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Bajwa, Neet Priya; Perry, Michelle – Mathematical Thinking and Learning: An International Journal, 2021
Elementary school students struggle in interpreting the equal sign as a symbol denoting equivalence. Although many have advocated using a pan-balance scale to help students develop this understanding, less is known about what features associated with this model support learning. To attempt to control and examine these features, the investigators…
Descriptors: Mathematics Skills, Mathematics Instruction, Elementary School Students, Concept Formation
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Björklund, Camilla; Ekdahl, Anna-Lena; Runesson Kempe, Ulla – Mathematical Thinking and Learning: An International Journal, 2021
We report here on an intervention implementing a structural approach to arithmetic problem-solving in relation to learning outcomes among preschoolers. Using the fundamental principles of the variation theory of learning for developing the intervention and as an analytical framework, we discuss teaching and learning in commensurable terms. The…
Descriptors: Preschool Education, Teaching Methods, Numbers, Intervention
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Hemmi, Kirsti; Bråting, Kajsa; Lepik, Madis – Mathematical Thinking and Learning: An International Journal, 2021
The aim of the study is to investigate and compare approaches to algebra in the Estonian, Finnish, and Swedish national core curricula (Grades 1-9). Despite the similarities in the school systems of these neighboring countries, the analysis reveals three quite different curricular approaches. The Estonian approach shows influences of the Russian…
Descriptors: Foreign Countries, Algebra, Mathematics Instruction, National Curriculum
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Lüken, Miriam M.; Sauzet, Odile – Mathematical Thinking and Learning: An International Journal, 2021
Despite increasing data on young children's patterning skills and evidence of a link between early pattern knowledge and later mathematics performance, little is known about the strategies children use to solve patterning tasks. This mixed-methods study examined 3- to 5-year-old children's informal strategies when solving eight patterning tasks…
Descriptors: Pattern Recognition, Early Childhood Education, Preschool Children, Mathematics Instruction
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Hackenberg, Amy J.; Creager, Mark; Eker, Ayfer – Mathematical Thinking and Learning: An International Journal, 2021
Three iterative, 18-episode design experiments were conducted after school with groups of 6-9 middle school students to understand how to differentiate mathematics instruction. Prior research on differentiating instruction (DI) and hypothetical learning trajectories guided the instruction. As the experiments proceeded, this definition of DI…
Descriptors: Mathematics Instruction, Teaching Methods, Individualized Instruction, Thinking Skills
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Kop, Peter M. G. M.; Janssen, Fred J. J. M.; Drijvers, Paul H. M.; van Driel, Jan H. – Mathematical Thinking and Learning: An International Journal, 2021
Student insight into algebraic formulas, including the ability to identify the structure of a formula and its components and to reason with and about formulas, is an issue in mathematics education. In this study, we investigated how 16- and 17-year-old pre-university students' insight into algebraic formulas can be promoted through graphing…
Descriptors: Algebra, Mathematics Instruction, Teaching Methods, Secondary School Students
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Nurnberger-Haag, Julie; Alexander, Anita N.; Powell, Sarah R. – Mathematical Thinking and Learning: An International Journal, 2021
Although the complexity of children's number learning is recognized, trade books about number have been treated as a simple, undifferentiated set. This analysis of 186 children's books, however, categorized a distinct subset of books about number as "counting books." These counting books were complex with regard to portrayal of counting…
Descriptors: Childrens Literature, Books, Computation, Numeracy
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Bråting, Kajsa; Kilhamn, Cecilia – Mathematical Thinking and Learning: An International Journal, 2021
This article investigates how the recent implementation of programming in school mathematics interacts with algebraic thinking and learning. Based on Duval's theory of semiotic representations, we analyze in what ways syntax and semantics of programming languages are aligned with or divert from corresponding algebraic symbolism. Three examples of…
Descriptors: Algebra, Computation, Thinking Skills, Semiotics
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González-Calero, José Antonio; Berciano, Ainhoa; Arnau, David – Mathematical Thinking and Learning: An International Journal, 2020
The reversal error is a prevalent phenomenon that consists of reversing the relationship between two variables when writing equations from comparison in verbal language. A study with 169 Basque/Spanish bilingual pre-service teachers examined whether this error is mainly due to the students' tendency to employ a direct-translation strategy based on…
Descriptors: Thinking Skills, Language Processing, Language Role, Equations (Mathematics)
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Soni, Meghna; Okamoto, Yukari – Mathematical Thinking and Learning: An International Journal, 2020
Competence in fractions is important in achieving advanced mathematics such as algebra and calculus. To foster students' understanding of fractions, intervention studies have found number lines to be an effective representational tool. Yet, it is unclear whether or not number lines are equally effective regardless of the ways in which they are…
Descriptors: Mathematics Instruction, Fractions, Mathematical Concepts, Numbers
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Rubel, Laurie H.; Nicol, Cynthia – Mathematical Thinking and Learning: An International Journal, 2020
Place-based education has traditionally had a limited focus on mathematics, and critical mathematics education often lacks explicit attention to place and space. We explore integrating theories of place, spatial justice, and critical mathematics education. To begin, we consider various frameworks of place--including Indigenous, urban, and critical…
Descriptors: Mathematics Education, Teaching Methods, Social Justice, Power Structure
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Björklund, Camilla; Palmér, Hanna – Mathematical Thinking and Learning: An International Journal, 2020
In this article we report on a study of children's attention to numerical content in picture books. Specific research questions are 1) how the content in a designed picture book directs children's attention to numbers, and 2) what kind of numerical reasoning the book reading entails. To answer these questions, we conducted an educational design…
Descriptors: Preschool Children, Picture Books, Mathematics Instruction, Numbers
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Tillema, Erik S. – Mathematical Thinking and Learning: An International Journal, 2020
Two-hour long developmental teaching interviews were conducted with each of 14 sixth grade students, ages 11-12. The purposes of the interviews were to investigate how students solved arrangement problems (APs), and how their solutions of these problems differed from their solution of Cartesian product problems (CPPs). The 14 students represented…
Descriptors: Mathematics Instruction, Multiplication, Mathematical Concepts, Teaching Methods
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Ayalon, Michal; Wilkie, Karina – Mathematical Thinking and Learning: An International Journal, 2020
Researching students' responses to tasks at different year levels and in varied curriculum contexts can provide insights that relate their understandings to prior learning experiences and teaching approaches. In this article, we discuss evidence of students from three curriculum contexts (English, Australian, and Israeli) (n = 350) ways of…
Descriptors: Secondary School Mathematics, Comparative Education, Foreign Countries, Mathematical Logic
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Baldinger, Erin E. – Mathematical Thinking and Learning: An International Journal, 2020
Analyzing and interpreting student thinking through written work is a key, often challenging, practice of teaching. It entails noticing students' mathematical thinking and drawing on mathematical knowledge for teaching. This study investigates how pre-service secondary teachers at the beginning of their preparation reason about students' written…
Descriptors: Preservice Teachers, Secondary School Teachers, Problem Solving, Logical Thinking
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