Classroom learning environment and motivation towards mathematics among secondary school students in Uganda

This article reports a study of secondary students’ perceptions of mathematics classroom learning environment and their associations with their motivation towards mathematics. A sample of 81 students (19 male and 62 female) in two schools were used. Student perceptions of the classroom environment were assessed using a modified What Is Happening In this Class? (WIHIC) questionnaire. Associations between student perceptions of the learning environment and motivation towards mathematics were examined using simple correlation and multiple regression analyses. The results of the t tests for independent samples indicated a statistically significant difference in student perceptions between different school types. Student perceptions on some of the modified WIHIC scales were statistically significantly associated with student motivation. The results suggest that teachers wishing to improve student motivation towards mathematics, in general, should emphasise the learning environment dimensions that are assessed by the WIHIC. The findings have implications for teachers of mathematics and head teachers, particularly those in secondary schools.     

A model for incorporating lesson study into the student teaching placement: what worked and what did not?

This article describes a model for incorporating lesson study into the student teaching placement and reports on the success of the implementation of such a model with student teachers and their cooperating teachers (CTs). Student teachers had the opportunity to discuss many important ideas with each other and their CTs, including “big ideas” of mathematics, and the anticipation of student questions and possible responses. Student teachers also had a built‐in opportunity for peer observation on a regular basis and the opportunity to collaborate with their peers. Certain important aspects of lesson study were not present in this implementation: the teachers involved did not discuss the gaps in their own knowledge with the goal of improving their own mathematical understanding, they did not refer outside sources for ideas for the lessons, and they did not have an overarching affective goal for students. Suggestions are made for teacher preparation in light of these findings.     

Investigating Elementary and Middle School Students’ Subjective Well-Being and Mathematical Performance in Shanghai

Students in Shanghai ranked at the top in mathematics on the past two assessments of the Program for International Student Assessment (PISA). However, even though Asian students in general, and Chinese students in particular, ranked at the top in mathematics, we know little about Shanghai students’ subjective well-being (SWB). This paper reports two studies that investigated the SWB of elementary and middle school students in Shanghai, as well as their mathematics performance. It is found that the mean scores of elementary school students on all scales of SWB are significantly higher than those of middle school students, representing a large drop for students when moving from elementary to middle school. Furthermore, students’ mathematics performance is moderately correlated with their SWB. And for Grade 6, students’ SWB affects their mathematics performance, especially from academic self-concept, attentiveness in the classroom, and relationship with teachers.     

Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices

This collective case study reports on an investigation into the relationship between mathematics teachers’ beliefs and their classroom practices, namely, how they organized their classroom activities, interacted with their students, and assessed their students’ learning. Additionally, the study examined the pervasiveness of their beliefs in the face of efforts to incorporate reform-oriented classroom materials and instructional strategies. The participants were five high school teachers of ninth-grade algebra at different stages in their teaching career. The qualitative analysis of the data revealed that in general beliefs were very influential on the teachers’ daily pedagogical decisions and that their beliefs about the nature of mathematics served as a primary source of their beliefs about pedagogy and student learning. Findings from the analysis concur with previous studies in this area that reveal a clear relationship between these constructs. In addition, the results provide useful insights for the mathematics education community as it shows the diversity among the inservice teachers’ beliefs (presented as hypothesized belief models), the role and influence of beliefs about the nature of mathematics on the belief structure and how the teachers designed their instructional practices to reflect these beliefs. The article concludes with a discussion of implications of teacher education.     

Teachers’ strategies of teaching primary school mathematics in a second language: A case of Botswana

This paper reports the results of a study of primary school mathematics teaching in northern Botswana in order to highlight the strategies teachers use in bi/multilingual classrooms. Questionnaire and interview data collection procedures were used. The findings, which are based on responses of randomly selected primary school teachers, confirmed that monolingual classes were fewer than bilingual and multilingual classes in those parts of Botswana. Furthermore, syllabus analysis confirmed the abstract nature of mathematical concepts. Teachers report to have devised strategies to overcome the difficulties imposed by this classroom situation.     

