REASONING ABOUT QUANTITIES INVOLVED IN RATE
OF CHANGE AS VARYING SIMULTANEOUSLY AND
INDEPENDENTLY
Abstract
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REASONING ABOUT QUANTITIES IN RATE OF CHANGE
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Quantities that Change Together
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Covariational Reasoning about Changing Quantities
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Drawing Parallels between Rate-related Reasoning Ratio-related Reasoning
REASONING ABOUT QUANTITIES IN RATE OF CHANGE
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REASONING ABOUT QUANTITIES IN RATE OF CHANGE
Drawing on Students’ Work on a Mathematical Task to Investigate Students’
Reasoning: Background Regarding Methods and Analysis
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Figure 1.
REASONING ABOUT QUANTITIES IN RATE OF CHANGE
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Figure 2.
Students’ Association of Amounts of Change
Covarying Quantities Involved in Rate of Change
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REASONING ABOUT QUANTITIES IN RATE OF CHANGE
Sketching a Graph that Related Volume and Height for a Narrow Bottle: Austin
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REASONING ABOUT QUANTITIES IN RATE OF CHANGE
Figure 3.
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REASONING ABOUT QUANTITIES IN RATE OF CHANGE
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Sketching a Bottle that a Given Graph Could Represent: Mason
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This area.
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REASONING ABOUT QUANTITIES IN RATE OF CHANGE
Figure 4.
REASONING ABOUT QUANTITIES IN RATE OF CHANGE
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Sketching a Graph that Related Volume and Height for Bottles of Varying Width: Jacob
REASONING ABOUT QUANTITIES IN RATE OF CHANGE
here.
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REASONING ABOUT QUANTITIES IN RATE OF CHANGE
Figure 5.
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REASONING ABOUT QUANTITIES IN RATE OF CHANGE
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Reasoning about Quantities Involved in Rate of Change
as Varying Simultaneously and Independently
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REASONING ABOUT QUANTITIES IN RATE OF CHANGE
Concluding Remarks
References
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REASONING ABOUT QUANTITIES IN RATE OF CHANGE
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