Connecting Mathematics and Science in Undergraduate Teacher Education Programs: Faculty Voices from the Maryland Collaborative for Teacher Preparation

The study reported in this paper investigated perceptions concerning connections between mathematics and science held by university/college instructors who participated in the Maryland Collaborative for Teacher Preparation (MCTP), an NSF-funded program aimed at developing special middle-level mathematics and science teachers. Specifically, we asked (a) “What are the perceptions of MCTP instructors about the ‘other’ discipline?” (b) “What are the perceptions of MCTP instructors about the connections between mathematics and science?” and (c) “What are some barriers perceived by MCTP instructors in implementing mathematics and science courses that emphasize connections?” The findings suggest that the benefits of emphasizing mathematics and science connections perceived by MCTP instructors were similar to the benefits reported by school teachers. The barriers reported were also similar. The participation in the project appeared to have encouraged MCTP instructors to grapple with some fundamental questions, like “What should be the nature of mathematics and science connections?” and “What is the nature of mathematics/science in relationship to the other discipline?”     

Relationship Between Science and Mathematics Teaching Efficacy of Preservice Elementary Teachers

The purpose of this study was to investigate the change in teacher efficacy beliefs about mathematics and science teaching during participation in methods courses and student teaching, as well as the relationship between mathematics and science teaching efficacy. Data revealed that, as science and mathematics teacher education in a methods course progressed, science and mathematics teaching efficacy significantly increased. This effect appeared to decrease slightly by the end of student teaching. Analysis of data indicated a significant difference in both the personal mathematics and personal science teaching efficacy scores, as well as mathematics outcome expectancy. Additionally, preservice teachers' personal mathematics and science teaching efficacies were directly related, as were their mathematics and science teaching outcome expectancies.     

Boundary Spanners as Bridges of Student and School Discourses in an Urban Science and Mathematics High School

A key to improving urban science and mathematics education is to facilitate the mutual understanding of the participants involved and then look for strategies to bridge differences. Educators need new theoretical tools to do so. In this paper the argument is made that the concept of “boundary spanner” is such a tool. Boundary spanners are individuals, objects, media, and other experiences that link an organization to its environment. They serve critical communicative roles, such as bridges for bringing distinct discourses together, cultural guides to make discourses of the “other” more explicit, and change agents for potentially reshaping participants' discourses. This ethnographic study provides three examples of boundary spanners found in the context of an urban public high school of science, mathematics, and technology: boundary media, boundary objects, and boundary experiences. The analysis brings to the foreground students' and teachers' distinct discourses about “good student identity,”“good student work,” and “good summer experience” and demonstrates how boundary spanners shaped, were shaped by, and sometimes brought together participants' distinct discourses. An argument is made for boundary spanners' practical and theoretical utility: practically, as a tool for enhancing meaning‐making between diverse groups, and theoretically, as a heuristic tool for understanding the reproductive and transformative aspects of urban science education.     

Research on mathematics education

This study addresses aspects that should be considered in every investigation concerning the reality of the subject being investigated, which in turn provide the basis for the procedures adopted to carry out the research. It speaks about the analysis of the procedures chosen to carry out the research. It is assumed that this care should be taken by the researcher at the moment the research procedures are being defined and made explicit. It is argued that the consonance between the ontological and epistemological dimensions of “what” and “how” to investigate the subject of investigation confers a degree of confidence to the research findings. The search for that confidence transcends analyses based only on calculations and explanations of methodological procedures, regardless of how well founded they are. This study addresses mathematics education specifically, adopting a phenomenological perspective. It is focused on the constitution of mathematical idealities and of mathematics as a science under the perspective of the Husserlian phenomenological conception of reality and knowledge. Characteristics of a phenomenological pedagogy are presented, which is carried out through work that is always intentional, with the educator taking account of what occurs with himself/herself, with the life world of the school, and with the student. The student is seen as a person and as being with others, his/her classmates, and the theme is addressed in the context of the field of inquiry under focus, with the teacher and with his/her “surroundings”.     

