Collaborative Learning Of Mathematics Research Articles

The underlying beliefs in Pirkko’s narrative about implementing collaborative learning in mathematics - ‘my job is to give individual instruction’

ABSTRACT Many teachers resist adopting collaborative learning despite its proven benefits. Beliefs play a role in this resistance, but exactly how they do so has yet to be understood. This narrative study provides a comprehensive analysis of one resisting teacher’s ambivalent perceptions and underlying beliefs about implementing a collaborative approach to learning mathematics in a Finnish seventh-grade class. Our results reveal how the seemingly noble goal of guiding students individually and associated beliefs may inhibit teachers from adopting collaborative learning even after successfully implementing it.

Scaffolding small groups at the group level: Improving the scaffolding behavior of mathematics teachers during mathematical discussions

Background Supporting students during collaborative learning in mathematics is challenging for teachers. We developed the Small-Group Scaffolding Tool (SGS-Tool) to assist teachers regarding how and when to offer support. The tool is based on three characteristics of scaffolding small groups at the group level: contingency to the group, phasing out content support when the group can continue independently, and transferring responsibility for learning to the group. Method We investigated whether the scaffolding behavior of teachers using the SGS-Tool was more adapted to the group level than that of teachers not using the tool. Participants were four teachers and their seventh grade classes. The topic was Early Algebra. We analyzed teachers’ scaffolding behavior with one group during five lessons. Findings The SGS-Tool offered teachers support when the groups discussed mathematics, but adaptations of the tool are needed. Overall, the SGS-Tool seems to be a promising tool for supporting mathematics teachers in scaffolding groups at the group level. Contribution Our study provides insight into what scaffolding small groups at the group level entails and how teachers can apply it.

表計算ソフト「Excel」とグループウェア「スタディノート」を使った、数学における協同学習

表計算ソフト「Excel」とグループウェア「スタディノート」を使った、数学における協同学習

The Case of Mitchell's Cube: Interactive and Reflexive Positioning During Collaborative Learning in Mathematics

Using positioning theory as a guiding framework, this qualitative research examined the experiences of students who appeared to be marginalized from collaborative learning in mathematics in a middle school setting. Positioning theory describes the discursive process whereby people are located in conversations as observably and subjectively coherent participants in jointly produced story lines. Interactive positioning describes when one or more persons position another individual. Reflexive positioning describes the positioning of oneself. In this research, I examined instances of (mis)alignment between interactive and reflexive positioning during collaborative learning. Factors potentially contributing to (mis)alignment are considered as well as implications for students, learning, and instruction.

Experiences in implementing and using a technological framework for mobile collaborative learning of mathematics and Chinese

This paper describes a technological framework for supporting mobile collaborative learning. The developers can reuse the framework's infrastructure to build content-specific mobile collaborative learning applications best suited for their content area of in-class or out-of-class learning. This paper reports on the experience in designing and using two such applications: for mathematics learning (FAO) and Chinese learning (Chinese-PP). The two applications were trialed with primary school students, the experience in using the system was collected and the benefits of the architecture are reflected upon. In a design-based research fashion the paper proposes a new cycle of system and approach redesign.

Learner-centred mathematics and statistics education using netbook tablet PCs

Tablet technology has been shown to support learner-centred mathematics education when this technology is available to both the lecturer and the students. However, cost is often the barrier to students’ use of tablet PCs for their university studies. This article argues that more affordable netbook PCs with tablet capabilities can be viable alternatives to full-sized tablet PCs to enhance active and collaborative learning in mathematics and statistics. For a whole teaching semester, netbook tablet PCs were given to volunteer students from two different cohorts. Students were enrolled in nursing mathematics or introductory statistics in non-mathematics majors at an Australian university. The aims were to gauge the suitability of this technology and to identify what active and collaborative learning emerged in these first-year classes. While the netbook tablet PCs were actively promoted in their tutorials, of additional interest was students’ use of the technology for any aspect of their studies both inside and outside the classroom. The outcome of this study was to inform a university decision to provide inexpensive tablet technology to larger cohorts of students. The results highlight different approaches required in the mathematics and statistics classes to achieve collaborative and active learning facilitated through the technology. Environmental variables such as the tutor, student, learning space, availability of other technologies and subject content had an impact on the nature of learning. While learner-centred education can be facilitated by inexpensive netbook tablet PCs, we caution that the savings may come at the expense of computing power.