Teaching anxieties revealed: pre-service elementary teachers’ reflections on their mathematics teaching experiences

Over the last 50?years, there has been ample research dedicated to mathematics anxiety in contexts of teaching and learning. However, there has been less attention focused on pre-service teachers’ anxieties about teaching mathematics in classroom settings. This study analyzed pre-service teachers’ reflections at the conclusion of an elementary mathematics field experience in order to determine common themes surrounding anxiety-related events based on mathematics practice-teaching experiences. Through qualitative analysis of pre-service teachers’ reflections using open and axial coding, three categories and ten themes surrounding elementary pre-service teachers’ anxiety-related events based on mathematics practice-teaching experiences emerged. Some of the themes presented were ones that increased pre-service teachers’ anxieties for teaching mathematics, whereas other themes reflected aspects of the field experience that decreased anxiety for teaching mathematics. Based on the themes revealed in this study, suggestions for strategies and materials that could be developed for university mathematics methods courses are discussed. Novel perspectives for considering mathematics teaching anxiety, such as locus of control and future time perspective, are shared.     

Technology Integration Barriers: Urban School Mathematics Teachers Perspectives

Despite the promise of technology in education, many practicing teachers face several challenges when trying to effectively integrate technology into their classroom instruction. Additionally, while national statistics cite a remarkable improvement in access to computer technology tools in schools, teacher surveys show consistent declines in the use and integration of computer technology to enhance student learning. This article reports on primary technology integration barriers that mathematics teachers identified when using technology in their classrooms. Suggestions to overcome some of these barriers are also provided.     

Game playing and fluctuations in emotional climate

The inclusion of games in mathematics programmes is widely believed to foster the enjoyment of mathematics. The focus of this paper is on fluctuations in emotional climate during the playing of whole-class mathematics games. A multimethod approach drawing on the sociology of emotions was employed to explore changes in the classroom emotional climate that were associated with game playing. The event-oriented inquiry was conducted with two teachers and a class of 10- to 13-year-olds in a New Zealand classroom during mathematics sessions. Over a series of eight mathematics lessons, there were three noticeable fluctuations in emotional climate, all of which occurred during whole-class games. Our analysis of these three events identified a successful interaction with dramatic emotional energy associated with a positive emotional climate, a successful interaction with undramatic emotional energy associated with positive emotional climate, and an unsuccessful interaction associated with negative emotional climate with interactional repair. The third event also illustrated how the incomplete nature of a game’s rules can provide an opportunity for a negative emotional climate to be associated with game playing. The taken-for-granted wisdom that whole-class mathematics games can enhance emotional aspects of a classroom learning environment is supported by some of our evidence.

     

Constructivism in Mathematics Classrooms: Listening to Ghanaian Teachers’ and Students’ Views

One of the challenges of implementing a new curriculum is how to bridge the gap between the underlining principles of the curriculum and the cultural and social orientations of the society which includes teachers and students. This article reports on a study that explored how the cultural and social orientations of teachers and students can influence the implementation of a constructivist curriculum in mathematics classrooms. The data for the study came from 250 students and 41 mathematics teachers, using questionnaires, observations, and interviews. The results showed that inasmuch as mathematics teachers and their students acknowledge the importance of student’s active participation and teamwork, these practices have not been fully conceptualised into the Ghanaian mathematics classroom due to some cultural factors. Two main cultural factors were discovered from the analyses of the results. Firstly, the culture of acknowledging only correct answers in class has a negative impact on individual students’ confidence and participation during mathematics lessons. Also, the culture of teamwork is not fully accepted within Ghanaian classrooms as most students find it difficult working in groups and accepting and appreciating each other’s view. It was evident in all lessons that students were ridiculed by their peers when they provide a wrong answer to a question and this affected individual students’ participation in the classroom. Therefore, we suggested that teachers should be pro-active in promoting a classroom environment which is free from fear and intimidation to motivate students to be actively involved in the classroom discourse.     

