Variables versus numbers: Effects of symbols and algebraic knowledge on students’ problem-solving strategies

Chan, Jenny Yun-Chen; Ottmar, Erin; Smith, Hannah; Closser, Avery H.

doi:10.1016/j.cedpsych.2022.102114

Cited by 8 publications

(5 citation statements)

References 42 publications

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“…A potential explanation for this select benefit of in‐game progress is that students with higher, as opposed to lower, foundational knowledge of algebra may be better equipped to make connections between the mathematical ideas hidden within DragonBox and algebraic concepts taught in classrooms, and in turn benefit more from DragonBox as they progress through the game. This explanation aligns with some prior work demonstrating that students with higher versus lower prior knowledge benefit more from mathematics interventions (Swanson et al, 2008; Wood et al, 2020) and that students with higher prior knowledge may be more likely to notice mathematical structures that support learning (Novick, 1988) and equation solving (Chan, Ottmar, et al, 2022; Lee et al, 2022). The moderating effect of students' prior algebraic knowledge, therefore, highlights its importance in the relation between in‐game progress and later algebraic performance.…”

Section: Discussionsupporting

confidence: 86%

Keep DRAGging ON: Is solving more problems in DragonBox 12+ associated with higher mathematical performance during the COVID‐19 pandemic?

Chan

Byrne

Jerusal

et al. 2023

Brit J Educational Tech

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Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between students' progress within DragonBox and their algebraic knowledge and general mathematics achievement, (b) the moderating effects of students' prior performance on these relations and (c) the potential factors associated with students' in-game progress. Among students with higher prior algebraic knowledge, higher in-game progress was related to higher algebraic knowledge after the intervention. Higher in-game progress was also associated with higher end-of-year mathematics achievement, and this association was stronger among students with lower prior mathematics achievement. Students' demographic characteristics, prior knowledge and prior achievement did not significantly predict in-game progress beyond the number of intervention sessions students completed. These findings advance research on how, for whom and in what contexts game-based interventions, such as

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Section: Discussionsupporting

confidence: 86%

Keep DRAGging ON: Is solving more problems in DragonBox 12+ associated with higher mathematical performance during the COVID‐19 pandemic?

Chan

Byrne

Jerusal

et al. 2023

Brit J Educational Tech

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“…Generating hypotheses directs the thinking process toward problem solutions. Hypotheses help the investigator collect the data needed to investigate the relationship between students' attitudes and performance in turning ideas into actions to find the information needed to solve problems (Chan et al, 2022;Wakhata et al, 2023).…”

Section: Resultsmentioning

confidence: 99%

Determining Students' Higher Thinking Skills Profile Using Creative Problem-Solving Model Indicators Integrated with Predict Observe Explain

Trisnayanti,

Sunarno,

Masykuri

et al. 2023

JPII

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This study intends to investigate the profile of students’ higher-order thinking skills through the model integration of Creative Problem Solving Predict-Observe-Explain (CPSPOE). Data collection was carried out both quantitatively and qualitatively (mixed method). The mixed method sequential explanatory design consisted of two distinct phases: quantitative and qualitative. In this design, the researchers first collected and analyzed quantitative (numeric) data, then proceeded with qualitative data to help decipher the quantitative results. Using a purposive sampling technique, the research sample used two junior high schools in the city of Bengkulu to determine the experimental and control classes in each school based on the average academic scores before the study. The research instrument was a high-level thinking cognitive test in the form of 10-item test items describing the interaction of living things with their environment. The results of student scores on the test were analyzed using the MANOVA significance test and obtained a p-value 0.05, meaning that there is a significant influence on classifying, problem-solving, generating hypothesizing, and decision-making. Based on the CPSPOE model reference, which is integrated with a complete and interactive sequence of learning stages that can facilitate students to be involved in efforts to train higher-order thinking skills and can effectively activate students, being facilitated by teachers, complex social systems are considered practical and easy to implement to train high-level thinking skills. This study concludes that the sequence of learning stages of the CPSPOE model can be effective in improving classifying, problem-solving, generating hypothesizing, and decision-making skills for junior high school students’ high-level thinking skills.

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“…The multilevel models were conducted in RStudio (RStudio Team, 2020) using the lme4 package (Bates et al, 2015). The final dataset is available on the Open Science Framework (Chan, Closser, et al, 2023; https://osf.io/ajtuh/).…”

Section: Methodsmentioning

confidence: 99%

Examining shifts in conceptual knowledge, procedural knowledge and procedural flexibility in the context of two game‐based technologies

Chan

Closser

Ngo

et al. 2023

Computer Assisted Learning

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Background Prior work has shown that middle school students struggle with algebra and that game‐based educational technologies, such as DragonBox and From Here to There!, are effective at improving students' algebraic performance. However, it remains unclear which aspects of algebraic knowledge shift as a result of playing these games and what game design features support algebraic learning. Objective Using the data from a randomized controlled trial conducted in the 2020–2021 academic year, we (a) examined students' relative performance on assessment items measuring conceptual knowledge, procedural knowledge and procedural flexibility in algebraic equation solving, and (b) identified changes in these aspects of algebraic knowledge after playing DragonBox or From Here to There!. Methods Eight hundred eighty‐seven seventh‐graders were randomly assigned to playing DragonBox or From Here to There! for nine 30‐min sessions throughout the school year. Students also completed a pretest, midtest and posttest measuring their algebraic knowledge. Results and Conclusion First, prior to the intervention, students scored the highest on procedural knowledge and lowest on conceptual knowledge. Second, students significantly improved and maintained learning gains on conceptual knowledge throughout the intervention. Their performance on procedural knowledge and procedural flexibility items increased at midtest but decreased at posttest. Third, the pattern of results was consistent for students in the DragonBox and From Here to There! conditions, suggesting that both games may support students' conceptual understanding of algebra. The findings have implications for research and practice on supporting algebraic learning through game‐based technologies during and beyond educational disruptions.

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Variables versus numbers: Effects of symbols and algebraic knowledge on students’ problem-solving strategies

Cited by 8 publications

References 42 publications

Keep DRAGging ON: Is solving more problems in DragonBox 12+ associated with higher mathematical performance during the COVID‐19 pandemic?

Keep DRAGging ON: Is solving more problems in DragonBox 12+ associated with higher mathematical performance during the COVID‐19 pandemic?

Determining Students' Higher Thinking Skills Profile Using Creative Problem-Solving Model Indicators Integrated with Predict Observe Explain

Examining shifts in conceptual knowledge, procedural knowledge and procedural flexibility in the context of two game‐based technologies

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