Preservice Teachers’ Conceptual and Procedural Knowledge of Fraction Operations: A Comparative Study of the United States and Taiwan

This study examined (a) the differences in preservice teachers’ procedural knowledge in four areas of fraction operations in Taiwan and the United States, (b) the differences in preservice teachers’ conceptual knowledge in four areas of fraction operations in Taiwan and the United States, and (c) correlation in preservice teachers’ conceptual knowledge and procedural knowledge of fractions in Taiwan and the United States. Participants were preservice teachers (N = 49) in a teacher education program in the United States and comparable Chinese preservice teachers (N = 47). Results indicated that Chinese preservice teachers performed better in procedural knowledge on fraction operations than American preservice teachers. No significant differences were found for conceptual knowledge on fraction division. Further, the correlation in this study showed that for Chinese and American preservice teachers, the relationship between conceptual and procedural knowledge of fraction operations was weak.     

Revisiting the STEBI‐B: Measuring Self‐Efficacy in Preservice Elementary Teachers

The Science Teaching Efficacy Belief Instrument‐Preservice (STEBI‐B) has been used in many studies to measure science teaching self‐efficacy and outcome expectancy in preservice elementary teachers. Since its development in 1990, there have been no studies that have re‐examined its internal validity and reliability. The purpose of this study was to do so. Two hundred ninety preservice elementary teachers participated in this study. The STEBI‐B was administered at the beginning of science methods courses. A factor analysis established that the two subscales, Personal Science Teaching Efficacy Belief (PSTE) and Science Teaching Outcome Expectancy (STOE), on the STEBI‐B were homogeneous, and loadings were comparable to those reported by Enochs and Riggs (1990) . Two items on the STOE were found to exhibit cross‐loading on the factor analysis, as well as low item‐total correlations. These two items were modified and the revised instrument administered to 86 new participants. Both revised items loaded more clearly on the STOE subscale, and item‐total correlations were stronger. Comparison of means analyses showed that gender, number of science courses taken, and school science experiences had significant associations with PSTE. The STEBI‐B continues to be employed in hundreds of studies to measure science teaching self‐efficacy. It is important to continue to monitor its reliability and validity, as well as check on associations with various background variables. The modified STEBI‐B is included in an appendix with this article.     

Web‐Based Instruction on Preservice Teachers' Knowledge of Fraction Operations

This study determines whether web‐based instruction (WBI) represents an improved method for helping preservice teachers learn procedural and conceptual knowledge of fractions.. The purpose was to compare the effectiveness of web‐based instruction (WBI) with the traditional lecture in mathematics content and methods for the elementary school course. The results of this study suggest that the use of WBI in learning fractions is more effective. When compared with the traditional instruction, the WBI treatment results were significantly more effective for procedural and conceptual knowledge of fraction operations.     

Science as a Learner and as a Teacher: Measuring Science Self‐Efficacy of Elementary Preservice Teachers

Academic science achievement of U.S. students has raised concerns regarding our ability as a nation to compete in a global economy. Additionally, research has shown that many elementary teachers have weak science content backgrounds and had poor/negative experiences as students of science, resulting in a lack of confidence regarding teaching science. However, efforts to increase science self‐efficacy (SE) in preservice teachers can help to combat these issues. This study looked at a sample of preservice elementary teachers engaged in a semester‐long science content course, using Bandura's concept of SE as a conceptual framework. Our quantitative data showed significant increases in science SE on both subscales (personal efficacy and outcome expectancy). Our qualitative data showed that students communicated an increased sense of confidence with regard to the discipline of science. In addition, students reported learning science pedagogy through the instructor's modeling. Combining our findings resulted in several meta‐inferences, one of which showed students growing as both confident learners of science and teachers of science simultaneously. We created a construct new to the literature to describe this phenomenon: “teacher‐learner,” for students are both learning science and learning to teach science simultaneously through the content course experience, resulting in increased science SE.     

