2013 Conference Proceedings - University of Nevada, Las Vegas

Figure 2. A Display of Student Strategies Used to Approach the Function Machine TaskConnecting Ideas from different TasksTable 3 is another example of how creating mathematical connections supportedalgebraic reasoning. In this example, a student made connections across tasks anddifferent student strategies to reason about the pentagon table task. When this student wasworking on the square table task, she seemed to have observed a pattern between inputand output values. She showed that for input of 1, the output is 1 + 3 and for 2 squaretables, the output is 2 + 4. Although this reasoning could lead to a generalization of x + (x+ 2) = y for x tables, she did not take it further using input of 1 and 2 and could notexplain it. From her drawing, it also seems she reasoned by considering available seats oneach train. It appears she was on track to generating an explicit rule although she did not.Table 3Student’s Connection of Mathematical IdeasTaskStudent’s Representations and GeneralizationsSquaretable taskPentagon table taskProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 186