Math Misconceptions and Considerations HSN-RN.A.1 & 2, B.3
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
Is it rational or irrational???? Students don’t have a clear understanding of what makes a number irrational. Misconception: Due to their lack of understanding of what constitutes an irrational number, students depend on their calculators to make the determination of rationality. A student may think that because a calculator says that √ 2=1.414213562 , it is a terminating decimal, and therefore rational.
What to do: Be sure that students understand that a calculator can only give a set number of decimal places and then it rounds the number. Therefore, √ 2 ≠ 1.414213562 and this can be proven by squaring 1.414213562.
1.999999999 is close to 2, but not equal to 2. Students can conclude that the √ 2 is a non-terminating, non-repeating decimal, therefore irrational. Adding radicals is as simple as adding integers. With their limited experience with irrational numbers, students have a difficult time performing simple operations, such as addition and subtraction, on them. Misconception: With a weak foundation for understanding irrational numbers, student resort to using the rules that apply to integers.
What to do: Compare adding irrational numbers to adding variables. If they are “likeradicals� then we add their coefficients.
Students should also check the reasonableness of their answer.