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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]

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]

This study proposes a computer‐assisted system with a design based on Polya's problem‐solving model. The system is designed to help average and low‐achieving second graders in mathematics with word‐based addition and subtraction questions. The emphasis of using the specific model was on dividing the problem‐solving procedure into stages and the concentration on the stages that are problematic for students. Specifically, we compared mathematical word problem‐solving performance and computational skills of students who utilized the computer‐assisted system with students who employed general strategy instruction. Participants consisted of 52 second‐grade students randomly assigned to treatment conditions. Students were pretested and posttested with mathematical problem‐solving and computation tests, and repeated measures of their progress with respect to word problem solving were registered. The results showed there was a significant difference between the experimental and control groups in terms of the word problem‐solving progress measure, favouring the experimental group. This confirms that providing students with a computer‐assisted system offered the opportunity to explore all stages of the problem‐solving procedure as one possible way to enhance their problem‐solving skills. Lay Description: What is currently known about the subject matter Problem‐based learning is recognized as an instruction method that positively influence learning outcomes along with higher order thinking skills.The use of computers to implement findings from qualitative research related to problem‐solving teaching strategies can develop reasoning skills in mathematics and problem solving of elementary students with learning difficulties in mathematics.Polya's model helps students to solve mathematical word‐based problems. What the paper adds to this subject This paper suggests that efforts to improve word problem solving should focus on episodes students neglect when solving problems.This study proposes a computer‐assisted system with a design based on Polya's problem‐solving model.This empirical study investigates whether providing students with computer‐based assistance at each stage of the problem‐solving process helps students to overcome their difficulties.This study explores whether students fail to solve the problem because they do not understand the specific relations among the three problem quantities, or in choosing a correct solution strategy, or in carrying out the solution strategy correctly. The implications of study findings for practitioners Combining Polya's model with computer assistance at each solving procedure stage enhances student's capabilities to solve mathematical word‐based problems.Students encountered problems when reviewing their solutions; this signifying that students did not recognize the variants of the problem. [ABSTRACT FROM AUTHOR]

Learning and teaching algebra concepts are frequent problems for both students and teachers alike. Students struggle to learn algebra, and teachers struggle to identify the best way to teach algebra. It is recurrent that teachers use instructional methods that promote memorization, and, consequently, the learning process may prove unsatisfactory. This paper introduces Virtual Algebra Tiles, an open educational resource whose purpose is to enable students to use algebra tiles from a computer to enhance their knowledge of algebra concepts. To evaluate the effectiveness of the system, we designed a case study. The participants were 40 students of engineering degrees who were randomly assigned to experimental or control groups. Results indicate that the system has a large effect size (ES = 0.83, p < 0.001) on learning effectiveness and a promising long‐term knowledge retention (ES = 0.79, p < 0.001). Students concluded that this version of algebra tiles is more motivating than other versions, because it is presented in a format that stands natural to them. Students feel more comfortable in virtual environments, and therefore, the learning process becomes a more pleasant task. Lay Description: What is already known about this topic: Inadequate teaching methodologies can lead to student failure.It is necessary to decrease the emphasis on memorization and to favour active learning techniques.The use of mathematical manipulatives increases students' learning gains.Algebra tiles are an educational resource that helps students understand algebra concepts by using geometric figures. What this paper adds: Virtual Algebra Tiles is a multimedia version of the educational resource algebra tiles.Virtual Algebra Tiles has a large effect size on students' learning achievements.Virtual Algebra Tiles improves students' long‐term knowledge retention. Implications for practices and/or policy: Teachers should participate in the development of digital pedagogical material to enrich their lectures.It is necessary to develop more open educational resources, which can be accessed by students and teachers.Digital educational resources must take into account the special needs of particular users. [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]

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]

Studies have shown that educational robotics (ER) may impact student learning, especially in relation to STEM (science, technology, engineering, and mathematics) areas. In the STEM framework, particularly for younger children, the "E" and the "T" are considered to be missing letters, because few studies have concentrated on teaching and evaluating technology and engineering through ER activities. This study aimed to develop and test the efficacy of an ER protocol to teach robotics in a sample of 389 students, hypothesizing that girls would be as successful as boys. A Robotics Questionnaire assessing the basics of robotics was developed for this study. A Wilcoxon nonparametric test was performed in order to evaluate improvements (p < 0.05). A Mann–Whitney nonparametric test was performed in order to test the presence of gender differences (p < 0.05). Data indicated significant improvements for all the age ranges considered. No gender differences were found. In order to evaluate the efficacy of a didactic intervention utilizing ER, it is important to assess the impact on children's technological and engineering (robotics, in particular) knowledge. Lay Description: What is already known about this topic: Studies have shown that educational robotics (ER) has a potential impact on student learning.In the STEM framework, the "E" and the "T" are considered the STEM missing letters.What this paper adds: This study aims at developing and testing the efficacy of an ER protocol to teach robotics.The hypothesis that girls will be equally successful than boys is explored too, and no gender differences were found.Implications for practice and/or policy: Our results suggest that ER can be utilized to learn robotics, bringing technology in the schools.ER could be considered as a tool able to contribute to girl's involvement in STEM. [ABSTRACT FROM AUTHOR]

The purpose of this study was to investigate the effect of a computer-based story, which was designed in anchored instruction framework, on sixth-grade students' mathematics word problem-solving achievement. Problems were embedded in a story presented on a computer as computer story, and then compared with the paper-based version of the same story and to a condition that presented the problems as typical, isolated word problems (i.e., a non-story condition including only problems). One hundred twenty-eight sixth-grade students from two public middle schools in Turkey participated in this study. In a pretest-posttest experimental design, students were randomly assigned to one of the treatment groups mentioned earlier in which they solved the same mathematics word problems. A one-way analysis of covariance was used to analyse students' achievement in the treatment groups. The results indicated that students who solved the problems in the computer story treatment had significantly higher achievement scores than students who solved the problems in the paper story and isolated word problems treatments. In addition, the story was found to be significantly more effective than the non-story treatment when it was presented on computer. [ABSTRACT FROM AUTHOR]