Math Misconceptions
K.CC.4-5
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
When the number of objects remains the same, regardless of their arrangement, it is referred to as conservation of number. Before students have gained a sense of conservation of number, they may believe the number of objects can increase or decrease when they are moved or rearranged. MISCONCEPTION:
WHAT TO DO:
”Did you add any?” “Did you take away any?” “How many objects do you have?” “How do you know?”
Students may need to recount the objects if one more is added to the group. 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 confidence and accuracy before moving on to larger numbers. MISCONCEPTION:
You counted 14 red objects. How many do I have if I have one more? (Student recounts the array.)
WHAT TO DO:
You counted 4 red objects. How many do I have if I have one more? (Student says 5.)
“How do you know?”
Students can easily count the same object more than once in any arrangement, most frequently when objects are scattered. When counting objects in this type of arrangement, students need a method for keeping the start number in mind. If not, they may continue to count and not know where to stop. Reinforce the understanding of cardinality by always asking, "How many?" MISCONCEPTION:
WHAT TO DO:
Some students might think that the count word used to tag an item is permanently connected to that item. So when the item is used again for counting and should be connected with a different count word, the student uses the original count word. For example, a student counts objects: triangle, square, circle and rectangle with the count words: one, two, three, four. If these items are rearranged as rectangle, triangle, circle and square, and counted, the student says these count words: four, one, three, two. Move objects around to show that a number name does not need to be permanently connected to the counted object. MISCONCEPTION: First, the teacher shows the shapes in a specific order: triangle, square, circle, & rectangle. Then the teacher rearranges the objects, and the student counts as shown.
WHAT TO DO: