Autonomy,beliefs and the learning of elementary mathematics teachers

Seven elementary teachers participated in a project designed to help them learn to teach mathematics according to reform recommendations. Teachers were provided opportunities to learn through both private reflection and public inquiry about their teaching and children's learning. The teachers’ instruction, reflection, and beliefs were studied. All of the teachers adopted some reform-based procedures including having children report problem-solving strategies. However, only three of them developed more complex practice in which children were involved in inquiry into one another's strategies. The groups had different beliefs about the autonomy of children to construct mathematics and their own autonomy to make instructional decisions.     

Effective teaching in elementary mathematics: Identifying classroom practices that support student achievement

Recent investigations into the education production function have moved beyond traditional teacher inputs, such as education, certification, and salary, focusing instead on observational measures of teaching practice. However, challenges to identification mean that this work has yet to coalesce around specific instructional dimensions that increase student achievement. I build on this discussion by exploiting within-school, between-grade, and cross-cohort variation in scores from two observation instruments; further, I condition on a uniquely rich set of teacher characteristics, practices, and skills. Findings indicate that inquiry-oriented instruction positively predicts student achievement. Content errors and imprecisions are negatively related, though these estimates are sensitive to the set of covariates included in the model. Two other dimensions of instruction, classroom emotional support and classroom organization, are not related to this outcome. Findings can inform recruitment and development efforts aimed at improving the quality of the teacher workforce.     

Theoretical beliefs and instructional practices used for teaching spelling in elementary classrooms

The current study aimed to examine teachers’ reported spelling assessment and instruction practices. Analysis of the match between teachers’ theoretical beliefs about spelling and their reported pedagogy was conducted to elucidate factors that may support or impede the use of evidence-based teaching strategies in the classroom. An electronic survey was completed by 405 randomly selected (stratified by region and socioeconomic status) elementary school teachers in New Zealand. The survey examined the following areas: spelling assessment, spelling instruction, beliefs about spelling, preparing teachers to teach spelling, and teachers’ perceived strengths and weaknesses of their spelling program. There was large variability in spelling assessment and instructional practices across teachers. Most respondents reported implementing some aspects of a developmental approach to spelling instruction through analysis of children’s spelling errors (64 %) and/or individualization of the spelling program (60 %). There was a large dissociation between teachers’ beliefs about spelling and their frequency of use of specific instructional practices associated with those beliefs (e.g., phonological awareness, orthographic knowledge). The mismatch between beliefs and reported practice appeared to be due to lack of professional knowledge regarding implementing explicit spelling instruction and finding time to teach spelling within the curriculum. Increasing teachers’ knowledge about language structure, practical implementation of key assessment and instruction activities, and the links between spelling and other areas of the curriculum are important factors in improving spelling pedagogical practices.     

The significance of mathematical knowledge in teaching elementary methods courses: perspectives of mathematics teacher educators

Our study investigates perspectives of mathematics teacher educators related to the usage of their mathematical knowledge in teaching “Methods of Teaching Elementary Mathematics” courses. Five mathematics teacher educators, all with experience in teaching methods courses for prospective elementary school teachers, participated in this study. In a clinical interview setting, the participants described where and how, in their teaching of elementary methods courses, they had an opportunity to use their advanced mathematical knowledge and provided examples of such opportunities or situations. We outline five apparently different viewpoints and then turn to the similar concerns that were expressed by the participants. In conclusion, we connect the individual perspectives by situating them in the context of unifying themes, both theoretical and practical.     

Comparing teaching practices,teacher content knowledge and pay in Punjab

This study utilises a unique school based survey of public, private and Public Partnership Programme (PPP) schools in Punjab, Pakistan to identify the correlates of: teacher behaviour in the classroom, teacher content knowledge mastery, and teacher pay. The study finds that private school teachers are associated with lower classroom observation scores than public school teachers, and both private and PPP school teachers are less likely to exhibit content knowledge mastery in Urdu than public school teachers (however, this is not the case for math and English). Public school teachers recruited after the introduction of test-based teacher recruitment are 30 percentage points more likely to demonstrate math content knowledge mastery than teachers recruited prior to test-based recruitment. The study also finds evidence of a pay gap between male and female teachers in both public and PPP schools after controlling for other characteristics. Teachers’ math content knowledge scores were found to be statistically significant correlates of teacher pay for private school teachers, but not for PPP or public school teachers. For female PPP school teachers, having higher academic qualifications is associated with higher wages however, this is not the case for male teachers in these schools.     

