For my final teaching experiment, I selected the “Pass the Problem” formative assessment activity. I designed this task as an introduction to linear inequalities, with the intent that students would make connections with their prior knowledge of inequalities in one variable and linear equations. The content goals of the task were for students to identify differences between linear inequalities and inequalities in one variable, and to construct arguments explaining how they thought about and demonstrated graphing linear inequalities. I formatted the task so that students had about 15 minutes to explore the problems with a partner, 15 minutes to interpret and add to the work of another pair, and 10 minutes to discuss the problems as a class.
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In this activity, the students will work in pairs to apply their knowledge of inequalities in one variable and linear equations to "figure out" how to graph linear inequalities. The purpose of the activity is for the students to explore challenging new material and to examine and explain the work of others. By examining and explaining what others may have been thinking, the students can deepen their own understanding of the new material. Their focus should be on both figuring out the problems and understanding the thinking of others. Because other students will be reading their work, they should explain their thought process as much as possible. It is okay to be wrong. I do not expect them to know exactly how to solve the problems, but I do expect them to take what they have learned about linear equations and inequalities in one variable so far and try to figure out what they can.
Common Core State Standards:
Standards for Mathematical Practice:
For my third teaching experiment, I chose to implement the Matching Representations Card Sort activity with my two seventh grade Algebra classes as a conclusion to our unit on Linear Equations. I selected this task because I had observed that my students were proficient at identifying the slope and y-intercept in a single representation, but struggled to identify these connections between different representations. My hope in selecting this task was that my students would solidify their understanding of how these connections can be seen across representations and improve their ability to calculate slope given different pieces of information. Our quiz on linear is set for the next class period, and many of the skills practiced in this lesson will be important in their success on the assessment.
In this task, students work in groups of four to match four representations of linear relationships: stories, equations, graphs, and tables. In order to ensure that all students participate equally, I designed the task so that each student was responsible for one representation. They were not allowed to show each other their cards; instead, they could only form the matches by verbally describing the information contained in their cards, such as the slope and the y-intercept. As groups completed the activity, they were given the opportunity to create their own set of matching representations for a single situation.
In this activity, students employed the following Math Practices:
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.
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.
In this activity, students work in pairs to begin work on one of two problems. After a few minutes, when pairs have completed approximately half of the problem, they trade problems with another pair, continuing from where the others had left off. As they complete the problem, I asked them to look for alternate strategies.
The purpose of this activity is to deepen student understanding of a familiar concept by examining other students' work. Often, learners become accustomed to solving problems in one way, limiting the growth of their conceptual understanding of the connections between strategies. Through examination of other students' strategies, more connections form in our learners' understandings. These connections continue to grow as the curriculum increases in complexity, giving the student a solid foundation upon which they can build as more knowledge and connections are acquired. This activity will be used as a review for the concluding assessment for our 8th grade "Thinking With Mathematical Models - Linear and Inverse Variation" unit. |
Teaching ExperimentsExperimental lessons used to assess students' mathematical understanding and make instructional decisions. Archives
March 2016
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