Diagnosing Students' Misconceptions in Number Sense via a Web-Based Two-Tier Test

A web-based two-tier test (WTTT-NS) which combined the advantages of traditional written tests and interviews in assessing number sense was developed and applied to assess students' answers and reasons for the questions. In addition, students' major misconceptions can be detected. A total of 1,248 sixth graders in Taiwan were selected to participate in this study. Results showed that the average percentage of correct answers was about 45%. Among the students who chose correct answers, about 22.9% of them used a number sense method to solve problems. In addition, students' misconceptions are classified by content domains. The major contributions of the WTTT-NS are to (1) avoid students using written computations answering number sense questions; (2) present a whole picture of students' misconceptions and the weight of these misconceptions; (3) include the strengths of quantitative and qualitative methods; (4) identify students' "true understanding" (a correct answer based on their correct understanding instead of guessing) by exploring reasons for their choices. In sum, the WTTT-NS is a new worthwhile method to assess students' number sense competence.