Fisher randomization tests for Neyman's null hypothesis of no average treatment effects are considered in a finite population setting associated with completely randomized experiments with more than two treatments. The consequences of using the F statistic to conduct such a test are examined both theoretically and computationally, and it is argued…

The cognitive development of prospective teacher needs to be taken into estimate so that proofs are presented in forms that are potentially meaningful for them. This requires educators and mathematicians to rethink consider the use of types of proof related to the logical thinking improvement of the singular. The purpose of the study is to…

The following report describes an assessment instrument called the Mathematics Performance and Cognition (MPAC) interview. The MPAC interview was designed to measure two outcomes of interest. It was designed to measure first and second graders' mathematics achievement in number, operations, and equality, and it was also designed to gather…

This report provides an overview of the development, implementation, and psychometric properties of a student mathematics interview designed to assess first- and second-grade student achievement and thinking processes. The student interview was conducted with 622 first- or second-grade students in 22 schools located in two public school districts…

The purposes of this study are to investigate whether pre-service middle school mathematics teachers evaluate discussions in the cases regarding proof by contradiction correctly, to what extent they explain their correct evaluations by referring to proof by contradiction, and the reasons of their misinterpretations of discussions in the cases…

By considering the example of proving the triangle postulate, this study aimed to explore Hong Kong preservice and novice teachers' knowledge competencies and their beliefs about preformal and formal proofs. The findings revealed that such teachers are not proficient in using preformal proofs and do not realize that preformal proofs are a useful…

This paper deals with the competence of Cultural (epistemological, historical and anthropological) Analysis of the Content (CAC), which is important for teachers' awareness and autonomy when dealing with educational choices in a changing cultural and institutional context. We report on an 18-hour intervention in a teacher education course at the…

Conventional methods for mediation analysis generate biased results when the mediator-outcome relationship depends on the treatment condition. This article shows how the ratio-of-mediator-probability weighting (RMPW) method can be used to decompose total effects into natural direct and indirect effects in the presence of treatment-by-mediator…

Conventional methods for mediation analysis generate biased results when the mediator--outcome relationship depends on the treatment condition. This article shows how the ratio-of-mediator-probability weighting (RMPW) method can be used to decompose total effects into natural direct and indirect effects in the presence of treatment-by-mediator…

This paper presents two studies of an intervention designed to help undergraduates comprehend mathematical proofs. The intervention used multimedia resources that presented proofs with audio commentary and visual animations designed to focus attention on logical relationships. In study 1, students studied an e-Proof or a standard written proof and…

The relationship between mathematical creativity (MC) and mathematical problem-solving performance (MP) has often been studied but the causal relation between these two constructs has yet to be clearly reported. The main purpose of this study was to define the causal relationship between MC and MP. Data from a representative sample of 480…

Recent research on the scaffolding of instruction has widened the use of the term to include forms of support for learners provided by, amongst other things, artefacts and computer-based learning environments. This paper tackles the important and under-researched issue of how mathematics lessons in junior high schools can be designed to scaffold…

This paper concerns communities of learners and teachers that are formed, develop and interact in university mathematics environments through the theoretical lens of "Communities of Practice." From this perspective, learning is described as a process of participation and reification in a community in which individuals belong and form…

This journal article discusses Advanced Mathematical Thinking (AMT) and how to enhance it. AMT is ability in representing, abstracting, creative thinking, and mathematical proving. The importance of AMT ability development in accord with government expectation who realize about the importance of mathematical competency mastery for student's life.…

Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…