J. Randy McGinnis & Carolyn Parker

Science Teaching Center

Department of Curriculum & Instruction

2226 Benjamin

University of Maryland

College Park, Maryland 20742

Amy Roth-McDuffie

Department of Teaching and Learning

Washington State University Tricities

2710 University Drive

Richland, Washington 99352

A paper presented at the annual meeting of the National Association for Research in Science Teaching, Boston, MA, March 28--April 1, 1999.

Abstract

There is currently considerable interest in preparing science teachers to make connections with mathematics. However, there are a dearth of empirical studies that systematically study the implementation of this teaching innovation. This study presents a detailed description and an interpretation of efforts made to prepare prospective upper elementary/middle level teachers to make connections between science and mathematics. The focus in this study is on the undergraduate teacher candidates’ senior year in which they take science methods in the fall and participate in student teaching in the spring. Participants in this year long study include the science methods professor and his co-researcher, thirty teacher candidates in the fall science methods course, and a sample of six select teacher candidates participating in student teaching in the spring. The six teacher candidates are distinguished from the other teacher candidates in this study by participating in a National Science Foundation funded undergraduate teacher preparation program (the Maryland Collaborative for Teacher Preparation, MCTP). A key implication from the science methods phase of the study is the assertion that while all participants benefited from the teaching innovation to blend mathematics and science in the methods course, the teacher candidates participating in the specialist program were particularly receptive to and accomplished in making connections between mathematics and science. We believe that they benefited preferentially due to their prior experience in content specialist classes in which the professors emphasized connections between the two disciplines. However, we also advise caution in implementing this innovation in all contexts. We learned that some teacher candidates are inclined to construct visions of the role of mathematics and science when making connections which specialists in the disciplines might find problematic. A key implication from the student teaching phase of this study is that while most of the benefits of the innovation continued, the process of encultration of the student teachers in extant cultures differentially supported aspects of the innovation. Of particular note is the tension that emerged between student freedom to engage in inquiry and a perceived need to limit student off task behavior and confusion through the use of more explicit instruction.

An Investigation in Preparing Teacher Candidates to Make Connections

Between Science And Mathematics

There is considerable interest currently in preparing science teachers to make connections with other disciplines, particularly mathematics. However, there are a dearth of empirical studies that systematically study the implementation of this teaching innovation. This study presents a detailed description and an interpretation of efforts made to prepare prospective upper elementary/middle level teachers to make connections between science and mathematics. The focus in this study is on the teacher candidates’ senior year in which they take science methods in the fall and participate in student teaching in the spring. This study first documents and interprets the extensive efforts made by one elementary science methods professor to make curricular connections between mathematics and science throughout a special section of an elementary science methods course at a major research university. The elementary science methods course included six teacher candidates participating in a special National Science Foundation funded undergraduate teacher preparation program designed to produce specialist mathematics and science upper elementary/middle level teachers, the Maryland Collaborative for Teacher Preparation (MCTP). This study second examines how these same teacher candidates in student teaching continue to construct their perspectives of making curricular connections between mathematics and science in the K-12 context.

Purpose and Relevant Background

In this study, the construction of a vision by teacher candidates for the role of mathematics and science when they are connected curricularly was of primary interest. For the first phase of the study, the senior level science methods course in the fall, the participants are the professor, his coresearcher, and thirty teacher candidates who were enrolled in the elementary science methods course. Special focus is on six teacher candidates participating in a National Science Foundation funded undergraduate teacher preparation program designed to produce specialist mathematics and science upper elementary/middle level teachers and on three elementary education majors with concentrations in mathematics or science. For the second phase of the study, the senior level student teaching semester in the spring which follows the methods semester, the participants are five of the six teacher candidates studied in the fall methods block. Insights are generated by the researchers as prompted in the fall semester by a comparison of the performance of the special teacher candidates’ and the other teacher candidate participants. In the spring semester, insights are generated solely from an examination of the five case study students. In their senior year of their teacher preparation program, the six MCTP teacher candidates brought to the senior level methods block extensive prior experience of being in reform-based classes. They had been taught by mathematics and science professors who were participants in the MCTP and structured their courses in a reform-based manner.

The context of this teaching innovation is a National Science Foundation funded undergraduate teacher preparation program, the Maryland Collaborative for Teacher Preparation [MCTP]. The MCTP is a statewide undergraduate program. A fundamental assumption of the MCTP is that changes in pre-secondary level mathematics and science educational practices require reform within the undergraduate mathematics and science subject matter and education classes teacher candidates take throughout their teacher preparation programs (NSF, 1993). While teacher candidates selected to participate in the MCTP program in many ways are representative of typical teacher candidates in elementary teacher preparation programs, they are distinctive by expressing an interest in teaching mathematics and/or science. The goal of the MCTP is to promote the development of professional teachers who are confident teaching mathematics and science using technology, who can make connections between and among the disciplines, and who can provide an exciting and challenging learning environment for students of diverse backgrounds (University of Maryland System, 1993). This goal is in accord with the educational practice reforms advocated by the major professional mathematics and science education communities (National Council of Teachers of Mathematics [NCTM], 1989, 1991; American Association for the Advancement of Science [AAA] 1989, 1993; National Research Council [NRC] of the National Academy of Sciences, 1989, 1996). Figure 1 contains a program overview of the MCTP.

