Gender-related beliefs of teachers in elementary school mathematics

In this quantitative study, questionnaire data of fifty-two third- and fourth-grade teachers were analyzed using MANOVA tools. Teachers were asked to consider boys' and girls' achievement in mathematics, giving their views on the reasons for the students' successes and failures and describing their learning characteristics. Teachers thought that their average achieving girls were less logical than equally achieving boys. The girls were thought to profit less than boys from additional effort and to exert relatively more effort to achieve the level of actual performance in mathematics. Teachers rated mathematics as more difficult for average achieving girls than for equally achieving boys. With regard to girls, teachers attributed unexpected failure more to low ability and less to lack of effort than with boys. The results increase our understanding of stereotypical teacher beliefs that might help explain gender differences in achievement and in subsequent occupational choices.This revised version was published online in September 2005 with corrections to the Cover Date.     

Training elementary mathematics teachers using interactive multimedia

Two studies were conducted wherein an interactive, multimedia-based instructional system was piloted with preservice elementary school teachers. Mathematics methods classes experienced conventional instruction with a new interactive technological-instructional system as supplemental course material. An analysis of interview data indicated that students were more likely to incorporate the knowledge they acquired from the system into their teaching repertoire. Many students thought that this mode of presentation enhanced their learning of mathematics teaching methods and their teaching in other fields.This project was supported, in part, by a grant from the National Science Foundation (Award # TPE-8950317) and International Business Machines.     

Worldviews,religions, and beliefs about teaching and learning: perception of mathematics teachers with different religious backgrounds

Beliefs about mathematics education and their influences on teaching practices have been widely investigated in recent decades. There have been numerous empirical studies on the influences of religions on teachers’ and students’ beliefs about subjects such as sciences and language. However, the influences of worldviews in general and religions in particular, as one of the major sources of beliefs in relation to mathematics education, are under-researched. The current study is a first step to unpacking the relationship between teachers’ religions and their beliefs about mathematics teaching and learning. By means of semi-structured interviews with mathematics teachers of different religious backgrounds, teachers’ perceptions on the connection between their personal religious beliefs and their beliefs about teaching and learning are investigated. In-depth analyses of the perceptions of three mathematics teachers reveal the complex relationship between teachers’ religious beliefs and their teaching beliefs. First, there are some common values shared by different religions, which influence the beliefs about mathematics teaching and learning as well as education in general. Second, religion is a rich belief system, and the teachers appear to apply only a portion of their religious beliefs to guide their teaching. It is also possible that a teacher is influenced by more than one religion or cultural tradition. Despite its subtleties, our study provides evidence to support the alignment between teachers’ personal religious beliefs and their beliefs about mathematics teaching and learning.     

Exploring student beliefs and understanding in elementary science and mathematics

This study had the goal of investigating the association among elementary students' (N = 276) science and math beliefs and the relationship between those beliefs and teachers' ratings of mathematical and science understanding. Results of structural path analysis indicate that in science, intellectual risk‐taking (IRT; the willingness to share tentative ideas, ask questions, attempting to do, and learn new things) was positively related to teachers' ratings of science understanding, while creative self‐efficacy (CSE) beliefs (i.e., students' confidence in their ability to generate ideas and solutions in science) were indirectly related (working through IRT). Results also indicate that students' scientific certainty beliefs (i.e., the belief that science knowledge is stable, fixed, and represented by correct answers) were negatively related to teachers' ratings of science understanding. With respect to math, results indicate that students' CSE beliefs were positively related to teachers' ratings of math understanding; whereas students' mathematical source beliefs (i.e., believing that math knowledge originates from external sources) were negatively related. © 2012 Wiley Periodicals, Inc. J Res Sci Teach 49: 942–960, 2012     

Motivation and learning in an online, unmoderated, mathematics workshop for teachers

As hypermedia, online teacher professional development (TPD) should ideally support diverse learners to work with online content effectively because it involves multiple representations and a nonlinear format. Differences among participants in motivation and learning provide challenges for design. The present study is a use-inspired, mixed-method study of 164 teachers’ motivation and learning in an unmoderated online workshop. It addresses participants’ demographic and motivational profiles, participation in this type of workshop (e.g., the frequency, duration, and focus, as well as their work with technology-enhanced, nonroutine challenge problems and journal assignments), the predictive value of the initial questionnaire, and implications for design. Findings indicate that while three clusters of motivational profiles could be identified (low interest, low self-efficacy, and less math; low interest, high self-efficacy, and more math; high interest, high self-efficacy, and more math), whether the teachers continue to participate appears to be related to the structure and content of the workshop, not just these profiles. Findings are interpreted as suggesting that the potential of hypermedia lies in its designers’ abilities to support participant stake by providing for multiple ways into thinking and working with disciplinary content—design that both accommodates and supports those with differing strengths and needs. Implications for studying motivation and learning online are also discussed.     

Infusing assessment into mathematics content courses for pre-service elementary school teachers

The present study aims to explore the use of assessment in mathematics content courses for future elementary school teachers. Analysis of self assessment data on mathematical understanding and peer assessment data on oral mathematical presentation showed that pre-service teachers had a balanced understanding of procedural knowledge and problem solving. Conceptual understanding was not in the structure of pre-service teachers’ mathematical knowledge. Understandings of conceptual knowledge, procedural knowledge, and problem solving had no meaningful effects on gains in mathematics performance. Aspects of oral mathematical presentation were associated with improved understanding of procedural knowledge and in particular conceptual knowledge. The result of the study calls for a conceptual approach to mathematical knowledge and sufficient mathematical problem solving in college-level mathematics content courses and in particular the infusion of assessment into college-level mathematics education for pre-service teachers.     

