Assisting teachers and students to reform the mathematics classroom

This study examines the usefulness of selected aspects of Tharp and Gallimore's (1988) theory of assistance as a theoretical framework for describing and analyzing change efforts in a middle school mathematics reform project. Drawing upon Tharp and Gallimore's redefinition of teaching as assisting performance and learning as the result of assisted performance, the social organization of a school-based mathematics reform effort in which teacher educators, mathematics teachers, and students both assist and are assisted is analyzed. In addition, one particular classroom assistance activity is presented and analyzed in terms of characteristics of assistance that, according to the theory, should lead to significant learning.     

Student perceptions of the classroom environment: Relations to motivation and achievement in mathematics

This study examined the relationship of 979 middle school students’ perceptions of their mathematics classroom environment to their motivation and achievement. Structural equation modeling indicated that motivational variables (utility, personal achievement goals, efficacy) mediated the influence of perceived teacher expectations, teacher support and use of reform practices on mathematics standardised test scores. Our study provides empirical evidence that students’ perceptions that their teachers believe that they are capable of learning and understanding mathematics positively relate to their Mastery and Performance Goal orientations and mathematics Utility. Further, we found an interaction between students’ perceptions of the frequency of reform practice use in their mathematics classroom and mathematics efficacy. For students with lower mathematics efficacy, their perceptions of more frequent use of reform practices in their mathematics class related to higher standardised test performance. For students with higher mathematics efficacy, perceived use of reform practices did not significantly relate to standardised test performance. These data suggest that frequent exposure to reform practices is especially critical for students who judge themselves as being less capable in mathematics and who are lower performers. This finding differs from prior research that has suggested that reform practice use benefits higher achievers but not lower achievers. An important implication of our study is the need for coordinated, ongoing professional development that highlights reform pedagogy and beliefs while also focusing on student motivation theories and strategies.     

What they notice in video: a study of prospective secondary mathematics teachers learning to teach

Most teacher preparation programs have embraced the use of video as an effective methodology for developing teachers’ noticing skills. This study focused on learning about what secondary mathematics prospective teachers (PSTs) were able to notice when viewing video of their own co-teaching, particularly in a microteaching setting that consisted of peers. PSTs documented their observations on an observation tool while re-watching their video and then identified and ranked their top three observations. The ranked noticing statements were analyzed based on a grounded theory approach. Overall, PSTs’ ranked observations were more likely to attend to students and had a strong focus on mathematics and student learning. Ranked observations equally demonstrated both broad and specific understanding of video moments and often made suggestions that something they noticed could be improved in the implementation stage, versus improvements in planning or changes in themselves. Results support PSTs’ use of video for developing noticing skills in teacher education programs.     

Working on What Works: working with teachers to improve classroom behaviour and relationships

The Working on What Works (WOWW) approach, which is based upon Solution-focused Brief Therapy, was implemented in a mainstream primary classroom over a 10-week period. The focus was on improving behaviour and relationships in class. Results demonstrated an improvement in teacher ratings for targets set by the class teacher compared with baseline. Pupils also set, and rated themselves on class targets. Observation of pupils, and their class-ratings, demonstrated a positive impact for these targets. Longer term follow-up suggested that this positive impact was maintained. It is concluded that WOWW had a positive impact on behaviour and relationships within this classroom.     

Sparking the imagination: creative experts working collaboratively with children,teachers and parents to enhance educational opportunities

This article suggests that child poverty and unequal educational opportunity are inextricably linked. It is argued that even from an early age children from poorer backgrounds are disadvantaged in terms of their preparedness to thrive in the formal school environment. Educational achievement is strongly influenced by attitudes and much research suggests that children from less advantaged backgrounds feel less in control at school and lack confidence in performing traditional school tasks. The ‘Sparking the Imagination’ project set out to try on a small scale to co‐ordinate efforts in raising educational opportunity for children from disadvantaged backgrounds by focusing on the context in which teaching and learning takes place. It was also deemed necessary to introduce measures to raise the motivation and aspirations of all involved and this was achieved through the engagement of children, teachers, parents and creative experts in collaborative learning within the classroom.     