In practice, the MCTP undergraduate classes are taught by faculty in mathematics, science, and education who make efforts to focus on "developing understanding of a few central concepts and to make connections among the sciences and between mathematics and science" (MCTP, 1996, p. 2). Faculty also strive to infuse technology into their teaching practices and to employ instructional and assessment strategies generally deemed compatible with the constructivist perspective (i.e., address conceptual change, promote reflection on changes in thinking, and stress logic and fundamental principles as opposed to memorization of unrelated facts) (Cobb, 1988; Driver, 1989; Tobin, Tippins, & Gallard, 1994; von Glasersfeld, 1987, 1989; Wheatley, 1991). A primary referent for MCTP faculty on teaching and learning from a constructivist perspective is The Case for Constructivist Classrooms (Brooks & Brooks, 1993). Faculty lecture is diminished and student-based problem-solving is emphasized in cross-disciplinary mathematical and scientific applications.

A. Phase one: Science Methods. As a result of the teacher candidates’ participation in the MCTP reform-based science and mathematics courses, the following research questions were investigated:

B. Phase two: Student Teaching. As a result of the teacher candidates’ participation in the MCTP reform-based science, mathematics and science and mathematics methods classes, the following research question was investigated:

"What beliefs and perceptions do the MCTP teacher candidates bring to their student teaching experiences?"

Research Methodological Approaches

This is an action research study (Collins, 1995; Gore & Zeicher, 1991; Hollingsworth, 1997; O’Hanlon, 1996; Zuber-Skerritt, 1996) using an N of one (a case study). A common focus of action research is to promote a self-reflective analysis that can improve teaching practice and our understanding of practices (Kyle, Linn, Bitner, Mitchell, & Perry, 1991; O’Hair, 1995). This study involved a cycle of four steps: planning, enacting, observing the plan, and reflection (Carr & Kemmis, 1986). While a case study has been applied to both quantitative and qualitative research methods and is itself not a methodology, a "qualitative case study is characterized by the main researcher spending substantial time, on site, personally in contact with activities and operations of the case, reflecting, revising meanings of what is going on" (Stake, 1994, p. 242). We chose a case study because we were interested in describing and interpreting the personal constructions of the college professor and his co-researcher as the professor examined his practice in the context of infusing innovation in his practice. A qualitative case study enables researchers to develop an in-depth narrative which provides a framework from which other teacher researchers can reflect on their experiences and which can inform future research (Romberg, 1992). For this study, the case is bounded by a unit of analysis that provides guidance on what is relevant and not relevant (Merriam, 1988; Ragin & Becker, 1992). The unit of analysis is the interdisciplary (mathematics and science) innovation of the one semester class.

The symbolic interaction theoretical stance makes the assumption that social reality is a social production (Blumer, 1969; Denzin, 1978). Meanings are constructed by humans through interaction; meanings are not inherently linked to inanimate objects or events. A central premise is that inquiry must be grounded in the empirical environment under study (van Sickle & Spector, 1996). This theoretical position places emphasis on the social construction of meaning in a culture through viewing the process of how individuals define and interpret each others acts. By carefully examining individual’s interpretations of each others acts assertions are made as to how the individual’s interpretations of each other sustain or transform the way they view their culture which guides they way they act and interact (Woods, 1992).

In this study, the symbolic interaction theory provided guidance for the roles of the researchers and the interpretative domain of the study (Goetz & LeCompte, 1984). Since the researchers held the belief that their research was "a social production symbolically negotiated between the researcher and participant" (p. 57) explicitly revealing the purpose of the research to the participants and maintaining an openness of mind regarding interpretations of the participants’ beliefs and actions complemented the action research methodological approach. Communication between the researchers and with the participants regarding subjective viewpoints became imperative to conduct in order to engage in meaning making within a group, the essence of symbolic interaction. Qualitative research assumes there are multiple realities constructed as a function of personal interaction and perception (Merriam, 1988). Respondent validation was desired as evidence of ongoing active communication between the researchers and the participants.

The professor, who was engaging in a prolonged self-study of his teaching practices, both during the science methods semester and during the subsequent student teaching semester, believed that the symbolic interaction theoretical stance supported the case study methodological approach. He also believed that it complemented a tenet of his philosophy of teaching which encouraged being intellectually honest with his teacher candidates regarding an analysis of the teaching of science. Since he expected to be a learner in this action research study, symbolic interaction supported him in a researcher role that allowed him to focus his attention on interpreting his prior self and his present self as a consequence of his understanding of the events and the participant perspectives throughout the study’s duration (Blumer, 1969).

Content Instruments. We used two instruments to assess the prior science knowledge of the teacher candidates enrolled in the science methods course. The GALT was used to assess process skills; a 60-item "Science Content Diagnostic" was crafted by the researchers from existing items in the literature (Gega, 1986) that aligned with the K-12 content recommendations made in the National Science Education Standards (1996). This instrument was divided into three sections (20 items each) that assessed a select knowledge in physical science, life science, and earth science. Table 1 includes sample items for inspection.

Observations. Roth-McDuffie observed the science methods class on several occasions throughout the semester-long class. The observed classes were video-taped for later analysis. Whenever the students were working in groups, the observations focused on the MCTP teacher candidates. In addition, McGinnis videotaped the MCTP teacher candidates’ and all non-MCTP teacher candidates’ majoring in mathematics and science "Science Investigations" poster displays. These displays contained the results of a consumer science investigation presented in graph and textual form.

