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Erbilgin, Evrim; Gningue, Serigne M. – Educational Studies in Mathematics, 2023
Representations are key to mathematical activities and meaning-making processes as they are part of modeling, connecting, communicating, and understanding mathematical ideas and concepts. The current study sought to examine a group of novice algebra learners' interactions with different representations from an onto-semiotic approach. A case study…
Descriptors: Novices, Algebra, Learning Processes, Mathematics Instruction
Lannin, John K.; Austin, Christopher; Geary, David C. – Mathematics Teacher: Learning and Teaching PK-12, 2023
In this article, the authors describe the two interpretations of mathematical expressions, as a process and as a product. They begin with an initial discussion of Tall's (2013) interpretations of expressions and connect this to state standards. Next, they describe the different interpretations of algebraic expressions based on their work with…
Descriptors: Mathematics Instruction, Teaching Methods, Middle School Students, High School Students
Lundberg, Anna L. V. – International Electronic Journal of Mathematics Education, 2022
This case study explores how 12-13-year-old students encounter proportional reasoning while working with geometric patterning tasks using concrete materials. The focus is on the students' use of spontaneous concepts when first dealing with such patterns in the context of collaborative work. Based on video recordings of a single lesson, a…
Descriptors: Middle School Students, Mathematics Skills, Logical Thinking, Geometric Concepts
Vlassis, Joëlle; Demonty, Isabelle – ZDM: Mathematics Education, 2022
To date, of the many studies on early algebraic thinking, none, to our knowledge, has examined the relationships between algebraic thinking and negative numbers. Students encounter persistent difficulties in dealing with these numbers, and we believe that these could be addressed through the development of algebraic thinking. We are particularly…
Descriptors: Algebra, Mathematics Instruction, Thinking Skills, Correlation
Hüseyin Kabadas; Hayal Yavuz Mumcu – Journal of Theoretical Educational Science, 2024
The aim of this study is to examine how middle school mathematics teachers diagnose and attempt to eliminate students' misconceptions in algebra. The study employed a case study method and embedded single-case design. The research was conducted with three mathematics teachers working in different state schools and having different professional…
Descriptors: Middle School Teachers, Middle School Students, Middle School Mathematics, Grade 8
Gembo Tshering – Mathematics Teaching Research Journal, 2024
Algebra is critical in shaping future mathematics success and is integral to the K-12 curriculum. Despite its inclusion, a common challenge arises as students' progress to higher grades without a solid foundation, resulting in challenging learning experiences. This action research study focuses on the algebraic learning experience of a Grade 7…
Descriptors: Grade 7, Intervention, Algebra, Mathematics Instruction
Christina Areizaga Barbieri; Elena M. Silla – Journal of Experimental Education, 2024
Prior research highlights a positive effect of incorrect worked examples on mathematics learning. Yet the mechanisms underlying these benefits are unclear. To investigate potential mechanisms of the benefits of various worked example types, we examined process data from a previously published classroom-based experiment. More specifically, we…
Descriptors: Middle School Students, Ethnic Diversity, Racial Relations, Public Schools
Nicole L. Fonger – Teachers College Press, 2024
An essential understanding of the uses and practices of algebra remain out of reach for many students. In this book, award-winning researcher Dr. Nicole Fonger addresses the issue of how to support all learners to experience algebra as meaningful. In a highly visual approach, the book details four research-based lenses with examples from 9th-grade…
Descriptors: Mathematics Instruction, Teaching Methods, Social Justice, Algebra
Khairunnisak, Cut; Johar, Rahmah; Yuhasriati; Zubainur, Cut Morina; Suhartati; Sasalia, Putri – Mathematics Teaching Research Journal, 2021
The mathematical representation ability is essential in solving mathematical problems, especially in algebraic expressions problems. Therefore, it is crucial to have a valid design of learning activities to support students' mathematical representation ability. Several previous studies claimed that realistic mathematics education is one of the…
Descriptors: Learning Processes, Learning Strategies, Algebra, Mathematics Skills
York, Toni; Greenstein, Steven; Akuom, Denish – North American Chapter of the International Group for the Psychology of Mathematics Education, 2022
Covariational reasoning and the creation and interpretation of graphs of covariational situations are important skills in math and science. Unfortunately, research shows that students often struggle to make meaningful connections between graphs and the covariational situations they represent. Educational activities designed to help students…
Descriptors: Mathematics Instruction, Graphs, Thinking Skills, Difficulty Level
Hunter, Jodie; Miller, Jodie; Bowmar, Alex; Jones, Ian – Mathematics Education Research Group of Australasia, 2022
In this paper, we explore student solutions to a free response mathematical assessment task which had opportunities for students to notice structural properties in the context of number systems. In total, 308 students aged between 10 years to 13 years participated in the study. Their responses were analysed to determine whether they noticed…
Descriptors: Middle School Students, Mathematics Instruction, Mathematics Skills, Thinking Skills
Ziegler, Esther; Trninic, Dragan; Kapur, Manu – Instructional Science: An International Journal of the Learning Sciences, 2021
Productive failure has shown positive effects on conceptual and transfer measures, but no clear effects on procedural measures. It is therefore an open question whether, and to what extent, productive failure methods may be used to enhance the learning of procedural skills. A typical productive failure study focuses on a single, complex concept;…
Descriptors: Algebra, Failure, Problem Solving, Mathematics Instruction
Peck, Frederick A. – For the Learning of Mathematics, 2022
In this paper I analyze a problem solving event in a secondary mathematics classroom. As the event unfolds, the teachers, including me, understand the event as involving interactions that were not related to learning. By adopting an expansive view of learning, I advance a different interpretation, that the interactions tell a story of student…
Descriptors: Mathematics Instruction, Secondary School Students, Learning Processes, Personal Autonomy
Marian Small – National Council of Teachers of Mathematics, 2025
This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…
Descriptors: Mathematical Concepts, Teaching Methods, Mathematics Instruction, Kindergarten
Knotts, Angela; Seago, Nanette; DePiper, Jill Neumayer – North American Chapter of the International Group for the Psychology of Mathematics Education, 2022
Asynchronous, online mathematics teacher professional development (PD) was designed to align with research on teacher professional learning as well as to support Communities of Inquiry (e.g., Garrison et al., 2000). The intervention included two actively facilitated formats and a structured independent condition, where facilitation was integrated…
Descriptors: Communities of Practice, Mathematics Instruction, Intervention, Teacher Attitudes