The influence of perceptually rich manipulatives and collaboration on mathematic problem-solving and perseverance

Carbonneau, Kira J.; Wong, Rachel M.; Borysenko, Nataliia

doi:10.1016/j.cedpsych.2020.101846

Cited by 14 publications

(12 citation statements)

References 37 publications

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“…Research on PP and PS in mathematics education has highlighted the relationship among mathematical PP, PS, and the advancement of mathematics (Cai et al, 2015;Căprioară, 2015;Hadamard, 1945;Kilpatrick, 1987;Singer et al, 2015). Commonly, PP and PS tasks were administered in mathematics learning to assess student's understanding of mathematics (Cai & Hwang, 2002;Carbonneau et al, 2020;Kotsopoulos & Cordy, 2009) and to improve student's motivation and creativity development (Căprioară, 2015;Christou et al, 2005;Crespo & Sinclair, 2008). There are several definitions of PP stated by researchers (Cai & Jiang, 2017;Cai et al, 2013;Crespo, 2003;Koichu & Kontorovich, 2013).…”

Section: Problem Posing and Problem-solving In Mathematics Educationmentioning

confidence: 99%

“…PP and PS have long been considered as central parts to develop high-quality mathematics thinking. Research in PP and PS found a significant relationship between problem-posing skills and general mathematical performance (Carbonneau et al, 2020;Limin et al, 2013). However, integrating PP and PS into mathematics learning practice to enhance the quality of learning outcomes has long been recognized as a critical and challenging task.…”

Section: Introductionmentioning

confidence: 99%

“…However, integrating PP and PS into mathematics learning practice to enhance the quality of learning outcomes has long been recognized as a critical and challenging task. Besides, mathematics is one of the difficult subjects and several previous research showed that students frequently struggle with PP and PS-related tasks (Carbonneau et al, 2020;Crespo & Harper, 2019). In terms of learning and instruction, much remained unknown about applying PP and PS in mathematics instruction with an effective approach.…”

Section: Introductionmentioning

confidence: 99%

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The impact of collaborative problem posing and solving with ubiquitous-decimal app in authentic contexts on math learning

Utami

Hwang

2021

J. Comput. Educ.

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The research focuses on integrating collaborative problem posing and solving (CPPS) activity into mathematics learning practice with authentic contextual support. We designed a ubiquitous learning application called "U-Decimal" to facilitate CPPS activity supporting decimal learning. The application facilitated the CPPS activity in three ways: designing questions in an authentic context, answering questions designed by students and teachers, and peer assessment. The study aimed to investigate the effect of student's learning behaviors in CPPS activity supported by U-Decimal on their decimal learning achievement. In total, 54 fourth graders from two different classes were engaged in the experiment. The experimental group completed CPPS activity using U-Decimal installed on tablet PCs, whereas the control group followed traditional CPPS activity with a paper-based approach. The results highlighted three main findings. First, the experimental students scored significantly higher on the post-test than the control students. Second, this study found the contributing functional aspects (i.e., picture-taking function, multimediatext and voice explanation, and peer assessment) and behavioral factors that predict learning achievement (i.e., quality of multiple-choice question design, quality of comment, and explaining answer using multimedia-text and voice explanation). Most importantly, our findings showed that U-Decimal is useful in supporting decimal learning achievement.

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Section: Problem Posing and Problem-solving In Mathematics Educationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The impact of collaborative problem posing and solving with ubiquitous-decimal app in authentic contexts on math learning

Utami

Hwang

2021

J. Comput. Educ.

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“…Most of the problems on the math subtest include application problems, which highlights how poorly the students score when it comes to solving word problems. Numerous factors influence how people adjust to and deal with the persistent social and environmental issues the world is facing, that includes the problems on how to help the students improve in their performance in mathematics which leads to the increasing recognition of cognitive and psychological factors that influence it [3].One reason that could be attributed to this is the limited exposure to non-routine problems and to the attitude towards and beliefs they hold about mathematics problem solving [4]. The variable 'attitude' is one of the most important factors that relates to achievement as much as students need to think and make decisions using appropriate strategies to solve mathematics problems [5].…”

Section: Introductionmentioning

confidence: 99%

Reflective Thinking Skills and Attitude towards Problem-solving as Mediated by Mathematical Resilience of the Students