Interviews. Roth-McDuffie conducted semi-structured interviews with the professor (McGinnis) and the six MCTP teacher candidates in the course. In addition, four non-MCTP teacher candidates in the course with concentrations in mathematics or science also agreed to be interviewed. The intent was to compare the MCTP teacher candidates’ interview responses with the responses of these four non-MCTP teacher candidates with similarly strong backgrounds in mathematics and science but who had not taken MCTP reformed-based content classes. The interviews were semi-structured in that we used a protocol (see Appendices A and B) for each interview, and Roth-McDuffie asked additional probing questions to clarify and/or pursue the participants’ ideas. The interviews were conducted at the beginning and the end of the semester in groups of two or three for the student participants. We opted to use small group interviews with the intent of providing a more conversation-like atmosphere which would allow one teacher candidate’s comments to encourage the others to share additional thoughts. This strategy was consistent with the interactionist perspective in that it allowed the participants to clarify and develop their thoughts and responses in an environment similar to that of their classroom learning environment.

At the beginning of the semester, the teacher candidates were grouped in pairs with the MCTP teacher candidates interviewed separately from the non-MCTP teacher candidates. During the semester one of the four non-MCTP teacher candidates dropped out of the methods courses, and consequently, three non-MCTP teacher candidates remained in the comparison group at the end of the semester. To maintain consistency between the MCTP and the non-MCTP interview groups, we decided to conduct the final interviews in groups of three (again, with the MCTP teacher candidates interviewed separately from the non-MCTP teacher candidates). Throughout both sets of interviews, Roth-McDuffie ensured that all participants were provided the opportunity to contribute to the conversation. Each of the group interviews lasted approximately 30 minutes.

In addition to the semi-structured interviews, McGinnis conducted an open-ended, informal group discussion with the MCTP teacher candidates in the science methods class. The group discussion focused on ideas about make connections between mathematics and science in teaching and learning. The discussion was prompted with the initial question, "What attempts have you observed your science methods professor making connections between mathematics and science in your science methods courses?" and from that prompt a conversation transpired. Roth-McDuffie video-taped and, in addition to McGinnis, participated in the discussion.

Artifacts. The teacher candidates’ products for the science methods class were collected for analysis. This included their weekly journal entries, written assignments, and poster displays.

Refer to Table 2 for a summary of these sources of data.

Class Evaluations. Three previous official student class evaluations of the professor’s elementary science methods class were item compared with the study class’s responses on the end of the semester class evaluation. Table 6 contains these class evaluations.

Observations. Carolyn Parker and another doctoral student majoring in mathematics education observed the teacher candidates in their semester-long public school placements. They made three separate classroom teaching observations spread out over the semester (beginning, middle, end). They took field notes of the participants’ science and mathematics teaching practices which were analyzed for this study.

Interviews. Carolyn Parker and the doctoral student majoring in mathematics education conducted two semi-structured interviews with the five MCTP teacher candidates during the student teaching semester. The interviews were semi-structured in that we used a protocol (see Appendix C) for each interview, and the interviewers asked additional probing questions to clarify and/or pursue the participants’ ideas. The interviews were conducted individually during the first third of the semester and at the end of the semester. The interviews were conducted following the observation of lessons and were incorporated seamlessly into the post-lesson observation debriefing(s). They were audio-recorded and transcribed.

Trustworthiness of the data. Criteria to enhance the trustworthiness of the data analysis were based on ways described by Eisner (1991), Elliot (1991), Erickson (1986), Feldman (1994), and Guba & Lincoln (1989). These methods involved the qualitative warrant checks of long-term observation in a setting, collection of data from multiple sources, active search for counter examples, and the triangulation of data.

Contextual Setting And Participants

The Science Methods Class. The three-credit elementary science methods course examined in this study was taught in the fall semester, 1997, at the University of Maryland, College Park. At this university, senior education students enroll in "Blocks," a cluster of five content methods courses (mathematics, language arts, reading, social studies and science) all of which meet for one hour and fifty minutes one day weekly. The science methods course is the only exposure to science education in the elementary teacher candidates’ program. In addition to classes at the University, students spend 2 full days each week in a field-based, public school placement. The field placements for non-MCTP teacher candidates were with regular classroom teachers in public elementary schools in the metropolitan region in which the university is located. The field placements for the MCTP teacher candidates were with specially trained MCTP cooperating mentors in upper elementary and middle level public schools in the metropolitan region in which the university is located.

