Mathematical Modeling for Preservice Teachers: A Problem from Anesthesiology

The study reported in this article deals with the observed actions of prospective Swedish mathematics teachers as they were working with a modeling situation. These prospective teachers were preparing to teach in Grades 4 to9 or in the gymnasium (Grades 10 to 12) and were students in a course in mathematical modeling. The larger study of which this study was a part focused on these students' understanding of modeling and how they related mathematical models to the real world. This article also attempts to illustrate how mathematics is intertwined with many other subjects, in this case medicine. This revised version was published online in July 2006 with corrections to the Cover Date.     

Computational estimation skill of preservice teachers: operation type and teacher view

Despite the importance of computational estimation skill for the improvement of number sense, little research exists on preservice teachers’ estimation skills and their view on estimation in the US context. This study examined the computational estimation skill of 58 preservice elementary teachers (PSTs) and its relationship to their views of the meaning of estimation and the importance of teaching it. Three sets of instruments were used: an estimation task, a computational task, and a belief survey. Results indicated that PSTs performed differently depending on the types of operations on the estimation test. It was also found that different types of problems elicited different strategies. Furthermore, the intervention of the study, along with five other factors were found to significantly correlate with estimation skills. The five factors include PSTs’ mathematical knowledge, their reported confidence about estimation skills, their self-reported knowledge about calculator use in instruction, their views of estimation in teaching mathematics, and their definition of estimation. A negative correlation was documented for the knowledge of calculator use in instruction, and positive correlations were present for other factors. Implications are discussed in accordance with these findings.     

Engineering design and the development of knowledge for teaching among preservice science teachers

The goal of this article is to inform professional understanding regarding preservice science teachers’ knowledge of engineering and the engineering design process. Originating as a conceptual study of the appropriateness of “knowledge as design” as a framework for conducting science teacher education to support learning related to engineering design, the findings are informed by an ongoing research project. Perkins’s theory encapsulates knowledge as design within four complementary components of the nature of design. When using the structure of Perkins’s theory as a framework for analysis of data gathered from preservice teachers conducting engineering activities within an instructional methods course for secondary science, a concurrence between teacher knowledge development and the theory emerged. Initially, the individuals, who were participants in the research, were unfamiliar with engineering as a component of science teaching and expressed a lack of knowledge of engineering. The emergence of connections between Perkins’s theory of knowledge as design and knowledge development for teaching were found when examining preservice teachers’ development of creative and systematic thinking skills within the context of engineering design activities as well as examination of their knowledge of the application of science to problem‐solving situations.     

The challenges facing initial teacher education: Irish prospective elementary teachers’ mathematics subject matter knowledge

Given the acknowledged relationship between teachers’ knowledge, their teaching and pupil learning, teachers’ mathematics subject matter knowledge (MSMK) has received increased attention internationally. As children's early mathematics experiences have been recognized as a critical stage, elementary teachers’ MSMK has become a focal point among researchers and policy makers alike. International research findings have uncovered that in many cases, there is a mismatch between what is perceived to be an appropriate MSMK for teaching elementary mathematics and that demonstrated by many qualified and prospective elementary teachers. Following repeated incidences of weak MSMK during interactions with prospective elementary teachers in one Irish College of Education (provider of initial teacher education programme for elementary teachers), this study sought to examine and address the issue purposefully through two cycles of action research. This article focuses on the data collected prospective teachers’ MSMK in the initial stage (reconnaissance) of these cycles, i.e. pre-test findings. While considerable differences were evident among the pre-test population, the findings suggest that prior to the intervention stage many participating prospective teachers; regardless of previous mathematics achievements or the level of mathematics study; demonstrate weaknesses and gaps in their ‘common’ MSMK. Particular difficulties were evident in relation to pre-test items requiring knowledge of rational numbers, conceptual understanding or problem solving. These findings highlight the inadequacy of previous mathematics achievements and indeed minimum entry requirements as predictors of MSMK for teaching. As well as its contribution at a local and national level, the findings provide an Irish perspective on this international issue.     

