Focusing on Units to Support Prospective Elementary Teachers' Understanding of Division in Fractional Contexts

This theoretical paper proposes a way to extend the partitive and measurement interpretations of whole number division to fractional contexts focusing on the issue of units. We define the unit‐changing and unit‐keeping interpretations for division and suggest a stronger and earlier focus on the concept of units in courses for prospective elementary teachers. As we highlight the importance of the concept of unit, we use the proposed interpretations in the analysis of one example that emerged in our methods course, discuss the idea of inverting and multiplying, and suggest implications for teacher education.     

The Effect of Process Approach Instruction upon Changing Pre-Service Elementary Teachers' Attitudes Toward Science

The responsibility of and the challenge to every teacher of science were never greater. At the same time the pleasure, the excitement, and the importance of teaching science grow in direct proportion to increasing responsibilities and challenge. It is absolutely essential that pre-service and in-service teacher education programs be the best possible—a goal attainable only if all those interested in science, in teaching and in the public welfare offer to assist teachers and contribute their special talents to the improvement of teacher education. (1)     

Investigating Elementary Teachers' Conceptions of Animal Classification

Numerous studies have been conducted regarding alternative conceptions about animal diversity and classification, many of which have used a cross‐age approach to investigate how students' conceptions change over time. None of these studies, however, have investigated teachers' conceptions of animal classification. This study was intended to augment the findings of past research by exploring the conceptions that elementary teachers possess about animal classification. Using interviews and written items, we documented teachers' conceptions about animal classification and compared them with student conceptions identified in previous research studies. Many of the teachers' conceptions observed in this study were similar to students' conceptions in that they were often too limited or too general compared with scientifically accepted conceptions. Also, the teachers in this study frequently used “non‐defining” characteristics, such as locomotion and habitat, to classify animals. As a result, several misclassifications were observed in the teachers' responses to the written items. Notably, the results of our study demonstrate that teachers often have the same alternative conceptions about animal classification as students. We explore some possible explanations for these alternative conceptions and discuss the instructional implications of the findings.     

Influence of a Mathematics Teachers' Circle on Elementary Teachers' Use of Problem Solving

Math teachers' circles are a form of professional development that is recommended by the Conference Board of the Mathematical Sciences in their publication Mathematical Education of Teachers II (2012). However, little research has been published on how effective math teachers' circles are in advancing the mathematical knowledge of teachers and influencing their actual teaching practice. This study reports how 25 elementary teachers from schools with minority and economically disadvantaged populations responded to a math circle experience. A pretest and posttest showed a significant increase in problem‐solving ability. Through analysis of journals, all but 4 of the 25 teachers indicated that participation in the math circle increased their understanding of problem solving and advanced their use of problem solving in the classroom.     

The Role of Reflection in Elementary Mathematics and Science Teachers' Training and Development: A Meta‐Synthesis

Meaningful and effective training and professional development programs for teachers are key to the improvement of teaching practices in our schools. In this paper, the authors offer a meta‐synthesis of the literature on the role of reflection for mathematics and science teachers within the context of professional development. The authors frame this review using Desimone's core components of professional development, a research‐based framework emphasizing components tied to positive outcomes (content focus, active learning, coherence, duration, and collective participation). A synthesis of literature in this area shows that few training and professional development programs include all five components of Desimone's core conceptual framework for effective professional development linked to positive outcomes. Further, the authors find in their review that increased contact hours included in a professional development program produce an increase in frequency, duration, and depth of reflective practice for teachers.     

Assessing Elementary Understanding of Multiplication Concepts

This article summarizes the basic concepts of multiplication and provides some evidence that the traditional third‐grade curriculum and instruction emphasizing memorization of multiplication facts produces much less understanding of the basic concepts of multiplication than a standards‐based curriculum and instruction emphasizing construction of number sense and meaning for operations. This study also describes a collection of assessment tasks that provided meaningful evidence of children's understandings of basic multiplication concepts, including understandings of the relationships between multiplication and addition.     

Preservice Teachers' Understanding of Perimeter and Area

Fifty-four postgraduate (elementary school) preservice teachers were given four tasks, two to assess their understanding of perimeter and two to assess their understanding of area. The teachers were asked to prepare a question that would assess student understanding of perimeter. Then they were given three problems and asked to decide whether the problems had sufficient information for a solution. The type of question prepared for the first task and the number of preservice teachers who stated that the other three tasks had insufficient information indicate a procedural understanding of perimeter and area, rather than a conceptual and relational understanding     

Developing Prospective Elementary Teachers' Flexibility in the Domain of Proportional Reasoning

Flexibility in the use of mathematics procedures consists of the ability to employ multiple solution methods across a set of problems, solve the same problem using multiple methods, and choose strategically from among methods so as to reduce computational demands. The purpose of this study was to characterize prospective elementary teachers' (n = 148) flexibility in the domain of proportional reasoning before formal instruction and to test the effects of two versions of an intervention that engaged prospective teachers in comparing different solutions to proportion problems. Results indicate that (a) participants exhibited limited flexibility before formal instruction, (b) the intervention led to significant gains in participants' flexibility that were retained six months after instruction, and (c) varying the source of the problem solutions that participants compared had no discernible effects on their flexibility. Implications for mathematics teacher preparation and for research on flexibility development are provided.     

