Reconstructing elementary teacher candidates' understanding of mathematics and science content

This paper examines the mathematics and science content knowledge of elementary teacher candidates. Data are presented which demonstrate that many elementary teacher candidates enter teacher education seriously deficient in their understanding of the subject matter they will teach to elementary students. The authors argue that these candidates are weakly prepared in content because of deficiencies in the pedagogy practiced in traditional didactic mathematics and science courses. They describe a conceptual approach to teaching mathematics and science content and contrast this with a didactic approach. Data are presented which demonstrate that these conceptual approaches significantly improved novice teachers understanding of content.     

Drawing Nature of Science in Pre-service Science Teacher Education: Epistemic Insight Through Visual Representations

Developing pre-service science teachers’ epistemic insight remains a challenge, despite decades of research in related bodies of work such as the nature of science (NOS) in science education. While there may be numerous aspects to this problem, one critical element is that the NOS is a meta-concept that demands higher-order cognitive skills. One possible strategy to facilitate pre-service teachers’ understanding of epistemic aspects of science is visualisation. Visual representations of objects and processes can be tools for developing and monitoring understanding. Although the NOS and visualisation literatures have been studied extensively, the intersection of these bodies of literatures has been minimal. Incorporating visual tools on the NOS in teacher education is likely to facilitate teachers’ learning, eventually impacting their students’ learning of the NOS. The objective of this paper is to illustrate how the visual tools of scientific knowledge and practices aspects of the NOS can be integrated in science teacher education in order to develop pre-service teachers’ epistemic insight. The paper presents an empirical study that incorporated visual tools about the NOS in primary science teacher education. Data on 14 pre-service teachers’ are presented along with in-depth case studies of 3 pre-service teachers illustrating the influence of the teacher education intervention. The qualitative analysis of visual representations before and after the intervention as well as verbal data suggests that there was improvement in pre-service teachers’ perceptions of the NOS. Implications for future research on visualisation of the NOS are discussed.     

Digital Simulation Games for Social Studies Classrooms

Data from ten teacher candidates studying teaching methods were analyzed to determine perceptions toward digital simulation games in the area of social studies. This research can be used as a conceptual model of how current teacher candidates react to new methods of instruction and determine how education programs might change existing curricula to better prepare their students toward methods that have the ability to evoke higher-order thinking skills and technology integration.     

Understanding Teacher Educators and Their Pre-Service Teachers through Multi-Media Case Studies of Practice

The challenges facing those who seek to prepare mathematics teachers are well established in the literature. Most of the research to date has focused on the perceptions and understandings of pre-service teachers, but not on the perceptions and understandings of teacher educators. In this study, we explore how four teacher educators understand their pre-service secondary teachers as the pre-service teachers attempt to make sense of teaching through the investigation of a multimedia case study of practice. We found that the teacher educators adopted two different implementation strategies: one strategy tended to be open-ended and exploratory; the other was more focused on the teacher educators' goals of anticipating student understanding and developing mathematical content knowledge for teaching. We also found that, in using the case study, teacher educators elicited pre-service teachers' thinking about the complexities of the teacher's role in small group work, about the value of explicitly revealing the teacher's reflections on the lessons, about the role of planning and preparation, and about the limits of pre-service teachers' abilities to understand and appreciate students' thinking and to extend lesson ideas. Both teacher educators and their pre-service teachers gained perspectives on the role of a teacher's mathematical content knowledge. These results imply that multimedia case studies of practice can serve as vehicles for revealing the knowledge and practice of teacher educators, as they engage in supporting the professional development of pre-service teachers.     

Cognitive and Attitudinal Predictors Related to Line Graphing Achievement among Elementary Pre-service Teachers

The purpose of this study was to determine the extent to which six cognitive and attitudinal variables predicted pre-service elementary teachers’ (N = 87) performance on line graphing. Predictors included reading comprehension and mathematics scores, logical thinking performance scores, as well as measures of attitudes toward science, mathematics and graphing. Results indicated that mathematical and logical thinking ability were the most significant predictors of line graph performance among the other variables, accounting for 41% of the total variability. Findings from this study suggest that elementary science education programs augment instruction to include aspects of mathematics and logical thinking.     

Development of Arithmetical Thinking: Evaluation of Subject Matter Knowledge of Pre-Service Teachers in Order to Design the Appropriate Course

One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of “number” and the development thereof, calculation methods and strategies. properties of operations on different sets of numbers, as well as the properties of the numbers themselves. Hence, the question arises: how to educate PMTs in order to supplement their mathematical knowledge with the required components? The present study explored the development of arithmetic thinking among pre-service teachers intending to teach mathematics at elementary school. This was done by matching the van Hiele theory of the development of geometric thinking to arithmetic. Analysis of findings obtained both in the present study and in many studies of geometry teaching indicates that this approach to considering the learners’ level of thinking development might lead to meaningful learning in arithmetic course for PMTs.     

