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Pino-Fan, Luis R.; Guzmán, Ismenia; Font, Vicenç; Duval, Raymond – PNA, 2017

This paper presents a study of networking of theories between the theory of registers of semiotic representation (TRSR) and the onto-semiotic approach of mathematical cognition and instruction (OSA). The results obtained show complementarities between these two theoretical perspectives, which might allow more detailed analysis of the students'…

Descriptors: Theories, Mathematics Education, Networks, Cognitive Psychology

Simon, Martin A. – PNA, 2016

This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the…

Descriptors: Instructional Design, Sequential Learning, Mathematics Instruction, Mathematical Concepts

Ruthven, Kenneth; Hofmann, Riikka – PNA, 2016

We define epistemic order as the way in which the exchange and development of knowledge takes place in the classroom, breaking this down into a system of three components: epistemic initiative relating to who sets the agenda in classroom dialogue, and how; epistemic appraisal relating to who judges contributions to classroom dialogue, and how; and…

Descriptors: Case Studies, Epistemology, Mathematics Curriculum, Mathematics Instruction

Barwell, Richard – PNA, 2016

Research on the socio-political dimensions of language diversity in mathematics classrooms is under-theorised and largely focuses on language choice. These dimensions are, however, likely to influence mathematics classroom interaction in many other ways than participants' choice of language. To investigate these influences, I propose that the…

Descriptors: Mathematics Curriculum, Mathematics, Mathematics Instruction, Mathematics Education

Edmonds-Wathen, Cris – PNA, 2016

This study focussed on the effect of grammar of Iwaidja, an indigenous Australian language, on mathematical conceptualisation. It investigated route description in Iwaidja. Spatial concepts such as direction, height and movement in relation to another object are briefly described using examples. Differences between English and Iwaidja are used to…

Descriptors: Foreign Countries, Grammar, Uncommonly Taught Languages, Indigenous Populations

Turner, Ross – PNA, 2016

Mathematics is central in school curricula around the world, yet outcomes are mixed at best. This is true both in relation to attitudes expressed towards mathematics, and in relation to observed assessment outcomes, showing how poorly individuals are prepared to use mathematics in a world in which the ability to do so is of increasing importance.…

Descriptors: Mathematics Skills, Numeracy, Outcomes of Education, Mathematics Anxiety

Matos, José Manuel – PNA, 2016

During the second half of the nineteenth century and early twentieth century the discipline of secondary mathematics was gradually built in Portugal and certified teachers, textbooks, programs, special teaching techniques emerge. This consolidation process ends with the emergency of school subjects that develop some kind of autonomy as Chervel…

Descriptors: Foreign Countries, Secondary School Mathematics, Secondary School Teachers, Educational History

Baroody, Arthur J. – PNA, 2016

Six widely used US Grade 1 curricula do not adequately address the following three developmental prerequisites identified by a proposed learning trajectory for the meaningful learning of the subtraction-as-addition strategy (e.g., for 13-8 think "what + 8 = 13?"): (a) reverse operations (adding 8 is undone by subtracting 8); (b) common…

Descriptors: Grade 1, Elementary School Mathematics, Arithmetic, Addition

Planas, Núria – PNA, 2016

A synthesis of reasons for the production of this monograph is presented with a focus on contemporary research in the context of the Ninth Congress of the European Society for Research in Mathematics Education. Within the domain of mathematics and language, three lines of concern are addressed: (1) classroom discourse, (2) language diversity, and…

Descriptors: Mathematics Education, Language Usage, Classroom Communication, Teaching Methods

Jaworski, Barbara – PNA, 2015

This paper addresses the design of teaching to promote engineering students' conceptual understanding of mathematics, and its outcomes for mathematical meaning-making. Within a developmental research approach, inquiry-based tasks have been designed and evaluated, through the use of competencies proposed for their potential to promote conceptual…

Descriptors: Sociocultural Patterns, Engineering Education, Concept Formation, Mathematical Concepts

Gómez, Pedro; Arias, Marlene – PNA, 2015

We study the relationship between mentors' and mathematics teachers' performance in an education program. To this end, we characterize the relationship between the changes made in the written productions of three groups of teachers and the characteristics of their mentors' comments that could motivate those changes--type of comment, content, and…

Descriptors: Mentors, Mathematics Teachers, Correlation, Feedback (Response)

Rivera, Ferdinand – PNA, 2015

Drawing on a review of recent work conducted in the area of pattern generalization (PG), this paper makes a case for a distributed view of PG, which basically situates processing ability in terms of convergences among several different factors that influence PG. Consequently, the distributed nature leads to different types of PG that depend on the…

Descriptors: Pattern Recognition, Algebra, Mathematical Concepts, Generalization

Otte, Michael F.; Mendonça, Tânia M.; de Barros, Luiz – PNA, 2015

The problems of geometry and mechanics have driven forward the generalization of the concepts of number and function. This shows how application and generalization together prevent that mathematics becomes a mere formalism. Thoughts are signs and signs have meaning within a certain context. Meaning is a function of a term: This function produces a…

Descriptors: Generalization, Geometric Concepts, Algebra, Mathematics Education

Santi, George; Baccaglini-Frank, Anna – PNA, 2015

We shift the view of a special needs student away from the acknowledged view, that is as a student who requires interventions to restore a currently expected functioning behaviour, introducing a new paradigm to frame special needs students' learning of mathematics. We use the theory of objectification and the new paradigm to look at (and…

Descriptors: Mathematics Instruction, Learning Problems, Generalization, Special Needs Students

Koichu, Boris – PNA, 2014

An iterative unpacking strategy consists of sequencing empirically-based theoretical developments so that at each step of theorizing one theory serves as an overarching conceptual framework, in which another theory, either existing or emerging, is embedded in order to elaborate on the chosen element(s) of the overarching theory. The strategy is…

Descriptors: Social Networks, Problem Solving, Heuristics, Mathematics Education