Math Misconceptions and Considerations HSA-CED.A.2 & 3
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
It doesn’t matter how the graph is labeled Students believe that the labels and scales on a graph are not important and can be assumed by the reader. Misconception: When students do not label their graphs properly, the information on the graph can be misinterpreted or unidentifiable. For example, on the graph below, without knowing the scale of the x or y-axis you cannot determine the point of intersection.
What to do: Show students examples of proper and improper labeling of graphs. Have a class discussion on how labeling a graph clears up any misconceptions that may occur while interpreting the information in the graph.
The graph must show all four quadrants When students first begin graphing they are accustomed to graphing on a coordinate plane in which all four quadrants are visible.
Misconception: When students interpret the problem over all real numbers, they may get answers that do not make sense in the context of the problem. In the example below, the student has graphed the inequalities correctly but may misinterpret the answer. It is possible, that a student would consider (-3, 4) and (8, -3) as possible solutions to the problem. However, if the x and y variables represent production of wheat and barley, then these are not viable solutions. It is not possible to produce negative acres of a crop.
What to do: Before graphing a problem, have a discussion on the limitations and natural constraints of the problem. Many real-world problems will have a natural constraint of positive integers. Have students explain what the natural constraints and limitations represent in the context of the problem.
Oops, which variable went with which solution?! Taking word problems and interpreting them as math equations and/or inequalities is a skill that requires students to organize the given information.
Misconception: At the conclusion of a problem, students should be able to interpret their answer in the context of the problem. When they do not keep track of their variable assignments, they may have difficulty doing this.
What to do: Organizing the information from a problem is a good strategy to help keep track of which variable is assigned to which value. Introducing students to a variety of methods for organizing their work and then allowing them to choose the method that works best for them is a good strategy. Highlighting important information and organizing information in a table are two possible strategies to explore with students.