Math Misconceptions
K.CC.6-7
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
Students may look at objects and focus on their size, arrangement, or area when making comparisons between groups. More and less are relative ideas; sometimes six is more, and sometimes six is less. When related to four, six is more, but when related to seven, six is less. Whenever students compare two quantities, they are trying to determine which of 3 relationships exists between them: is greater than, is less than, or is equal to. An important component of assessing a student’s understanding is to probe for more information, proof, and justification. This questioning clarifies what the child is thinking and what strategies are being used. MISCONCEPTION: Student states, “Group 1 is less than Group 2.”
WHAT TO DO:
Group 1 is greater than Group 2.
Students possibly have misconceptions about comparing the numbers between 1 and 10 when only using written numerals because the numeral is an abstract representation of a quantity. Students must have mastery of the concrete representations of written numerals and quantities long before they would be asked to compare the written numerals alone. Many models of concrete representations can be used such as nonstandard unit lengths. Additionally, it is not in the CCSS for Kindergartners to use inequality symbols to represent comparisons. Rather, students should be using the terminology such as: “5 is less than 9”; “8 is greater than 3”; 4 is equal to 4”; or “7 is not equal to 1” in either verbal discussions or written math journals. MISCONCEPTION:
WHAT TO DO: