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Janet Metcalfe; Judy Xu; Matti Vuorre; Robert Siegler; Dylan Wiliam; Robert A. Bjork – British Journal of Educational Psychology, 2025
Background: Although the generation of errors has been thought, traditionally, to impair learning, recent studies indicate that, under particular feedback conditions, the commission of errors may have a beneficial effect. Aims: This study investigates the teaching strategies that facilitate learning from errors. Materials and Methods: This 2-year…
Descriptors: Error Patterns, Error Correction, Direct Instruction, Test Preparation
Benjamin Tatira – Mathematics Teaching Research Journal, 2024
Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…
Descriptors: Mathematics Instruction, Teaching Methods, Schemata (Cognition), Problem Solving
Muslim; Toto Nusantara; Sudirman; Santi Irawati – Mathematics Teaching Research Journal, 2023
This study aims to describe students' commognitive in solving algebraic problems. This research is a qualitative research with descriptive approach. The subjects of this research were fifth semester students of the mathematics education study program at the College of Taman Siswa Teacher Training and Education. The research subjects were 9…
Descriptors: Algebra, Mathematics Instruction, Problem Solving, Teacher Education Programs
Tsamir, Pessia; Tirosh, Dina – International Journal of Science and Mathematics Education, 2023
This paper aims to broaden the scope of the construct concept image by addressing the mathematically oriented notion of "solution of an algebraic equation." The notion solution of an algebraic equation is not mathematical per se, but it is most prevalent in mathematical communications and in mathematics education. The paper describes…
Descriptors: Problem Solving, Algebra, Equations (Mathematics), Mathematics Education
Philile Nobuhle Mathaba; Anass Bayaga; Daniela Tîrnovan; Michael J. Bossé – Journal on Mathematics Education, 2024
This research investigates errors and misconceptions among learners in algebraic education by utilizing Koch's error analysis method alongside the Structure of the Observed Learning Outcome (SOLO) taxonomy. The primary aim of the investigation is to discern the kinds of errors and cognitive stages demonstrated by Grade 9 students when engaged in…
Descriptors: Algebra, Misconceptions, Cognitive Ability, Mathematics Education
Brain-Anatomy Differences in the Commission of Reversal Errors during Algebraic Word Problem Solving
Ventura-Campos, Noelia; Ferrando Esteve, Lara; Miró-Padilla, Anna; Ávila, César – Mind, Brain, and Education, 2022
An important line of research related to the resolution of word problems is the study of the cognitive processes involved when subjects translate problems into the language of algebra. One of the most common errors in problem-solving is the reversal error (RE), which occurs when students reverse the relationship between two variables when…
Descriptors: Brain Hemisphere Functions, Word Problems (Mathematics), Algebra, Problem Solving
Sükrü Ilgün; Solmaz Damla Gedik Altun; Alper Cihan Konyalioglu – Educational Policy Analysis and Strategic Research, 2023
The aim of this study is to examine the ability of pre-service mathematics teachers to detect errors made in solving questions about matrices. The study particularly focused on revealing the internalization of the teachings such as the meanings and relational dimensions of concepts and operations about matrix. The study was conducted with 26…
Descriptors: Preservice Teachers, Mathematics Teachers, Error Patterns, Matrices
Nadia M. Theba; Craig Pournara; Shikha Takker – Pythagoras, 2024
Developing structure sense is an important part of learning algebra. We investigated learners' structure sense of algebraic expressions involving brackets. This led us to propose the constructs "surface structure" sense and "systemic structure" sense. Using a random sample of 58 Grade 10 learners scoring above 40% in a test, we…
Descriptors: Algebra, Grade 10, Mathematics Instruction, Error Patterns
Soneira, Carlos – International Journal of Science and Mathematics Education, 2022
In this article, we examine how 10th graders make use of different intertwined representations when solving algebraic word problems. It is structured in a quantitative phase, with 61 students and a subsequent follow-up case study with nine pairs of students. We found that drawings and tables, used as auxiliary representations within variants of…
Descriptors: Problem Solving, Word Problems (Mathematics), Algebra, Error Patterns
Barbieri, Christina Areizaga; Booth, Julie L. – Applied Cognitive Psychology, 2020
Although findings from cognitive science have suggested learning benefits of confronting errors (Metcalfe, 2017), they are not often capitalized on in many mathematics classrooms (Tulis, 2013). The current study assessed the effects of examples focused on either common mathematical misconceptions and errors or correct concepts and procedures on…
Descriptors: Mathematics Skills, Problem Solving, Algebra, Misconceptions
Aydin-Güç, Funda; Aygün, Derya – International Online Journal of Education and Teaching, 2021
The study aimed to determine the mistakes of students in operations with algebraic expressions, and their misconceptions that may lead to errors. The study adopted case study method, one of the qualitative research models. The participants were composed of 48 (24 boys, 24 girls) randomly selected among 8th grade students in three different classes…
Descriptors: Error Patterns, Misconceptions, Mathematical Concepts, Equations (Mathematics)
Melhuish, Kathleen; Larsen, Sean; Cook, Samuel – International Journal of Research in Undergraduate Mathematics Education, 2019
Over the years, we have noticed our students constructing proofs that commutativity is preserved by isomorphism that do not explicitly use the fact that the isomorphism is surjective. These proofs are typically valid otherwise. However, such proofs are invalid because they would prove the false claim that commutativity is preserved by any…
Descriptors: Mathematical Logic, Problem Solving, Algebra, Error Patterns
Burhan Ogut; Blue Webb; Juanita Hicks; Ruhan Circi; Michelle Yin – Grantee Submission, 2024
In this study, we explore the application of process mining techniques on assessment log data to explore problem-solving strategies in Algebra. By analyzing sequences of student activities, we demonstrate the significant potential of process mining in identifying problem-solving strategies that lead to successful and unsuccessful outcomes. Our…
Descriptors: Mathematics Skills, Problem Solving, Learning Analytics, Algebra
Jeffrey Kramer Bye; Jenny Yun-Chen Chan; Avery H. Closser; Ji-Eun Lee; Stacy T. Shaw; Erin R. Ottmar – Journal of Numerical Cognition, 2024
Students often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order…
Descriptors: Middle School Students, Middle School Mathematics, Arithmetic, Mathematics Skills
Jones, Dustin L.; Zientek, Linda Reichwein; Sharon, Valerie V.; Swarthout, Mary B. – School Science and Mathematics, 2020
We analyzed the solution pathways and errors found in the written responses of 469 prospective teachers solving an equation containing fractions. The majority (332, or 70%) used an algebraic method; 141 of the 332 (42%) were correct, and 22% of the algebraic methods were abandoned before a solution was obtained. We identified the steps in the…
Descriptors: Problem Solving, Equations (Mathematics), Fractions, Error Patterns