I chose to enact the “Create the Problem” teaching experiment as the culminating activity for the Word Problems investigation in our 7th grade “Expressions and Equations” unit. In this unit, students were introduced to solving word problems without being asked to use a specific strategy. Throughout the investigation, students learned the guess-check-generalize method of solving, building into developing the skills to generalize and create an equation to represent a word problem using key words that indicate mathematical operations. The “Create the Problem” teaching experiment seemed to be an ideal conclusion to this unit, as it requires students to apply their knowledge of generalizing using key words to execute the process in reverse by taking an equation and creating a corresponding word problem. I also selected this activity to assess how students worked together to overcome a challenging problem, as it requires a different sort of creativity than is typical in the mathematics curriculum that these students have experienced.
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In this activity, students work in pairs to create a word problem that corresponds to a given equation. They will focus on developing creative problems with clear language that is not operations-based. Once they have created their problem, they will partner with another pair with the same original equation to edit their work and write a final word problem to be solved by another pair in the classroom.
The purpose of this activity is to help the students develop an understanding of what language can be used to communicate mathematical operations (beyond add, subtract, multiply and divide). They will also be developing their ability with several math practices:
This activity will be used as a review for the concluding assessment for our 7th grade "Expressions and Equations" unit. I chose to enact my teaching experiment, “Pass the Problem”, as a review to conclude our unit on linear and inverse variation. This task seemed particularly well suited to a review activity for several reasons. First, I have observed that these students seem to have a reasonably good understanding of linear and inverse variation, but are often inclined to confuse the two, attempting to write a linear equation for inverse variation or vice versa. The students have demonstrated that they can successfully work with either when used in an isolated context, but this confusion seems to arise when the students are looking at both types of relationships in close succession. As such, the two- question structure of this activity enabled me to have students engaging in both types of problems in quick succession. Second, the activity can be completed individually or in pairs, which gave me flexibility with how many students were in attendance, while also giving the vast majority (all but either one or two, depending on the hour) a partner with whom they could discuss ideas and process how to work through the task. Third, the structure of a “Pass the Problem” task requires that students interpret the work of other students and analyze how to proceed from where the others had left off. As a result, the cognitive demand of the task is raised, helping students to build connections between different strategies and advance their understanding of the mathematical concepts.
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Teaching ExperimentsExperimental lessons used to assess students' mathematical understanding and make instructional decisions. Archives
March 2016
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