An assessment of the sources of the reversal error through classic and new variables

Calvo, Carlos Soneira; González‐Calero, José Antonio; Arnau, David

doi:10.1007/s10649-018-9828-1

Cited by 16 publications

(25 citation statements)

References 18 publications

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“…Currently, fewer literature has been found related to reversible reasoning investigations in conceptual relationships for inverse function problems. The focus of previous researchers are more on the operational aspects, for example by identifying error reversals that students make for the problem of "students and professors" (González-Calero, Arnau, & Laserna-Belenguer, 2015;Soneira, González-Calero, & Arnau, 2018;Tunç-Pekkan, 2015), reversible multiplication relationships (Hackenberg, 2010), cognitive conflict and insufficient mental processes to reverse problem situations (Ramful, 2014), the type of task that causes reversible reasoning (B. Dougherty, Bryant, Bryant, & Shin, 2017;B. J. Dougherty, Bryant, Bryant, Darrough, & Pfannenstiel, 2015;Sangwin & Jones, 2017;Simon, Kara, et al, 2016;Vilkomir & O'Donoghue, 2009).…”

Section: Discussionmentioning

confidence: 99%

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Ikram¹,

Purwanto²,

Parta³

et al. 2020

Journal for the Education of Gifted Young Scientists

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Researchers have argued that reversible reasoning is involved in all topics in mathematics. The study employed a qualitative research approach, consisted of three sessions (pre-assessment, thinking-aloud, and interview), and involved eight participants enrolled in Algebra class. The aim was to explore the potential role of reversible reasoning on students' inverse functions. The result of study indicated that there three categories of reversible reasoning that refer to the consistency of students in completing inverse function tasks, which are relational-harmonic, relationalvisual, and relational-identity. Mental activities performed by the students in constructing and reasoning inverse functions were also explained. In addition, potential aspects of the students' reversible reasoning created during the process of constructing meaning were highlighted. These findings provide perspectives on reversible reasoning, students' understanding of inverse functions, and areas of future research

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Section: Discussionmentioning

confidence: 99%

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Ikram¹,

Purwanto²,

Parta³

et al. 2020

Journal for the Education of Gifted Young Scientists

View full text Add to dashboard Cite

show abstract

“…Research has also identified that some students may display the reversal error even in statements without syntactic obstruction (Cohen & Kanim, 2005;MacGregor & Stacey, 1993;Martin & Bassok, 2005;Soneira et al, 2018). It can be inferred in this case that these students did not rely on the word order matching strategy because if they did so consistently, then they would not have obtained the reversal error.…”

Section: Static Comparison Strategymentioning

confidence: 98%

“…It was argued that the use of these first letters as symbols may prompt students to use the symbols as labels rather than as variables (Crowley et al, 1994;Fisher, 1988). However, research by Cohen and Kanim (2005) as well as Soneira et al (2018) did not find any differences in the rate of the reversal error in problems that took the variable as the first letter of the quantity and those that took the variable as a more general symbol.…”

Section: Literature Reviewmentioning

confidence: 99%

Insights into the reversal error from a study with South African and Spanish prospective primary teachers

2021

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This study, using a quantitative approach, examined Spanish and South African pre-service teachers’ responses to translating word problems based on direct proportionality into equations. The participants were 79 South African and 211 Spanish prospective primary school teachers who were in their second year of a Bachelor of Education degree. The study’s general objective was to compare the students’ proficiency in expressing direct proportionality word problems as equations, with a particular focus on the extent of the reversal error among the students’ responses. Furthermore, the study sought to test the explanatory power of word order matching and the static comparison as causes of the reversal error in the two contexts. The study found that South African students had a higher proportion of correct responses across all the items. While nearly all the errors made by Spanish students were reversals, the South African group barely committed reversal errors. However, a subgroup of the South African students made errors consisting of equations that do not make sense in the situation, suggesting that they had poor foundational knowledge of the multiplicative comparison relation and did not understand the functioning of the algebraic language. The study also found that the word order matching strategy has some explanatory power for the reversal error in both contexts. However, the static comparison strategy offers explanatory power only in the Spanish context, suggesting that there may be a difference in curriculum and instructional approaches in the middle and secondary years of schooling, which is when equations are taught.

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“…Lima & Tall (2008) mengklasifikasi persamaan bentuk aljabar bentuk "persamaan = angka" sebagai bentuk evaluasi karena melibatkan bilangan numerik dari ekspresi aljabar, dimana nilai input dapat ditemukan dengan "membongkar" atau memanipulasi bentuk aljabar untuk memperoleh penyelesaiannya. Disisi lainnya, jika solusi persamaan linear melibatkan konsep kesamaan yang direalisasikan secara konseptual, maka siswa justru mengalami kesulitan dengan kasus itu (Soneira et al, 2018). Persamaan 3 + 2 = + 6 dapat dengan mudah diselesaikan dengan konsep keseimbangan dengan membayangkan sebagai objek yang tidak diketahui dengan berat yang sama dan mereprsentasikan persamaannya dengan 3 dan 2 disebelah kiri dan dan 6 disebelah kanan.…”

Section: Pendahuluanunclassified

Meningkatkan Pengetahuan Siswa Tentang Sistem Persamaan Linear Dua Variabel (SPLDV) Melalui Model Pembelajaran Kooperatif

2021

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Sejumlah permasalahan dalam Sistem Persamaan Linear Dua Variabel (SPLDV), mendorong para peneliti melakukan kajian yang beragam. Namun, masih sedikit peneliti yang mengintegrasikan antara model pembelajaran dengan materi tersebut. Oleh karena itu, penelitian ini bertujuan untuk mendeskripsikan bagaimana peningkatan pengetahuan SPLDV siswa melalaui pembelajaran kooperatif. Kami melakukan Penelitian tindakan kelas bersama dengan guru di kelas atau dilokasi penelitian dengan melibatkan siswa di tingkat menengah. Data yang dikumpulkan berupa observasi, tes, dan dokumentasi. Kami menggunakan analisa kuantitatif dan kualitatif untuk mendeskripsikan temuan. Dari hasil tersebut, kami menemukan bahwa terjadi peningkatan pengetahuan siswa tentang SPLDV melalui model kooperatif. Lebih lanjut, peningkatan ini berdampak pada peningkatan aktivitas guru dan siswa dalam kelas serta meminimalkan kesalahan siswa dalam menyelesaikan masalah SPLD

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An assessment of the sources of the reversal error through classic and new variables

Cited by 16 publications

References 18 publications

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Insights into the reversal error from a study with South African and Spanish prospective primary teachers

Meningkatkan Pengetahuan Siswa Tentang Sistem Persamaan Linear Dua Variabel (SPLDV) Melalui Model Pembelajaran Kooperatif

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