We all want our students to develop their mathematical abilities.
We have repeatedly heard how well-developed problem-solving skills and mathematical thinking can positively influence students’ future careers. However, the only way students will improve their mathematics abilities is if we give them a chance to struggle along the way.
I recently had a chance to support a group of third grade teachers as they began to collaboratively plan a task for students to explore during their next unit of study. One teacher suggested the following question:
A farmer has 12 animals in his barn. He counts 32 legs.
If only horses and chickens live in the barn, what is the total number of horses?
A few weeks later the team met to look at students’ work on the task and decide what action steps needed to be taken as a result of their review. Towards the end of the discussion, one teacher announced, “I didn’t think that my kids could do that task. So, I just told them that there were 12 heads and asked them to predict how many horses might be in the barn.”
Teachers are dedicated to their students’ learning and desperately want to support them in any way possible. Sometimes, like in the case above, teachers feel compelled to make the content easier so their students can quickly complete the task and feel successful.
This practice hinders students’ mathematical development.
By lowering the cognitive demand of the task, we deny opportunities for students to challenge themselves to make sense of the situation and apply what they know. We also prevent students from learning as a result of their mistakes and deny them the opportunity to understand the importance of perseverance.
Glenda Lappan and Diane Briars summarize the critical importance of implementing meaningful tasks (1995). They explain that “there is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is, than the selection or creation of the tasks with which the teacher engages students in studying math”.
Three strategies to help students in the classroom.
Rather than simply deciding that students won’t be successful with a cognitively demanding task, here are three strategies you can use to help students without taking the challenge out of the task itself.
Do the task yourself and if possible, compare your work with other colleagues. Look for different approaches that students might take. Think of ways to extend students’ thinking or redirect students’ work if they need support. Consider how students will work on the task. Decide if they need to work individually, in pairs or in small groups.
Monitor students’ work without disrupting their thinking. Avoid questions such as “How is it going?” Look for those students’ approaches that you think will benefit the whole class to hear. Consider the order in which you want students to present.
Provide sentence frames such as “I think we need to find…” , “So far, we know that…” and “Help me understand how you….”.
Implement a protocol, such as pause, reflect, discuss, to encourage discussion.
We want all of our students to develop their abilities to think mathematically. They will only be able to do so if we give them a chance!
Lappan, G., & Briars, D. (1995). “How should mathematics be taught?” in In I. M. Carl (Ed.), Prospects for School Mathematics. National Council of Teachers of Mathematics, Reston VA.