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Background: Game‐based learning can frame problem‐solving as a sense‐making experience with domain‐specific tasks for school students. However, multiple challenges arise when trying to support learners in such a complex, problem‐oriented learning environment. Objectives and Methods: With an architecture‐themed mathematics learning game, we conducted two mixed‐method studies to explore the impact and design of game‐based mathematical experience on the math problem‐solving performance of middle school students. Results and Conclusions: The study findings suggested a positive impact of game‐based math experience on math problem‐solving for middle school students. Problematization‐oriented game‐based math tasks with structuring features enhanced students' reasoning with problems and channelled it to doing mathematics. Takeaways: The current research findings support the initiative to frame learning as a sense‐making experience with domain‐specific tasks and inform the design of game‐based mathematical experience and learning support. Lay Description: What is already known about this topic: Realistic mathematical practices frame learning as a sense‐making experience.Challenges arise when involving learners in realistic mathematical experiences driven by domain‐specific tasks. What this paper adds: Game‐based simulation of math tasks framed learning as sense‐making experience.Game‐based math experiencing promoted math contextual problem‐solving performance.Structuring features enhanced problematized experiencing with math tasks. Implications for practice and/or policy: Teachers can integrate and facilitate game‐based math experiencing in class.Efforts should be made to make game‐based math tasks meaningful for students. [ABSTRACT FROM AUTHOR]

Background Study: The effects of the flipped classroom (FC) on students' academic performance remain ambiguous, and the use of pre‐class videos may be one of the main factors hindering students' progress. A software package called GeoGebra has been proposed as a substitute for pre‐class videos to aid students' learning. Objective: This study investigates the effect of the FC using GeoGebra (FCG) on mathematical performance and memory among senior secondary students. Methods: One hundred and sixty students of a senior high school in China were selected. A quasi‐experimental design was implemented in which the classes were split into the intervention group (FCG), control group A (FCV) and control group B (TL) by random assignment. Pretest, Post‐test 1 and Post‐test 2 were introduced. Results and Conclusion: The results indicate that both the FCG and the FC with pre‐class videos (FCV) were more effective than traditional lectures in enhancing students' academic test scores, and that the effect of the FCG was comparable to its video counterpart, F(2, 136) = 3.752, ρ = 0.026, η2 = 0.052. Although their effects were similar, the qualitative results revealed some hidden benefits associated with the replacement of pre‐class video with GeoGebra. Furthermore, although they were equally effective in promoting students' performance in the short‐term, the long‐term effects on academic performance of both forms of FC were non‐significant when compared with traditional lectures. Lay Description: What is already known about this topic: Flipped classroom is an effective strategy in teaching mathematics.Among those challenges, video may be one of the main factors hindering the effect of flipped classroom. What this paper adds: GeoGebra could be an effective alternative to video.Effect between the flipped classroom using GeoGebra and the flipped classroom using video were similar.Both the flipped classroom with GeoGebra and the flipped classroom with videos were more effective than traditional lectures. Implications for practice and/or policy: Students' short‐term performance could be enhanced by visualisation provided by flipped classroom.To enhance students' long‐term performance, an appropriate amount of homework is suggested. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate the effect of using dynamic geometry software (GeoGebra) on the eighth‐grade students' conceptual understanding and the retention of learning regarding linear equations and slope. In this study, a quasi‐experimental design with pre‐test, post‐test and delayed post‐test was employed. This study was conducted with 52 eighth‐grade Turkish students (experimental group, n = 25; control group, n = 27). While GeoGebra software‐supported instruction was carried out in the experimental group, textbook‐based direct instruction was continued in the control group. Data were collected with the conceptual understanding test (CUT) which consists of 38 questions including open‐ended, multiple choice and fill in the blanks. CUT was applied to the experimental and control groups as a pre‐test and post‐test at both the beginning and the end of the instruction, respectively. Seven weeks after the instruction, CUT was applied to both groups as a retention test. Data were analysed through SPSS 17.0 statistical software by using a t‐test and ANCOVA test. It was indicated in the study results that GeoGebra software‐supported instruction for eighth‐grade students regarding linear equations and slope did significantly improve both their conceptual understanding and retention of learning in comparison to textbook‐based direct instruction. Lay Description: What is already known about this topic?: The subject of functions and their graphs are the basis of many mathematical concepts and subjects such as logarithm, limit, derivative and integral.It is indicated in many studies that middle‐grade students have some misconceptions and difficulties in learning the concept of a straight line and slope.It was determined in previous studies conducted at different grade level that using dynamic geometry software (DGS) increases students' mathematics achievement according to traditional instruction.There is a need for research investigating the effect of using GeoGebra software on eighth grade students' conceptual understanding and retention of learning regarding linear equations and slope. What this paper adds?: A quasi‐experimental design with pre‐test, post‐test and delayed post‐test was conducted.Using GeoGebra software had positive effects on eighth‐grade students' conceptual understanding regarding linear equations and slope.The learning environment with GeoGebra software increased the retention of learning. The implications of study findings for practitioners: This research provided evidence regarding the effects of using GeoGebra software on eighth‐grade students' conceptual understanding and retention of learning in mathematics.In future studies, the long‐term effects of GeoGebra on other mathematics topics and other learning outcomes within similar settings should be examined. [ABSTRACT FROM AUTHOR]