Simacon

Veloria²

2022

AJESS

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Aims: This paper explored the mediating effect of mathematical resilience on the relationship between reflective thinking skills and student’s attitude towards problem-solving. Study design: This study utilized a non-experimental quantitative research design utilizing the descriptive-correlational technique. Place and Duration of Study: The study was conducted at public high schools in the Province of Bukidnon, Philippines in the school year 2021-2022. Methodology: The respondents of the study were 469 Junior High School students. The respondents were chosen using stratified sampling to simple random sampling. There were three questionnaires utilized to collect the data. The items in each indicator revealed a good interpretation for both validity and reliability of the questionnaires. Results: The result revealed that the respondents have a high level of both reflective thinking skills and mathematical resilience and has moderate level in their attitude towards problem-solving. The relationship between reflective thinking skills and attitude towards problem-solving; reflective thinking skills and mathematical resilience; and mathematical resilience and attitude towards problem-solving revealed an r-values of .521, .348, and .356 respectively, with a p- value of <.001 which is highly significant at 0.01 level of significance. Furthermore, the result also shows that mathematical resilience partially mediates the relationship between reflective thinking skills and attitude towards problem-solving. Conclusion: The attitude towards problem-solving is directly impacted by one’s capacity for reflective thinking. On the other hand, the ability to engage in reflective thinking has an effect, albeit an indirect one, on students' mathematical resilience, which in turn influences the students' attitude toward problem solving.

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“…Although it is not immediately obvious, the obscured value of Cuisenaire rods may be an affordance as part-whole structure, and regularity is not detracted from by the numerical value of the manipulative. Perceptual richness of manipulatives has been shown to detract from mathematical learning (Carbonneau, Wong, & Borysenko, 2020). It is possible that explicit teaching with Cuisenaire rods would have helped learners to identify additive reasoning structure more clearly.…”

Section: The Impact Of Structured Manipulatives On Additive Reasoningmentioning

confidence: 99%

Do structured manipulatives aid understanding of additive reasoning, and addition and subtraction fluency in a sample of Year 7 and 8 students?

Green¹

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<p>Mathematical achievement may impact on outcomes in later life; thus, identifying and improving key mathematical skills is a focus of a large body of educational research. Both additive reasoning, and knowledge of addition and subtraction facts, appear to predict later mathematical achievement. The current study explores the impact of a short intervention with a small group of year 7 and 8 students working at lower than expected academic levels. The current study is based on Cognitive Load Theory and research suggesting that counting strategies overload working memory. A mixed-methods approach was used to identify whether structured manipulatives improved the additive reasoning and, addition and subtraction fluency in a sample of ten participants. Participants attended after-school intervention sessions of 45 minutes for seven weeks. The intervention focused on teaching additive reasoning and fluency using structured manipulatives. Inferential statistical analysis showed a statistically significant mean improvement in participants’ ability to answer simple addition and subtraction questions. Tests constructed to operationalise additive reasoning also showed statistically significant mean improvement. Participants answered diagnostic questions operationalising various aspects of additive reasoning. Individual differences in understanding of additive reasoning were observed, and the inverse relationship between addition and subtraction proved to be a challenging concept. Semi-structured interviews provided themes of valuing the intervention and the manipulatives used. Due to the size and design of this study, it is not possible to extrapolate findings to other learners. However, the study may provide directions for future research. Structured manipulatives may have a role to play in enabling learners to begin to learn additive relationships and further securing recall of addition and subtraction facts. Students at years 7 and 8 may still need considerable exposure to additive concepts; moreover, returning to manipulatives may develop this knowledge. Finally, the findings from the diagnostic questions help show the complexity of additive reasoning. Classroom practitioners may need to further develop their knowledge of additive reasoning, its importance, and the individual differences and misconceptions that learners hold in order to provide considered learning experiences.</p>

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The influence of perceptually rich manipulatives and collaboration on mathematic problem-solving and perseverance

Cited by 14 publications

References 37 publications

The impact of collaborative problem posing and solving with ubiquitous-decimal app in authentic contexts on math learning

The impact of collaborative problem posing and solving with ubiquitous-decimal app in authentic contexts on math learning

Reflective Thinking Skills and Attitude towards Problem-solving as Mediated by Mathematical Resilience of the Students

Do structured manipulatives aid understanding of additive reasoning, and addition and subtraction fluency in a sample of Year 7 and 8 students?

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