Math Misconceptions and Considerations HSA-SSE.A.1 & 2
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
Understanding the use of variables in mathematics Students already understand that variables can be used for labels of objects, but they have difficulty understanding they can also be used for values of unknown quantities. Students may believe that the use of variables in algebraic expressions is only the abstract manipulation of symbols. Misconception:
In this example, the student was asked to combine like terms. Many times teachers will explain to students to think of “a� as apples so they remember how to combine like terms. The students will remember how to combine like terms, but when they are asked to interpret the meaning of the expression, they do not understand that variables can also be used to represent unknown numbers. What to do:
To prevent this error, make sure you specifically define what the variables represent in the problem. For example if you are solving a problem with nickels and dimes, d is the unknown number of dimes and n is the unknown number of nickels. You can also use more real-world examples to help combat this misconception.
Factoring Students may believe that an expression cannot be factored because they do not recognize the form. Misconception: Students may think expressions like the following cannot be factored. x 2−49 3 2 12 a −9 a +20a −15 What to do: Encourage students to re-write polynomials into different forms. Students will see different number patterns depending on which math facts they know. This can help with the development of factoring patterns. At first, students may need help reorganizing the terms until they recognize a pattern. Here are some ways
2
x −49
and 12 a 3−9 a 2 +20a −15 can be re-written.