This study has two parts: phase I designed activities to support all students’ learning preferences, and phase II used open-ended questions and activities based on these preferences to develop students’ mathematical critical thinking skills in polynomials at all performance levels (i.e., high-achieving, fair-achieving, and low-achieving students). This research used an embedded mixed-method design. The subjects selected were 28 out of 98 seventh graders at a boys’ junior high school in Bangkok, Thailand, who were chosen by cluster random sampling technique. The instruments, which were validated by five experts, included a questionnaire, lesson plans, exit tickets, interview protocols, and tests of critical thinking skills in polynomials. The content validity was assessed via expert judgment, and reliability was assessed by item analysis. The quality and effectiveness of the instruments were acceptable. The research results showed the following: (1) most students at all performance levels prefer activities in which they can learn from participating in classroom activities, such as games, activities with real-life applications, and activities involving listening instead of reading and writing, and (2) critical thinking skills in high-achieving and fair-achieving students were at the fair level, while those of low-achieving students were poor. Analysis was the highest critical thinking subskill among high-achieving and low-achieving students, while interpretation was the highest subskill in among fair-achieving students. Open-ended questions and activities based on students’ preferences appear to be practical for developing critical thinking skills among students of all achievement levels.

This research aims to study and classify errors in polynomials made by secondary school students. The data for error identification was collected from exercise books of 72 eighth grade students. Three types of errors were examined: careless, computational, and conceptual errors. The errors were considered according to four topics in polynomials: similar terms of monomials; addition of polynomials; subtraction of polynomials; and multiplication of polynomials. It is found that students made the highest computational errors in identifying monomials’ similarity, which accounts for 17.86%. They have the highest percentage of making computational errors in the addition and subtraction of polynomials, which account for 10.88% and 12.04%, respectively. Lastly, they have the highest percentage of making careless errors in the multiplication of polynomials, which accounts for 14.44%. Furthermore, it can be seen that the source of errors is learners’ carelessness when writing the question and its answer. In addition, the basic knowledge of computing addition, subtraction, and multiplication of integers is the most crucial factor that leads to incorrect answers. Nevertheless, most students understand the principle of polynomials, but frequently make errors on other issues.

This research studied the effectiveness of the simulation-based learning assisted with scaffolding approach to address students’ misconceptions (MCs) about projectile motion. The five MCs were related to the direction of the force acting on an object (MC1), the acceleration of an object at the top of the trajectory (MC2), the directions of velocity and acceleration during projectile motion (MC3), the time of flight of objects (MC4), and the relationship between the range of projectile motion and angle of projection (MC5). This study was a pre-experimental design using both quantitative and qualitative data. The sample comprised 35 tenth-grade Thai high school students who were chosen using the cluster sampling technique. The teaching method consisted of three steps: a briefing, simulation, and debriefing. Each step was assisted with scaffolding to guide and help the students. The MCs tests consisted of five multiple-choice questions with a four-tier diagnostic test, and the tests were used as a pre-test, end-of-class test, and end-of-topic test. Six semi-structured interview questions were used to obtain in-depth data. The results indicated that MC1, MC2, MC3, MC4, and MC5 were addressed by 11.1%, 85.7%, 57.2%, 57.2%, and 61.5%, respectively, at the end-of-topic test. Students who had MCs in the pre-test changed their understanding of the concepts in MC2, MC3, MC4, and MC5 by 57.1%, 14.3%, 28.6%, and 53.8%, respectively. None of the MC students in MC1 understood the concept at the end-of-topic test. Nevertheless, the overall results showed increased students’ understanding of all conceptions.