Common neural functions during children's naturalistic and controlled laboratory mathematics learning

A major goal of human neuroscience is to understand how the brain functions in the real world, and to measure neural processes under conditions that are ecologically valid. A critical step toward this goal is understanding how brain activity during naturalistic tasks that mimic the real world, relates to brain activity in more traditional laboratory tasks. In the present study, we used intersubject correlations to locate reliable stimulus-driven cerebral processes among children and adults in a naturalistic video lesson and a laboratory forced-choice task that shared the same arithmetic concept. We show that relative to a control condition with grammatical content, naturalistic and laboratory arithmetic tasks evoked overlapping activation within brain regions previously associated with math semantics. The regions of specific functional overlap between the naturalistic mathematics lesson and laboratory mathematics task included bilateral intraparietal cortex, which confirms that this region processes mathematical content independently of differences in task mode. These findings suggest that regions of the intraparietal cortex process mathematical content when children are learning about mathematics in the real world.

Routines for Learning Modeling Practices and Content

The authors share a teacher-designed mathematical modeling routine geared to support teachers and to leverage opportunities for their students in learning important modeling practices and mathematical content.

QUATÉRNIOS: GENERALIZAÇÃO DOS NÚMEROS COMPLEXOS NA PERSPECTIVA DO USO DO SOFTWARE EDUCATIVO GEOGEBRA E O SOFTWARE ON-LINE LIVRE QUATERNION

This article was carried out under the Tutorial Education Program (PET Mathematical Knowledge connections), of the Mathematics Degree Course at the Federal University of Mato Grosso do Sul (UFMS) - Três Lagoas Campus (CPTL). Our objective was to present both the consolidation of Complex Numbers (1833) and the class of hyper-complex Quaternions (1843), both conceptualized by Sir William Rowan Hamilton, as well as using the Free Educational Software GeoGebra and the Free Online Software QUATERNION, as alternative pedagogical resources facilitating the development of the teaching and learning process of abstract mathematical content.

Features of the content of teaching test tasks in mathematics for students of secondary vocational education institutions

The paper discusses the possibilities of using educational mathematical content in the implementation of educational testing. Distance learning requires a significant revision of educational content. This research is based on the analysis of the accumulated experience in the implementation of training testing. An analysis was carried out in the field of improving educational content and the main directions were determined. Variants of designing the content of test tasks for students of secondary vocational education institutions are proposed, taking into account the specifics of educational activities in the specialty 15.02.07 Automation of technological processes and production (by industry). A new methodological approach to the development and testing process is proposed. The test tasks and their sequence, designed adequately to the logical structure of the educational material, contribute to the formation of systemic knowledge and ways of working with them. It is advisable to include in the content of test materials tasks that focus on building logical conclusions. These techniques and tests are carried out at the Nizhnevartovsk Oil College.

Mediating Wor(l)ds: Teaching and Learning of Mathematics in English in Malaysia

<p>This study investigates the implementation of ETeMS (English for the Teaching of Mathematics and Science) policy in Malaysia. Teachers, who learnt mathematics and were trained to teach mathematics in Bahasa Melayu, have had to teach mathematics in English since the implementation of ETeMS. This study observes two teachers and their teaching of mathematics in English to ten-year-old students. The study draws on sociocultural and sociolinguistic theories of classroom research which strongly advocate that education is a process of interaction. Both theories place importance on the joint construction of meaning through classroom interaction. The research mainly seeks to understand how teaching and learning is mediated in classrooms through the new medium of instruction. Adapting Erickson’s (1982) proposed constructs: academic and social participation structures, the study investigates the academic world and social world of linguistically altered mathematics classrooms. Sinclair and Coulthard’s (1975) discourse analysis tool has been adapted to study the teaching and learning of mathematics in English. Principles from conversation analysis and critical discourse analysis have been drawn upon to study the social world of linguistically altered classroom. Analysis of the classroom interaction showed that the academic world of linguistically altered classrooms is still heavily reliant on triadic dialogue. Despite that, teacher talk, through various discursive practices, was found to be an important mediating tool for mathematical content and mathematical English. Mathematical content and mathematical English were also shown to be jointly constructed through the use of several other mediating tools. The study revealed that there is more of an emphasis on teaching for testing than teaching for understanding, hence more attention to procedural fluency than to conceptual understanding, thus more emphasis on calculation discourse than on conceptual discourse. However, once the content and concept has been jointly constructed, students take some ownership of the classroom interaction. As well as the academic world, the study investigates how the new language of instruction mediates the social world of the classroom. The study found that the new medium (re)creates the social world of the classroom as teachers and students position and (re)position themselves and each other, and (re)establish their identities and sense of agency through the new language. From the insights gleaned from this study, the inter-relationship between ETeMS policy on paper and ETeMS policy in practice is explored. Some important implications for policy, practice and inter-disciplinarity in mathematics education and applied linguistics are discussed. The thesis concludes by proposing an adapted and extended model of mathematics education and directions for future research.</p>

