The aim of this qualitative case study is to investigate prospective mathematics teachers’ subject matter knowledge of the underlying concepts of standard and nonstandard algorithms used to solve the problems with whole numbers. Twenty three prospective mathematics teachers enrolled in the Elementary Mathematics Education Program of one of the most successful universities in Turkey were the participants of the study. The data was collected through four tasks containing basic algorithms. More specifically, the Ones Task assessed participants’ understanding of the underlying place value concepts of standard algorithms. The Andrew Task and the Doubling Task required participants to conceptualize and interpret nonstandard strategies. In the Division Task, participants were expected to provide in-depth explanation for the difference between multiplication and division and between partitive division and measurement division. The content analysis method was used to analyze the data. The results of the study revealed that more than half of the prospective mathematics teachers had knowledge about the place value of 1 in addition and subtraction, and also multiplication. However, most of the prospective teachers could not explain the underlying principle and the meaning of the nonstandard algorithm in subtraction. Similar to their knowledge on subtraction, prospective teachers’ knowledge on division was limited.

This study investigated the development of problem-solving strategies demonstrated by 42 elementary pre-service mathematics teachers in problem-solving mathematics classes. The study used a mixed methods approach of quantitative and qualitative research by analyzing the collected data.. The quantitative portion calculates the frequencies and percentage of the participants’ responses to the problems posed in three different phases of the intervention: before, during, and after receiving the mathematics lessons. The qualitative approach was used for in-depth investigation to describe various mathematical problem-solving strategies demonstrated by participants across the three different research phases. Findings of the study indicated a limited number of problem-solving strategies present during the first phase of research such as “use arithmetic operation strategy,” and “make a drawing strategy,”. During the implementation of the problem-solving lessons and classroom discussion, the participants began to develop more strategies such as  “use logical reasoning,” “solve a simpler problem,” “guess and check,” “organize data in a table or a list,” “look for a pattern,” “work backwards,” and “solve an equation,”. However, the research findings nonetheless revealed participants’ weakness in applying the variety of skills required for success in problem solving, such as interpreting information, mathematical working, and logical thinking. Results also demonstrated a limited and incorrect use of mathematical terminology, as well as a lack of problem comprehension. The discussion of the study addresses different features and issues related to mathematical problem-solving strategies. In light of its findings, this study presents recommendations and suggestions for the future development of pre-service teachers’ problem-solving strategies.

This study was to support the understanding of the set structure, binary operations, and their properties as a prerequisite of group theory material categorized as 9 structure senses. This study aimed at investigating the process of students’ structure sense in recognizing the structure of mathematical properties or objects as a prerequisite of group theory material. A task-based case study by exploring 9 categories of structure senses through three integrated process frameworks in the questionnaire was employed in this study. It involved 26 students who had obtained a prerequisite of group theory material and would take abstract algebra course. The choice of subjects was determined based on the results of the questionnaire, in which it identifies the type of structure sense processes. There were 6 out of 26 subjects were chosen. The 6 subjects consisted of 2 subjects from the first path process, 2 subjects from the second path process, and 2 subjects from the third path process. Then, the 6 subjects were interviewed. The choice of 2 subjects for each path process was because it used a fixed comparison theory. Then, the data were validated by using triangulation methods by comparing the students’ work on assignments and questionnaires as well as audio recordings of interviews. The results show the tendency of the process of structure sense was more dominated by students from the second type of path process, in which the subjects still depend on the well-known structure of the properties or mathematical objects in the form of sample questions. The subjects were unable to understand definitions in order to construct structures of properties or mathematical objects.

This meta-analysis study investigates the effect of computer-based tests on motivation. The random effect model is the basis for calculating the summary effect, and it is found that the 30 articles obtained through the PRISMA method, which consist of four parts, namely identification, screening, eligibility, and included, can be generalized. Data analysis was performed using R studio and OpenMEE. Based on the research results, the p-value <.05 was obtained, so it was concluded that using a computer-based test significantly affected motivation. In the moderator analysis, it was found that computer-based tests were most effective for intrinsic motivation for the motivation variable, university students for the participants variable, and the country of Iran for the region variable. Evaluation of publication bias using the funnel plot and regression method shows no publication bias, proving that the 30 articles analyzed represent all existing studies on computer-based tests.