Teaching teachers to teach Boris: a framework for mathematics teacher educator pedagogical content knowledge

The notion of pedagogical content knowledge (PCK) was posited in the context of school teaching and the knowledge used by teachers teaching school students. It has been examined for a number of discipline areas, notably mathematics. There are, however, other teaching contexts, including those of teacher educators, whose students are pre-service teachers (PSTs). The content these teacher educators teach is not subject discipline knowledge (or not solely), but the PCK for teaching a subject discipline. What knowledge do teacher educators use as they teach PCK? This paper presents a framework for the PCK required of mathematics teacher educators as they work to develop PSTs’ PCK for teaching mathematics. The framework builds on existing research into PCK and categorises aspects of the work of teacher education. The framework’s usefulness is examined by studying the PCK used by the first author in building PSTs’ understanding of mathematics teacher PCK.     

One speaker,two languages: Learning opportunities in the mathematics classroom

The data reported in this article come from a large project whose goal was to explore how Latin American students in Catalonia, Spain use their two languages—Spanish and Catalan—to support their learning of mathematics in small groups with other students who are Spanish- or Catalan-dominant. For 5 years, lessons from bilingual mathematics classrooms in three public secondary schools were video-recorded and transcribed. In the presentation of findings, I discuss three language practices that emerged from the analyses of several classroom instances as follows: (1) caution with mathematical vocabulary, (2) invention of terms, and (3) word-for-word translation. One example is chosen to represent each practice and some of its situated effects. The first two examples support the view that the experience of language difficulties, either real or presumed, contributes to generating opportunities that may be beneficial to mathematics learning. The third example, where the focus on the mathematics is hindered, points to a contrasting finding. Unlike other studies in the field, which have reported the difficulties and obstacles that arise in learning and teaching due to bilingualism in the classroom, I propose a change of focus through the conceptualization of language as a potential for thinking and doing, and particularly for learning and teaching mathematics.     

Learning to lose in the mathematics classroom: a critique of traditional schooling practices in the UK

“Back‐to‐basics” policies fit easily within many mathematics classrooms. Features such as order, control, rule following, uniformity, and conformity are relatively commonplace and are now more generally in demand with the current political backlash against progressive forms of schooling. This paper examines some of the influences of these traditional features of classrooms through a case study of one mathematics department in the United Kingdom. Interviews with students, lesson observations, results of questionnaires, and other case study data are analysed to show the ways in which traditional forms of learning can inhibit understanding, reify the divide between school and the “real world,” and suppress the transfer of knowledge. The findings suggest that two key elements of British Conservative education policy the commitment to traditional forms of schooling and the drive to produce school leavers capable of adapting to the demands of the 21st century — are fundamentally in conflict.     

Learning to teach mathematics through inquiry: a focus on the relationship between describing and enacting inquiry-oriented teaching

This article is based on one of the several case studies of recent graduates of a teacher education programme that is founded upon inquiry-based, field-oriented and learner-focussed principles and practices and that is centrally concerned with shaping teachers who can enact strong inquiry-based practices in Kindergarten to Grade 12 classrooms. The analysis draws on interviews with one graduate, and on video data collected in his multi-aged Grade 1/2 classroom, to explore some of the ways in which this new teacher enacted inquiry-based teaching approaches in his first year of teaching and to consider his capacity to communicate his understanding of inquiry. This article presents implications for beginning teachers’ collaborative practices, for the assessment of new teachers and for practices in preservice teacher education.     

浅谈小学数学教学中师生的课堂关系

进入21世纪的孩子们面临着更多的机遇和挑战,所以社会各界对教育的要求更高,实施素质教育已迫在眉睫.素质教育要求教学教学更重视学生的主体地位,重视数学思想的渗透,重视智力的开发和能力的培养,重视非智力因素的作用.在素质教育的课堂上应体现新的师生关系.     

