A Mathematics Teachers’ Perspective and its Relationship to Practice

In this paper we try to characterize the pedagogical approaches that mathematics teachers are developing to meet the challenges posed by education reforms. A key aspect is the identification of the perspectives that underlie those pedagogical approaches, using the term perspective to include a broad pedagogical structure composed of multiple conceptions that are related to some aspects of a teacher’s practice. Through the study of the practice of a secondary mathematics teacher, we try to explore how his/her pedagogical approaches on mathematics, mathematics learning, and mathematics teaching are related to the relational architecture that is established in the classroom during the development of an instructional unit of similarity at a secondary school level, and we examine if that relationship can be explained in terms of the underlying perspective. The results of the study have shown the characteristics of that relationship, and the important role that the teacher’s knowledge of the students’ difficulties plays both in making decisions and in developing the teachers’ actions.     

Commitment to Teach in Under-Resourced Schools: Prospective Science and Mathematics Teachers’ Dispositions

In this exploratory study, we sought to gain an understanding of what motivates prospective teachers who are Noyce Scholars at a research-intensive southeastern US university to commit to teaching secondary level science or mathematics in school districts that have a high proportion of students who come from low-socioeconomic households. An interpretive methodology revealed three themes associated with Noyce Scholars’ motivations to teach (1) awareness of educational challenges, (2) sense of belonging to or comfort with diverse communities, and (3) belief that one can serve as a role model and resource. The paper describes and compares the significance of each theme among six prospective teachers who identify with the schooling experiences of students who came from low-income or poor households and nine prospective teachers who identify with the schooling experiences in a middle-income school or district. The implication of this study supports the importance of recruiting prospective science and mathematics teachers who have knowledge of and a disposition to work with learners from low-income or poor households, even if those prospective teachers are not themselves the members of under-served populations.     

K-12 Science and Mathematics Teachers’ Beliefs About and Use of Inquiry in the Classroom

A survey instrument was developed and administered to 1,222 K-12 mathematics and science teachers to measure their beliefs about and use of inquiry in the classroom. Four variables (grade level taught, content area taught, level of support received, and self-efficacy for teaching inquiry) were significantly correlated to two dependent variables, percentage of time that students are engaged in inquiry during a typical lesson and the perceived ideal percentage of instructional time that should be devoted to inquiry. Specifically, elementary school teachers reported using inquiry-based practices more than either middle-school or high-school teachers; similarly, elementary-school teachers believed such practices should be used more often. All groups, however, reported believing in an ideal percentage of time devoted to inquiry instruction that was significantly greater than their reported percentage of time actually spent on inquiry instruction. A disordinal effect was found between grade level taught and content area taught; at the elementary level, science teachers reported both an ideal and actual percentage of time on inquiry higher than those reported by the math teachers, while at the high school level math teachers reported both an ideal and actual percentage of time on inquiry higher than those reported by the science teachers. No correlations were found between typical and ideal percentage of time devoted to inquiry and subject matter content knowledge training, gender, years of teaching experience, or maximum degree earned.     

Factors that Affect Science and Mathematics Teachers’ Initial Implementation of Technology-Enhanced Formative Assessment Using a Classroom Response System

The purpose of this study is to uncover and understand the factors that affect secondary science and mathematics teachers?? initial implementation of Technology-Enhanced Formative Assessment (TEFA), a pedagogy developed for teaching with classroom response system (CRS) technology. We sought to identify the most common and strongest factors, and to understand the general process of how teachers adopt TEFA. We identified ten main hindering factors reported by teachers, and found that time limitations and question development difficulties are reported as the most problematic. In this paper we provide five vignettes of teachers?? initial implementation experiences, illustrating different courses that TEFA adoption can follow. We classify our ten factors into four groups: contextual factors that directly hinder teachers?? attempts to implement TEFA (extrinsic type I); circumstances that affect teachers?? teaching in general (extrinsic type 0); gaps that teachers have in the knowledge and skills they need to adopt TEFA (intrinsic type I); and ways of being a teacher that describe teachers?? deeper perspectives and beliefs, which may be consonant or dissonant with TEFA (intrinsic type II). Finally, we identify four general categories that describe the teachers?? initial TEFA implementation.     

