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Preschoolers’ different ways of structuring part-part-whole relations with finger patterns when solving an arithmetic task

In this paper we report on findings from a study of 5-to-6-year-old children’s ways of structuring part-part-whole relations using finger patterns. We focused our analysis on data from interviews with 28 children who during their last year of preschool learned to enact a structural approach. We used this data set to analyze their different ways of structuring a task with one part unknown, and what constitutes the ability to structure the task in a conceptually powerful way. The way children stru...

What makes mathematical word problem solving challenging? Exploring the roles of word problem characteristics, text comprehension, and arithmetic skills

In this study we investigated word-problem (WP) item characteristics, individual differences in text comprehension and arithmetic skills, and their relations to mathematical WP-solving. The participants were 891 fourth-grade students from elementary schools in Finland. Analyses were conducted in two phases. In the first phase, WP characteristics concerning linguistic and numerical factors and their difficulty level were investigated. In contrast to our expectations, the results did not show a cl...

This research addressed Hungarian pre-service and in-service (both elementary and lower secondary) teachers’ pedagogical content knowledge concerning the teaching of word problem solving strategies. By means of a standardized interview protocol, participants (N = 30) were asked about their judgement on the difficulty of teaching word problems, the factors they find difficult, and their current teaching practice. Furthermore, based on a comparative analysis of Eastern European textbooks, we teste...

Informal strategies reflecting the representation of a situation described in an arithmetic word problem mediate students’ solving processes. When the informal strategies are inefficient, teaching students to make way for more efficient ways to find the solution is an important educational issue in mathematics. The current paper presents a pedagogical design for arithmetic word problem solving, which is part of a first-grade arithmetic intervention (ACE). The curriculum was designed to promote a...

Math MOOC UniTo: an Italian project on MOOCs for mathematics teacher education, and the development of a new theoretical framework

This paper focuses on MOOCs (massive open online courses), a fairly recent paradigm in e-learning educational projects. Despite the high dropout rate, and the impossibility of benefiting from the opportunities that bring with it a face-to-face dialogue, several factors make MOOCs a good option for ongoing teacher professional learning. The MOOCs on which we focus address mathematics teacher education. In particular, we illustrate our experience based on four MOOCs that we organized in Italy in t...

Observing the transition from industrial work to more and more digitalised work in the last decades, in this paper we discuss changes in employment and the relevance of numeracy in adult basic education and in working environments. In a knowledge society, the demand for highly qualified professionals is growing. It is questionable what effects this need will have on other occupational groups. Is there a higher risk of becoming more vulnerable as a result of a so-called ‘polarisation of the labou...

Numeracy in Youth and Adult Basic Education: syntactic, semantic, and pragmatic dimensions of a discursive practice

The diversity of vulnerability conditions, that have prevented children and adolescents from exercising their right to school education, also produces a diversity of cultural references of the public that comes to Basic Education programs for Youth and Adults in developing countries. This diversity often forges appropriation processes of numeracy practices that defy the rationality assumed by hegemonic mathematics and confront us with the insufficiency of not only the syntactic approach, but als...

Is it a subspace or not? Making sense of subspaces of vector spaces in a technology-assisted learning environment

The purpose of this research study was to understand how linear algebra students in a university in the United States make sense of subspaces of vector spaces in a series of in-depth qualitative interviews in a technology-assisted learning environment. Fourteen mathematics majors came up with a diversity of innovative and creative ways in which they coordinated visual and analytic approaches in the exploration of subspaces of a number of vector spaces such as \({\mathbb{R}}^n ,{\mathbb{R}}^{n \t...

In this survey paper, we describe the state of the field on linear algebra research. We synthesize themes, questions, results, and perspectives emphasized in the papers that appear in this issue, as well as a selection of those published between 2008 and 2017. We highlight the extensive base of empirical research detailing how students reason about a variety of topic areas in linear algebra, as well as studies that provide evidence of promising directions for supporting students’ success through...

Word problem solving and pictorial representations: insights from an exploratory study in kindergarten

The aim of this study was to investigate how pictorial representations with different semiotic characteristics affect additive word problem solving by kindergartners. The focus of the study is on three categories of additive problems (change problems, combine problems and equalize problems) and on representational pictures with different semiotic characteristics: (a) pictures in which the problem quantities are represented in pictorial form, that is, as groups of illustrated objects (PP pictures...

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