Examining the supervision of mathematics student teachers through analysis of conference communications

Student teaching is often a capstone experience in the preparation of mathematics teachers. Thus, it is essential to better understand key aspects of the experience. We conducted a qualitative study of post-lesson conferences led by supervisors (classroom cooperating teachers and a university supervisor) working with mathematics student teachers. Analysis of conference communications revealed differences in the types and content of communications in conferences led by the cooperating teachers and by the university supervisor. Cooperating teachers tended toward evaluative supervision that lacked a focus on the mathematics of the lessons while the university supervisor tended toward educative supervision, guiding student teachers to reflect on and learn from their own classroom experiences including the mathematics of their lessons. Differences are discussed, and suggestions concerning the supervision of student teachers are made along with recommendations for further research.     

Primary School Mathematics Teacher Reflection through a Modelling-Based Professional Development Programme

This article contributes to the discussion on mathematics teacher reflection. Reflection was included in a study of the didactisation practices of primary school mathematics teachers as one of nine didactisation practices. The study involved five volunteer primary school mathematics teachers. A qualitative design-research approach was designed which employed model-eliciting tasks to create new experiences for teachers. This article reports on the nature and development of mathematics teacher reflection. Teacher reflection was gauged at various times during the programme through written responses to open-ended reflective questionnaires. Teachers were involved in three types of sessions for a period of one year: 1) modelling sessions whereby they collaboratively solved a mathematical modelling task; 2) observing primary school students/learners solve the same problems; and 3) sessions discussing traditional and problem-centred teaching and learning. It was found that modelling tasks provided reflective platforms and a window to teacher resources, orientations and goals. It is recommended that further research into mathematics teacher reflection be conducted where teachers specifically implement modelling in their own classrooms.     

Reinscribing urban: teaching high school mathematics in low income, urban communities of color

This article reports findings from a research and professional development project at two high schools located in low-income, urban communities of color. The project collaborates with teachers on improving their instructional practices, using a framework of culturally relevant mathematics pedagogy, which is described in detail here. We present results from a qualitative and quantitative analysis of mathematics instruction in 68 classroom observations of seven teachers. In particular, we use culturally relevant mathematics pedagogy as a lens through which to analyze instruction and the associated opportunities to learn mathematics provided to students.     

The nature of Chinese Language classroom learning environments in Singapore secondary schools

This article reports findings from a classroom environment study which was designed to investigate the nature of Chinese Language classroom environments in Singapore secondary schools. We used a perceptual instrument, the Chinese Language Classroom Environment Inventory, to investigate teachers’ and students’ perceptions towards their Chinese Language classroom learning environments using six dimensions, namely, Student Cohesiveness, Teacher Support, Involvement, Cooperation, Task Orientation and Equity. The investigation was carried out using a sample of 1,460 secondary three (Grade 9) students from 50 Chinese Language classes in 25 Singapore government secondary schools. The nature of the Chinese Language classroom learning environments was interpreted from analyses of the perception scores obtained, as well as from various comparisons of the perception scores between different groups. Although both the Chinese Language teachers and students perceived their present classroom learning environments positively, they would like improvements in all the six dimensions of the classroom learning environments under investigation. Also teachers perceived a more positive classroom learning environment than their students in the same class. In addition, female students perceived their actual and preferred classroom environments more positively than their male counterparts.     

