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Hopkins, Sarah; Russo, James; Siegler, Robert – Mathematical Thinking and Learning: An International Journal, 2022

There is a growing awareness that many children are not developing fast and accurate retrieval-based strategies for solving single-digit addition problems. In this study we individually assessed 166 third and fourth grade children to identify a group of children (called accurate-min-counters) who frequently solved simple single-digit addition…

Descriptors: Addition, Grade 3, Grade 4, Elementary School Students

Earnest, Darrell – Mathematical Thinking and Learning: An International Journal, 2022

Around the globe, young students are expected to learn about time, yet how is it that they themselves make sense of this topic? From a sociocultural perspective, sense-making about time emerges in relation to properties of available tools and representations, such as analog clocks or digital notation. Such interactions with the symbols and…

Descriptors: Time, Grade 2, Elementary School Mathematics, Problem Solving

Stephens, Ana; Sung, Yewon; Strachota, Susanne; Torres, Ranza Veltri; Morton, Karisma; Gardiner, Angela Murphy; Blanton, Maria; Knuth, Eric; Stroud, Rena – Mathematical Thinking and Learning: An International Journal, 2022

This research focuses on ways in which balance scales mediate students' relational understandings of the equal sign. Participants included 21 Kindergarten-Grade 2 students who took part in an early algebra classroom intervention focused in part on developing a relational understanding of the equal sign through the use of balance scales. Students…

Descriptors: Equations (Mathematics), Kindergarten, Elementary School Students, Symbols (Mathematics)

Rathé, Sanne; Torbeyns, Joke; Smedt, Bert De; Verschaffel, Lieven – Mathematical Thinking and Learning: An International Journal, 2022

Children's spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a separate construct from spontaneous focusing on numerosity (SFON) and examined whether it is uniquely related to numerical abilities and mathematics…

Descriptors: Numbers, Symbols (Mathematics), Numeracy, Mathematics Skills

Supply, Anne-Sophie; Van Dooren, Wim; Onghena, Patrick – Mathematical Thinking and Learning: An International Journal, 2022

Previous research has shown that early numerical abilities are predictive of later mathematical achievement. In line with these previous studies, we investigated whether early numerical abilities are also associated with later probabilistic reasoning abilities. In the present study, we examined children's numerical abilities in the second grade of…

Descriptors: Mathematics Skills, Numeracy, Mathematics Achievement, Preschool Children

Johnson, Heather Lynn – Mathematical Thinking and Learning: An International Journal, 2022

It is well known that students benefit from opportunities to interpret and create different representations (e.g., diagrams, graphs, tables, symbols) of mathematical ideas. Employing Marton's Variation theory as a lens, I argue for an expansion of the use of multiple representations in task design for graphs: Incorporate two different forms of the…

Descriptors: Task Analysis, Mathematics Instruction, Thinking Skills, Graphs

Bas-Ader, Sinem; Carlson, Marilyn P. – Mathematical Thinking and Learning: An International Journal, 2022

This study examined the spontaneous teacher-student interactions that occurred in three graduate student instructors' [GSIs] precalculus classrooms. We classified these interactions relative to these instructors' actions to make sense of and use student thinking to inform their in-the-moment interactions with students. Our characterizations of…

Descriptors: Teaching Assistants, Teacher Student Relationship, Teacher Behavior, Teacher Attitudes

Nedaei, Mahboubeh; Radmehr, Farzad; Drake, Michael – Mathematical Thinking and Learning: An International Journal, 2022

Previous studies have suggested that problem-posing activities could be used to improve the teaching, learning, and assessment of mathematics. The purpose of this study is to explore undergraduate engineering students' problem posing in relation to the integral-area relationship. The goal is to help fill a gap in tertiary level research about…

Descriptors: Engineering Education, Undergraduate Students, Calculus, Mathematics Instruction

Choppin, Jeffrey; Roth McDuffie, Amy; Drake, Corey; Davis, Jon – Mathematical Thinking and Learning: An International Journal, 2022

We studied how the distal policy mechanisms of curricular aims and objectives articulated in official curriculum documents influenced classroom instruction, and the factors that were associated with the enactment of those curricular aims and objectives. The study was set in the U.S. context, where there is an ambitious effort to transform…

Descriptors: Instructional Materials, Common Core State Standards, Mathematics Education, Mathematics Curriculum

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

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

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

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

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

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