The science methods class was taught in a manner consistent with the education philosophy of the professor. In McGinnis’s case, he chose to place emphasis on the construction of science content in conjunction with knowledge construction in science education theory. Science education topics typically that form the substance of the course include: concept mapping; the nature of science and science teaching; inclusive science education practices; the fair test; the learning cycle; science process skills; safety; alternative conceptions; alternative assessments; science talks; and science-technology-society. In practice, teacher candidates in McGinnis’s class begin each class in small cooperative learning groups that engage in a student-centered, problem-based science learning activity that serve as a referent during subsequent pedagogy discussions facilitated by the professor. The activities are taken from existing sources, such as "Moon Gazing" (Schatz, 1991), or instructor created, such as an investigation of the causes of middle ear infections (McGinnis & Graeber, 1994). The activities are selected to represent different grade levels, all the sciences, and connections with other disciplines, particularly mathematics. McGinnis facilitates discussions by posing questions that unpack the pedagogical implications inherent in the activities. His goal is to assist the teacher candidates in constructing a schema of science teaching practice consisting of the categories "Science Content," "Pedagogical Content Knowledge," "Curricular Knowledge," "Attitude," and "Context." General questions, such as "What science content was taught/learned in the activity?" and "What pedagogical strategies were used to teach/learn that content?" serve as conversation catalysts. The professor also serves the role of an expert of science education research that is relevant to science education topics, such as the fair test, concept mapping, and inclusive science education practices. The teacher candidates take the lead in several class sessions in which they engage in a type of peer coaching in which they demonstrate and discuss with their small cooperative learning teams science lesson plans they developed for use with elementary students. In addition, the teacher candidates make presentations near the end of the semester in which they discuss a consumer science inquiry they facilitated that semester with young learners in a school setting.

The teacher candidates are assessed by their ability to research a science content topic; to interview young learners on their conceptions of the topic and report their findings in a concept map; to carry out instruction (and reflect on that experience) with a small group of elementary students in a public school setting; to carry out a scientific investigation and present it to the class in a poster format; and to write an end of the semester essay in which they delineate their perception of the theoretical structure of science education and provide practical examples on how to enact that schema in an elementary school setting.

The Student Teaching Semester

During the student teaching semester, the participants were assigned to mentor teachers who participated in a summer MCTP Mentor Teacher Workshop. The participants spent 8 weeks in an upper elementary grade placement and 8 weeks in a middle grade placement. In both placements, there were significant opportunities to teach mathematics and science.

Participants. As previously mentioned, during the first semester of this study, participants included the professor of the science methods class (McGinnis), a coresearcher, and the thirty teacher candidates in the course. Special focus was on six teacher candidates participating in the MCTP and four non-MCTP teacher candidates with concentrations in mathematics or science. We wanted a comparison group of non-MCTP teacher candidates that was most similar to our MCTP group in terms of prior content preparation, so we selected four who were concentrating in mathematics or science elementary education (2 mathematics, 2 science). One of the participants (science concentration) in the non-MCTP comparison group dropped out of the methods block before the end of the semester. Refer to Table 3 for a more detailed of each of these nine teacher candidates. During the second semester of this study, participants were the six MCTP teacher candidates (one of whom dropped out of the study when her health concerns did not allow her to continue enrollment in the student teaching semester).

In preparation for my innovation to make connections between mathematics and science in the science methods course, Roth-McDuffie and I conducted a review of the literature. Our intent was to survey what was promoted as a rationale for making connections between the disciplines and what theorists understood about attempting such an innovation. In particular, two areas were examined: professional associations’ call for mathematics and science integration and theoreticians’ conceptualization of mathematics and science integration.

Professional Associations’ Call for Integration of the Disciplines. From our review of the literature, we learned that professional associations concerned with the teaching of mathematics and science have long called for the integration of the disciplines. Prominent among these associations is The School Science and Mathematics Association, the National Council of Teachers of Mathematics (NCTM), and the American Association for the Advancement of Science (AAAS). Indeed, faced with a burgeoning body of work on the integration of the two school disciplines, School Science and Mathematics in 1905 decided it was necessary to publish a bibliography of the literature on that topic to assist interested professionals. This interest in integrating mathematics and science continued in these associations throughout this century. Currently, this interest has manifested itself strongly in the mathematics and science education reform documents promoted by the NCTM, AAAS, and the National Research Council (NRC). Influential documents such as Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989), Science for All Americans (Rutherford & Algren, 1990), Benchmarks for Scientific Literacy (AAAS, 1993), and most recently, National Science Education Standards (NRC, 1996) all promote linking the teaching of the two disciplines. For example, Program Standard C in the National Science Education Standards (NRC, 1996, p. 214) states a science perspective of this linkage:

Theoreticians Conceptualization of Mathematics and Science Integration. We found Berlin’s (1991) comprehensive bibliography on the integration of mathematics and science particularly helpful to begin our search. We were surprised to learn from Berlin’s review that research had played a subsidiary role in the literature on this topic. In discussing her review of the literature, Berlin (1994) stated there existed a "marked paucity of research documents" (p. 32) with only 41 of the 555 citations relating to research. She stated there was a need for "conceptualization and additional research on integrated science and mathematics in teaching and learning" (p. 4). In a more recent, comprehensive review of the literature on this topic, Huntley (1997) also found a dearth of research on integrating mathematics and science in education. Committed to guiding our teaching innovation by insights from scholarship, we devoted considerable attention to reviewing the relatively few theory-based articles on this topic. What follows is a summary of the articles arranged by date, from oldest to most current, that informed us.

