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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]

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]

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]

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]

We describe three iterations of a Massive Open Online Course (MOOC) developed from online preparation materials for a reformed introductory physics classroom at the Massachusetts Institute of Technology, in which the teaching staff interact with small groups of students doing problems using an expert problem-solving pedagogy. The MOOC contains an e-text, simple checkpoint problems and homework. We show how certain course design aspects affect student behaviour: (a) frequent quizzes correlated with students reading a large fraction of the e-text, and (b) When homework sets are arranged by increasing (instructor-estimated) difficulty, we found strong correlations between difficulty and time to solution, but weak correlations with percent correct. Modifications to the second offering of the course resulted in higher retention. These modifications included targeting physics teachers and posting materials well in advance. We define retention as certificates earned relative to participants who make a significant effort on the second assignment. Retention measured this way varied between 44% and 72%, being highest in the course aimed at teachers. We show that there is significant learning among MOOC participants. Applying item response theory to common homework problems showed that the MOOC participants had significantly higher ability than students in a Massachusetts Institute of Technology course and that they maintained this advantage over the duration of the MOOC. [ABSTRACT FROM AUTHOR]