Promoting sophisticated fraction constructs through instructional changes in a mathematics course for PreK-8 prospective teachers

Stevens, Alexis; Wilkins, Jesse L. M.; Lovin, LouAnn H.; Siegfried, John; Norton, Anderson; Busi, Richard

doi:10.1007/s10857-018-9415-5

Cited by 11 publications

(5 citation statements)

References 36 publications

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“…Pada materi pecahan, siswa dapat menghasilkan beragam alternatif dan penyelesaian ketika mereka diberikan masalah yang sifatnya kontekstual (Adu-Gyamfi et al, 2019). Akant tetapi, siswa cenderung salah dalam memaknai pecahan secara konseptual, dimana mereka kurang memaknai pecahan sebagai bagian dari sesuatu yang utuh, dalam ilustrasi gambar yang biasanya ditandai dengan arsiran yang dinamakan pembilang dan bagian yang utuh dianggap sebagai satuan yang disebut dengan penyebut (Baek et al, 2017;Stevens et al, 2018). Selain itu, ketidakkontekstualan permasalahan yang diberikan siswa juga menjadi masalah saat mereka bekerja dengan konsep pecahan, misalkan siswa gagal dalam memaknai perkalian dan pembagian pecahan (Purnomo et al, 2022).…”

Section: Pendahuluanunclassified

Buku Ajar Pecahan Berorientasi pada Pemecahan Masalah Matematis Siswa: Riset Pengembangan pada Siswa Sekolah Dasar

Rismala,

Ilyas,

Ma'rufi

et al. 2023

JRHotsPM

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Penelitian ini bertujuan untuk mengetahui: strategi yang digunakan dalam mengembangkan buku ajar matematika materi pecahan dan untuk mengetahui efektifitas buku ajar matematika materi pecahan dalam meningkatkan kemampuan menyelesaikan masalah pada siswa kelas IV SD. Pengembangan media pembelajaran yang dilakukan berdasarkan prosedur penelitian & pengembangan menggunakan model ADDIE yang terdiri dari tahapan Analisis (Analysis), Desain (Design), Pengembangan (Development), Implementasi (Implementation), dan Evaluasi (Evaluation). Penelitian ini menghasilkan produk berupa buku ajar matematika yang berorientasi pada pemecahan masalah pada materi pecahan.. Hasil penelitian menunjukkan bahwa buku ajar matematika berorientasi pemecahan masalah pada materi pecahan di kelas IV SDIT Insan Madani Palopo, berada pada kategori valid. Dilihat dari nilai rata-rata validasi buku ajar matematika berorientasi pemecahan masalah dengan kategori sangat valid, praktis, dan efektif

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Section: Pendahuluanunclassified

Buku Ajar Pecahan Berorientasi pada Pemecahan Masalah Matematis Siswa: Riset Pengembangan pada Siswa Sekolah Dasar

Rismala,

Ilyas,

Ma'rufi

et al. 2023

JRHotsPM

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“…Developing this anticipatory thinking gives students flexibility and allows them to build more complex structures and relations. First, children learn to coordinate units in activity, as seen in Figure 5 (Hackenberg, 2010;Stevens et al, 2020). A child who can coordinate three levels of units in activity cannot hold all three levels of units in mind simultaneously; they cannot view the piece of pie in Figure 5 flexibly as made up of 2 parts, each of which is 1/5 of an unseen whole.…”

Section: Hackenberg (2010) Calls Interiorized Schemes Conceptsmentioning

confidence: 99%

“…Finally, some of the proposed mechanisms may be more accurately considered a subset of fractions knowledge rather than a result of fractions knowledge. For example, I have suggested that the interiorization of multiplicative schemes may be a mechanism, but in multiple studies these schemes are used to characterize fractions knowledge itself (Hackenberg, 2013;Hackenberg & Lee, 2015;Norton & Hackenberg, 2010;Stevens et al, 2020). Similarly, arithmetic fluency, which I consider a potential mediator between fractions and algebra knowledge, has been considered an aspect of fractions knowledge in many psychological studies (DeWolf et al, 2015a;Hurst & Cordes, 2018a;2018b;Powell et al, 2019;Siegler et al, 2012).…”

Section: Questioning Assumptions: Causal Directionalitymentioning

confidence: 99%

Causal pathways from fractions to algebra: Integrating psychology and math education perspectives

Viegut¹

2021

Preprint

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Algebra knowledge is an important gatekeeper to educational and economic opportunity. Both math education researchers and psychologists have shown that fractions may be a key to this gate (e.g., Hackenberg, 2013; Siegler et al., 2012). However, psychological and educational research on the fractions-algebra association has been disconnected, with separate frameworks, definitions, and designs. This integrative review synthesizes evidence from both disciplines about how and why fractions knowledge leads to stronger algebra knowledge. I suggest that the strength of causal evidence is limited by idiosyncratic measurement, limited longitudinal research, and imprecise definitions. I also review six plausible fractions-to-algebra mechanisms, which future research should empirically test. Throughout, I argue that more nuanced understanding of the fractions-algebra association will require interdisciplinary teams. Finally, I propose an integrative conceptual model of how fractions knowledge may lead to success in algebra and suggest new directions for collaborative investigation to inform developmental theory and educational practice.

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“…All misconceptions more or less relate to natural number bias (Alibali and Sidney, 2015;van Dooren, Lehtinen and Verschaffel, 2015), a tendency to use considerations and procedures learned in the domain of natural numbers and transfer them unjustifiably to the domain of integers or rational numbers. One of the misconceptions combines natural number bias with a similar tendency related to the transfer from the domain of proper fractions to the domain of all fractions (Stevens et al, 2020).…”

Section: Diagnostic Instrument -Particularitiesmentioning

confidence: 99%

A Joint Assessment of Reasoning about General Statements in Mathematics and Biology

2021

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This contribution belongs to a larger empirical study that focuses on issues related to the implementation of inquiry-based learning and formative assessment in science and mathematics education, while it also refers to the issue of STEM education. Here, we discuss the two topics from the perspective of professional preparation of primary school teachers. We employ an educational tool called Concept Cartoons and perceive it as a common diagnostic tool for investigating modes of reasoning about general statements in arithmetic, geometry and biology. The presented qualitative exploratory empirical study maps and codes various kinds of reasoning that can be identified with the tool and investigates possibilities of a joint coding procedure. As a result, it provides a conversion table between various modes of reasoning in the three subject domains. The arisen code categories cover the field of generic examples, including the initial stages so that they can be used for scaffolding the process of learning the foundations of deductive reasoning. The joint approach to reasoning in mathematics and biology shows how argumentation and formative assessment can be understood equally and developed simultaneously in both school subjects. It helps us to see how the two school subjects can be integrated didactically.

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Promoting sophisticated fraction constructs through instructional changes in a mathematics course for PreK-8 prospective teachers

Cited by 11 publications

References 36 publications

Buku Ajar Pecahan Berorientasi pada Pemecahan Masalah Matematis Siswa: Riset Pengembangan pada Siswa Sekolah Dasar

Buku Ajar Pecahan Berorientasi pada Pemecahan Masalah Matematis Siswa: Riset Pengembangan pada Siswa Sekolah Dasar

Causal pathways from fractions to algebra: Integrating psychology and math education perspectives

A Joint Assessment of Reasoning about General Statements in Mathematics and Biology

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