In 1916, John Dewey engaged in one of the earliest discussions about integrating all disciplines in teaching and learning and about learning through meaningful activities. Dewey’s rationale for the teaching of subject matter in an integrated manner was founded on his belief that there was too much subject matter in the respective disciplines to be mastered by a separate study of each in school settings. He states:

Furthermore, Dewey thought that the disciplines would by necessity be taught in an integrated manner if schooling were concerned with assisting learners to make sense of everyday experience that did not come separated into separate domains of study. He states:

In regards to science Dewey thought that it was in particular danger of being distant from learners’ everyday concerns if it were taught as a separate discipline. As he states:

Brown and Wall (1976) in an influential article discusses a continuum model of integration that emerged from the Cambridge Conference that focused on the integration of mathematics and science. They present the integration of mathematics and science in terms of common processes and describes the six areas of learning that are common to mathematics and science that can be dealt with in a hands-on laboratory setting. The areas are: (1) sorting and classifying; (2) measuring; (3) using spatial and time relationships; (4) interpreting data; (5) communicating; and (6) formulating and interpreting models.

In Goals for the correlation of elementary science and mathematics: The report of the Cambridge Conference on the correlation of science and mathematics in the schools (Education Development Center, 1976), a model of relating science and mathematics in a curriculum is presented. The report states that,

A good curriculum comprises units and activities which relate the science in mathematics in different ways, which could be described as: mathematics for mathematics; mathematics for science; mathematics and science; science for mathematics; and science for science. (p. 19).

Lehman and McDonald (1988) present a study designed to assess whether an integrated approach to teaching mathematics and science would change preservice teachers’ perception toward integrating the two disciplines. Also, the researchers compared preservice teachers’ (in the integrated program) and practicing teachers’ perceptions of mathematics and science. They found that preservice teachers increased their awareness of curricular materials for math/science integration and believed that integration mathematics and science is a preferable method for teaching. The science student teachers began the semester thinking that their high school teachers integrated mathematics and science and ended the semester thinking that they did not integrate the disciplines. Lehman and McDonald posited that this change shows that the student teachers developed a more sophisticated definition of integration after starting the semester with an oversimplified definition of integration. However, they also found that mathematics student teachers changed their thinking in the reverse direction. They started out saying that their high school mathematics teachers did not integrate the two disciplines but ended saying they did integrate them. Lehman and McDonald attribute this change to possible recognizing some activities as integrated under a more sophisticated understanding of integration, or possibly recalling some activities that they previously had not.

Among practicing teachers, science teachers indicated that they integrated mathematics and science more often than did mathematics teachers. Although mathematics teachers believed that integrating is a preferred teaching method, less than half of the sample indicated that they made attempts to integrate the two disciplines. The mathematics teachers were concerned about the time required to integrate the disciplines. From these findings, Lehman and McDonald contend, "Their concern about time may also be indicative of a belief that integrating mathematics and science would require their adding science into what they perceive as an already crowded curriculum" (p. 648).

Bagheri and Kretschmer (1991), described a model and their teaching experiences integrating science and mathematics methods courses and the student teaching. The four main features of the model are as follows: (1) the same professor that teaches the methods course also supervises the teacher candidate in student teaching; (2) emphasis on curriculum development and evaluation; (3) focus on teacher candidates "growth in their capacity for analytical and evaluative work" for all aspects of teaching including "assessment of broader educational issues, observing in classrooms, or reviewing curricular materials" (p. 18); (4) "nurture teacher candidates as reflective practitioners who make pedagogical decisions in light of what they know of subject matter, learners, social contexts, cultures, and the purposes of an elementary education" (p. 18).

As previously mentioned, Berlin (1991) conducted an exhaustive review of the literature on the topic of integrating mathematics and science. Authors included classroom teachers, teacher educators, curriculum developers, and educational researchers. Most helpful for our purposes of preparing teacher candidates to make connections between mathematics and science was her finding of how science and mathematics had been most commonly presented in attempts to integrate the two disciplines. She states:

McBride (1991) provides a brief history of the integration efforts made to link mathematics and science. In a synthesis of the literature, McBride discusses a rationale for integrating mathematics and science. The four reasons given are:

McBride identifies several research questions that need to be addressed. One of these questions is "How can preservice teachers be prepared so that they can integrate science and mathematics instruction when they can become teachers?" (p. 288). Also, McBride identifies five problems of integrating that must be addressed: (1) math and science are currently organized and taught as separate subjects in most schools; (2) teaching math concepts through science activities requires more time; (3) classroom management can be more complicated when using integrated activities as opposed to whole class mathematics instruction; (4) mathematics teachers often do not have the science materials necessary; (5) few teachers have access to or awareness of integrated curriculum materials. McBride lists and provides a brief description of commercial resources, professional organizations, projects, and other resource materials available to support teachers. Among several recommendations, McBride states, "Teacher educators must implement ideas of integration into their methodology classes. Preservice teachers must be given both rationale and methodology for integrating science and mathematics instruction" (p. 290).

In light of theories on constructivism and cognitive apprenticeship that suggest that school curriculum should integrate subject matter with real-world problems, Roth (1993) provides an example of mathematics and science learning being integrated through a case study of a high school physics student. Roth demonstrates the benefits of linking mathematics and science (with the use of technology) through an in-depth analysis of one students’ learning.

