Math Misconceptions and Considerations HSF-IF.B.4, 5, 6
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
Calculating rate of change incorrectly Students learned about slope in middle school and were likely introduced to it as the ratio of rise over run. When finding slope using a graph, the student’s first instinct it to count the squares on the graph paper and then write a ratio for the rate of change. The problem arises when the scale of the x and y axes are not the same. Misconception: In this example, the student counted the grid lines to find the change in the y-values and the change in the x-values. Another possible error would be that the student 5 writes the slope as . 9
What to do: To prevent this error, have students look at the scale of the axes before beginning. Also, when students determine the rate of change, have them analyze it in the context of the problem. Remind students that the slope is the change in y over the change in x.
Obtaining an incorrect domain Students get in the habit of just applying the rules they have learned for finding the domain and forget to interpret their answer in terms of the problem. The result is a domain that does not make sense in the context of the problem. Misconception:
Students may realize that the function is linear and simply look at the problem from a formulaic point of view and say that the domain is all real numbers. What to do:
Discuss with the students why a domain of all real numbers in the context of the problem does not make sense. Students should approach each problem individually instead of employing a “one size fits all� method to every domain situation.