Exploring Mathematical Representations in Solving Ill-Structured Problems: The Case of Quadratic Function

Santia, Ika; Purwanto, Purwanto; Sutawidjadja, Akbar; Sudirman, Sudirman; Subanji, Subanji

doi:10.22342/jme.10.3.7600.365-378

Cited by 34 publications

(36 citation statements)

References 27 publications

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“…As the techno-mathematical resources are being integrated, allowing her to think-with-diagrams, they become increasingly independent from particular dimensions, and the model evolves to a greater abstraction level. This is in line with results indicating that students' abilities in finding appropriate representations affect their competency in problem-solving (Santia et al, 2019).…”

Section: Techno-mathematical Fluency: the Combined Use Of Paper-and-pencil And Digital Toolssupporting

confidence: 91%

Digital Tools and Paper-and-Pencil in Solving-and-Expressing: How Technology Expands a Student’s Conceptual Model of a Covariation Problem

Jacinto

Carreira

2021

J. Math. Educ.

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This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.

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Section: Techno-mathematical Fluency: the Combined Use Of Paper-and-pencil And Digital Toolssupporting

confidence: 91%

Digital Tools and Paper-and-Pencil in Solving-and-Expressing: How Technology Expands a Student’s Conceptual Model of a Covariation Problem

Jacinto

Carreira

2021

J. Math. Educ.

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“…From some of the studies above, research is a representation process involving algebra (Anwar & Rahmawati, 2017), Geometry (Anwar et al, 2016;Ulusoy & Argun, 2019), and quadratic functions (Santia et al, 2019). If viewed from the type of problem, the word problem (Anwar & Rahmawati, 2017;Boonen et al, 2016;Ulusoy & Argun, 2019) and ill-structured problems (Anwar et al, 2016;Santia et al, 2019). This study involves geometrical problems about the perimeter and area of a rectangle by using ill-structured problems.…”

Section: Research Bymentioning

confidence: 99%

“…When the students solve the same problem, they do not rule out the possibility of using different representations. This is because the representation used by the students in the problem-solving process is influenced by their learning experiences (Anwar & Rahmawati, 2017) The results of some research on representation in problem solving (Anwar & Rahmawati, 2017;Anwar et al, 2016;Boonen et al, 2016;Santia, et al, 2019;Ulusoy & Argun, 2019) shows that representation is effective in problem solving. Anwar & Rahmawati (2017) conducted a qualitative study involving four 8 th grade students to describe the construction process of students' symbolic and verbal representations when solving problems based on Polya's stages.…”

Section: Introductionmentioning

confidence: 99%

Exploring Student’s Representation Process in Solving Ill-Structured Problems Geometry

Prayitno

Purwanto

Subanji

et al. 2020

Participatory Educational Research

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This study is to reveal the construction process of student representation in solving of ill-structured geometry problems. The three phases involved in the construction process are interpreting the problem, giving opinions, and concluding. A total of four high school students participated in Surabaya and Sidoarjo in this qualitative study. They used visual and symbolic representations to solve the ill-structured problems. The research data were obtained from the sheets of ill-structured geometry problems (ISGP), video recordings, and interviews. The data analysis through three stages, data identification, data presentation, and conclusion. The results of data analysis show that the process of constructing the visual and symbolic representations was carried out by the students when interpreting the problem. The subjects provide data to support problem-solving process, such as initial length and width. The construction process through the visual representation began with the process of giving meaning. They drew rectangle with a length and width. Likewise, when giving an opinion, they referred to the drawings they made with length and width of different sizes. They used symbolic representation as a length and width for the initial situation in the process of giving meaning. Through the use of variables, they could perform calculations so as to determine the proposals used as a solution. Two patterns that the students did during the process of the representation construction, are deductive and inductive. It is important for teachers to know the process of representation of students when solving illstructured problems. It needs to be enlarged and in line with the criteria to obtain the general description of the representation of the construction process when solving the problem. Then, teachers should design meaningful learning so they can connect concepts that their students can use to solve problems.

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“…2018; Mukuka, Balimuttajjo, et al, 2020b) but also in other contexts (Hong & Choi, 2014;Santia et al, 2019;Zaslavsky, 1997). Second, these two topics are considered necessary and as pre-requisites for various advanced courses in mathematics and other physical sciences at tertiary levels of education.…”

Section: Experimental Conditionsmentioning

confidence: 97%

Mediating Effect of Self-Efficacy on the Relationship Between Instruction and Students’ Mathematical Reasoning

2021

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Literature is well-stocked with studies confirming that an instructional approach, self-efficacy, and mathematical reasoning skills are critical for enhancing students’ conceptual understanding and achievement in mathematics. However, there has been little emphasis on establishing whether being able to reason mathematically depends only on the instructional approach or students’ self-efficacy beliefs about mathematics also play a hidden role. A quasi-experimental study involving 301 grade 11 students from six public secondary schools in one district was carried out to investigate the mediating effect of self-efficacy on the relationship between instruction and students’ mathematical reasoning. Participants of the study were selected using the cluster random sampling method. Data were collected before and after the intervention via a mathematical reasoning test and a mathematics self-efficacy beliefs questionnaire. A Parallel Multiple Mediator Model in SPSS using the PROCESS custom dialogue version 3.4 was employed for data analysis. Findings suggest that mathematics self-efficacy and task-specific self-efficacy beliefs collectively and significantly mediate the effect of the instructional approach on students’ mathematical reasoning. The Student Teams-Achievement Division (STAD) was found to be an effective approach for enhancing students’ mathematical reasoning alongside self-efficacy beliefs. These findings provide evidence on the need to select an instructional approach that does not only focus on developing students’ cognitive abilities such as mathematical reasoning but also fosters students’ affective attributes such as maths self-efficacy beliefs.

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Exploring Mathematical Representations in Solving Ill-Structured Problems: The Case of Quadratic Function

Cited by 34 publications

References 27 publications

Digital Tools and Paper-and-Pencil in Solving-and-Expressing: How Technology Expands a Student’s Conceptual Model of a Covariation Problem

Digital Tools and Paper-and-Pencil in Solving-and-Expressing: How Technology Expands a Student’s Conceptual Model of a Covariation Problem

Exploring Student’s Representation Process in Solving Ill-Structured Problems Geometry

Mediating Effect of Self-Efficacy on the Relationship Between Instruction and Students’ Mathematical Reasoning

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