Stuessy (1993) discusses the rationale behind integrating mathematics and science in a methods course and describes the course and its development. The similarities between the disciplines is discussed in terms of both content knowledge and pedagogical knowledge, and in terms of the reform movements for both mathematics and science. The instructors of the methods courses noticed, in particular,

Stuessy used the following data sources as indicators of the relevance of the course in preparing preservice teachers to teach mathematics and science: (1) a multiple choice measure of students’ self-efficacy in teaching mathematics and science (the STEBI and the MTEBI); (2) students performance data (measured by 3 portfolio grades and a final examination); (3) students’ responses informal exit interviews and course evaluations. These data sources indicated that the integrated methods course was very successful. Scores on the self-efficacy instruments "showed significant positive gains in students’ beliefs about themselves as successful teachers of mathematics and science" (p. 61). Also, the students portfolio scores showed higher levels of performance on teaching related tasks. Finally, students’ indicated a high level of satisfaction with the course.

Steen (1994) discusses possible ways to integrate mathematics and science. These methods include: (1) using mathematical methods in science; (2) using science examples and methods in math instruction; (3) teaching math entirely as a part of science; (4) teaching science entirely as a part of mathematics; (5) employing math methods in science and science methods in math, coordinating both subjects. Steen describes each of these options and uses this description to make the point that while mathematics and science can contribute to each other, the two disciplines are "fundamentally different enterprises" (p. 9). He states that "science seeks to understand nature, [and] mathematics reveals order and pattern" (p. 9). He concludes, therefore, that an effective educational program must teach students the ways not only in which mathematics and science are similar, but also the ways they are different. Steen questions whether it is possible "to teach an entire curriculum that integrates science and mathematics" (p. 10). He believes that it is not possible because science and mathematics teachers are not sufficiently prepared to understand mathematics and the multiple sciences within science (e.g., physics, biology, chemistry). To avoid this overwhelming constraint to successfully integrating mathematics and science, Steen suggests that instead of attempting to integrating content, practitioners should integrate instructional methodologies (e.g., exploratory, investigative, and discovery learning).

Dossey (1994) reviews models for the integration of mathematics and science: (1) a simultaneous model where ties are made between the content in math and science courses; (2) a braided model where content from the disciplines are viewed as strands to be visited every year; (3) a topical model where the curriculum focuses on specific topics; (4) a unified model where unifying ideas are used to examine and relate concepts, principles and procedures from both disciplines (e.g., sets, functions, and structures); (5) a full interdisciplinary model which "completely merges the disciplines and draws from each when content is needed to move the topic forward" (p. 14). Dossey notes that while we have many examples of the simultaneous model taking place in our schools, the little contact between teachers prevents teachers from making rich ties to integrate mathematics and science. Moreover, Dossey concludes that careful development of examples of the other models have not been attempted. Dossey suggests that the recently developed Standard documents in mathematics and science may provide the support to achieve integration. However, he lists several barriers and actions that need to be taken to overcome these barriers: (1) curricular materials need to be developed; (2) assessment instruments need to be developed to appropriately measure progress in an integrated curriculum; (3) teacher education programs need to change to prepare teachers to teach integrated curricula; (4) public relations efforts need to be initiated to educate the various constituencies involved in education.

Lehman (1994) presents a study that extends the previous work of Lehman and McDonald (1988). Lehman summarizes the reasons for integration as:

The purpose of Lehman’s study was to understand how practicing and preservice teachers perceive the idea of integrating mathematics and science. Lehman administered an eight item questionnaire to 161 undergraduate elementary education majors and 60 elementary teachers. From an analysis of the survey results, Lehman detected three findings. First, preservice teachers were more likely to prefer integrating mathematics and science in teaching than practicing teacher (75% of preservice compared to 50% of practicing). Second, less than 50% of the practicing teachers believed they had sufficient background to integrate mathematics and science. Of the preservice teachers, approximately one-third believed they had sufficient background to integrate. Third, 41% of practicing teachers believed that there is not enough time to integrate mathematics and science as compared to 12% for preservice teachers. Thus, for many practicing teachers, integrating is seen "as another add-on topic" (p. 62). Included among Lehman’s recommendations are the following: (1) preservice elementary teachers should receive instruction in mathematics and science integration and should have opportunities to teach integrated lessons in field experiences; and (2) alternative models for integrating in preservice and inservice training should be explored.

Lonning and De Franco (1997) propose a continuum model of integration as a tool for curriculum development and for modifying lessons to enhance math and science connections. To effectively integrate mathematics and science in a lesson, content from both areas must be at the appropriate grade level (part of the curriculum for a specified grade level). The authors content that using the curriculum is helpful in answering the following important questions:

The authors caution that not all mathematics or science concepts can or should be taught through integration, and we should focus on the question, "‘How can the concepts best be taught’ rather than ‘How can they be integrated?’" (p. 215).

Austin, Hirstein, & Walen (1997) examined whether students participating in a high school curriculum designed to implement the NCTM Standards and integrate mathematics and science had better attitudes and achievement than control classes. They found significant attitude improvement in the experimental students’ mathematical confidence, no significant differences between experimental and control classes PSAT scores, and significant differences on the a problem solving test at the end of the year (favoring the experimental students). "These results suggest that a Standards-based curriculum can improve students’ mathematical attitude and problem-solving skills" (p. 45).

Enactment of Plans/ Observation. McGinnis structured science methods for elementary teachers, EDCI 372A, along three intellectual themes: constructivism, multiculturalism, and curriculum connections. The intent was to foster a learning community in which the elementary teacher candidates would reflect on these constructs as they developed skills, knowledge, and dispositions appropriate for the teaching of elementary science.

