Much research has come to the same conclusion. Contrary to what we may believe, many students are not thinking in math class. Students who are good at math are usually good at following a list of steps required to get them to the answer. However, when given a problem that requires students to problem solve and think critically, they become stuck and quickly give up.

Denise Cowdrey, a math teacher at Lord Dorchester Secondary School, has used the work of Dr. Peter Liljedahl to create a "thinking classroom" where her students can practice the important skills of critical thinking and reasoning. 

"I was in search of a way to engage my students and develop deeper understanding of content and curriculum," says Denise. "I was noticing students did not retain information from year to year. They were good at mimicking teachers but when evaluating their thinking the results were poor."

In a thinking classroom, students work daily with different groups of students in the class on vertical surfaces, such as chalkboards and whiteboards. According to Denise, these two concepts have revolutionized both the way she teaches and the way students in her class learn.

Since introducing randomized groups and whiteboards to her lessons, Denise has noticed important changes in her class dynamic: communication among students has increased as they teach one another and look to other groups for help, not her, when they get stuck on a math problem.

"I can't tell you what a difference just working vertically has made to students' understanding of alternative methods to finding an answer," says Denise. "I think in the past I was getting in the way of my students' learning by showing them step to step how to perform tasks and solve problems. Now, we consolidate after the students have made a first attempt to solve the problem."

Her findings line up with Dr. Lilijedahl's research. According to Lilijedahl, when randomization of groups is done in full view of students and students work on non-permanent vertical surfaces, changes in classroom behaviour can be profound: there is an elimination of social barriers within the classroom; mobility of knowledge between students increases; reliance on the teacher for answers decreases; increase in class and group discussion, increased participation and persistence, and students become more enthusiastic about math class.

Denise is thrilled with the results. By letting her students take control of their learning and guiding them in a safe way to deepen their understanding of concepts, Denise has watched their confidence grow. "In the past, exams and summatives have been difficult, but now with a thinking classroom the students have a greater depth of knowledge and the confidence to apply their skills in novel situations - their performance on exams has been impressive."

By building a thinking classroom, Denise has allowed her students ownership of their learning. "I can't tell you how excited I am to go to work each day," says Denise. "I love my job but I am amazed at what my students can do without direct instruction. The students realize that the answer is in the room and it doesn't have to come from me. They depend on one another for help and this builds an incredible classroom community."