Student Perceptions of a Summer Ventures in Science and Mathematics Camp Experience

“As the world becomes increasingly technological, the value of (the ideas and skills of its population) will be determined in no small measure by the effectiveness of science, technology, engineering, and mathematics (STEM) education in the United States” and “STEM education will determine whether the United States will remain a leader among nations and whether we will be able to solve immense challenges in such areas as energy, health, environmental protection, and national security” (President's Council of Advisors on Science and Technology, 2010, p. vii). Research on the effectiveness of STEM‐focused school and other learning experiences (e.g., short‐term camps) on student attitudes and performance outcomes is sparse. In this study, we documented the influence of an intensive STEM summer program on high school students’ attitudes toward STEM concepts and interests in STEM careers. Attending the summer program was associated with gains on students’ attitudes toward some aspects of STEM as well as specific career interests. Notably, students reported statistically significant views of important aspects of STEM and their attitudes toward science and mathematics were more positive than their attitudes about engineering and technology.     

Turkish Preservice Primary School Teachers' Science Teaching Efficacy Beliefs and Attitudes Toward Science: The Effect of a Primary Teacher Education Program

The main purpose of this study was to investigate the effectiveness of a primary teacher education program in improving science teaching efficacy beliefs (personal science teaching efficacy beliefs and outcome expectancy beliefs) of preservice primary school teachers. The study also investigated whether the program has an effect on student teachers' attitudes toward science. Data were collected by administering the “Science Teaching Efficacy Beliefs Instrument” and “Attitudes toward Science Scale” to 282 preservice primary teachers (147 freshmen, 135 seniors). Statistical techniques such as means and t‐test were used to analyze the data. Results of the study showed that the primary teacher education program has a medium positive effect on science teaching efficacy beliefs of the primary preservice teachers (t = 4.791, p = .000) and that there were no gender differences in terms of efficacy beliefs. Results also indicated that preservice primary teachers' attitudes toward science were moderately positive and differ by class level. Fourth‐year preservice teachers' attitudes toward science were found to be significantly more positive than the first years (t = 5.494, p = .000). There were no gender differences in attitudes toward science.     

Beliefs and beyond: affect and the teaching and learning of mathematics

The importance of beliefs for the teaching and learning of mathematics is widely recognized among mathematics educators. In this special issue, we explicitly address what we call “beliefs and beyond” to indicate the larger field surrounding beliefs in mathematics education. This is done to broaden the discussion to related concepts (which may not originate in mathematics education) and to consider the interconnectedness of concepts. In particular, we present some new developments at the conceptual level, address different approaches to investigate beliefs, highlight the role of student beliefs in problem-solving activities, and discuss teacher beliefs and their significance for professional development. One specific intention is to consider expertise from colleagues in the fields of educational research and psychology, side by side with perspectives provided by researchers from mathematics education.     

A Preservice Secondary Teacher's Moves to Protect Her View of Herself as a Mathematics Expert

This paper discusses the experience of a preservice secondary mathematics teacher during lesson study. Although the preservice teacher was a strong undergraduate mathematics student, she used compensation “moves” to deflect attention away from her insecurities about her conceptual understanding of secondary mathematics. She feared being labeled as “dumb” and redirected conversations in order to protect her identity as a knower of mathematics. This paper investigates the culture in which preservice teachers develop confidence in their personal mathematics knowledge and how that confidence may influence behavior.     

Student Attitudes and Calculus Reform

This paper compares the attitudes about mathematics of students from traditionally taught calculus classes and those from a “reformed” calculus course. The paper is based on three studies, which together present a consistent picture of student attitudes about calculus reform. The reformed course appeared to violate students' deeply held beliefs about the nature of mathematics and how it should be learned. Although during their first months in the reformed course most students disliked it, their attitudes gradually changed. One and 2 years after, reform students felt significantly more than the traditionally taught students that they better understood how math was used and that they had been required to understand math rather than memorize formulas.     

