characterized the subject. Flexible thinking has replaced rigid rules, unleashing student creativity in the process. This pedagogical shift has helped positively redefine the subject, which has led to better math teaching and learning. Still, the practice is commonly mismanaged and overemphasized.

### Elementary math teachers frequently provide questions that stimulate multiple solutions, and encourage students to share their solving strategies in front of the class. In theory, this methodology creates a dynamic classroom experience that engages everyone. In reality, however, it usually has the reverse effect, puzzling already confused children. Many students initially pay attention, but their focus wanes with each passing explanation. Learning becomes passive and the lesson more resembles a collection of oral reports than an instructive learning session. By the time the last presenter shares, the majority of students have stopped listening and forgotten the earlier solving methods.

### This lesson design is most dynamic and effective when teachers use the following approach. The mental math topic *Add 98 to three-digit numbers* will be used as a catalyst.

### While lesson planning, the instructor selects a few strategies that they want their students to learn, e.g.

### Standard algorithm

### Add 100, subtract 2

### Make 100

### At the beginning of the lesson, they present a problem such as

**98 + 394 =**and allow students an exploratory time to solve. As students try out different solving methods, the teacher probes the room, carefully selects which strategies will be presented, and the order in which they’re given. If there is a valuable method that no child uses, the teacher will demonstrate it.

### Strategies are shared from simplest to most complex. When the latter is demonstrated before the former, struggling students often become confused, frustrated, and stop paying attention.

### Presenters understand that they are providing instruction. Therefore, the selected students need to articulate their strategies, or the teacher needs to efficiently paraphrase their mini-lesson. Long-winded presentations lead to disengaged learners.

### After a child presents, all of their classmates practice the strategy using analogous examples. For the problem

**98 + 394**, three different presenters might demonstrate the following three solutions:

### After each student shares, the class practices the problems **98 + 496**, **98 + 795**, and **98 + 597**, using methods I, II, and III, respectively.

### Regardless of how brilliant or creative a strategy is, the teacher doesn’t select students, whose explanation will confuse their classmates. This can be frustrating for both students and teachers, but resisting is critical to maximize learning. Teachers can recognize and commend individual students at a different time of the day.