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Saba Gerami; Eric Khiu; Vilma Mesa; Thomas Judson – Educational Studies in Mathematics, 2024
Using Balacheff's (2013) model of conceptions, we inferred potential conceptions in three examples presented in the spanning sets section of an interactive linear algebra textbook. An analysis of student responses to two similar reading questions revealed additional strategies that students used to decide whether a vector was in the spanning set…
Descriptors: Foreign Countries, Mathematical Concepts, Algebra, Textbooks
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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
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Aiyub Aiyub; Didi Suryadi; Siti Fatimah; Kusnandi Kusnandi; Zainal Abidin – Mathematics Teaching Research Journal, 2024
This study aimed to interpret and describe students' mathematical thinking processes of non-routine mathematical problems that were solved based on didactic situation theory. This study uses a qualitative method, a phenomenological hermeneutics study for grade 8 students at a junior high school in Banda Aceh in the 2021-2022 academic year.…
Descriptors: Thinking Skills, Mathematics Instruction, Problem Solving, Hermeneutics
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Lilin Rofiqotul Ilmi; Abdussakir – International Society for Technology, Education, and Science, 2024
This research aims to describe students' level of algebraic reasoning based on the adversity quotient types of climber, camper, and quitter in solving PISA model mathematics problems. This research is descriptive research with a qualitative approach. The research began by administering a questionnaire to determine the student's adversity quotient…
Descriptors: Algebra, Thinking Skills, Problem Solving, Mathematics Tests
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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
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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
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Jahudin, Janet; Siew, Nyet Moi – Problems of Education in the 21st Century, 2023
Diagnostic tests have been developed previously to measure algebraic thinking skills; however, the tests do not specifically address algebraic problem-solving. Thus, an Algebraic Thinking Test (ATT) Instrument was developed to measure algebraic thinking skills in problem-solving involving linear equations. ATT comprises nine open-ended questions…
Descriptors: Algebra, Thinking Skills, Foreign Countries, Problem Solving
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Eva Hejnová; Petr Eisenmann; Lucie Loukotová; Jirí Pribyl – Journal on Efficiency and Responsibility in Education and Science, 2024
The paper describes the results of a study whose main aim was to find the interrelationship between pupils' school grades in Czech language (native), mathematics, and physics and pupils' cognitive predispositions to problem-solving in science and mathematics diagnosed by the Lawson Classroom Test of Scientific Reasoning and the Culture of Problem…
Descriptors: Cognitive Ability, Problem Solving, Slavic Languages, Grades (Scholastic)
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Jahudin, Janet; Siew, Nyet Moi – Problems of Education in the 21st Century, 2023
Algebraic Thinking Skills (ATS) are one of the skills that students need to master in order to solve nonroutine problems. These skills are also necessary as a foundation for students preparing to enter university studies and fields of work that require logical and analytical thinking. However, Malaysian students' performance in solving algebraic…
Descriptors: Algebra, Thinking Skills, Mathematics Skills, Problem Solving
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Tšhegofatšo Phuti Makgakga – Online Submission, 2023
This article provides insights into Grade 11 learner understanding of the roots of quadratic equations, how learners used solution strategies to find equations with given roots, how they determine the unknown values and the other root when one root is given and how they determine the unknown values when two roots of the equation are given. The…
Descriptors: Grade 11, High School Students, Mathematics Instruction, Teaching Methods
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Hannah Smith; Avery H. Closser; Erin Ottmar; Jenny Yun-Chen Chan – Applied Cognitive Psychology, 2022
Worked examples are effective learning tools for algebraic equation solving. However, they are typically presented in a static concise format, which only displays the major derivation steps in one static image. The current work explores how worked examples that vary in their extensiveness (i.e., detail) and degree of dynamic presentation (i.e.,…
Descriptors: Algebra, Mathematics Instruction, Equations (Mathematics), Problem Solving
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Powell, Sarah R.; Berry, Katherine A.; Fall, Anna-Maria; Roberts, Greg; Fuchs, Lynn S.; Barnes, Marcia A. – Journal of Educational Psychology, 2021
The purpose of this study was to explore the paths by which word-problem intervention, with versus without embedded prealgebraic reasoning instruction, improved word-problem performance. Students with mathematics difficulty (MD; n = 304) were randomly assigned to a business-as-usual condition or 1 of 2 variants of word-problem intervention. The…
Descriptors: Word Problems (Mathematics), Problem Solving, Algebra, Mathematics Instruction
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Barbieri, Christina Areizaga; Booth, Julie L.; Chawla, Kamal – Educational Psychology, 2023
The current study assessed whether adding worked examples with self-explanation prompts focused on making connections between mathematical principles, procedures, and concepts of rational numbers to a curriculum focused on invented strategies improves pre-algebra students' fraction number line acuity, rational number concepts and procedures.…
Descriptors: Fractions, Mathematics Instruction, Teaching Methods, Algebra
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Chirove, Munyaradzi; Ogbonnaya, Ugorji Iheanachor – Journal of Research and Advances in Mathematics Education, 2021
The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge in some branches of mathematics, the relationship between learners' procedural and conceptual knowledge of…
Descriptors: Algebra, Grade 11, High School Students, Correlation
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Özdemir, Ercan – Shanlax International Journal of Education, 2022
The present study investigates the understanding of the equals sign among middle school students. The study data were gathered from a total of 433 middle school students (111 in the fifth grade, 106 in the sixth grade, 95 in the seventh grade and 121 in the eighth grade) using a ten-item equals sign test developed by the researcher. The study…
Descriptors: Middle School Students, Mathematics Instruction, Symbols (Mathematics), Concept Formation
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