Level of Inquiry as Motivator in an Inquiry Methods Course for Preservice Elementary Teachers

Of great importance for achieving science education reform may be teachers' interest in science and enjoyment of science. This study explores the motivational qualities (rated for interest, fun, and learning value) of different levels of inquiry of hands‐on class activities. The participants, 53 preservice teachers in two sections of a science methods course, rated the activities at the end of each class. At the end of the course, these activities were categorized by level of inquiry (levels 0–3), with 30% rated as level 0 (no inquiry), 40% as level 1, 22% as level 2, and 8% as level 3, according to how much choice was given for posing questions and designing investigations. Ratings of each hands‐on activity indicated that participants perceived activities of higher levels of inquiry to be more fun and more interesting. They also perceived that they had learned more. These findings suggest that course instructors should determine level of inquiry when planning course activities, and degree of participant input into course activities may be important in the development of interest in science. A focus on hands‐on learning especially at higher levels of inquiry may serve both to capture the interest of teachers and to model how they can make science more authentic and engaging for children.     

The DESTIN: Preservice Teachers' Drawings of the Ideal Elementary Science Teacher

The aim of this study is to report findings from the Drawing‐Elementary‐Science‐Teacher‐Ideal‐Not, or the DESTIN procedure. The study utilizes a simple drawing procedure accompanied by a narrative and discussion for understanding preservice teachers' images of science, science teaching, and the science teacher. Ninety drawings from two sections of an elementary science methods course were analyzed. Looking at the pre‐drawings from the beginning of the semester and post‐drawings done at the end of the semester, the findings relate the value of using drawings in teacher education and the usefulness of this procedure to promote discussions about science teaching, the construction of new images and practices for teaching elementary science, and teacher identity. The DESTIN procedure has potential as a productive activity for teacher education and long‐term professional development by making more explicit teachers' views of science teaching and learning and their past experiences as science learners.     

Preservice Elementary Teachers' Conceptions of What Causes Night and Day

Two different procedures were utilized to study 50 preservice elementary teachers' conceptions of what causes night and day on earth. The numbers of responses representing alternative conceptions for the models with written and verbal explanation procedures were 27 and 14, respectively. The alternative conception most frequently expressed for both procedures was that night and day are caused by the earth revolving around the sun. The frequency with which alternative conceptions were expressed by future teachers is a problem which should be addressed with instruction using models.     

伽马函数余元公式的证明

本文整理介绍伽马函数余元公式的几种可在数学分析课程中讲解的证明,以供广大师生们参考.其中一些证明略有改进.     

Metaphors Reveal Preservice Elementary Teachers' Views of Mathematics and Science Teaching

Typically, experiences shape one's attitudes toward the “thing” that is being experienced, whether it is a person, pet, movie, etc. Classroom experiences also shape one's attitudes toward a subject, teacher, learning, and so forth. Studies have shown that attitudes become more negative as students move from elementary to secondary schools. Elementary preservice teachers have had many classroom experiences by the time they reach their methods courses. These varied experiences have shaped their attitudes about the learning and teaching of mathematics and science.     

Changes in Preservice Elementary Teachers' Sense of Efficacy in Teaching Science

This paper reports progress to date on a longitudinal study of changes in preservice teachers' sense of efficacy in teaching science. The study involved procedures designed to validate, in an Australian context, the Science Teaching Efficacy Beliefs Instrument (STEBI-B) comprised of two scales: Personal Science Teaching Efficacy Belief Scale (STE) and Science Teaching Outcome Expectancy Scale (STO). Concomitantly, the instrument was used to monitor changes in teachers' sense of science teaching efficacy employing a pretest and repeated posttest, one group research design. The subjects were students enrolled in a three-year Bachelor of Teaching (Primary) program. Correlations between pretest scores on STEBI-B and other measures of personal beliefs and behaviors, namely academic self concept and academic locus of control, supported the validity of STEBI-B. The results indicate that, over three semesters of the program, there was significant difference between the pretest and posttest scores on the STE scale. Possible explanations of the results obtained are discussed and evaluated and a justification for further long term research into teachers' sense of efficacy in teaching science is provided. Implications of the results for the teaching of elementary school science are discussed.     

Supporting Preservice Teachers' Understanding of Place Value and Multidigit Arithmetic

This article provides an analysis of a teaching experiment conducted in the context of teacher education designed to support preservice teachers' understandings of place value and multidigit addition and subtraction. The experiment addresses the following research question: Can the results from research conducted in elementary mathematics classrooms guide preservice elementary teachers' development of conceptual understanding of the same concepts? In both cases, the students (e.g., elementary students and preservice teachers) participated in activities from an instructional sequence designed to support conceptual understanding of both place value and multidigit addition and subtraction. Analyses of the episodes from the teaching experiment document the learning of the preservice teachers and how that learning was supported by initial conjectures grounded in the research on elementary students' ways of reasoning.