Analysis of student conception of exponentiation using three-tier test

This study aimed to (1) describe the students’ conception of grade X in exponentiation and (2) describe the misconceptions experienced by students of grade X in exponentiation. Subjects in this study were the students of grade X at one vocational school in West Kalimantan. The instrument used in this study was a three-tier test, a test consists of three levels. The first level is a multiple-choice question on the concept of exponents, the second level is a matter of reasoning about the reason for the answer from the first step, and the third level questions the students’ confidence on their answers. The results of this study indicate that 69.71% of students comprehended the concept, 14.71% of students miscomprehended, 0.59% of students miscomprehended (false positive) and 0.88% miscomprehended (false negative), 7.65% of students did not comprehend the concept, and 6.45% of students were identified as answering correctly because of luck or answering without confident. The most common misconception experienced by students in learning exponentiation was they did not comprehend the properties of exponents which lead them making mistakes in using exponential properties to simplify exponential equations involving the operation of addition, subtraction, multiplication, division, and rank. Another misconception that also occurred was students’ miscomprehension of the definition of negative exponential.