A Reappraisal of Online Mathematics Teaching Using LaTeX

The mathematics language LaTeX is often seen outside of academic circles as a legacy technology that is awkward to use. MathML - a verbose language designed for data-exchange, and to be written and understood by machines - is sometimes by contrast seen as something that will aid online mathematics and lack of browser support for it bemoaned. However LaTeX can already do many of the things that MathML might promise. LaTeX is here proposed as a language from which small fragments, with concise syntax, can be used by people to easily create and share mathematical expressions online. The capability to embed fragments of LaTeX code in online discussions is described here and its impact on a group of educators and learners evaluated. Here LaTeX is posited as a useful tool for facilitating asynchronous, online, collaborative learning of mathematics.

Diagram-Based Support for Collaborative Learning in Mathematical Exercise

This paper focuses on the collaborative learning of mathematics in which learners effectively acquire knowledge of common exercises through discussion with other learners. During collaborative learning, learners sometimes cannot solve exercises successfully, because they cannot derive answers by themselves or they hesitate to propose answers through discussion. To cope with such situations, this paper proposes two support functions using diagrams to encourage active discussion, since diagrams are often used to graphically illustrate mathematical concepts. One function indicates the differences between learner diagrams and the group diagram in order to encourage participation in discussions. To compare the characteristics of diagrams drawn by different learners, internal representation of the diagram, which consists of types of figures and remarkable relations to other figures, is introduced. The other function provides hints in the group diagram so that all learners can consider their answers collaboratively through discussions. Since preparing hints for all exercises is difficult, rules for drawing supplementary figures, which are general methods for drawing supplementary figures that correspond to individual answering methods/formulas, are also developed. By applying available rules to current group diagram, appropriate supplementary figures that can solve current learning situations may be generated. The experimental results showed that the generated hints successfully increased the number of utterances in the groups. Moreover, learners were also able to derive answers by themselves and tended to propose more opinions in discussions when the uniqueness of their diagrams was indicated.

Students’ Activity in Computer-Supported Collaborative Problem Solving in Mathematics

The purpose of this study was to analyse secondary school students’ (N = 16) computer-supported collaborative mathematical problem solving. The problem addressed in the study was: What kinds of metacognitive processes appear during computer-supported collaborative learning in mathematics? Another aim of the study was to consider the applicability of networked learning in mathematics. The network-based learning environment Knowledge Forum (KF) was used to support students’ collaborative problem solving. The data consist of 188 posted computer notes, portfolio material such as notebooks, and observations. The computer notes were analysed through three stages of qualitative content analysis. The three stages were content analysis of computer notesin mathematical problem solving, content analysis of mathematical problem solving activity and content analysis of the students’ metacognitive activity. The results of the content analysis illustrate how networked discussions mediated mathematical knowledge and students’ questions, while the mathematical problem solving activity shows that the students co-regulate their thinking. The results of the content analysis of the students’ metacognitive activity revealed that the students use metacognitive knowledge and make metacognitive judgments and perform monitoring during networked discussions. In conclusion, the results of this study demonstrate that working with the networked technology contributes to the students’ use of their mathematical knowledge and stimulates them into making their thinking visible. The findings also show some metacognitive activity in the students’ computer-supported collaborative problem solving in mathematics.

Supplemental instruction sessions in college algebra and calculus

AbstractLook at the kinds of things that happen in specific Supplemental Instruction sessions and see h collaborative learning in mathematics takes place.