Integrating Science and Mathematics: Perceptions of Preservice and Practicing Elementary Teachers

One hundred and sixty-one undergraduate elementary education majors and sixty elementary teachers completed an eight-item questionnaire designed to assess their perceptions toward integrating science and mathematics in the elementary grades. The two groups of subjects differed significantly on their responses to five of the eight items. Chi square analyses suggest that practicing elementary teachers felt they had more background in mathematics and science, were more aware of curriculum materials in this area, did not think that integration was currently a common practice, and were more likely to indicate that there was not sufficient time in the school day to integrate the subjects. Preservice teachers were more likely to indicate that integrating the disciplines was preferred to teaching them separately. In addition to the analyses of data, a list of recommendations are provided for teachers, curriculum developers, and policy makers interested in advancing the concept of integrating science and mathematics in instruction.     

Exploring the Role of Individual and Socially Constructed Knowledge Mobilization Tasks in Revealing Preservice Elementary Teachers' Understandings of a Triangle Fraction Task

This study compares the effectiveness of two forms of a knowledge mobilization task on preservice elementary teachers' (n= 65) performance in solving a triangle fraction problem. The study then identifies the source of the successful solutions by linking solutions to earlier activities. One group worked with the triangle fraction task individually; a second worked with the triangle fraction task in a social constructivist setting; a control group had no knowledge mobilization pretask. Although there was no significant difference in the frequency of successful solutions among treatment groups, a chi‐square analysis found that the social‐constructivist pretask group applied fewer ideas from the manipulative lessons as solutions to the posttask than did the comparison groups. The social constructivist group was, however, most successful at generating novel solutions to the triangle problem. The potential benefits of individual and socially constructed knowledge mobilization tasks are discussed.     

Mathematics Anxiety and Learning Styles: What Is the Relationship in Elementary Preservice Teachers?

The study investigated the relationship between elementary preservice teachers' mathematics anxiety levels and learning style preferences. Subjects included 72 preservice teachers at a midsized southeastern U.S. university who were at the end of their third year of study. The subjects completed the Mathematics Anxiety Rating Scale and the Style Analysis Survey (SAS). Scores obtained on the two instruments were analyzed using Pearson product‐moment correlations. Eleven of the SAS subscales were examined. The global subscale was the only one related to mathematics anxiety at the p < .05 level of significance. Findings revealed a low (r= .28) but significant (p < .05) positive correlation between mathematics anxiety and a global (right‐brain dominant) learning style. As global orientation scores increased, mathematics anxiety scores increased as well. This study indicated that there is tendency for global learners to possess higher levels of mathematics anxiety.     

Community‐Based Service‐Learning as a Source of Personal Self‐Efficacy: Preparing Preservice Elementary Teachers to Teach Science for Diversity

Bandura (1997) contends that when compared to other sources of efficacy, mastery experiences, when presented appropriately, have the most powerful influence on self‐efficacy. The purpose of this study was to investigate the effects of community‐based service learning (CBSL) experiences on preservice elementary teachers' personal self‐efficacy beliefs about equitable science teaching and learning. Data were collected using pretests‐posttests and post‐questionnaires with the study sample. Findings from this study support Bandura's assertion. CBSL experiences were an important source of personal self‐efficacy and significantly influenced preservice elementary teachers' personal self‐efficacy beliefs about equitable science teaching and learning.     

Writing Papers in Math Class: A Tool for Encouraging Mathematical Exploration by Preservice Elementary Teachers

This paper describes the author's attempt to design assignments that engage preservice elementary teachers in original mathematical thinking. In particular, the choice of integer operations as the focus of a structured writing assignment that takes students two weeks to complete is explained and justified. Exemplary student work is quoted.     

Gender‐Related Beliefs and Mathematics Performance of Preservice Primary Teachers

The aim of this study was to examine whether there are gender differences in mathematics achievement and in beliefs about mathematics of preservice teachers over a period of four years. Data were collected from preservice teachers (156 males and 155 females) from the Ad?yaman University Faculty of Education in Turkey. The Mathematics as a Gendered Domain instrument was used to investigate preservice teachers' beliefs about the gender differences in mathematics. The results indicated that gender had no effect on mathematics performances of the preservice primary teachers. Findings of this research show that most of the male and female preservice primary teachers do not gender‐stereotype mathematics and believe that mathematics is gender neutral, although there are gender differences on some types of items of instrument.     