Learning environment,self-efficacy for teaching mathematics,and beliefs about mathematics

Learning environment research has a long history of significant relationships between the learning environment and student outcomes. This study investigated relationships between the learning environments of mathematics courses in a teacher education program and two outcomes, mathematics teaching self-efficacy and beliefs about mathematics. These two outcomes have been repeatedly shown to influence the future teaching practices of preservice teachers but, to date, their relationships with learning environment have been investigated neither with preservice teachers nor at all in the United Arab Emirates or wider Gulf region. The learning environment was found to be significantly related to preservice teachers’ mathematics teaching self-efficacy and beliefs about mathematics. Learning environments perceived more favourably by preservice teachers were associated with higher self-efficacy for teaching mathematics, but also with more-traditional beliefs, making these findings important for higher education institutes and teacher educators.

     

小学教育专业高等数学教学探析

从三个方面对小学教育专业高等数学的教学进行了探讨，即：充分展示数学思维过程；突出数学思想方法；突出高等数学与初等数学在内容上的互补性。     

GCSE mathematics in further education: challenging beliefs and practices

This paper describes the outcomes of a two-year study on the beliefs and practices adopted by four FE teachers in their attempt to teach one-year GCSE retake classes and the subsequent effects on students' learning. In the second year of the study, an attempt was made to perturb these practices by introducing a substantial collection of classroom discussion resources. These focused on well-known conceptual obstacles and were intended to provoke cognitive conflict and reflection. Modest, yet significant learning gains were observed with two of the classes, but not with the others. Reasons for this appear to be related to teachers' beliefs about learning.     

The longitudinal influences of computer-intensive learning experiences on at-risk elementary students

This evaluation study examined the school achievement and adjustment by at-risk students one year following their participation as fifth and sixth graders in computer-intensive classrooms using the Apple Classrooms of Tomorrow (ACOT) program. Comparisons between the former ACOT subjects and a matched control group who had attended the same elementary school were made on attitudes toward school, teacher evaluations, grades, computer skills, and standardized test scores. Results showed some advantages for the ACOT students in the seventh grade, but on most measures they were indistinguishable from the control group. Specifically, both groups appeared to remain at risk based on their poor performance and relatively poor adjustment. A key factor in interpreting outcomes for the ACOT group was the limited availability of computers in the seventh grade, which thus restricted their opportunities to apply or transfer the skills they had learned. This research was supported by a grant from Apple Classrooms of Tomorrow, Apple Computer, Inc.     

Prospective teacher beliefs about liberative and oppressive mathematics teaching practices: a first step toward equitable instruction

This article reports findings from a study conducted within a teacher education program to help highlight the importance of equitable instruction of mathematics for all students. The researcher developed four scenarios of her oppressive and liberative teaching practices. Prospective teachers were then asked to write scenarios describing their oppressive and liberative teaching practices. Results showed that prospective teachers found it easier to write liberative teaching practices of themselves than oppressive examples. Scenario themes centered on allowing students ample time to understand mathematical concepts, having high expectations for all students, and addressing individual student’s needs. Developing prospective teachers who are aware of equity in teaching requires ample time to discuss authentic issues in diversity. Teacher educators need to be aware of their own oppressive and liberative teaching practices in doing such work.     

The PISA mathematics regime: knowledge structures and practices of the self

Within mathematics education research, the responses to the Programme for International Student Assessment’s (PISA’s) international testing regime tend to accept its framework and results as necessary points of reference, even when offering a critical reinterpretation or challenging national policy discourses based on PISA. In this article, we offer a different approach to the critique of PISA, drawing on theoretical tools provided by Bernstein and Foucault, to ask what the PISA regime achieves. Our understanding of this achievement encompasses both the production of knowledge structures and the production of students, teachers and other agents as subjects. We propose that the theoretical approach we offer provides a methodological entry point into analysis of the texts comprising the PISA mathematics regime. Analysis of a single PISA item is used to illustrate the insights that may be gained from such a theoretical lens. Such insights into the logic of PISA have the potential to allow us better to understand and hence contest the role that PISA and other large-scale assessment regimes may play in global and local policy discourses.     

