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In 1998 Marzano proposed a taxonomy of learning that integrated three domains or systems: the self system, which involves student motivation; the metacognitive system, involving goal setting and planning; and the cognitive system, required to complete the task at hand. Although extant for 20 years, a paucity of studies have utilized this taxonomy, even though employing Marzano's taxonomy as a framework is particularly appropriate for studies involving student affect. This study provides an exemplar of the use of Marzano's taxonomy as a framework to investigate the impact of a classroom intervention using active and social strategies to enhance student participation. Further, this paper provides suggestions for employing Marzano's taxonomy in other areas for practising teachers, teacher educators, and educational researchers.

There is a dream, among mathematics educators, for a common direction that would unite teachers, policy makers and researchers, with researchers collaborating to accumulate knowledge and thus contribute to the understanding and improvement of school practice. But this dream becomes less and less realistic in view of the tendency of mathematics education to multiply and diversify its epistemological foundations, theoretical approaches, methodologies and research questions. In response to concerns and challenges, mathematics educators started engaging in "meta-studies" such as attempts at outlining a definition of the domain, more or less comprehensive syntheses of research approaches and theories, comparison of theories, and analyses of articles published in leading journals and conference proceedings over the past 10 or more years. The author decided to take a more empirical approach and have a good look at a more or less "random sample" of papers, in the sense that they were not specially selected to represent this or that issue, theme, theoretical perspective or mathematical topic. In reading the reports, the author had several questions in mind. In this article, the author will initially give an overview of the results from this empirical study, and then elaborate a little more on one particular issue (namely, task problematization). She will give examples of task problematization from the 55 PME papers, but she shall also go beyond the sample and speak more broadly on various approaches to this kind of work, known to her from other publications.

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and findings from mathematics education. Teacher beliefs about mathematics, learning and self-efficacy were expected to have a major impact on their classroom practices. We therefore assessed teacher beliefs about the usefulness of mathematics, learning (constructivist and socio-constructivist beliefs) and teacher self-efficacy when teaching modeling (teacher or class level variable). The student level variables assessed were modeling competence and other individual factors, such as basic mathematical skills and cognitive abilities. The effectiveness of the intervention was measured in a pre-post control group design using multilevel structural equation modeling. The results showed no direct effect of the intervention on student modeling competence. However, they did reveal that the intervention had a significant effect on teacher beliefs about learning (constructivist and socio-constructivist view) and an effect of these teacher beliefs about learning on student modeling competence. Further, the results showed that students' gains in modeling competence is not only mediated by teacher beliefs, but also influenced by individual factors. Implications for teaching as well as limitations of the study are discussed.

This paper is centered on creating equitable opportunities for learners in mathematics education. Through observations of teacher practice, the paper seeks to theorize how teachers enact their dispositions toward mathematics instruction. These observed propensities, in relation to teachers' aims for students to "take up their space" in and beyond the mathematics classroom, then inform a model of equitable mathematics instruction. Teachers' dispositions are considered in relation to Mason's discipline of noticing and Bourdieu's notion of the symbolic violence of dominant discourses.

Drawing on ecological psychology, this paper considers how student engagement is an accomplishment of the classroom system. Specifically, this paper presents an analysis of two teachers and their students who were using a project-based unit in their mathematics classes. The two teachers used identical curricular materials, but had dramatically different personal histories of teaching and different instructional practices. Our goal is to investigate the role of the teacher in supporting student engagement by considering the kinds of opportunities to learn that were presented by the teacher, and the relationship between those opportunities to learn and the ways their students engaged. Pragmatically, this paper contributes to our understanding of how teachers' framing of activity significantly impacts the ways that students are likely to engage tasks. Theoretically, this paper highlights the interactional nature of learning, with the goal of clarifying why learning is not simply an individual accomplishment.

