Motivation and students’ use of learning strategies: Evidence of unidirectional effects in mathematics classrooms

Considerable evidence indicates that student motivation and use of learning strategies are related. There is insufficient understanding, however, about their reciprocal effects—whether motivation affects strategy use, the converse, or whether the effects are bidirectional—and which components of motivation and strategies are involved. A two-wave longitudinal design was used to examine this issue among 9th grade students (N = 306) enrolled in high school mathematics classes during an academic term. A cross-lagged structural model found that students’ self-efficacy in mathematics and value predicted their reported use of learning strategies. There was no evidence, however, that learning strategy use predicted motivation and, thus, support for unidirectional effect of motivation during that time interval. Implications for models of self-regulated learning and instruction are discussed.     

Response groups as learning resources when working with portfolios

This article, based on the guidance of 17 teacher education students during their final term, presents the theoretical framework, procedures and results of an extensive experiment with portfolio assessment combined with peer tutoring. A recent reform programme in higher education in Norway has as one of its aims to improve the quality of teaching and better facilitate learning in universities and university colleges. One important aspect of the reform programme is to encourage greater diversity in student assessment, and to establish a closer link between the learning process and the methods of examination. Following up on those intentions, the students are encouraged to work more systematically on written texts as a strategy for learning, accompanied by responses to their drafts offered by the course tutors. The idea of portfolio assessment is central in the reform programme, as also is the concept of reflection. During a term 17 student teachers worked regularly in peer groups giving responses to each other's drafts, which also included separate reflection papers related to their work in the response groups. This way of working seems to have had a positive impact on their learning both as students and as a basis for their further development as professional teachers.     

Reflection on the teaching-learning process in the initial training of teachers. Characterization of the issues on which pre-service mathematics teachers reflect

Our aim was to highlight the issues of the reflections of pre-service mathematics teachers in their learning portfolio about the teaching-learning process taking place in a university teacher-training classroom. Category systems were designed which, together with the analysis system used, could provide a method helpful to teacher educators, teachers and to future research. The pre-service teachers showed difficulty in considering themselves as ‘authentic’ mathematics teachers. The study revealed that the preparation of a portfolio can help pre-service teachers learn more about themselves and provide educators insight into how to help pre-service mathematics teachers engage in the teaching-learning process.     

Social representations as mediators of practice in mathematics classrooms with immigrant students

This article suggests that a critical perspective of the notion of social representations can offer useful insights into understanding practices of teaching and learning in mathematics classrooms with immigrant students. Drawing on literature using social representations, previous empirical studies are revisited to examine three specific questions: what are the dominant social representations that permeate the mathematics classroom with immigrant students? What impact do these social representations have on classroom practices? What are the spaces for changing these practices through becoming reflective and critically aware of these representations? These questions are addressed mostly in relation to teachers’ representations, though the article also draws on data from research with students and parents to illustrate the diversity of representations and to argue for a critical and reflective perspective.     

Using a video-based curriculum to develop a reflective stance in prospective mathematics teachers

Although video cases are increasingly being used in teacher education as a means of situating learning and developing habits of reflection, there has been little evidence of the outcomes of such use. This study investigates the effects of using a coherent video-case curriculum in a university mathematics methods course by addressing two issues: (1) how the use of a video-case curriculum affects the reflective stance of prospective teachers (PTs); and (2) the extent to which a reflective stance developed while reflecting on other teachers’ practice transfers for reflecting on one’s own practice. Data sources include videotapes of course sessions and PTs’ written work from a middle school mathematics methods course that used a video-case curriculum as a major instructional tool. Both qualitative and quantitative analytical methods were used, including comparative and chi-square contingency table analyses. The PTs in this study showed changes in their level of reflection, their tendency to ground their analyses in evidence, and their focus on student thinking. In particular, they began to analyze teaching in terms of how it affects student thinking, to consider multiple interpretations of student thinking, and to develop a more tentative stance of inquiry. More significantly, the reflective stance developed via the video curriculum transferred to the PTs’ self-reflection in a course field experience. The results of this study speak to the power of using a video-case curriculum as a means of developing a reflective stance in prospective mathematics teachers.

The popularization of China’s higher education and its influence on university mathematics education

This paper introduces the current situation of the popular Chinese university education, points out the impact of popularized Chinese higher education on its university mathematics education, and presents the actualities and existing problems of university mathematics education research in China.     

Searching for evidence of curricular effect on the teaching and learning of mathematics: Lessons learned from the two projects

The two research projects described and discussed in the special issue provided much needed longitudinal empirical data to show the curricular influence on classroom instruction and student learning outcomes. The findings have helped to advance our understanding of whether the reform curricula can bring about positive changes in classroom instruction and student learning outcomes and how such changes might be sustained. In this article we synthesize the results from the two studies and discuss several lessons learned from the projects about investigating and understanding curricular effects on the teaching and learning of mathematics.     