The Influence of Teachers’ Efficacy and Beliefs Regarding Mathematics Instruction in the Early Childhood Classroom

This was a correlational study conducted with a population of prekindergarten educators from a large, metropolitan school district. The purpose was to examine if there were relationships between and among early childhood teachers’ sense of self-efficacy, their beliefs about the importance of mathematics, and their mathematics instructional practices. Examining teachers’ efficacy and beliefs can inform educational practice and help to differentiate between more and less successful instructional practices when teaching mathematics in the early childhood classroom. Data were collected on teacher efficacy and teacher beliefs about the importance of mathematics with two self-report questionnaires. The hypothesis that the teachers higher in efficacy will rate the importance of mathematics higher on the teacher-belief scale than the teachers with lower efficacy was found to be true with this sample, but the correlation was weak. The level of efficacy of the early childhood teachers in this sample confirmed that in assessing their capabilities, they rate themselves high in instructional strategies, classroom management, and student engagement. The early childhood teachers did not rate their belief in mathematics as high as their efficacy. Observations of mathematics instructional practices were conducted with twenty teachers. It was hypothesized that the combination of high teacher efficacy and high teacher mathematics beliefs would show alignment with the presence of standards-based mathematics instructional practices. The results were not statistically significant. No correlation signals a need for more research to explore what other personal or external factors relate to mathematics instructional practices in the early childhood classroom. The research may inform pre kindergarten teachers and teacher educators about effective instructional strategies and knowledge needed to launch early childhood students on a developmentally appropriate pathway to mathematical literacy.     

Development in South African Primary Mathematics Teacher Educators’ Work with In-Service Teachers

This paper focuses, empirically, on the developments seen in a group of South African early grades’ mathematics teacher educators in the course of a university-provincial education department partnership project. This project sought to support the district Mathematics Subject Advisers to support, in turn, teachers to implement an intervention consisting of a sequence of four lessons focused on multiplicative reasoning. Outcomes based on pre- and post-tests administered by the Subject Advisers suggested substantial pre- to post-test improvement at the student level. Subject Adviser observations and reflections pointed to successes in engendering more dialogic conversations between mathematics teachers and mathematics teacher educators focused on mathematics and its teaching and learning. The ‘double move’ of increasing overlap between the subject adviser and teacher communities, coupled with evidence that implementing the intervention had enabled the Subject Advisers to develop their mathematical and pedagogical understandings, provides a useful way of considering development in the capacity of mathematics teacher educators to support mathematics teaching and learning.

     

Students’ Motivation in the Mathematics Classroom. Revealing Causes and Consequences

Students’ affective domain has been popular in the mathematics education community in an ongoing attempt to understand students’ learning behavior. Specifically, enhancing students’ motivation in the mathematics classroom is an important issue for teachers and researchers, due to its relation to students’ behavior and achievement. This paper utilized achievement goal theory—an important theoretical prospect on students’ motivation in school settings—to investigate the existence of a model presenting the relation between motivation and other affective constructs and students’ performance in mathematics. In this regard, two types of tests were administered to 321 sixth grade students measuring their motivation and other affective constructs and their performance in mathematics. Using structural equation modeling, we examined the associations among the affective constructs, motivation, and the extent to which these constructs influence students’ performance and interest in mathematics. The data revealed that students’ performance and their interest in mathematics were influenced by fear of failure, self-efficacy beliefs, and achievement goals. We discuss these findings in terms of teaching implications in the mathematics classroom.

     

Students’ Motivation in the Mathematics Classroom. Revealing Causes and Consequences

Students’ affective domain has been popular in the mathematics education community in an ongoing attempt to understand students’ learning behavior. Specifically, enhancing students’ motivation in the mathematics classroom is an important issue for teachers and researchers, due to its relation to students’ behavior and achievement. This paper utilized achievement goal theory—an important theoretical prospect on students’ motivation in school settings—to investigate the existence of a model presenting the relation between motivation and other affective constructs and students’ performance in mathematics. In this regard, two types of tests were administered to 321 sixth grade students measuring their motivation and other affective constructs and their performance in mathematics. Using structural equation modeling, we examined the associations among the affective constructs, motivation, and the extent to which these constructs influence students’ performance and interest in mathematics. The data revealed that students’ performance and their interest in mathematics were influenced by fear of failure, self-efficacy beliefs, and achievement goals. We discuss these findings in terms of teaching implications in the mathematics classroom.     