Teachers’ assessments of students’ learning of mathematics

This paper reports a study of the classroom assessment practices of 12 sixth form college mathematics teachers in Malta. It explores the extent to which these teachers are knowledgeable about their students’ learning of mathematics and the implications that this has for their classroom practices. It reveals that these teachers’ knowledge of their students’ understanding of certain mathematical concepts is fairly limited. It then goes on to discuss this phenomenon in terms of a process that can hinder rather than promote learning. The research illuminates the position of teachers who appear to lack certain detailed information about their students which, it can be argued, could inform more effective teaching strategies. The paper concludes by exploring possible implications for similar situations where learning could be enhanced by more effective classroom assessment strategies and their use to inform future teaching and learning activities.     

Including students’ diverse perspectives on classroom interactions into video-based professional development for teachers

Video is often used in professional development courses to sensitize mathematics teachers to students’ thinking and issues of classroom interaction. This article presents an approach that incorporates students’ perspectives on mathematics classroom interactions into video-based professional development in order to enhance teachers’ reflection on diverse awareness of students concerning demands within mathematics classroom interactions. This approach is theoretically justified by the empirical research on equal participation in classroom interaction and practically elaborated by video material from Grade 5 students. Empirical snapshots from design experiments with teachers demonstrate that teachers’ sensitivity can be enhanced.     

Student teachers’ discipline strategies: relations with self-images,anticipated student responses and control orientation

Teacher discipline strategies are well documented when it comes to its effects on students and the working climate in the classroom. Although it is commonly acknowledged that for student teachers classroom management is a major concern, student teachers’ use of discipline strategies is largely unknown. In this paper, we examine student teachers’ beliefs in relation to their discipline strategies. Three clusters of discipline strategies are distinguished: sensitive, directive and aggressive discipline strategies. Beliefs that were taken into account are self-images on control and affiliation, control orientation and anticipated student responses on control and affiliation. All participants were student teachers of a one-year teacher education programme for secondary education in the Netherlands. Student questionnaires were used to measure discipline strategies (n?=?2506). Student teachers’ (n?=?104) self-images, control orientation and anticipated student responses were measured with student teacher questionnaires. Results of the multiple regression analyses showed that student teachers’ sensitive and directive discipline strategies are explained best by self-images on control; aggressive discipline strategies are explained best by self-images on affiliation and by control orientation. Apart from the possible academic interest in these particular findings, results are believed to be useful in a practical sense, in particular for teacher education programmes.     

教师变量对小学生数学学习成绩影响的多水平分析

32名小学数学教师与这些教师所教班级的1691名学生参与了本研究。两个测量工具评价了教师的数学学科知识与学科教学知识,对教师的55节数学课进行了录像,并按照学习任务的认知水平与课堂对话的特点进行了编码,同时测查了学生的期末数学学习成绩。多水平分析结果表明:教师的学科教学知识、课堂学习任务的认知水平、课堂对话中教师提问问题的类型与对话的权威来源对学生的数学成绩具有显著的预测作用;而教师的学科知识对学生数学成绩的影响未达到显著性水平。     

Challenges of critical colleagueship: examining and reflecting on mathematics teacher study group interactions

This article examines mathematics teacher collegiality by focusing on both the ways in which teachers interacted as critical colleagues in a long-term professional development project and the evolving role of the teacher–educator–researcher as the facilitator of this project. The professional development collaboration comprised two phases: one focused on reading classroom discourse literature and one focused on supporting each other through cycles of action research related to mathematics classroom discourse. Lord’s (1994) critical colleagueship framework is used to examine how a study group of middle-grades (ages 11–16) mathematics teacher–researchers took (or did not take) a more critical stance toward their own teaching practice and that of their colleagues. We found that challenging interactions were related to instances in which the teachers interacted as critical colleagues and were marked by particular features including the use of particular words and the use of personal experience as a form of evidence. We present the ways in which we came to understand what it might look like to scrutinize one’s practice and findings related to the development of this type of collegiality across the two different phases of this project. We end with a section in which the teacher–educator–researcher who facilitated the professional development project reflects on the ways in which the analysis caused her to reconsider both the nature of argumentation in mathematics study group settings and what implications this has with respect to her own practice as a facilitator.