Mediating Wor(l)ds: Teaching and Learning of Mathematics in English in Malaysia

<p>This study investigates the implementation of ETeMS (English for the Teaching of Mathematics and Science) policy in Malaysia. Teachers, who learnt mathematics and were trained to teach mathematics in Bahasa Melayu, have had to teach mathematics in English since the implementation of ETeMS. This study observes two teachers and their teaching of mathematics in English to ten-year-old students. The study draws on sociocultural and sociolinguistic theories of classroom research which strongly advocate that education is a process of interaction. Both theories place importance on the joint construction of meaning through classroom interaction. The research mainly seeks to understand how teaching and learning is mediated in classrooms through the new medium of instruction. Adapting Erickson’s (1982) proposed constructs: academic and social participation structures, the study investigates the academic world and social world of linguistically altered mathematics classrooms. Sinclair and Coulthard’s (1975) discourse analysis tool has been adapted to study the teaching and learning of mathematics in English. Principles from conversation analysis and critical discourse analysis have been drawn upon to study the social world of linguistically altered classroom. Analysis of the classroom interaction showed that the academic world of linguistically altered classrooms is still heavily reliant on triadic dialogue. Despite that, teacher talk, through various discursive practices, was found to be an important mediating tool for mathematical content and mathematical English. Mathematical content and mathematical English were also shown to be jointly constructed through the use of several other mediating tools. The study revealed that there is more of an emphasis on teaching for testing than teaching for understanding, hence more attention to procedural fluency than to conceptual understanding, thus more emphasis on calculation discourse than on conceptual discourse. However, once the content and concept has been jointly constructed, students take some ownership of the classroom interaction. As well as the academic world, the study investigates how the new language of instruction mediates the social world of the classroom. The study found that the new medium (re)creates the social world of the classroom as teachers and students position and (re)position themselves and each other, and (re)establish their identities and sense of agency through the new language. From the insights gleaned from this study, the inter-relationship between ETeMS policy on paper and ETeMS policy in practice is explored. Some important implications for policy, practice and inter-disciplinarity in mathematics education and applied linguistics are discussed. The thesis concludes by proposing an adapted and extended model of mathematics education and directions for future research.</p>

Epistemic Complexity of the Mathematical Object “Integral”

The literature in mathematics education identifies a traditional formal mechanistic-type paradigm in Integral Calculus teaching which is focused on the content to be taught but not on how to teach it. Resorting to the history of the genesis of knowledge makes it possible to identify variables in the mathematical content of the curriculum that have a positive influence on the appropriation of the notions and procedures of calculus, enabling a particularised way of teaching. Objective: The objective of this research was to characterise the anthology of the integral seen from the epistemic complexity that composes it based on historiography. Design: The modelling of epistemic complexity for the definite integral was considered, based on the theoretical construct “epistemic configuration”. Analysis and results: Formalising this complexity revealed logical keys and epistemological elements in the process of the theoretical constitution that reflected epistemological ruptures which, in the organisation of the information, gave rise to three periods for the integral. The characterisation of this complexity and the connection of its components were used to design a process of teaching the integral that was applied to three groups of university students. The implementation showed that a paradigm shift in the teaching process is possible, allowing students to develop mathematical competencies.

Taxonomy of Key Terms for Mathematics Education

We present the process of developing a taxonomy of key terms for Mathematics Education. We build on the existing taxonomy of key terms that has been used in an open access document repository. Additionally, we took into account terms that have been established in encyclopedias of the discipline and the frequency of use of keywords in specialized journals that were indexed in Scopus and Web of Science. We made a review of synonymy between these terms and the terms of the existing taxonomy. We included in our proposal the terms that are relevant given their frequency of use in the journals. We removed from the existing taxonomy the terms that are little used in practice. The new taxonomy is organized in six main categories: approach, educational level, foundations of Mathematics Education, research in Mathematics Education, pedagogical notions and mathematical content. This proposal was validated in three phases by researchers, innovators in Mathematics Education, and editors of specialized journals and experts who lead associations and events in the discipline.

Mathematics textbooks and curriculum resources as instruments for change

In this survey paper we aim to provide an overview of research on mathematics textbooks and, more broadly, curriculum resources as instruments for change related to mathematical content, instructional goals and practices, and student learning of mathematics. In particular, we elaborate on the following themes: (1) The role of curriculum resources as instruments for change from a theoretical perspective; (2) The design of curriculum resources to mediate the implementation of reform ideas and innovative practice; (3) Teachers’ influence on the implementation of change through curriculum resources; (4) Students’ influence on the implementation of change through curriculum resources; and (5) Evidence of curriculum resources yielding changes in student-related factors or variables. We claim that, whilst textbooks and curriculum resources are influential, they alone cannot change teachers’ teaching nor students’ learning practices in times of curricular change. Moreover, more knowledge is needed about features of curriculum resources that support the implementation of change. We contend that curriculum innovations are likely to be successful, if teachers and students are supported to co- and re-design the relevant curriculum trajectories and materials in line with the reform efforts and their own individual needs.

Preschool children’s mathematical arguments in play-based activities

The present study examines the structure and mathematical content of children’s mathematical arguments as part of communication in play-based activities. It shows how Nordin and Boistrup’s (The Journal of Mathematical Behavior 51:15–27, 2018) framework for identifying and reconstructing mathematical arguments, which includes Toulmin’s model of argumentation, the notion of anchoring (Lithner, Educational Studies in Mathematics 67:255–276, 2008) and a multimodal approach, can be used to identify and explore preschool children’s mathematical arguments. Two different types of argument that occurred during play-based activities were identified: partial arguments and full arguments. The findings reveal the extensive use of multimodal interactions in all parts of the children’s mathematical arguments. Moreover, the findings point to the crucial role of adults as dialogue collaborators in the argumentation that emerges in the play-based activities.