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by John Woodward on Aug 27, 2020
Learn More About TransMath
When I began my career as a special education teacher, I felt I entered the classroom with a number of strengths. I had a good understanding of behavior management, curriculum design, effective interventions, and how to teach in what has generically been described as direct instruction. However, I quickly realized that I knew little about motivation, and this was critical to understanding how each student approached a subject like math and, more importantly, how they processed success and failure.
After five years of working with low-achieving students and those with learning disabilities, I realized that a diet of tasks which were broken down into small steps “to ensure success” wasn’t enough. Albert Bandura, among others, wrote that this kind of diet leads to a false sense of self-efficacy. Routine problems are just that, and success can be highly likely. When the same students are given something nonroutine and challenging, the sense of success in math evaporates. Also, repeated practice on small-step, routine problems was sometimes monotonous to my students. The more I read about motivation theory, the more I understood that a variety of tasks—particularly ones that occasionally challenge students—were instrumental to good teaching. For example, the definition of problem solving in math requires that at the onset, the answer is not immediately clear. That’s just not the case with routine tasks where the thinking required to solve a problem is simply a matter of following a rule.
The downside of asking students to solve challenging math problems is that if the teacher doesn’t do a good job introducing the problem and then scaffolding when appropriate, students can end up more discouraged about their learning than empowered as problem solvers. Failure only reinforces what students already think about themselves and the subject matter.
Fast forward to today. Teachers and students across the country are returning to instructional settings that are simply abnormal. Let’s just focus on the online world that began last spring and is likely to continue in many districts through the fall. So many teachers I’ve read about and talked to say the same thing about their new world of online teaching: “It’s hard to engage students, especially if I don’t have five days a week to teach math.” To me, this is partly a motivation issue, and there are any number of answers. I’ll focus on one.
An element we take for granted in a normal classroom is community. In an online world, the community is fragmented. That means before we begin instruction, we need to be checking in and giving students the opportunity to express “how things are going.” This is ongoing and often subtle in a regular classroom. It needs to be explicit in online classes, even if it robs you of five to 10 minutes of instruction.
As for increasing engagement, here’s just one approach to think about, and it’s something we’ve had a great deal of success with in our research. Here’s how it worked.
Rather than have students work by themselves on typical word problems from a text, we worked with students in small groups using novel or “logic/puzzle-like” problems. Tons of these problems can be found on the Internet today, and here’s just one that we used.
Planet Fiesta has a party that lasts for 1,000 days. The number of days in the year on Planet Fiesta are the same as on Earth, but there are no leap years on Planet Fiesta. The party starts on a Monday. What day does it end?
One reason why this is a good problem is obvious—the answer is not immediately clear. The key to making this kind of problem solving successful, especially with struggling students, is to have the group (or community) work on the problem. This relieves students from the pressure of individual accountability and eventual success or failure. Time and again we found that by devoting 15 to 20 minutes of work on just one problem, almost every student made a contribution, especially when prodded in the right way. Suzanne Chapin, Catherine O’Connor, and Nancy C. Anderson’s book, Classroom Discussion in Math, is an excellent resource for these kinds of questioning techniques.
In our work, the teacher introduced the problem and then had students talk about what made the problem difficult as well as what the problem was asking for. As students worked together and occasionally hit “a dead end,” he scaffolded their thinking and gently guided them in a different direction by asking questions about their strategies. When students found an answer, the teacher guided them through the final evaluation step of problem solving that almost never occurs when students work on a bank of word problems by themselves. In achieving the answer, the community of students found success. The teacher was also able to use this particular problem to make connections to division and the concept of the remainder.
Apply this to an online world. Teachers could post the problem for students to think about before class starts. After checking in with students about their emotional wellbeing—a critical aspect of classroom community—the teacher could introduce the problem again and follow the steps described above. A key instructional strategy in this kind of work is to get everyone to make a contribution, even if it means restating what someone else said and elaborating slightly.
This suggestion is certainly not a panacea for all of the instructional dilemmas that online instruction has created for teachers and students, but it’s one small way to and a variation to everyday math as well as present challenging problems where students can feel a collective success.
John Woodward, Ph.D., is a nationally recognized mathematics author, writer, and speaker. He is the author of TransMath® and NUMBERS professional development.
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