Electronic portfolios: Perspectives of students, teachers and parents

This study explores the perspectives of students, teachers and parents to evaluate the use of digital portfolios as an additional way to capture and enhance the learning of elementary students in a public school setting and as an opportunity to communicate this learning to parents. The research questions address four problems: complex assessment of learning, parental participation, and student and teacher satisfaction and the impact of the portfolio on teaching methods. Particularly, we are interested in the subjective satisfaction of students, teachers and parents in the portfolio development process. We are also interested in whether students learn to reflect constructively on their work, whether teachers have changed their teaching methods and whether parents believe the portfolio was used or could be used for enhanced communications.     

Quantitative and qualitative measures of student learning at university level

This paper reports the use of quantitative and qualitative measures of university student learning during teaching in psychiatry. Concept mapping, pre-and post test scores and performance in written assignments were used to measure the quality of change in personal understanding and to show the ways that the knowledge-targets of the course were achieved. The data show that: (1) Concept mapping can be used to explore personal understanding because it facilitates discrete statements of meaning. (2) These personal statements can be compared through time to assess change. (3) Specific criteria can be used to measure the quality of the change from one statement to another so that the different qualities of change that occur can be made-visible in the course of teaching. The approach is discussed in the broader context of learning theory and teaching practice. We show in particular, that prior-knowledge is an important determinant of learning because it affects the sense that can be made of taught material.     

The development and use of an instrument to measure willingness to seek help from peers and teachers when studying college mathematics

As part of a three-phase study, 18 items were developed to measure aspects of a student’s willingness to seek help from and/or work with peers and teachers when studying college mathematics. In the first phase, 24 items were developed and administered to 165 undergraduate college students. During the second phase, 20 items, modified from the first instrument, were completed by a sample of 314 undergraduate college students. The sample was randomly divided in half and principal factor analysis with varimax rotation was performed on the first half. Two factors emerged and were interpreted as: Willingness to Work with Students (nine items); and Willingness to Seek Help from Teachers (nine items). Based on the results of the exploratory factor analysis, confirmatory factor analysis was performed on the second half of the sample. Coefficient α estimates were calculated to assess internal consistency. In the third phase, the final 18-item survey was given to 140 undergraduate college students and confirmatory factor analysis was again performed based on the results of the exploratory factor analysis from Phase II. Recommendations for future uses of these scales are given.     

Numerical competence in young children and in children with mathematics learning disabilities

A longitudinal study was conducted on 82 children to investigate, firstly the numerical competence of young children and the predictive value of (pre)-numerical tests in kindergarten, and, secondly, whether children's knowledge of the numerical system and representation of the number size is related to their computation and logical knowledge and to their counting skills. In an additional cross-sectional study on 30 children with a clinical diagnosis of mathematical learning disability (MLD) of 8,5 years, age- and ability-matched with 2 × 30 children the same parameters of numerical competence were assessed. The longitudinal data showed individual differences in numerosity, as well as the relationship between a delay in arithmetics in grade l and problems on numerosity in kindergarten. In the cross-sectional results some evidence was found for the independence of numerical abilities in MLD-children. About 13% of them had still severe pre-numerical processing deficits (in number sequence production, cardinality skills and logical knowledge) in grade 3. About 67% had severe difficulties in executing calculation procedures and a lack of conceptual knowledge. A feature of 87% of the MLD-children was severe translation deficits, with a significantly worse knowledge of number words compared with the knowledge of Arab numerals. Finally a severe deficit in subitizing was found to be present in 33% of the MLD children. On a group level the processing deficits were linked to understanding numerosity, since the ability-matched younger children and the MLD-children had the same pre-numerical and numerical profile. Implications for the assessment of mathematical disabilities and the value of TEDI-MATH® as an instrument in this process are discussed.     

Experimental evaluation of the effects of cooperative learning on kindergarten children's mathematics ability

The aims of this study were to investigate the effects of cooperative learning on the mathematics ability and cooperative social behaviours of kindergarten children and to evaluate teachers’ perspectives on the application of the program. One control (n = 17) and one experimental group (n = 17) were studied. In the experimental group, a curriculum based on cooperative learning method activities was used. Significant improvements in mathematics abilities were found for children in the experimental group that utilised cooperative learning.     

Lacan,subjectivity and the task of mathematics education research

This paper addresses the issue of subjectivity in the context of mathematics education research. It introduces the psychoanalyst and theorist Jacques Lacan whose work on subjectivity combined Freud’s psychoanalytic theory with processes of signification as developed in the work of de Saussure and Peirce. The paper positions Lacan’s subjectivity initially in relation to the work of Piaget and Vygotsky who have been widely cited within mathematics education research, but more extensively it is shown how Lacan’s conception of subjectivity provides a development of Peircian semiotics that has been influential for some recent work in the area. Through this route Lacan’s work enables a conception of subjectivity that combines yet transcends Piaget’s psychology and Peirce’s semiotics and in so doing provides a bridge from mathematics education research to contemporary theories of subjectivity more prevalent in the cultural sciences. It is argued that these broader conceptions of subjectivity enable mathematics education research to support more effective engagement by teachers, teacher educators, researchers and students in the wider social domain.

