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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: Providing students with worked out problem solutions is a beneficial instructional technique in STEM disciplines, and studying examples that have been worked out incorrectly may be especially helpful for reducing misconceptions in students with low prior content knowledge. However, past results are inconclusive and the effects of incorrect worked examples alone or in combination with correct examples remains unclear. Objectives: We aim to address whether studying incorrect examples alone or in combination with correct examples can support the reduction of students' fraction misconceptions, operationalized as errors made with high confidence. Methods: After incorrectly solving a sampling problem, 130 students in 4th through 11th grade in the U.S. were randomly assigned to a condition in an online problem set focused on fraction equivalence. Students studied either single‐type worked examples (i.e., correct or incorrect; n = 49) or combination‐type worked examples (correct and incorrect; n = 41) or engaged in a problem‐solving control (n = 50). Results: Studying a combination of correct and incorrect worked examples was as effective as the problem‐solving control with feedback at improving fraction equivalence knowledge and reducing the rate of high‐confidence errors. Students in both the combination condition and the problem‐solving with feedback condition outperformed those who studied either correct or incorrect worked examples alone. Conclusions: Results support the inclusion of a combination of correct and incorrect worked examples when teaching students with low prior content knowledge. Studying a combination of example types within an online tutor helps to reduce misconceptions about fractions, a topic students commonly struggle with. A problem‐solving task with corrective feedback worked equally well. Lay Description: What is already known about this topic: Studying worked examples of mathematical solutions improves student learning.Incorrect examples, either alone or in combination with correct examples, are particularly effective for improving learning for students with low prior knowledge in the target content.Comparing correct and incorrect examples is also effective at improving problem‐solving but this effect may be specific to those with high prior knowledge.Still unknown are the impacts of these different combinations of examples on misconceptions in particular. What this paper adds: We show that studying a combination of correct and incorrect examples reduces math misconceptions.Problem‐solving with corrective feedback within an online tutor also has this effect. Implications for practice and/or policy: Using a combination of example types will help reduce students' misconceptions about fractions. [ABSTRACT FROM AUTHOR]

Background: Eye movement modelling examples (EMME) are demonstrations in which learners' not only see a model's (e.g., a teacher's) task performance on a computer screen (as in regular video examples) but also the model's eye movements (represented as moving coloured dots overlaid on the screen). Thereby EMME help guide learners' attention towards the relevant information and can model cognitive strategies which are otherwise unobservable for learners. Objectives: This study investigated whether EMME can help to learn deductive reasoning strategies and how the presence/absence of a teacher's verbal explanation affects learning from EMME. Methods: Secondary education students (N = 137) were randomly assigned to study video examples under one of four conditions in a 2 (EMME: yes/no) x 2 (verbal explanations: yes/no) between‐subjects design. Results and Conclusions: Results revealed only a beneficial effect of the presence of verbal explanations on performance on the practice problems, but no pretest‐to‐posttest learning gains. Implications: Seeing the teacher's eye movements does not appear to enhance learning of deductive reasoning. The presence/absence of the teacher's verbal explanation does not seem to affect learning deductive reasoning. Lay Description: What is currently known about the subject matter?: Eye movement modelling examples (EMME) are demonstrations in which learners not only see a teacher's task execution on a computer screen (as in video examples) but also the teacher's eye movements.The eye movements in EMME were visualized as moving coloured dots overlaid on the screen recording.EMME help direct attention to relevant information and enhance learning; it is not yet known if this also applies to reasoning problems.It is unknown if and how presence/absence of a teacher's verbal explanation affects learning from EMME. What our paper adds to this?: Secondary education students watched EMME or regular video examples with/without a teacher's verbal explanation.The examples demonstrated how to solve deductive reasoning problems (adapted version of the Mastermind game).Performance and learning gains were examined and revealed no differences between conditions. The implications of study findings for practitioners: Seeing the teacher's eye movements does not appear to enhance learning of deductive reasoning.The presence/absence of the teacher's verbal explanation does not seem to affect learning deductive reasoning. [ABSTRACT FROM AUTHOR]

With the advent of mobile technologies, well‐designed fraction apps can be used to help children gain fraction knowledge, a challenging topic for both teachers and students. The present pilot study adopted a quasi‐experimental design to investigate whether children can learn fraction concepts equally well if half of the lesson time (20 min) is replaced with game‐based learning. Keeping the total lesson time (40 min) identical, the control group (N = 33) received traditional instruction, and the experimental group (N = 32) was presented with a blended learning approach spending half of the class time (20 min) playing tablet‐based fraction games, where each of the learners had their own tablet. The results suggested that in the posttest, the experimental group achieved similar learning gains to the control group and appear to have achieved better performance in the transfer test than the control group. This paper also discusses the efficiency of game‐based learning, the mechanism of how fraction games might enhance learning, and the potential of integrating game‐based learning in educational settings. Lay Description: What is already known about this topicAs a significant mathematical concept in daily life, fractions are crucial for later success in math learning.As a promising new technology, educational games show a great potential for improving learning.Well‐designed fraction apps can be used to help children gain fraction knowledge.What this paper addsGame‐based fraction learning can be combined with formal learning in school education.Game‐based fraction learning might provide a more efficient approach to increasing students' conceptual knowledge of fractions.The result showed that the experimental group achieved a similar cognitive level as the control group although they spent half of the time playing a game, suggesting that children can gain knowledge from the experiences of playing games.What are the implications for practice and/or policyThe result suggests that the proper use of educational games in teaching fractions can make learning more efficient.Further research needs to be done to determine whether the fraction understanding gained through playing these games will have an impact on students' future learning of more complicated fraction concepts. [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]

A promising method to support game‐based learning is to facilitate learners' externalization of cognitive and metacognitive processes. Externalizing Problem Representation (EPR) refers to a cognitive behaviour in which a learner constructs her own representations overtly. The purpose of this study is to investigate whether learning supports promoting EPR enhance qualitative understanding and quantitative proficiency in ratios and proportional relationships in a learning game (i.e., E‐Rebuild) context. Specifically, this study investigated the effects of representation format in problem representation on qualitative understanding and quantitative proficiency in a learning game context. The results of this study indicate that (a) symbolic learning supports better facilitate comprehension of math concepts and their relations than iconic learning supports in video game contexts, (b) symbolic learning supports better facilitate players' reflection for implicit understanding and promote their math problem‐solving skills, (c) participants in the symbolic learning support group increased significantly in qualitative understanding but not in quantitative proficiency after gameplay, and (d) participants in the iconic learning support group experienced significant growth in quantitative proficiency but not in qualitative understanding after gameplay. Lay Description: What is already known about this topic: Video games potentially facilitate implicit qualitative understanding more than quantitative knowledge test performance.Educational game designers lack a good understanding of the design and development of effective learning supports in educational games. What this paper adds: Symbolic learning supports for problem representation better facilitate comprehension of math concepts and their relations than iconic learning supports in video game contexts.Participants experienced significant growth in quantitative proficiency after they processed the iconic in‐game learning supports in game‐based math tasks.Participants' qualitative understanding in the symbolic learning support group increased significantly after playing E‐Rebuild‐based math game task. Implications for practice and/or policy: This study informs scholars and designers of game‐based learning about designing learning support and its properties in video game contexts: Learning support design to promote math problem representation across problem translation and problem integration.This study provides design principles for learning supports in math learning game; symbolic learning supports facilitate qualitative understanding whereas iconic learning supports facilitate quantitative proficiency in math learning game. [ABSTRACT FROM AUTHOR]