MATHEMATICS STUDENT TEACHERS’ RESPONSES TO INFLUENCES AND BELIEFS

This article forms part of an ongoing study of student teachers of secondary mathematics. The aspect reported on in this article is an analysis of the effects of the influences brought to bear upon four individual student teachers of secondary mathematics as they progress through a one-year postgraduate course of teacher training (PGCE) based at a British University. The students have differing initial beliefs about teaching, learning and mathematics. As anticipated in the literature, the student's initial beliefs survive virtually intact throughout the year. However, the study suggests that the link between initial beliefs and teaching approach is not deterministic. The study suggests ways of encouraging student teachers to employ a range of pupil activities in their teaching.     

The Border Crossings of a Multicultural Science Education Enthusiast

Jill was a preservice science education student who wanted to make science more accessible to all students. This study is an examination of the “borders” she encountered as she completed her student teaching in a cultural setting that was different from her own. Her student teaching experience was documented through interviews, participant observations, field notes, lesson plans, and a journal. An inductive analysis of the documents and a context chart of the coded data revealed that Jill encountered the (a) cultural border of her students, (b) cultural border of science instruction, and (c) cultural border of the school. While some borders were crossed, others were not. This study suggests that during field experiences, preservice teachers may encounter multiple cultural borders, some consistent and some inconsistent with their instructional philosophy. As student teachers work with diverse populations, supervisors and cooperating teachers need to recognize the borders student teachers will encounter and encourage student teachers to examine their beliefs about practice as a means to acknowledge and understand the encountered borders.     

Gender,Prior Academic Performance and Beliefs as Predictors of Attitudes Toward Biology Laboratory Experiences

The purpose of this study was to investigate the relationships between gender, prior academic performance, beliefs and student attitudes toward biology laboratory experiences. The sample consisted of 294 students from 10th, 11th and 12th grades enrolled in a Catholic high school in a major metropolitan area in the Southeast. Two 11-item scales were created; one to measure student attitudes toward biology laboratory experiences, and the other to measure student beliefs about the benefits of biology laboratory. A three-way analysis of variance (gender × prior academic performance × beliefs) was conducted with the attitudes toward biology used as the dependent variable. Gender had a significant effect on attitudes, with females reporting more positive attitudes toward biology laboratory than males. Prior academic experience was also a significant predictor of attitudes; students who received lower GPAs in previous science courses reported more positive attitudes toward biology laboratory than students with higher GPAs. Based on previous research this finding was surprising; however, it appears that lower achieving students may perceive that there is a higher benefit from “hands on” laboratory experiences than high achieving students. The data also indicated that beliefs had the strongest correlations with attitudes; students who believed laboratory experiences were beneficial had more positive attitudes. The implications for research, theory and practice are also presented.     

Expanding Notions of “Learning Trajectories” in Mathematics Education

Over the past 20 years learning trajectories and learning progressions have gained prominence in mathematics and science education research. However, use of these representations ranges widely in breadth and depth, often depending on from what discipline they emerge and the type of learning they intend to characterize. Learning trajectories research has spanned from studies of individual student learning of a single concept to trajectories covering a full set of content standards across grade bands. In this article, we discuss important theoretical assumptions that implicitly guide the development and use of learning trajectories and progressions in mathematics education. We argue that diverse theoretical conceptualizations of what it means for a student to “learn” mathematics necessarily both constrains and amplifies what a particular learning trajectory can capture about the development of students’ knowledge.     

A comprehensive theory of representation for mathematics education

Representation is a difficult concept. Behaviorists wanted to get rid of it; many researchers prefer other terms like “conception” or “reasoning” or even “encoding;” and many cognitive science resarchers have tried to avoid the problem by reducing thinking to production rules.There are at least two simple and naive reasons for considering representation as an important subject for scientific study. The first one is that we all experience representation as a stream of internal images, gestures and words. The second one is that the words and symbols we use to communicate do not refer directly to reality but to represented entities: objects, properties, relationships, processes, actions, and constructs, about which there is no automatic agreement between two persons. It is the purpose of this paper to analyse this problem, and to try to connect it with an original analysis of the role of action in representation. The issue is important for mathematics education and even for the epistemology of mathematics, as mathematical concepts have their first roots in the action on, and in the representation of, the physical and social world; even though there may be a great distance today between that pragmatical and empirical source, and the sophisticated concepts of contemporary mathematics.     