Epistemic profiles and self-regulated learning: Examining relations in the context of mathematics problem solving

Relations were examined between epistemic profiles, regulation of cognition, and mathematics problem solving. Two hundred sixty-eight students were sampled from undergraduate mathematics and statistics courses. Students completed inventories reflecting their epistemic profiles and learning strategies, and were profiled as rational, empirical, or both. Based on their profiles, 24 students participated in two problem-solving sessions. Episodes were coded for planning, monitoring, control, use of empirical and rational argumentation, and justification for solutions. For both self-reported metacognitive self-regulation and regulation of cognition during problem solving, students profiled as rational had the highest self-reported mean and actual frequency of regulation of cognition compared to students profiled as predominantly empirical. Moreover, students profiled as predominantly rational correctly solved more problems than the other two groups. Finally, students’ approaches to problem solving were consistent with their epistemic profiles. Relations are discussed in the context of various theoretical frameworks.     

Metaphors in mathematics classrooms: analyzing the dynamic process of teaching and learning of graph functions

This article presents an analysis of a phenomenon that was observed within the dynamic processes of teaching and learning to read and elaborate Cartesian graphs for functions at high-school level. Two questions were considered during this investigation: What types of metaphors does the teacher use to explain the graphic representation of functions at high-school level? Is the teacher aware of the use he/she has made of metaphors in his/her speech, and to what extent does he/she monitor them? The theoretical framework was based on embodied cognition theory. Our findings include teachers’ expressions that suggest, among other ideas: (1) orientation metaphors, such as “the abscissa axis is horizontal”; (2) fictive motion, such as “the graph of a function can be considered as the trace of a point that moves over the graph”; (3) ontological metaphors; and (4) interaction of metaphors. We also show that teachers were not aware of using metaphors.     

The meaning of mathematics instruction in multilingual classrooms: analyzing the importance of responsibility for learning

In the multilingual mathematics classroom, the assignment for teachers to scaffold students by means of instruction and guidance in order to facilitate language progress and learning for all is often emphasized. In Sweden, where mathematics education is characterized by a low level of teacher responsibility for students’ performance, this responsibility is in part passed on to students. However, research investigating the complexity of relations between mathematics teaching and learning in multilingual classrooms, as well as effect studies of mathematics teaching, often take the existence of teachers’ responsibility for offering specific content activities for granted. This study investigates the relations between different aspects of responsibility in mathematics teaching and students’ performance in the multilingual mathematics classroom. The relationship between different group compositions and how the responsibility is expressed is also investigated. Multilevel structural equation models using TIMSS 2003 data identified a substantial positive influence on mathematics achievement of teachers taking responsibility for students’ learning processes by organizing and offering a learning environment where the teacher actively and openly supports the students in their mathematics learning, and where the students also are active and learn mathematics themselves. A correlation was also revealed between group composition, in terms of students’ social and linguistic background, and how mathematics teaching was performed. This relationship indicates pedagogical segregation in Swedish mathematics education by teachers taking less responsibility for students’ learning processes in classes with a high proportion of students born abroad or a high proportion of students with low socio-economic status.     

谈如何在小学数学教学中培养学生独立思考的习惯

在当今多元化教育模式下,教师侧重于培养小学生自我探索、独立思考的能力,格外重视小学生逻辑思维能力的培养,让学生在潜移默化中形成独立思考的习惯。小学阶段的数学教育教学对学生来说非常重要,教师要让学生养成独立思考的习惯,提高独立思考的能力,要学会活学活用知识,避免死板地吸收数学内容。     

Integrating social justice with mathematics and science: An analysis of student teacher lessons

Student teachers have difficulty planning lessons that fully integrate social justice with mathematics/science content. This study was a content analysis of 26 poster presentations of mathematics or science lessons incorporating social justice issues made by student teachers (20F, 6M) at a mid-sized college in central New York State. The presented lessons applied four pedagogical approaches to integration (data collection followed by graphing analysis; discussion of text/video; modeling; library/internet investigation) and addressed three major social justice themes (diversity, system disparities in human communities, and in stewardship of earth). Deeper content knowledge, faculty lesson modeling/reflection and practice delivering lessons are recommended.     

关于高师院校“中学数学教材教法”课程改革的设想

根据国内外教学教育的发展趋势,认为我国高师院校“中学教学教材教法”课程应顺应形势的发展,积极进行改革,并提出了改革的具体设想。