The version of constructivism emphasized was a fusion between ideas voiced by von Glasersfeld (1989), and Brooks and Brooks (1993). This meant that classroom science knowledge was represented as being constructed by individuals who actively participated in group problem solving learning experiences. Knowledge claims were evaluated as to their fit with evidence and were characterized by their openness to change as determined by additional information. The focus in science methods was not on finding the truth but on building testable theories.

The version of curriculum connections emphasized was adapted from Goals for the correlation of elementary science and mathematics: The report of the Cambridge conference on the correlation of science and mathematics in the schools (Educational Development Center, 1969) and Brown and Hall (1976) as presented in Lonning and DeFranco (1994). Efforts to connect science and mathematics were evaluated along the continuum suggested by Brown and Hall. Points on the continuum included "Independent Science, Science Focus, Balanced Mathematics and Science, Mathematics Focus, and Independent Mathematics." Considerable consideration was placed on the type (and appropriateness) of making connections between science and mathematics in specific lessons.

The following are activities/circumstances that were unique to this course during the study period and were facilitated by participation in/connection with MCTP:

Analysis. We collected and analyzed the textual data through the use of the qualitative technique of analytic induction to construct patterns of similarities and differences between the professor's and his co-researchers perceptions (Bogdan & Biklen, 1992; Gee, 1990; Goetz & LeCompte, 1984; LeCompte, Millroy, & Preissle, 1992). In analyzing the data and looking for patterns, we used both the emic and etic perspectives. The etic perspective imposes the researchers’ theoretical framework on the data; while the emic perspective uses the participants’ own words to develop the narrative (Van Maanen, 1995). We collected the quantitative data through the use of two instruments that measure science process and content knowledge. These were analyzed using non-parametric statistics.

Findings: Science Methods Semester

To answer our first research question ("Are the MCTP teacher candidates distinguished from the non-MCTP teacher candidates in the science content knowledge they bring to their science methods class?") we administered two instruments at the beginning of the semester. In analyzing these data we performed the Mann-Whitney U Test using the SPSS version 6.0 statistical analysis software package. The Mann-Whitney U Test is commonly used in place of a t-test for the equality of two means when sample sizes are small and correspondingly the assumption of normality is questionable (McGhee, 1985). This test is regarded as "one of the most powerful of the nonparametric tests for comparing two populations" (McGhee, 1985, p. 509).

In determining our two groups, we compared the MCTP teacher candidates with the following groups: (1) all of the other teacher candidates in the class; (2) the teacher candidates who had a science concentration; and (3) the teacher candidates who had a mathematics concentration

The results from the Mann-Whitney U analysis of the GALT scores are shown in Table 4 (Note: a higher rank signifies a better score.) The results show that the MCTP teacher candidates performed significantly better than the other teacher candidates in the class on the GALT at the 0.10 level of significance (p=0.08). While the MCTP scores, as a group, were better than the other sub-groups (i.e., science and or mathematics concentration) a significant difference did not exist between the MCTP teacher candidates scores and any of the sub-groups. Thus, the MCTP teacher candidates performed as well as either the mathematics concentration or the science concentration teacher candidates.

The Science Diagnostic Instrument scores were analyzed as follows: (1) total score; (2) physical science score; (3) life science score; (4) earth and space science score. The results from the Mann-Whitney U analysis for these scores and for the various groups described above are shown in Table 5. The results from the Mann-Whitney U analysis of the GALT scores are shown in Table 1 (Note: a higher rank signifies a better score.) The results show that the MCTP teacher candidates performed significantly better than the other teacher candidates in the class on the GALT at the 0.10 level of significance (p=0.08). While the MCTP scores, as a group, were better than the other sub-groups (i.e., science and or mathematics concentration) a significant difference did not exist between the MCTP teacher candidates scores and any of the sub-groups. Thus, the MCTP teacher candidates performed as well as either the mathematics concentration or the science concentration teacher candidates, and the MCTP teacher candidates performed better than the other teacher candidates as a whole.

In examining the sub-scores in the areas of physical, life, and earth and space science, we see that the MCTP teacher candidates’ mean rank scores are higher than the mathematics concentration teacher candidates for both the life and the earth and space sciences sub-scores. In addition, the MCTP teacher candidates performed better than their classmates as a whole on the earth and space science section of the instrument, but this was not statistically significant. In general, the MCTP teacher candidates performed better than those teacher candidates whose concentrations were science, but these scores were not significantly different.

Given that the MCTP teacher candidates were prepared with a focus on both mathematics and science content areas, these results indicated to us that the dual focus and the MCTP content professors commitment to a more problem-centered, student-centered pedagogy did not diminish the scientific knowledge gained as compared to the teacher candidates who focused only on science in more traditionally taught science content classes.

To answer our second research question ("Are the MCTP teacher candidates distinguished from the non-MCTP teacher candidates in the beliefs and perceptions they bring to their science methods course concerning [a spectrum of areas]") we analyzed the data we collected from the beginning of the semester teacher candidate interview. What follows are assertions we generated from a careful reading and comparison of all the participants’ responses to the interview questions. These assertions are presented in the order of the sub-sections of the second research question. Included in each are exemplar comments from the participants that support the claims made by our assertions.

a. Content preparedness to teach elementary students. The MCTP teacher candidates were distinguished from the other teacher candidates by expressing that preparedness to teach young students science content required their being taught content in a manner that modeled good practices. However, as a result of being taught science content by MCTP faculty in a constructivist manner, the MCTP teacher candidates recognized that a high level of comfort with science content was required. Consequently, the MCTP teacher candidates tended to express they felt less prepared as compared with the responses of the non-MCTP teacher candidates who were taught content in a lecture-based manner. The non-MCTP teacher candidates expressed a somewhat naive confidence of their content preparedness.