Exploiting the potential of primary historical sources in primary school: a focus on teacher’s actions

Integrating history of mathematics in classes could be a hard task with young pupils. Indeed, original historical sources have a language that is far from the modern one. Such texts represent cultural artefacts that can give access to mathematical knowledge. The teacher can exploit such potential acting as a mediator between the mathematical signs of the source and those signs that are accessible to students. Through a case study, we investigate the role of the teacher in the process of semiotic mediation during a collective discussion. The analysed intervention is made of two phases: firstly, students work collaboratively and secondly, the teacher mediates a discussion aimed at institutionalizing the knowledge. During the discussion, working on a text from Tartaglia’s translation of Euclid’s Elements, a group of fifth graders constructs a definition of prime numbers. Referring to the Theory of Semiotic Mediation, we analyse the role of the teacher in building up semiotic chains linking students’ productions to an institutionalized knowledge emerging from the collective discussion. We highlight how teacher’s focalization on students’ words allows the progress of the discussion: the potential of the historical text is exploited fostering a definition that is close to culturally shared mathematics.     

新手-熟手高中化学教师PCK个案比较研究* ——以“氧化还原反应”主题为例

采用访谈法与质性资料分析法,测查了6名(3名新手与3名熟手)高中化学教师关于氧化还原反应主题的PCK。结果表明:(1)新手教师与熟手教师在CTO,KoL与KoS组分上存在较明显的差异。新手教师倾向于采用“教师-传授”教学取向,对学生知识的把握相对不足,更强调使用习题巩固策略;而熟手教师倾向于采用“学生-建构”教学取向,对学生知识的把握更为全面,更强调学生自主建构知识的过程。(2)新手教师与熟手教师在KoC与KoA组分上存在较明显的相似之处。在课程知识方面,教师对课程标准与教材中氧化还原反应主题内容具有较好的理解,但对化学基本观念、学科核心素养认识尚浅;在评价知识方面,教师偏向于传统的评价方式,且集中在形成性评价和总结性评价,但相对缺乏对学生的课前诊断性评价。文末据此对我国化学教师教育及其研究提出相关建议。     

理科职前教师科学模型理解的调查研究

就科学模型的理解对553名理科职前教师进行问卷调查。结果发现：（1）职前教师对科学模型的认识处于中上水平,仍需进一步提高;（2）科学模型的多个维度之间职前教师的理解水平相当;（3）职前教师对科学模型的认识并非随年级逐渐递增,具有不稳定性、反复性;（4）专业学习内容的差异对教师科学模型的认识有着重要影响;（5）科学模型的认识性别差异不明显。基于此提出了关于理科职前教师教育中加强科学模型教学的3点启示。     

国外科学教师信念的理论与实证研究评述

评述国外科学教师信念的理论与实证研究,前者主要包括信念的定义内涵与理论框架,后者主要涵盖信念的测评方式、以及信念与实践的关系等;并据此探讨这类研究对我国化学教师教育的启示,以期对我国化学教师信念研究与化学教师发展提供有益思路。     

University−Urban High School Partnership: Math and Science Professional Learning Communities

This study focused on science and math professional learning communities (PLCs) that were implemented through a university‐urban high school partnership. These PLCs were part of mandated school‐wide, content‐based PLCs implemented as part of the reform efforts initiated in an urban school to address the school's failure to meet Adequate Yearly Progress (AYP) for four years consecutively and low graduation rate (less than 25%) for male students. The key issues were (a) students had continually earned low test scores; (b) there was continuous principal turnover; (c) faculty morale was at an all‐time low, and the quality of teaching was very poor; and (d) the students were not effectively disciplined. The study examined the impact that university faculty‐led mandated PLCs have on teachers' practices and students' learning and achievement. Analysis of data revealed practices that were effective in developing and implementing these successful math and science PLCs. Three themes emerged: ethics of care, teacher agency, and aesthetics of professional interactions. Each theme contained key features that appeared to contribute to the implementation of a successful PLC.     

同伴指导影响师范生课堂教学基本技能的实验研究

为了找寻训练师范生课堂教学行为的有效策略，对某师范大学的38名师范生进行教育实验，探讨了教师单向指导训练策略和同伴相互指导训练策略对师范生课堂教学行为变化的影响。结果表明，相比教师单向指导策略，同伴相互指导策略能激发全体师范生的积极主动性，是一种低消耗、高效率的训练师范生教学基本技能的有效策略。