Math Misconceptions

1.OA.1-2

Look closely at errors in students’ work (formative assessment) to help you reflect and

make instructional decisions to suit all students’ needs.

Students begin to formulate misconceptions and generalizations about addition and subtraction, particularly when they associate certain words or phrases with only one particular operation. For example, students may incorrectly conclude that when they are working with subtraction, they are always “taking away” something. Teachers more often relate addition to “joining” and subtraction to “taking away” and may or may not realize that there are other models and situations for each operation. Students need to have experiences with different types of addition and subtraction word problems that model different situations. Refer to the CCSS common addition and subtraction situations table (page 4 sidebar of this module and page 88 of the CCSS for Mathematics) for examples of problem variations and footnote explanations. MISCONCEPTION:

“There are 5 total apples on the table. 3 are red and some are green. How many apples are green?”

WHAT TO DO:

This is a situational example of “addend unknown”.

As students begin to write their own equations, they may write the symbols and numbers out of order, as they do not have a solid understanding of how each symbol contributes to the meaning of the equation. Writing an expression or equation is an abstract representation of math, and should only occur when students are developmental ready – meaning they have a firm grasp of addition and subtraction first with concrete materials, then moving to pictorial, and on to the abstract equation. Repeated practice with composing and decomposing a number into its smaller numbers in many different ways is the key to students having a firm grasp of what it really means to put together, add to, take apart, take from, and compare numbers. Without the process of acting out situations, using objects, or creating drawings, showing the equations is meaningless to a student. MISCONCEPTION:

Susan had 5 flowers. She gave one to her friend. How many flowers does she have now?

Student says, “I had 5. I took away 1. Now I have 4.” Student records: 5 = 4 - 1

WHAT TO DO:

Go back to including context, objects, and drawings to build an understanding of the action in the situation to connect to equations.