This is the first in a two-part blog series that explores math intervention.
Several years ago, I did some math coaching with a group of teachers who told me they wanted their first graders engaged in more problem solving activities, including opportunities to grapple with tasks and explain their thinking.
Together, we created relevant problems to use with students in the class. My memory is foggy about the exact problem we used for the first lesson, but what remains clearly in my mind is that while introducing the problem to the students, one little fellow shouted out the answer in a matter of seconds. I was flabbergasted! Even though every student had yet to determine the answer (or even have pencil in hand), my whole idea of what constitutes “problem solving” was shaken by this one individual first grader.
As I was walking down the hallway after the lesson some questions were spinning in my head:
- Was it the numbers that we selected?
- Was it the ability of that one student and not the problem itself that created the situation?
- Is there more to selecting problems than just looking at the numbers?
- What makes a problem problematic for ALL students?
I worked with this group of first grade teachers for about six weeks. Over that time we refined our ideas about what problem solving looks like. But in my continued work over the years with teachers across the country, these questions continue to bubble up as I look at published materials used in classrooms and math problems posted on the internet. Oftentimes the problems that I see labeled as “problem solving” are what I think of as traditional word problems. So I ask, what is the difference between students doing word problems and students doing problem solving?
When I turn to one of my favorite resources by Marilyn Burns, About Teaching Mathematics, A K-8 Resources, Third Edition, Marilyn helps me to answer my question, “What makes a problem problematic for ALL students?
Criteria for Mathematical Problems
- There is a perplexing situation that the student understands.
- The student is interested in finding a solution.
- The student is unable to proceed directly toward a solution.
- The solution requires use of mathematical ideas.
What I have learned over time is that when students are doing word problems they are building their understanding of the operations and their ability to think algebraically. When students are doing rich problems that involve extended thinking, they are also building mathematical understanding, but additionally their ability to think and reason. The point is not whether students should be doing word problems or problem solving, but rather, as teachers we need to have clearly in our minds the kinds of problems we are presenting to students and why we are presenting them. We need to look carefully at published materials and lesson ideas we use in our classrooms to make the best choices to meet the goals for any given day for our students.
This is one of the most difficult things for any teacher to do. Do you have any strategies for creating rich math problems that you can share?