Mathematical connection skills and their relationship with productive thinking among secondary school students

Jawad, Lina Fouad

doi:10.21533/pen.v10i1.2667

Cited by 8 publications

(9 citation statements)

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“…Thus, learners with good mathematical connection skills succeed in solving mathematical problems well, while poor mathematical connection skills cause students to fail in solving mathematical problems. This concurs with the findings of Hine (2021) and Jawad (2022).…”

Section: Feature and Different Representations Connectionssupporting

confidence: 93%

“…Mathematical connections are defined as networks and the associations that learners create between mathematical concepts and topics (intra-mathematical connections), between mathematics and other fields (extra-mathematical connections), and between mathematics and the real world or everyday life (extra-mathematical connections) (García-García & Dolores-Flores, 2018;Nabilah et al, 2019;Hasbi et al, 2019;Quilang & Lazaro, 2022;Rodríguez-Nieto et al, 2022). According to Jawad (2022), learners who possess mathematical connection skills can recognize and connect mathematical ideas; understand how mathematical ideas interconnect and build on one another to produce a coherent whole. A learner who can make mathematical connections has a deep understanding and long-lasting knowledge of the subject (Saminanto & Kartono, 2015).…”

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confidence: 99%

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Exploring grade 11 learners’ mathematical connections when solving two-dimensional trigonometric problems in an activity-based learning environment

2023

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In this paper, we explored the type of mathematical connections Grade 11 learners make when solving two-dimensional (2D) trigonometric problems in an Activity-Based Learning (ABL) environment. We followed a qualitative case study design within an interpretive paradigm. Convenience sampling was used to select a whole class of 45 Grade 11 learners from one of the public non-fee-paying secondary schools in Capricorn District, Limpopo Province of South Africa. Group work presentations and classroom interactions were used to collect data. Data were analyzed using deductive thematic analysis guided by the mathematical connections’ framework. The findings indicated that learners managed to make procedural, meaning, reversibility, different representations, feature, and inclusion part whole as well as integrated connections as they worked on 2D trigonometric problems in an ABL environment. We established that learners did not make generalization part-whole connections. In addition, we found that some learners lacked mathematical connections skills and failed to solve the problems. Engaging learners in an ABL environment provided a fine-grained approach that allowed them to make mathematical connections. We, therefore, recommend that teachers should create an ABL environment to enable learners to make different types of mathematics connections during the teaching and learning of trigonometric concepts.

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Section: Feature and Different Representations Connectionssupporting

confidence: 93%

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confidence: 99%

Exploring grade 11 learners’ mathematical connections when solving two-dimensional trigonometric problems in an activity-based learning environment

2023

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“…From the questionnaire and the interviews, when reflecting on the use of tools and addressing CT in the mathematics lessons, students showed a high level of awareness of the relevance of the use of spreadsheets and CT in mathematics and a positive perception of the benefits of CT and its importance for their (future) work and daily life. Indeed, there is an important relationship between mathematics and daily life in the sense that mathematics prepares for real-life challenges (Jawad, 2022). In addition, offering real-life problems is an effective pedagogical approach to developing CT skills (Bocconi et al, 2022).…”

Section: Reflections On Resultsmentioning

confidence: 99%

Spreadsheets in Secondary School Statistics Education: Using Authentic Data for Computational Thinking

Borkulo

Chytas

Drijvers

et al. 2023

Digit Exp Math Educ

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Computational thinking (CT) is gaining attention in education as a part of digital literacy and can be addressed in several disciplines, including mathematics. Through the lens of Brennan and Resnick’s framework, we investigated how computational concepts, practices, and perspectives can be addressed in upper-secondary statistics lessons using spreadsheets through design-based research. Three classes of, in total, 58 16- to 17-year-old 11th-grade students explored several authentic real-life data sets in three 2-h sessions using spreadsheets. We evaluated the intervention by analyzing students’ workbooks, spreadsheet files, interviews, and questionnaires. The findings indicate that (1) students successfully engaged in computational concepts through using formulas, parameters, and conditional statements, (2) fruitfully applied data practices, and (3) demonstrated awareness of the relevance of CT for their everyday and future lives. These results highlight the potential of the use of spreadsheets in secondary school for developing computational thinking skills. Implications for further integration of CT in the mathematics curriculum are discussed.

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“…Mathematical connection is not a method, an educational theory, or a product students come up with at the end of mathematical activities, but it is a process through which students build mathematical ideas (Jawad, 2022). It is a cognitive process in which a person finds real relationships among ideas, concepts, definitions, theorems, procedures, and representations either within mathematics or with other disciplines or real-world (Dolores-Flores et al, 2019;Garcia-Garcia & Dolores-Flores, 2018).…”

Section: Literature Review Mathematical Connection Abilitymentioning

confidence: 99%

Mathematical Connection is at the Heart of Mathematical Creativity

Bicer,

Capraro

et al. 2023

Creativity. Theories – Research - Applications

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Although teaching mathematics for creativity has been advocated by many researchers, it has not been widely adopted by many teachers because of two reasons: 1) researchers emphasized and investigated mathematical creativity in terms of product dimension by looking at what students have at the end of problem-solving or -posing activities, but they neglected the creative processes students use during mathematics classrooms, and 2) creativity is an abstract construct and it is hard for teachers to interpret what it means for students to be creative in mathematics without further guidance. These can be eliminated by employing techniques of mathematical connections as tools because using mathematical connections can help teachers make sense of how to promote the creative processes of students in mathematics. Because making mathematical connections is a process of linking ideas in mathematics to other ideas and this is a creative act for students to take to achieve creative ideas in mathematics, using the strategies of making mathematical connections has the potential for teachers to understand what it means for students to be creative in mathematics and what it means to teach mathematics for creativity. This paper has two aims to 1) illustrate strategies for making mathematical connections that can also help students’ creative processes in mathematics, and 2) investigate the relationship among general mathematical ability, mathematical creative ability, and mathematical connection ability by reviewing theoretical explanations of these constructs and several predictors (e.g., inductive/deductive ability, quantitative ability) that are important for these constructs. This paper does not only provide examples and techniques of mathematical connection that can be used to foster creative processes of students in mathematics, but also suggests a potential model depicting the relationship among mathematical creativity, mathematical ability, and mathematical connection considering previously suggested theoretical models. It is important to note that the hypothesized model (see Figure 4) suggested in the present paper is not tested through statistical analyses and it is suggested that future research be conducted to show the relationship among the constructs (mathematical connection, mathematical creativity, mathematical ability, and spatial reasoning ability).

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Mathematical connection skills and their relationship with productive thinking among secondary school students

Cited by 8 publications

References 0 publications

Exploring grade 11 learners’ mathematical connections when solving two-dimensional trigonometric problems in an activity-based learning environment

Exploring grade 11 learners’ mathematical connections when solving two-dimensional trigonometric problems in an activity-based learning environment

Spreadsheets in Secondary School Statistics Education: Using Authentic Data for Computational Thinking

Mathematical Connection is at the Heart of Mathematical Creativity

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