The juxtaposition of instructor and student perspectives on mathematics courses for elementary teachers

This qualitative study examined perspectives of two key stakeholder groups, instructors and students, on mathematics content courses for prospective elementary teachers (Mathematics for Teachers [MFT] courses). A collective case study approach, which drew from the data of two cases in different but comparable settings, contributed to the robustness of the findings. Cross-case analysis of the interview data revealed several convergent themes: the role of affect in student learning, pedagogy and instructor disposition, connections to the elementary classroom, and mathematics content. The findings included both conflicting and complementary perspectives between the two key stakeholder groups. When juxtaposed, the multiple viewpoints offer insights into some of the central issues related to teaching and learning in MFT courses and suggest potential avenues for improving experiences in these courses.     

The cognitive effects of a mathematics in-service workshop on elementary school teachers

Siegler's rule assessment methodology was used to investigate the cognitive effects of a 32 hour mathematics in-service workshop on 28 elementary shool teachers. This paper reports on attempts (a) to assess the levels of cognitive understanding of the basic concepts of proportion, probability, and correlation among elementary teachers, and (b) to change teachers' levels in understanding these concepts by a method of direct instruction. Significant improvements were noted in the levels of cognitive development associated with the concept of proportion. Though nonsignificant improvements were noted in the concepts of probability and correlation, all the teachers were assigned to the highest cognitive rule associated with the probability concept at the end of the workshop.     

Science knowledge and efficacy beliefs among preservice elementary teachers: A follow-up study

Slightly over two years ago aspects of knowledge and efficacy beliefs among preservice elementary teachers regarding science education were examined. Those results indicated a low level of science knowledge and a marked lack of confidence toward teaching science among prospective teachers. In the interim suggestions from that study have resulted in an increase in the number of required science courses that have been implemented in the teacher education program. The current, follow-up, study, found no increase in science content knowledge but did identify positive changes in efficacy beliefs. The results are discussed relative to Locus of Control theory.     

The preparation experiences of elementary mathematics specialists: examining influences on beliefs,content knowledge,and teaching practices

Many in the field of mathematics education call for elementary schools to have elementary mathematics specialists (EMSs) who provide needed mathematical expertise and support for children and teachers. EMSs serve as a reasonable, immediate alternative to the challenges generated by elementary teachers needing improved mathematical knowledge for teaching in the classroom. However, limited inquiry has explored how to best prepare EMSs and how program features and learning activities influence their development. This mixed-method study identifies some of the interrelated benefits from a K-5 Mathematics Endorsement Program designed to prepare EMSs through examining changes in mathematical beliefs, specialized content knowledge (SCK), and classroom teaching practices during the program. Data (n = 32) were collected over the 2-semester program via belief surveys, a content knowledge assessment, observations of teaching practices, and individual interviews from elementary teachers participating in the program. The findings show some changes in beliefs can be made relatively quickly, other shifts in beliefs take more time and continued support, and changes in SCK and adoption of various aspects of standard-based pedagogy require considerably greater opportunities to learn. The described program features and learning experiences provided a context for these changes and offer considerations for EMS preparation programs.     

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.

     

Exploring the impact of written reflections on learning in the elementary mathematics classroom

The authors examined the implementation of written reflections in a Grade 4 mathematics classroom over the course of 8 weeks. Students in this case study engaged in a workshop modeled after Calkin's Writers' Workshop and within this workshop the use of writing as a reflective tool in mathematics was introduced. The authors explore how students used writing to evaluate their learning and how the teacher used the students' written reflections as a formative assessment for instructional purposes. Students' written reflections were coded and these codes were used to conduct an inductive thematic analysis. Analysis of written reflections via constant-comparison analysis was used for further differentiation. The findings show students' ability to accurately self-evaluate their problem-solving skills and highlighted students' confidence level with certain mathematical concepts. Teachers were able to use students' reflections as a place to begin conferring with a student for further clarification. The written reflections aided in instructional decisions and increased individual instruction when needed. The authors include implications for teacher practice and areas for future research.     

Learner control of context and instructional support in learning elementary school mathematics

Learner-control strategies for selecting problem context and the level of instructional support were examined separately and in combination on a computer-based mathematics unit on the metric system. Subjects were 240 sixth-grade students assigned to 15 treatments formed by crossing five context conditions (animals, sports, clothing, nocontext, and learner control) with three instructional support conditions (minimum, maximum, and learner control). As hypothesized, comparisons of instructional support conditions on posttest achievement showed performance to be lowest under learner control. Subjects opted to view very few items and to decrease the amount they selected over the course of the instruction. No effects were associated with the context variable, although on one of the three lessons, learner-control subjects made significantly fewer on-task errors than did no-context subjects. Further analyses showed a strong tendency by learner-control context subjects to vary their selection of contexts across lessons. Subjects in the context and instructional support learner-control strategies indicated positive attitudes toward the strategies.