A Comparison of Preservice Elementary Teachers' Beliefs About Mathematics and Teaching Mathematics: 1968 and 1998

The study replicates Collier's (1972) work. It focuses on the beliefs of a large sample of elementary education students at four stages of teacher preparation, about both the nature of and the teaching of mathematics. The instrument measures what Collier termed a “formal‐informal” dimension of belief. The data suggest that initially the 1998 students held significantly more informal (constructivist) beliefs than did their 1968 counterparts. In both years, students moved toward more informal beliefs during the course of their programs, with the most significant changes occurring in their beliefs about how mathematics should be taught. However, apparent contradictions in belief structures were observed both at the start and at the end of their programs. Thus, it appears that though many students acquired new, more informal beliefs during the course of their programs, they did not develop robust, consistent philosophies of mathematics education.     

Assessing Preservice Teachers' Beliefs about the Teaching and Learning of Mathematics and Science

With increased study of teachers' beliefs about science and mathematics teaching in recent years, there is a need for instruments that assess beliefs in both content areas. Moreover, early field experiences in schools and professional development efforts may influence the beliefs that preservice and in‐service teachers develop, and instruments for this purpose are limited. This article describes the development and validation of the Confidence, Commitment, Collaboration, and Student thinking in Mathematics and Science (CCCSMS) beliefs scales, a set of 10 six‐item scales. Collectively, these scales measure teachers' self‐confidence in doing and teaching science and mathematics, confidence in understanding children's thinking and building models of that thinking, commitment to teaching science and mathematics from a standards‐based perspective, and commitment to collaborating with peers. The scales represent an efficient and effective way of assessing beliefs of large groups. Although this article focuses predominantly on development of the scales, results from initial use indicate that there are positive correlations between beliefs related to mathematics and beliefs related to science, but the correlations are low enough to show that many teachers think differently about the two subjects.     

Facilitating parental engagement in school mathematics and science through inquiry-based learning: an examination of teachers’ and parents’ beliefs

This study examined teachers’ and parents’ beliefs on the implementation of inquiry-based modeling activities as a means to facilitate parental engagement in school mathematics and science. The study had three objectives: (a) to describe teachers’ beliefs about inquiry-based mathematics and science and parental engagement; (b) to describe parents’ beliefs about inquiry-based mathematics and science and their engagement in inquiry-based problem solving; and (c) to explore the impact of an inquiry-based learning environment comprising a model-eliciting activity and Twitter. The research involved three sixth-grade teachers and 32 parents from one elementary school. Teachers and parents participated in workshops, followed by the implementation of a model-eliciting activity in two classrooms. Three teachers and six parents participated in semi-structured interviews. Teachers reported positive beliefs on parental engagement in the mathematics and science classrooms and the potential positive role of parents in implementing innovative problem-solving activities. Parents expressed strong beliefs on their engagement and welcomed the inquiry-based modeling approach. Based on the results of this aspect of a four-year longitudinal design, implications for parental engagement in inquiry-based mathematics and science teaching and learning and further research are discussed.     

The Relationship Between Teacher and Student Beliefs About Mathematics

In this study the relationship between teacher (n = 7) beliefs about mathematics, the learning and teaching of mathematics and their respective students' beliefs about mathematics (n = 158) are examined. The data were collected by means of two instruments specifically designed to measure belief systems about mathematics. Teacher scores were adjusted so that a higher score reflected beliefs in aligntnent with the National Council of Teachers of Mathematics (NCTM) Standards. Results indicated that the students of teachers whose beliefs were in alignment with the NCTM Standards had significantly different beliefs about factors that lead to success in mathematics than did other students. Specifically these students felt that working hard to solve problems and striving for understanding would lead to success. No student differences were found for subscales of ego orientation, competitiveness, interest and extrinsic factors such as neatness and cooperation. These findings suggest that this group of teachers practiced what they believed and that these practices affected what their students believed about mathematics. We suggest that using these two assessments in tandem give a clearer picture of the mathematical environment within a classroom and can be used in professional development workshops to initiate teacher reflection about classroom practices.