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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]

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]

Task solving processes and changes in these processes have long been expected to provide valuable information about children's performance in school. This article used electronic tangibles (concrete materials that can be physically manipulated) and a dynamic testing format (pretest, training, and posttest) to investigate children's task solving processes and changes in these processes as a result of training. We also evaluated the value of process information for the prediction of school results. Participants were N = 253 children with a mean age of 7.8 years. Half of them received a graduated prompts training; the other half received repeated practice only. Three process measures were used: grouping behaviour, verbalized strategies, and completion time. Different measures showed different effects of training, with verbalized strategies showing the largest difference on the posttest between trained and untrained children. Although process measures were related to performance on our dynamic task and to math and reading performance in school, the amount of help provided during training provided the most predictive value to school results. We concluded that children's task solving processes provide valuable information, but the interpretation requires more research. Lay Description: What is already known about this topic: Dynamic testing provides information on a child's ability to learn.Solving process information provides indications for intervention.Computerized testing can be of great help in recording process information. What this paper adds: Process‐oriented dynamic testing provides explanatory information beyond traditional tests.The use of a tangible user interface (TUI) console uncovers valuable information on solving processes.Process measures are related to series completion performance, math, and reading.Need for instruction is the best predictor of math and reading ability.Implications for practice and/or policy: A framework for interpreting process information is necessary in dynamic testing.Process‐oriented dynamic testing may be more suitable to inform education.TUIs provide a more natural testing environment. [ABSTRACT FROM AUTHOR]