Math Misconceptions and Considerations HSA-CED.A.1
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
Improper use of the equal sign It is a good idea to require students to develop the habit of always properly labeling their variables using short descriptions. Misconception: After reading a problem, students will begin compiling their known and unknown information. When doing so they will write statements like:
Such statements do not make sense – printers aren’t numbers. What to do: Modeling proper use of the equal sign is necessary. Also, explain to the students how the equal sign is being misused in the example above. An alternative, proper way to label values would be:
We got different equations?? Because there are a number of ways to setup a correct equation, students will inevitably create several solutions paths. Misconception: With the two equations below, students will arrive at different answers. This will contribute to them believing their work is wrong. In actuality, both answers are correct but each student is finding a different unknown in the problem.
What to do: Take the time to explore the different solution paths with the class to validate the fact that both equations and solutions are correct. Real world application problems Whenever possible, students should be exposed to problems that contain relevant applications. Misconception: Students may believe that the equations of linear, quadratic, and other functions are abstract and exist only “in a math book,” without seeing the usefulness of these functions as modeling real-world phenomena. What to do: Make constant connections in the classroom between the topic at hand and a real-world application. This should be done throughout the year and will help enforce the realization that algebraic expressions, variables, equations, etc., represent actual values. “Translating” the equation/inequality incorrectly Students will likely make mistakes when they begin “translating” descriptions into algebraic equations. Misconception: Students misinterpret the description and the result is an algebraic equation that doe not make sense.
What to do: Students need to be aware of the context of a problem, multiple meanings of keywords, and the validity of the resulting equation/inequality. Students should always be encouraged to question the reasonableness of an answer and be prepared to justify their own thought processes.