Math Misconceptions

K.OA.1-5

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

make instructional decisions to suit all students’ needs.

Misconceptions with understanding addition and subtraction may be linked to problems with cardinality. Cardinality is knowing that the number word said tells the quantity you have and that the number you end on when counting in sequence represents the entire amount counted. Students need a firm grasp of the counting sequence in order to fluidly find one more without recounting. Have students work with small numbers for an extended period of time to build their understanding and accuracy before moving on to larger numbers. MISCONCEPTION:

WHAT TO DO:

“How do you know?”

You  counted  9  red  objects.    How  many  do  I  have  if  I  add  one  more?  (Student  recounts  the  array.)  

You  counted  4  red  objects.    How  many  do  I  have  if  I  add  one  more?  (Student  says  5.)  

Students may make errors in their understanding of addition and subtraction when they move too quickly to abstract representations, which are numbers and symbols. As students use methods to represent addition and subtraction and solve word problems, they should always use some sort of counters that allow for direct modeling. Any physical materials can be selected (by the teacher and by the students) to aid with problem solving. After continued experiences with concrete manipulatives, students should also use drawings or pictorial representations. These drawings do not need specific details, and digits may often be shown within the drawings. Abstract expressions and equations can be shown and modeled by the teacher to show connections, and over time, students will write abstract representations along with their drawings and concrete materials to make their own connections. MISCONCEPTION:

WHAT TO DO:

Concrete, pictorial, and abstract representations

In Kindergarten, students represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations. 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 developmentally ready – meaning they have a firm grasp of addition and subtraction with concrete materials. Repeated practice with composing (joining smaller numbers to make larger numbers) 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 and take from. Without the process of acting out situations, using objects, or creating drawings, showing the equations may be too advanced and not developmentally appropriate for a student. MISCONCEPTION:

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.