Balancing Acts: Negotiating authenticity and authority in shared reflection

In this self-study, a teacher educator and an experienced teacher analyze an unexpected shared opportunity to mentor pre-service elementary educators. Our partnership arose during a graduate course on literacy development for elementary students, serendipitously captured during an extended electronic conversation with the pre-service candidates. We uncovered an interplay between authenticity and authority that generated enhanced professional development for each of us and for the teacher candidates who were enrolled in the course. As well as reflections on our own practices, implications for teacher education development and pedagogy are noted.     

An Exploration of the Relationship Between Case Study Methodology and Learning Style Preference

The purpose of this study was to look at the use of the case method approach in relation to the preferred learning style of students in an elementary science methods course. Ninety-seven students enrolled in an elementary and elementary/middle level science methods course at Midwest university participated in this study. Participants completed a Barsch Learning Styles Inventory to determine learning style preference. At the end of the semester, students were asked to rate the eight identified teaching methods utilized throughout the semester as to their effectiveness. This research shows that pre-service teachers found the use of case studies as potentially useful in helping them learn and process course content no matter what learning style preference the pre-service teacher has.     

重视数学阅读,打造深度学习课堂

许多小学数学教师已然认识到了开展小学数学阅读活动和制定科学的教学方法,对提高学生的计算能力和思维能力的重要作用。所以,教师在教学过程中要积极探索科学的教学方法培养学生的有效阅读能力,这样学生才能够更好地理解和学习数学知识,提高学生的解题思维能力和学习有效性。以下便对数学阅读活动的开展和深度学习课堂的构建进行分析和探究。     

Values in the mathematics classroom

Abstract

Values, moral values and democratic values are attracting the attention of education researchers in general and mathematics education researchers in particular. Little research has studied pre-service teachers’ perceptions of values in the classroom, their perceptions of the relationship between the different variables of values in the classroom, as well as their relationship with the democratic society. The present research attempts to do so. Twenty-two graduate pre-service teachers who participated in ‘New trends in mathematics education’ course discussed how to cultivated values in the mathematics classroom. Moreover, they answered survey questions related to the cultivation of values in this classroom. We used a combination of deductive and inductive content analysis to characterize the pre-service teachers’ texts. The research results indicate that the pre-service teachers perceived values as encouraging students’ activity in the mathematics classroom. In addition, the pre-service teachers perceived values as encouraging specific categories of values needed as skills for the citizen in a democratic society, as creativity, critical thinking and metacognition.     

In Pursuit of a Connected Way of Knowing: The Case of One Mathematics Teacher

In this paper, we offer illustrations of a mathematics teacher’s difficulties with content knowledge when trying to find connections between school mathematics and science; we do so by describing the development of this teacher’s thinking and learning in her pursuit of connections between the concepts of slope of a line and density of matter. The paper is based on a sub-study that is part of a larger Colombian project, PROMESA (Creating Science and Mathematics Connected Learning Experiences that Open Opportunities for the Promotion of Algebraic Reasoning), which incorporated a Professional Learning Programme (PLP) seeking to integrate school science and mathematics teachers into working teams, in order to create science and mathematics connected learning experiences that considered the promotion of algebraic reasoning. The ‘challenging questions’ that emerged for this teacher, during the workshops of the induction stage of the PLP, became the driving force for her continued engagement in learning mathematics content in a connected way, as opposed to the compartmentalised content-item thinking that she had experienced as a school student. We provide illustrations of first steps in the development of a teacher’s mathematical understanding, which can support growth of mathematical knowledge for teaching.     

The Mathematics of Estimation: Possibilities for Interdisciplinary Pedagogy and Social Consciousness

The purpose of this article is to report on the importance of providing pre-service and in-service teachers with experience and specific training in critical thinking skills. The essential concepts in elementary mathematics curricula can be augmented to include and cultivate critical thinking skills that have tremendous ramifications for future leaders and for those who move on to more technical training. A sample problem, along with pre-service teacher responses, is used here to show the necessity and importance of this kind of training as the responses show clear evidence of a certain naivete on the part of these college level students. The responses do show evidence of budding social conscience in the students, but the level of expertise in critical thinking is not at all sophisticated. We discuss and explore the implications of our approach.     