Affect is an important element of the learning process both in the classroom and with educational technology. This paper presents analyses in relation to the identification of Action Units (AUs) related to affective states and their impact on learning with a tutoring system. To assess affect, a tool was devised to identify AUs on pictures of human faces. Action Units are combinations of individual facial muscles or groups of muscles that create facial expressions in association with affect. Pictures from a population of students were taken while using an intelligent tutoring system for mathematics in a secondary school in a suburban school in Veracruz, Mexico. The students were asked to interact with the tutoring system for 40 minutes and they were photographed with the tool at a rate of 1 picture every 5 seconds acquiring a dataset consisting of 16,800 photos. To achieve identification, the software analyzes individual pictures using Principal Component Analyses (PCA) and Euclidian distance. The tool developed to classify affective states shows 88.88% accuracy in the identification of AUs when matching the recognized AU to the Cohn-Kanade AU-Coded facial expression database. The analyses also elicited the most common AUs for the population and their association with learning with the intelligent tutoring system. These preliminary results shed light on the issues of affect in relation to learning mathematics with tutoring systems and pave the way for the implementation of coping strategies based on the automatic recognition of facial expressions.

In this paper, we engage in a thought experiment about how students might notate their reasoning for composing fractions multiplicatively (taking a fraction of a fraction and determining its size in relation to the whole). In the thought experiment we differentiate between two levels of a fraction composition scheme, which have been identified in prior research, and discuss differences in systems of notation that students might produce, depending on the level of their scheme. We situate this discussion within a framework for learning in order to articulate how developing systems of notation with students can contribute to their learning.

This article documents teacher learning through participation in lesson study, a form of professional development that originated in Japan and is currently practiced widely in the US. Specifically, the paper shows how teachers in three different lesson study teams 1) expanded their mathematical content knowledge, 2) grew more skillful at eliciting and analyzing student thinking, 3) became more curious about mathematics and about student thinking, 4) emphasized students' autonomous problem-solving, and 5) increasingly used multiple representations for solving mathematics problems. These outcomes were common across three lesson study teams, despite significant differences among teams composition, and content foci. [ABSTRACT FROM AUTHOR]

The purpose of this study was to identify the interactional strategies that one teacher used in a discourse-rich tenth-grade classroom to develop her students' facility with the mathematical register. Viewing the mathematical register as multi-semiotic and having a specific grammatical patterning, we used discourse analysis () to examine the teacher's initiation and feedback moves that supported students in using symbolic and natural language in mathematical ways during three consecutive lesson episodes. Our findings suggest that, while teacher interactional strategies which focus or probe student thinking are effective for supporting students' learning of the mathematical register, strategies that funnel or lead student contributions towards predetermined answers may also serve that purpose through creating opportunities for meaningful language practice. [ABSTRACT FROM AUTHOR]

The purpose of this study was to explore the views of students enrolled at a small United States Midwestern community college toward learning mathematics, and to examine the relationship between student beliefs about mathematic learning and educational experiences with mathematics using Q methodology and open-ended response prompts. Schommer’s ( Journal of Educational Psychology, 82, 495–504, ) multidimensional theory of personal epistemology provided the structural framework for the development of 36 domain specific Q sort statements. Analysis of the data revealed three distinct but related views of learning mathematic which were labeled Active Learners, Skeptical Learners, and Confident Learners. Chi-square tests of independence revealed no significant differences based on gender. Additionally, there was no evidence for differences based on level of mathematics completed, age, or college hours accumulated. Student’s previous experiences in instructional environments, however, were closely associated with beliefs. Results are discussed in view of the implications for establishing learning environments and considerations in implementing Standards-based curricula in higher education. [ABSTRACT FROM AUTHOR]

The results of an intervention program for students with difficulties learning mathematics are reported. Two kinds of math intervention, guided versus structured instruction, were compared to regular math instruction. A total of 75 students from regular and special education, aged seven to thirteen, participated. Ability and automaticity multiplication tests were administered before and after the four-month training period. The results show that the students in both of the experimental conditions improved more than the students in the control condition. Some additional differences were found between the two experimental interventions. Guided instruction appeared to be more effective for low performing students than structured instruction and especially for those students in regular education. Special education students appear to benefit most from structured instruction for the automaticity of multiplication problems. A three month follow-up test showed the acquired knowledge to be well-established in both groups. [ABSTRACT FROM AUTHOR]