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Claire Wladis; Benjamin Sencindiver; Kathleen Offenholley – North American Chapter of the International Group for the Psychology of Mathematics Education, 2023
Here we investigate how college students may conceptualize symbolic algebraic properties. This work uses the theory of Grundvorstellungen (GVs) to analyze how learners' conceptions may or may not align with some desired goals of instruction. Through the analysis of interviews with students across a variety of courses, we describe several…
Descriptors: College Students, Algebra, Mathematics Instruction, Symbols (Mathematics)
Margaret Walton; Janet Walkoe – Mathematics Teacher: Learning and Teaching PK-12, 2025
Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…
Descriptors: Mathematics Instruction, Prior Learning, Knowledge Level, Algebra
Reilly Norum; Ji-Eun Lee; Erin Ottmar; Lane Harrison – British Journal of Educational Technology, 2024
Well-designed online educational games can improve students' math knowledge, skills and engagement; however, more research is needed to understand how to formatively assess components of students' mathematical understanding and learning as students solve problems in online educational games. In this study, we examined how 7th-grade students' (N =…
Descriptors: Educational Games, Computer Games, Student Evaluation, Mathematics Skills
Zhao, Yilang – ProQuest LLC, 2023
This study explores learning vector addition and demonstrating the understanding of vector addition. Vector addition is a key skill in mathematics and science education, but there is a limited amount of research that focuses on this topic. My study investigates how an instructional design framework "concreteness fading" can be used for…
Descriptors: Mathematics Skills, Grade 8, Middle School Students, Knowledge Level
Arnawa, I. Made; Yanita; Yerizon; Ginting, Bukti; Nita, Sri – International Journal of Instruction, 2021
The study examines the impact of APOS theory on students' achievement in Elementary Linear Algebra (ELA) in accordance with their adequate prior knowledge (APK) and inadequate prior knowledge (IAPK). The mixed methods were used to determine the problem-solving test in ELA. Data were obtained from 65 industrial engineering students at Andalas…
Descriptors: Constructivism (Learning), Educational Theories, Mathematics Achievement, Algebra
Wakhata, Robert; Balimuttajjo, Sudi; Mutarutinya, Védaste – Mathematics Teaching Research Journal, 2023
The present study explored 285 11th-grade students' preconceptions, misconceptions, and errors in solving mathematics tasks by graphical method. A descriptive-explorative study design was adopted. Cluster sampling was used to select students from sampled secondary schools in eastern and central Uganda. Students' paper and pen solution sketches…
Descriptors: Foreign Countries, Secondary School Mathematics, High School Students, Grade 11
Prasad, Priya V.; Barron, Victoria – The Mathematics Educator, 2019
Students' ability to reason for themselves is a crucial step in developing conceptual understandings of mathematics, especially if those students are preservice teachers. Even if classroom environments are structured to promote students' reasoning and sense-making, students may rely on prior procedural knowledge to justify their mathematical…
Descriptors: Preservice Teachers, Mathematics Teachers, Mathematics Instruction, Knowledge Level
Fries, Laura; DeCaro, Marci S.; Ramirez, Gerardo – Journal of Educational Psychology, 2019
Research demonstrates that seductive details negatively impact learning from instructional materials such as textbooks and learning modules. Yet, anecdotally, teachers and students consider seductive details an enhancement to classroom lectures. We examined this apparent disconnect by exploring the impact of seductive details in mathematics…
Descriptors: Lecture Method, Instructional Materials, Mathematics Instruction, Educational Environment
Makhubele , Yeyisani Evans – International Electronic Journal of Mathematics Education, 2021
This paper presents an analysis of fractions errors displayed by learners due to deficient mastery of prerequisite concepts. Fractions continue to pose a critical challenge for learners. Fractions can be a tricky concept for learners although they often use the concept of sharing in their daily lives. 30 purposefully sampled learners participated…
Descriptors: Foreign Countries, Middle School Students, Secondary School Mathematics, Algebra
Barbieri, Christina A.; Miller-Cotto, Dana; Booth, Julie L. – Journal of the Learning Sciences, 2019
The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students' (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during…
Descriptors: Middle School Students, Algebra, Mathematics Instruction, Cues
Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul – Physical Review Physics Education Research, 2016
We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque…
Descriptors: Mechanics (Physics), Motion, Graphs, Classification
Wilkie, Karina J. – Educational Studies in Mathematics, 2016
Algebra has been explicit in many school curriculum programs from the early years but there are competing views on what content and approaches are appropriate for different levels of schooling. This study investigated 12-13-year-old Australian students' algebraic thinking in a hybrid environment of functional and equation-based approaches to…
Descriptors: Secondary School Mathematics, Algebra, Thinking Skills, Problem Solving
Bardini, Caroline; Pierce, Robyn; Vincent, Jill; King, Deborah – Indonesian Mathematical Society Journal on Mathematics Education, 2014
Concern has been expressed that many commencing undergraduate mathematics students have mastered skills without conceptual understanding. A pilot study carried out at a leading Australian university indicates that a significant number of students, with high tertiary entrance ranks, have very limited understanding of the concept of function,…
Descriptors: Undergraduate Students, College Mathematics, Mathematical Concepts, Pilot Projects
Sun-Lin, Hong-Zheng; Chiou, Guey-Fa – Educational Technology & Society, 2017
This study examined the interaction effects of self-explanation and game-reward strategies on sixth graders' algebra variable learning achievement, learning attitude, and meta-cognitive awareness. A learning system was developed to support the learning activity, and a 2×2 quasi-experiment was conducted. Ninety-seven students were invited to…
Descriptors: Algebra, Grade 6, Mathematics Achievement, Student Attitudes
Barbieri, Christina; Booth, Julie L. – Grantee Submission, 2016
Middle school algebra students (N = 125) randomly assigned within classroom to a Problem-solving control group, a Correct worked examples control group, or an Incorrect worked examples group, completed an experimental classroom study to assess the differential effects of incorrect examples versus the two control groups on students' algebra…
Descriptors: Middle School Students, Algebra, Secondary School Mathematics, Randomized Controlled Trials
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