数学思想方法在小学数学教学中的渗透路径

数学课程的精华在于数学思想方法。以下将小学数学教学作为载体,先对小学数学教学中渗透数学思想方法的意义进行分析,随后探讨小学数学教学中渗透数学思想方法的路径,希望提供有利参考。     

Designing and implementing authentic investigative proportional reasoning tasks: the impact on pre-service mathematics teachers’ content and pedagogical knowledge and attitudes

In this study we created, implemented, and evaluated the impact of proportional reasoning authentic investigative tasks on the mathematical content and pedagogical knowledge and attitudes of pre-service elementary and middle school mathematics teachers. For this purpose, a special teaching model was developed, implemented, and tested as part of the pre-service mathematics teacher education programs conducted in Israeli teacher colleges. The conclusion of the study is that application of the model, through which the pre-service teachers gain experience of and are exposed to authentic investigative proportional reasoning tasks with incorporation of theory (reading and analyzing relevant research reports) and practice, leads to a significant positive change in the pre-service teachers’ mathematical content and pedagogical knowledge. In addition, improvement occurred in their attitudes and beliefs towards learning and teaching mathematics in general, and ratio and proportion in particular.     

Mapping the social side of pre-service teachers: connecting closeness,trust, and efficacy with performance

This exploratory study foregrounds the important, but often understudied social side of pre-service teacher development and its relation to teaching performance in one university-based teacher preparation program in the US. We examine the extent to which pre-service elementary teachers’ social relationships and perceptions of peer trust and efficacy are associated with performance on a high stakes mathematics teaching assessment. Findings suggest that social and emotional support through close social ties, peer trust, and self-efficacy are significantly and positively associated with pre-service teachers’ teaching performance. Our work further contributes to the development and discourse about teacher education in university-based teacher preparation programs.     

Pre-service teachers’ future-oriented mathematical identity work

Research on identity has been a growing domain in the contexts of teacher education and mathematics education; however, identity work has been explored to a much lesser extent, with a future orientation overlooked. In addition, earlier studies have not provided sufficient knowledge on how different elementary teacher education programs might facilitate pre-service teachers’ identity work. In this study, we compare future-oriented mathematical identity work through a narrative framework considering six pre-service teachers undergoing two different teacher education programs. All pre-service teachers reported having had negative experiences with mathematics during their school years. Based on the results we conclude that despite the striking similarities in pre-service teachers’ mathematical backgrounds, the ways in which these cases are conducting their identity work differ substantially. It seems that the main reasons for these differences are different emphases and pedagogical practices in mathematics education courses. Additionally, we further elaborate on our earlier conceptualisation of identity work.     

小学课程中的数学文化:内涵特点、主要内容与学习价值

数学文化是指数学的思想、精神、语言、方法、观点以及它们的形成与发展,还包括数学在人类生活、科学技术、社会发展中的贡献和意义,以及与数学相关的人文活动。与纯粹的数学知识相比较,数学文化体现了人文性与科学性交融、开放性与包容性并存、民族性与统一性共生,以及价值理性与工具理性互推的特点。适合小学生学习的数学文化内容主要有数学知识的发展历史、数学家的成长故事、数学的游戏活动、数学的生活应用和学科应用。小学生学习数学文化有助于他们理解数学知识、掌握数学思想方法、提高数学思维水平、加强数学应用意识和培养数学精神。     

Mathematical myths: Teacher candidates' beliefs and the implications for teacher educators

Abstract

For more than 2 decades, professional, state, and federal agencies have adopted educational standards aimed at improving mathematics instruction. One way of measuring the success of these adopted standards is to examine their impact on the mathematics attitudes and beliefs of students who received their education during this reform period. How teachers approach and implement these mathematics standards is heavily influenced by what they believe about mathematics content and pedagogy. For those who seek to improve mathematics education, examining beliefs regarding mathematics and the factors that influence those beliefs is imperative. In this paper we explore the persistence of teacher candidates' beliefs in myths despite changing educational standards. The beliefs of 76 current elementary teacher candidates were compared to beliefs of 131 elementary teacher candidates from 1990. The results confirm the pervasiveness and persistence of math myths among female elementary teacher candidates.     

Contrasting Research Perspectives: What the evidence yields

This paper reviews pre-service elementary teachers' beliefs about mathematics and mathematics teaching and, learning from an earlier study of the mathematics methods course of a teacher education program, then overviews the data triangulation, and discusses the inconsistencies and contradictions in the data. Thus, the study offers further insight into the complexities of pre-service teachers' unwavering conceptions and their acquisition of innovative pedagogy. Questions emerged about the inconsistencies between what was said and what was done. For example, why were the pre-service teachers' responses in surveys and interviews inconsistent with their instructional behavior? Explanations to this and other questions are offered to shed some light on two of the most unsettling features of teacher education: changing pre-service teachers' beliefs and their learning of mathematics pedagogy.