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Figure 2: Arrow diagram set 1

Figure 4: Arrow diagram set 3

Several patterns are more obvious than others in this inquiry, and they quickly emerge—especially if the arrow diagrams conformed to the proposed structure (i.e., two parallel axes vertically oriented, with the same scale, and 0’ s aligned). Observe sev eral groups of arrow diagrams, drawn by me to de pict the types of groupings that a group of learners might have organized from one of my courses; these figures show groups of sorted arrow dia grams, but do not include all groups of diagrams that might be created during a single class. Before reading on, examine Figures 2, 3, and 4 to see what type of conjectures you can make about patterns. Examining the set of arrow diagrams in Figure 2, some reasonable conjectures might be: 1) functions with negative slopes, where the rays intersect be tween the axes; 2) functions with positive slopes, where the rays do not intersect; and 3) functions with zero slope, the rays intersect on the y - axis. An extension one might reach even without an arrow diagram based on the previous conjectures is that

Figure 3: Arrow diagram set 2

Virginia Mathematics Teacher vol. 47, no. 1

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