Preservice Mathematics Teachers’ Noticing in Action and in Reflection

International Journal of Science and Mathematics Education - The aim of this paper is to discuss preservice mathematics teachers’ in-the-moment noticing of mathematical opportunities and how...     

Constructivism in Mathematics Classrooms: Listening to Ghanaian Teachers’ and Students’ Views

One of the challenges of implementing a new curriculum is how to bridge the gap between the underlining principles of the curriculum and the cultural and social orientations of the society which includes teachers and students. This article reports on a study that explored how the cultural and social orientations of teachers and students can influence the implementation of a constructivist curriculum in mathematics classrooms. The data for the study came from 250 students and 41 mathematics teachers, using questionnaires, observations, and interviews. The results showed that inasmuch as mathematics teachers and their students acknowledge the importance of student’s active participation and teamwork, these practices have not been fully conceptualised into the Ghanaian mathematics classroom due to some cultural factors. Two main cultural factors were discovered from the analyses of the results. Firstly, the culture of acknowledging only correct answers in class has a negative impact on individual students’ confidence and participation during mathematics lessons. Also, the culture of teamwork is not fully accepted within Ghanaian classrooms as most students find it difficult working in groups and accepting and appreciating each other’s view. It was evident in all lessons that students were ridiculed by their peers when they provide a wrong answer to a question and this affected individual students’ participation in the classroom. Therefore, we suggested that teachers should be pro-active in promoting a classroom environment which is free from fear and intimidation to motivate students to be actively involved in the classroom discourse.     

Prospective Elementary Teachers’ Understanding of the Nature of Science and Perceptions of the Classroom Learning Environment

This study investigated prospective elementary teachers’ understandings of the nature of science and explored associations with their guided-inquiry science learning environment. Over 500 female students completed the Nature of Scientific Knowledge Survey (NSKS), although only four scales were analyzed–Creative, Testable, Amoral, and Unified. The learning environment was assessed using previously-validated and reliable scales from What Is Happening In this Class? (WIHIC) and the Science Laboratory Environment Inventory (SLEI). Analyses indicated moderate multiple correlations that were statistically significant (p?<?0.01) between Creative (R?=?0.22), Testable (R?=?0.29), and Unified (R?=?0.27), and a positive learning environment. Regression coefficients revealed that Open-Endedness was a significant independent predictor of students’ understanding of the role of creativity in science (β?=?0.16), while Cooperation, Open-Endedness, and Material Environment were linked with understanding the testable nature of science (β?=?0.10–0.12). Interview questions probed possible relationships between an improved understanding of the nature of science and elements of a positive classroom environment. Responses suggested that an appropriate level of open-endedness during investigations was very important as this helped students grapple with abstract nature of science concepts and shift their conceptions closer to a more realistic view of scientific practice.     

Elementary Teachers’ Preferences for Pre-Service and In-Service Training in the Teaching of Reading

Abstract

The purpose of this study was to discover guidelines for improving the pre-service and in-service training of elementary teachers to teach reading. Three hundred and eight elementary teachers were queried regarding (1) their attitudes toward their pre-service education, (2) their educational needs, and (3) their preferences for in- service program formats. Responses were analyzed according to grade levels taught and years of service. The main conclusion was that elementary teachers of different grades and with different terms of service express different attitudes, needs and preferences regarding their training to teach reading. Implications for pre-service and in-service training programs are discussed.     

