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. I launched the activity with a “Do Now” with four representations of the same linear situation: a story, an equation, a table, and a graph. Students were told that the four representations corresponded to the same situation, and were asked to explain how they could tell. In the past, these students have practiced writing story problems that match a given equation and writing equations that match a given story problem, writing the equation that matches a graph and drawing a graph from its equation, making tables from an equation or a graph, and drawing a graph using data from a table. However, they have never looked at all four representations simultaneously, so I designed the “Do Now” to ensure that all students had access to all parts of the task (see Figures A-D below for a range of student responses). I used the discussion of the “Do Now” as a medium to provide students with the tools that they would need to identify the slope and y-intercept in each of the representations. The students have learned multiple techniques of calculating slope and finding the y-intercept, and as we looked at each representation I recorded the methods described by the students on the board. My hope with this was to provide the students with the tools that they would need to complete the task with less reliance on my help. After reviewing the video, I have mixed feelings on this part of the lesson. I believe that it was helpful to many students, as when I reviewed the students’ written work from the “Do Now”, not all students were sure of how to find the slope and y-intercept in every representation. During the activity, I overheard teammates referencing the board and the techniques we discussed while describing to each other how to find the necessary information in their representation. However, I noticed in the video that several students were not engaged in this discussion, particularly during the moments when I was recording the strategies on the board. I suspect that this was because we have been working on this material for a while and these students are ones who feel comfortable with the material. From my observations, these students are confident with their knowledge but this was not reflected in their work on the “Do Now.” If I were to do this lesson again, I think that I would revise this portion of the lesson by designing a structured note-taking sheet to encourage all students to be recording important information from the discussion and ensure that students are actively engaged. In this lesson, I hoped for my students to employ several of the Math Practices:
I found that students in both classes were successful with the added difficulty created by not being able to show each other their cards. I overheard multiple conversations in which one group member described to another how to identify the slope or y-intercept in their representation. If I were to implement this task again, regardless of content, I would retain this aspect of the task, because it required all group members to be engaged and to contribute to the group’s efforts. If I were to implement it again with this content, I might create a second tier of card difficulties for groups that I expect to work quickly by removing some of the scaffolding. These changes could include not specifying how to calculate the rate of change in each situation on the story cards, aligning the table and graph so that few points are shared between the two, selecting points in the table so that the change in x is not one, or writing equations in point-slope or standard form. These changes would add cognitive demand by reducing the amount of regularity and requiring that students employ different techniques on different cards. More than the card sort itself, my addition of the student created problems (see Figures E-G) provided me with a means to assess student understanding; however, it only allows me to assess group understanding, not individual understanding (beyond what I heard in the discussions). One lesson I learned from this is that I need to ensure that my formative assessment includes an individual written portion if I want to be able to assess each individual student’s understanding. For the purpose of this task, this was not a problem, because my “Do Now” gave me a view into each student’s understanding before the task, and the group-created problems allow me to see where that group stands after the task.
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Teaching ExperimentsExperimental lessons used to assess students' mathematical understanding and make instructional decisions. Archives
March 2016
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