The overarching goal of this research project is to develop a set of theoretical and empirical based design principles to support student engagement in flipped mathematics learning. We used a design‐based research approach in which a series of studies was conducted in a secondary school. First, an analysis of practical problems was performed via exploratory studies (Studies 1A and 1B), randomized experiments (Studies 2A and 2B), and a literature review (Study 3). Second, a basic flipped lesson prototype was developed based on our empirical findings and relevant theoretical work of student engagement and self‐determination theory. Third, we refined and evaluated our practice with two empirical studies (Studies 4 and 5). Finally, we reflected on each stage of our research project to produce a set of design principles for future practice. This study thus contributes to our knowledge of methods to support student engagement in flipped mathematics learning. Lay Description: What is already known about this topic: Flipped learning can increase student achievement in mathematics education.After flipping, studies reported non‐significant or even negative results in terms of student engagement.Little work has been done to support student engagement in flipped learning. What this paper adds: This study investigated methods to support student engagement in flipped mathematics learning.A 2‐year design‐based research was conducted consisting of a series of five studies.Theoretical work of student engagement and self‐determination theory were drawn. Implications for practice and/or policy: The use of group competitions increased student engagement in flipped mathematics learning.Peer interaction inside the classroom fostered students' cognitive engagement.Design principles are proposed to support student engagement in future practice.The principles cover five major instructional activities of flipped learning. [ABSTRACT FROM AUTHOR]

This study investigates the effect of E‐learning (EL), blended learning (BL) and flipped learning (FL) approaches on the mathematics achievement, self‐regulation and mathematics self‐efficacy. Participants consist of 163 first‐year students attending an associate degree program (a 2‐year program) of a state university. The EL, BL and FL settings in the research were designed based on Merrill's 'First Principles of Instruction Design Theory'. In the research in which a quasi‐experimental pre‐test–post‐test research design was used, the data were obtained by means of mathematics achievement test, self‐regulation and self‐efficacy questionnaires. The experimental results showed that the mathematics achievement post‐test scores of FL students were significantly higher than those of the students of EL and BL. No significant difference was found between BL and EL settings. In addition, FL students showed significantly higher self‐regulation and mathematics self‐efficacy than the other groups' students. According to these results, it can be said that the usage of FL approach in mathematics courses has a positive effect on the learning process of students. It is expected that the findings will be helpful in the future design and implementation of mathematics courses at vocational colleges. Lay Description: What is already known about this topic?: The flipped learning approach has the potential to develop mathematics teachingThe ability of student's own learning regulation becomes one of the key concepts of flipped learning setting.Little is known about the design and implementation of flipped learning settings in mathematics courses. What this paper adds: This study investigates the effect of E‐Learning (EL), Blended Learning (BL) and Flipped Learning (FL) approaches on the mathematics achievement, self‐regulation and mathematics self‐efficacy.The EL, BL and FL settings in the research were designed based on Merrill's 'First Principles of Instruction Design Theory'.The usage of FL approach, developed in line with Merrill's First Principles of Instruction design theory, improves the mathematics achievement, self‐regulation and mathematics self‐efficacy levels of students. Implications for practice and/or policy: This research provided evidences for effects of Merrill's "First Principles of Instruction Design Theory" on online learners.The FL approach, developed in line with Merrill's First Principles of Instruction design theory, may serve as a reference for improving students' learning performance.It is expected that the findings will be helpful in the future design and implementation of mathematics courses at vocational colleges. [ABSTRACT FROM AUTHOR]