An Eastern Learning Paradox: Paradoxes in Two Korean Mathematics Teachers’ Pedagogy of Silence in the Classroom

Eastern philosophies of education such as Confucianism and Taosim advocate the use of silence in the teacher–pupil tradition of pedagogy. We investigate contemporary classrooms in Korea, and study whether teachers in Korea today incorporate this method implicitly or explicitly in their classrooms. Empirical data in the form of video-taped classroom lessons and the analysis of the videos reveal the learning paradoxes that arise from a rote adherence to constructivism by teachers that are trained within a larger Confucian society.     

Why Use Multiple Representations in the Mathematics Classroom? Views of English and German Preservice Teachers

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice teachers affords identifying corresponding needs for teacher education. However, specific empirical research is scarce. Taking into account the possible role of culture, this study consequently focuses on views about using multiple representations held by more than 100 English and more than 200 German preservice teachers. The results indicate that there are culture-dependent aspects of preservice teachers’ views, but also that there are common needs for professional development.     

Why Use Multiple Representations in the Mathematics Classroom? Views of English and German Preservice Teachers

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice teachers affords identifying corresponding needs for teacher education. However, specific empirical research is scarce. Taking into account the possible role of culture, this study consequently focuses on views about using multiple representations held by more than 100 English and more than 200 German preservice teachers. The results indicate that there are culture-dependent aspects of preservice teachers’ views, but also that there are common needs for professional development.

     

Preservice and Inservice Teachers’ Challenges in the Planning of Practical Work in Physics

Practical work in school science plays many essential roles that have been discussed in the literature. However, less attention has been paid to how teachers learn the different roles of practical work and to the kind of challenges they face in their learning during laboratory courses designed for teachers. In the present study we applied the principles of grounded theory to frame a set of factors that seem to set major challenges concerning both successful work in the school physics laboratory and also in the preparation of lessons that exploit practical work. The subject groups of the study were preservice and inservice physics teachers who participated in a school laboratory course. Our results derived from a detailed analysis of tutoring discussions between the instructor and the participants in the course, which revealed that the challenges in practical or laboratory work consisted of the limitations of the laboratory facilities, an insufficient knowledge of physics, problems in understanding instructional approaches, and the general organization of practical work. Based on these findings, we present our recommendations on the preparation of preservice and inservice teachers for the more effective use of practical work in school science and in school physics.     

Does Physical Activity of Preschool Teachers Impact the Planning and Implementation of Movement Activities in the Kindergartens？

The authors of this paper compared the views of Slovenian and Portuguese preschool teachers about the importance of play and movement for the preschool children. In the paper, they focused on the question： Does physical activity of preschool teachers （spontaneous or planned） impact the planning and implementation of movement activities in their kindergarten group？ They also analyzed the influence of subjective theories on the planning of movement activities and the realization of the curriculum objectives in the field of movement. Most of the preschool teachers in Slovenia and Portugal give priority to natural forms of movement in nature and play, allowing the movement of the fingers, palms, and hands. Research has shown a link between physical activity of preschool teachers and their views on the importance of the implementation of the movement activities of preschool children. The authors also noted that the quality of the implementation of the education process in kindergartens in the area of movement activities depends on their subjective theories to a great extent and on the level of professional competence referred to the discussed topic.     

Technology Integration in a Science Classroom: Preservice Teachers’ Perceptions

The challenge of preparing students for the information age has prompted administrators to increase technology in the public schools. Yet despite the increased availability of technology in schools, few teachers are integrating technology for instructional purposes. Preservice teachers must be equipped with adequate content knowledge of technology to create an advantageous learning experience in science classrooms. To understand preservice teachers’ conceptions of technology integration, this research study explored 15 elementary science methods students’ definitions of technology and their attitudes toward incorporating technology into their teaching. The phenomenological study took place in a science methods course that was based on a constructivist approach to teaching and learning science through science activities and class discussions, with an emphasis on a teacher beliefs framework. Data were collected throughout the semester, including an open-ended pre/post-technology integration survey, lesson plans, and reflections on activities conducted throughout the course. Through a qualitative analysis, we identified improvements in students’ technology definitions, increased technology incorporation into science lesson plans, and favorable attitudes toward technology integration in science teaching after instruction. This research project demonstrates that positive changes in beliefs and behaviors relating to technology integration in science instruction among preservice teachers are possible through explicit instruction.