There is a lot of talk these days about children growing up as “digital natives.” They have never known a world without computers, cell phones, or social networking. Digital media is their “first language.”
With the shift in emphasis from coverage to depth of understanding in the Common Core State Standards for Mathematics, it is clear that what we need to create in our classrooms are problem solving natives: students for whom critical thinking and problem solving are their primary “language,” students who are equipped to face the challenges of our increasingly complex twenty-first century world.
In my last post, I talked about the need for a problem-solving toolbox to equip students to deal with word problems and to think in the ways expected by the Common Core State Standards for Mathematics. In this post, we’ll open the toolbox and discuss a great all-purpose tool—drawing (or acting) out the problem.
The first Standard for Mathematical Practice in the Common Core State Standards for Mathematics is “Make sense of problems and persevere in solving them.” This requires students to explain to themselves the meaning of a problem and decide how they could go about solving it.
Let’s say the problem is something like this: “Cecilia and Kayuana have some stickers. Kayuana has 18 stickers. They have 31 stickers altogether. How many more stickers does Kayuana have than Cecilia?”
If students have been taught the “trick” of looking for key words, they will see the word “altogether,” which they have been told means “add.” And we know from experience that many students will do just that and come up with an answer of 49—as this third grader did. (Although you can see he changed his response to another—incorrect—answer, his original solution was 49.)
They may also see “how many more,” which they have been told means “subtract,” and come up with an answer of 13, as this student did.
Neither of these solutions, obviously, answers the question that is actually being asked, which is how many more stickers Kayuana has than Cecilia.
Because this is a two-step word problem, students who are inexperienced problem-solvers may be unsure as to how to approach the problem. Using a picture to represent the problem makes the scenario, and the solution, much more evident.
Here you can see examples of student work from four students who were able to successfully solve this problem using a picture. Although most of them did use the subtraction algorithm as well, you can see that one student was able to solve the problem entirely based on the drawing, without using any algorithms at all.
All of these students were able to make sense of the problem and correctly identify the steps they needed to take to arrive at a solution. It is evident from their drawings that the pictures helped them to represent the problem and determine the numbers they needed to use in their calculations.
The ability to represent problems in pictures (or to act them out) is a valuable problem-solving skill for students to develop for their problem-solving toolbox. To help you further this skill in your students, we are offering the activity Schmoos ’n’ Goos from Solve It! 3rd. This activity is well suited to being solved with this strategy, and can be adapted up or down for younger or older students.
I would love your feedback as you try this activity or others with your students. Stay tuned for a discussion of more tools for that problem-solving toolbox in future posts.