Graphical Representations of Speed: Obstacles Preservice K‐8 Teachers Experience

This study examines the difficulties college students experience when creating and interpreting graphs in which speed is one of the variables. Nineteen students, all preservice elementary or middle school teachers, completed an upper‐level course exploring algebraic concepts. Although all of these preservice teachers had previously completed several mathematics courses, including calculus, they demonstrated widespread misconceptions about the variable speed. This study identifies four cognitive obstacles held by the students, provides excerpts of their graphical constructions and verbal interpretations, and discusses potential causes for the confusion. In particular, misconceptions arose when students interpreted the behavior and nature of speed within a graphical context, as well as in situations where they were required to construct a graph involving speed as a variable. The study concludes by offering implications for the teaching and learning of speed and its interpretation within a graphical setting.     

A Longitudinal Study of Elementary Pre‐service Teachers' Mathematics Beliefs and Content Knowledge

This study investigated the mathematics beliefs and content knowledge of 103 elementary pre‐service teachers in a developmental teacher preparation program that included a two course mathematics methods sequence. Pre‐service teachers' pedagogical beliefs became more cognitively‐oriented during the teacher preparation program with these changes occurring during the two methods courses. Pedagogical beliefs remained stable during student teaching. The pre‐service teachers also significantly increased their personal efficacy for teaching mathematics throughout the program with these shifts occurring across both methods courses and into student teaching. Pedagogical beliefs and teaching efficacy beliefs were not related at the beginning of the program, but, in general, were positively related throughout the program. In addition, the pre‐service teachers' pedagogical beliefs were positively related to their specialized content knowledge for teaching mathematics at the end of the program.     

Science Self‐Efficacy of Preservice Teachers in Face‐to‐Face versus Blended Environments

Using a quasi‐experimental mixed methods concurrent design, this study measured the science self‐efficacy of pre‐service elementary teachers before and after a survey of science content course. Further, this course was delivered in two different formats: face‐to‐face and hybrid (approximately 50% online), and compared pre‐and post‐science self‐efficacy of students in the two different course formats. Our quantitative results showed increases in personal efficacy, but not outcome expectancy for both formats, and no significant differences between the increases for either format. Our qualitative data showed that participants attributed their increased levels of personal efficacy to the hands‐on components of the course, as well as perceived teacher attitudes toward science, both of which would be challenging to replicate in a purely online format, as opposed to the hybrid format included in this study.     

Preservice Elementary Teachers' Use of Mathematics in a Project‐Based Science Approach

The use of a project‐based science (PBS) approach to teaching encourages students to integrate mathematics and science in meaningful ways as they create projects. As a beginning study of how students use mathematics in such an approach, an analysis of 23 projects developed by preservice elementary teachers enrolled in an elementary science course was conducted. Findings showed that students made a number of different types of mathematical errors and underutilized data representation and summary forms. Implications included the importance of developing methods for supporting the use of mathematical tools in utilizing a project‐based approach and considering ways that such tools mediate scientific thinking.     

Autobiographical Stories from Preservice Elementary Mathematics and Science Students: Implications for K‐16 Teaching

Autobiographies are an effective tool for assessing students' predispositions toward science and mathematics content and identifying any changes in attitude over time. The purpose of this study was to analyze autobiographies of students enrolled in elementary education methods classes to determine the kinds of K‐12 and college content course experiences affecting their perceptions of mathematics or science. Special attention was given to recollections of events that had positive or negative effects on students' interest in and attitudes toward science or mathematics, their confidence in these areas, and transitions in attitude throughout their experiences. Ninety‐eight autobiographies were collected and analyzed, revealing attitudes that were generally more positive than expected, five major emergent themes, and important information about when and why transitions in attitudes occurred.