This activity, adapted from Barton and Heidema’s Teaching Reading In Mathematics (2009), helps students to develop their ability to solve math word problems by collaborating on problems as a group, and then communicating as a group the steps and thought process they followed. By describing their process both in speech and writing, students are able to clarify and solidify their understanding of the problem and its solution. In addition to improving math proficiency, this activity develops metacognitive skills.
Identify or write a relatively challenging word problem that you want students to solve.
Determine the groups you want students to work in.
- Students get to assigned groups.
You will want to think about both student ability and student affinity in assigning groups.
- Teacher explains that students will work on solving a problem through discussion, and that they will initially avoid writing and drawing. Teacher distributes problem.
By forcing students to think aloud about the problem and their process, you help them to make explicit connections and to clarify concepts.
- Students discuss the problem, and decide how to solve the problem through oral conversation only.
You will want to circulate during this time and listen to student thinking and conversation. Ask them what they are noticing and thinking, and help guide them towards greater sophistication.
- After students have discussed the problem and agreed on a solution, teacher distributes a piece of paper and a pencil to each group.
You will want to wait for this step to ensure that they really just talk through the first step as intended.
- One student in each group writes the first step of solving the problem. The student may ask for help from other group members if she or he is stuck.Encourage students to write in regular language, not using mathematical symbols or numbers.Circulate as students are working, leading mini-conferences and listening to and guiding their thinking about how to interpret the word problem.
- When the first student is done writing, she or he passes the paper and pencil to the right, and the next group member writes the second step of solving the problem, asking for help from group members as needed.
Encourage students to write down the steps in as detailed a manner as possible, and not to miss small steps. Their response should describe every aspect of the solution process.
- Students continue passing the paper and writing steps until they have written the entire solution to the problem.
Remind students that the more detailed the steps, the better. Discourage them from combining steps or from omitting steps that might seem obvious. They will benefit from thinking through the full process really clearly.
- After all groups are done recording the process, each group exchanges their sheet with another group. Students prepare to use the other group’s solution sheet to solve the problem.
Consider assigning which groups will exchange, especially if groups are at different levels or are finishing at different times.
- One student in each group is chosen as “reader,” another as a “writer.” The remaining students in each group are “solvers.”
You can assign roles, or allow students to do so.
- The reader reads aloud the steps in the exchanged solution sheet in exactly the order and manner they are written. The solvers help follow the steps, and the writer records the work using mathematical symbols as they solve the problem.Circulate as students are working and help them to follow the process. Help them to evaluate any differences between their method and the other group’s method.At this point you will want to monitor whether any group’s solution sheet contains an error, and if so, to guide the group with it towards identifying and correcting the error.
- The writer from each group records the solution to the problem in mathematical symbols on the board. Students examine the various solutions to see differences and similarities, and discuss a variety of ways to solve problem.
You will want to guide a discussion about the various ways students decided to solve the problem, and discussing similarities and differences, pros and cons.
- Alone or in groups, in conversation or in writing, students reflect on their learning process.Students respond to questions including:How does writing about your process help you to solve a word problem?How does thinking through all your steps ahead of time change the way you solve a problem?How does collaborating with a group help you to solve a word problem?What were two different ways to solve this problem? What is a pro and con of each method?