探讨小学数学课堂教学的有效性提问

随着我国经济社会的不断发展和进步,以及新课改和素质教育的推进和落实,我国教育事业发展也越来越快越来越好,教学理念和教学方法也在不断改革和创新。各个学校在提升学生文化知识能力的同时,更加注重学生综合素质和能力水平的培养。在小学数学教学中,有效性的提问教学能够有效提升小学生的学习兴趣和能力,促进小学生全面发展和进步。     

The purpose, design and use of examples in the teaching of elementary mathematics

This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching, and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the analysis of these lessons was to discover, and to construct theories around, the ways that these novice teachers could be seen to draw upon their mathematics teaching knowledge-base in their lesson preparation and in their observed classroom instruction. A highly-pervasive dimension of the findings was these teachers’ choice and use of examples. Four categories of uses of examples are identified and exemplified: these are related to different kinds of teacher awareness.

Linking reform-oriented experiences to teacher identity: The case of an elementary mathematics teacher

Novice teachers often have difficulty transferring what they learn in teacher education programs to classroom practice. This is especially true for elementary school teachers who are expected to teach mathematics with reform-oriented methods. The purpose of this longitudinal case study was to examine the experience of one novice elementary school teacher over a 3-year period, and understand the factors that supported her to enact a reform-oriented practice in mathematics as she transitioned from being a preservice to inservice teacher. Influential mathematics education models, her commitment to learning, and school-based contexts affected her teaching identity and practices. To conclude, an argument is made for teacher education experiences to explicitly address mathematics teacher identity to support the enactment of reform-oriented practices.     

Opening the black box of field experiences: How cooperating teachers' beliefs and practices shape student teachers' beliefs and practices

This study employed ethnographic methods to describe and explain changes to beginning science teachers' (n = 6) practices and beliefs during a year long internship. Teaching practices were strongly influenced by the cooperating teachers. Initially, all six interns attempted to re-enact lessons they witnessed their cooperating teachers teach, including following lesson structures and borrowing representations, anecdotes, and jokes. Later, they independently implemented instruction that emphasized similar strategies as their mentors, regardless of whether or not they were experiencing success. Interns who were successful also shifted their beliefs to match their mentors.     

Teacher voices from an online elementary mathematics community: examining perceptions of professional learning

Journal of Mathematics Teacher Education - This study compares web usage data with interviews from 41 participants, who are members of an online professional development site called the Everyday...     

情境教学在小学数学教育中的应用研究

数学新课程的教学设计尤其注重充分发挥学生的主体作用,这就要求教师要在教学中设计合适的教学情境和教学条件,充分调动学生的学习热情和动力,引导学生主动参与到教学之中。本文以情境教学在小学数学教学中作用、实现情境教学的方法和应注意事项为重点,对情境教学在小学数学教育中的应用开展了较为详细的研究。     

The development of beginning mathematics teacher pedagogical content knowledge

Recent research efforts (Schmidt et al. in The preparation gap: teacher education for middle school mathematics in six countries, MSU Center for Research in Mathematics and Science Education, 2007) demonstrate that teacher development programs in high-performing countries offer experiences that are designed to develop both mathematical knowledge and pedagogical knowledge. However, identifying the nature of the mathematical knowledge and the pedagogical content knowledge (PCK) required for effective teaching remains elusive (Ball et al. in J Teacher Educ 59:389–407, 2008). Building on the initial conceptual framework of Magnusson et al. (Examining pedagogical content knowledge, Kluwer, Dordrecht, pp 95–132, 1999), we examined the PCK development for two beginning middle and secondary mathematics teachers in an alternative certification program. The PCK development of these two individuals varied due to their focus on developing particular aspects of their PCK, with one individual focusing on assessment and student understanding, and the other individual focusing on curricular knowledge. Our findings indicate that these individuals privileged particular aspects of their knowledge, leading to differences in their PCK development. This study provides insight into the specific aspects of PCK that developed through the course of actual instructional practice, providing a lens for future research in this area.