How to Encourage Independent Thinking in Math

High school math teacher Michelle Russell noticed that when she gave her students a tough math problem, they would often shut down rather than risk answering incorrectly. Being wrong, however, is part of the math learning process. “It’s like putting together a puzzle: You do the wrong things first before you figure out the right things,” Russell, who teaches math at Florence High School in Alabama, writes in MiddleWeb.

Still, she knew she had inadvertently contributed to her students’ unwillingness to roll up their sleeves and engage in the productive struggle that’s necessary for working through complex math problems. “As much as I hate to admit it, part of the problem is that I’ve probably conditioned them to think that I’ll jump in quickly if they need help,” Russell writes. “I will often provide step-by-step instructions, which removes any responsibility from the student to think for themselves.”

ASK OPEN-ENDED QUESTIONS

Determined to get her students thinking for themselves, Russell skipped her usual technique for introducing a new subject—lecturing students on the concept—and instead encouraged them to take a more active role in their learning.

“We started looking at different tables of values, and I asked them what they noticed,” Russell recalls. “What happened? I learned that asking students what they noticed is a pretty effective question.”

To build students’ confidence and reduce anxiety, she paired them up and asked them to share their findings with each other—a strategy Russell recommends for both middle and high school students.

Russell opened up exercises she had previously assigned as independent work for classroom discussion. “We worked each problem as a class, and I started out letting them confer with a partner until they got comfortable,” she writes. “Students would give an answer, and the class would debate whether it was correct or not. This resulted in a lot of thinking and good conversations…. Importantly, the students enjoyed it.”

PAIR STUDENTS UP 

Russell next implemented a strategy called a row game, in which students first solved problems independently and then paired up to compare their answers. Russell explains, “The pair of problems in each row will have the same answer. If students’ answers don’t match, they have to check each other’s work and look for the mistake.”

When she challenged her students to work together to solve problems like this, she found that they tended to engage more deeply and were more willing to stick with tough math work longer.

Encouraging students to think for themselves, says Russell, takes time—both for the teacher creating lessons and for students working through the material. But she found the benefits for her students made the approach worth the extra time. “If you want students to think and reason, you have to give them the time and space to do it,” she says. “Without giving notes and step-by-step instructions, it took three days to fully introduce exponential graphs. I could have given them the notes in less than one day. I know which one is better, but it is a fact that allowing students to discover and think for themselves will take longer.”