Learning to teach mathematics and to analyze teaching effectiveness: evidence from a video- and practice-based approach

Although emerging consensus exists that practice-based approaches to teacher preparation assist in closing the distance between university coursework and fieldwork experiences and in assuring that future teachers learn to implement innovative research-based instructional strategies, little empirical research has investigated teacher learning from this approach. This study examines the impact of a video- and practice-based course on prospective teachers’ mathematics classroom practices and analysis of their own teaching. Two groups of elementary prospective teachers participated in the study—one attended the course and one did not. Findings reveal that the course assisted participants in making student thinking visible and in pursuing it further during instruction and in conducting evidence-based analyses of their own teaching. Conclusions discuss the importance of teaching these skills systematically during teacher preparation.     

Sustainable changes in teacher practices: a longitudinal analysis of the classroom practices of high school mathematics teachers

This study examines the effects of professional development on various aspects of teachers’ mathematics instruction. Using data collected between 2005 and 2009, we examined the extent to which the instructional practices of 49 US high school teachers who participated in content-based, sustained professional development changed over time. We found that changes in several aspects of their instructional practices followed somewhat different patterns. Teachers made statistically significant and steady changes in mathematical discourse, instructional clarity, and the development of students’ mathematical habit of mind, but not in student interactions or in the use of multiple representations.     

Mathematical knowledge for teaching teachers: knowledge used and developed by mathematics teacher educators in learning to teach via problem solving

In this study, we report on what types of mathematical knowledge for teaching teachers (MKTT) mathematics teacher educators (MTEs) use and develop when they work together and reflect on their teaching in a Community of Practice while helping prospective primary teachers (PTs) generate their own mathematical knowledge for teaching in learning mathematics via problem solving. Two novice MTEs worked with an experienced MTE and reflected on the process of learning to teach via problem solving and supporting PTs in developing deep understandings of foundational mathematical ideas. Taking a position of inquiry as stance, we examined our experiences teaching mathematics content courses for PTs via problem solving. We found that all of the MTEs used and developed some MKTT through (a) understanding and deciding on the mathematical goals of both the individual lessons and the two-course sequence as a whole, (b) choosing and facilitating tasks, and (c) using questions to scaffold PTs learning and engage them in mathematical processes such as making conjectures, justifying their reasoning, and proving or disproving conjectures.     

On some psychological aspects of mathematics achievement assessment and classroom interaction

The way students and teachers evaluate mathematics achievement differs in certain respects. To which causal performance is ascribed determines the teacher's strategy to interact with the student on the one hand and influences the student's willingness to invest additional effort on the other. Certain possible causal factors for success and failure in mathematics and their relation to teacher-student-interaction are discussed in the present article. A rather general cognitive scheme, the teachers reference norm, explains differences between the teacher's perception and assessment of student characteristics and subsequent teaching interventions.     

Learning to learn: Learning therapy in a college classroom

This paper describes the structure and rationale of the Language and Learning Seminar, a college course that grapples with learned helplessness issues that are frequently associated with LD. Peer/mentors play a vital role in its dynamic oral, written, and electronic communications. Elements of the course work synergistically to bypass long-standing emotional and linguistic barriers to learning. Yalom’s classification of therapeutic elements in group therapy serves as a context in which to explain the learning therapy provided by York University since 1987.     

Joining the Learning Society and working in the NHS: some issues

In this paper we discuss the concept of the Learning Society in relation to staff working in the NHS (National Health Service) and taking part in formal courses. We outline the changing context within the NHS and draw on evidence from interviews with 38 participants on two courses. While motives for participation in courses were mixed, many staff felt under some pressure to engage in formal courses and in some cases undertook work‐related training in their own time and at their own expense. We conclude by discussing the implications of these findings for the development of a Learning Society.