MCTP Teacher Candidate Beliefs and Perceptions. The distinguishable feature of the MCTP teacher candidates’ comments on content preparedness was that they believed their MCTP professors taught content in a manner that modeled good pedagogy, and they could emulate this approach with young learners. They believed this approach promoted lifelong retention of content.

Non- MCTP Teacher Candidate Beliefs and Perceptions. A distinguishable feature of the non-MCTP teacher candidates’ comments on content was a perception that while they believed that they had gained a sufficient body of science content knowledge, it had been learned in isolation from a good model of how to teach young students.

b. A vision of an appropriate science learning environment for elementary students. The MCTP teacher candidates expressed a vision of an elementary science learning environment in alignment with the reform movement (student-centered and problem-based, with an emphasis on students’ prior knowledge) that they believed was modeled by their MCTP science content professors. They also could contrast this reform-based vision with a traditional, lecture and textbook-based science content environment. The non-MCTP teacher candidates expressed dissatisfaction with a traditional learning environment based on teacher lecture but could not express an alternative vision of good teaching for elementary science students except for the increased use of labs involving equipment and manipulatives. Moreover, when they referred to using equipment and manipulatives, the non-MCTP teacher candidates did not indicate that they had developed a vision for how they would use these things or for what purpose.

MCTP Teacher Candidate Beliefs and Perceptions. Drawing on their recent undergraduate experience learning science content in MCTP classes, the MCTP teacher candidates expressed a well-developed vision of an elementary science learning with specific examples of their vision. The learning environment that they described included inquiry, cooperative learning, a concern for students prior knowledge, the teacher as a facilitator, and a commitment to achieving equity between males and females. Furthermore, they indicated they had developed personal theories/rationales for why these modes of learning are appropriate for young learners.

Non- MCTP Teacher Candidate Beliefs and Perceptions. In the context of their recent undergraduate experiences of learning content in a lecture-based manner that they believed was inappropriate for young learners, the non-MCTP teacher candidates’ alternative vision of good pedagogy for young learners was one based on instances of good teaching in their own K-12 educational histories or on brief field-based education experiences observing young students. These alternative visions were not thoroughly developed.

c. Rationale for and intent to make connections between science and mathematics in elementary teaching. The MCTP teacher candidates evidenced considerable reflection based on the firsthand MCTP experience of learning science and mathematics in a connected manner for a rationale making connections between science and mathematics. They intended to make extensive connections between the disciplines in their future practices. The non-MCTP teacher candidates were characterized by not having reflected on a rationale for making connections between the disciplines nor having experienced learning the disciplines in that manner except in cases where mathematics was used as a tool in science. They expressed a willingness to make connections between mathematics and science but based that connection solely on the use of mathematics as a tool. In addition, while both the MCTP and the non-MCTP groups seem to discuss mathematics as a tool for science when discussing what mathematics as a discipline brings to science, the MCTP group seems to recognize common processes of the disciplines (unlike non-MCTP group).

MCTP Teacher Candidate Beliefs and Perceptions. The MCTP teacher candidates’ brought to their science methods course the ability to articulate a rationale for making connections between science and mathematics based on extensive prior experience of learning the disciplines in that manner. Through their MCTP experiences, they perceived mathematics and science to be so intrinsically connected that they had difficulty conceiving teaching them as separate subjects. Their rationale included the belief that both disciplines could contribute, and in the case of mathematics, assist the other, in developing a better holistic understanding of an area of interest. They professed a shared intent to make extensive connections between the two disciplines in their future teaching practices.

Non- MCTP Teacher Candidate Beliefs and Perceptions. The non-MCTP teacher candidates brought to the science methods course a restricted rationale for making connections between mathematics and science. While they voiced a willingness toward attempting to make connections between science and mathematics, they based the connection fundamentally between science and mathematics on mathematics use as a tool in science.

d. the role of science methods in their teacher preparation program. The MCTP teacher candidates brought to the science methods class an inclusive vision of teacher preparation program composed of a seamless linkage between their undergraduate content courses and their science methods course. As a result of being taught content in a manner that modeled good pedagogy, they had a vision of how they wanted to teach. However, they recognized that the science methods course was essential to teach them the skills and knowledge base to enact that vision of teaching. The non-MCTP teacher candidates brought to science methods a vision of content classes taught in a manner they believed was inappropriate for young learners. They saw the science methods as their first opportunity to gain skills in teaching science appropriately.

MCTP Teacher Candidate Beliefs and Perceptions. The MCTP teacher candidates held the vision of science methods as performing an important next step role in their teacher preparation program by assisting them in enacting their vision of teaching content to young learners appropriately. They believed the primary purpose of science methods was to give them the opportunity to develop the strategies and knowledge necessary to create learning opportunities and environments similar to what they previously experienced in their MCTP content classes

Non- MCTP Teacher Candidate Beliefs and Perceptions. The non-MCTP teacher candidates saw the science methods course as their first opportunity in their undergraduate program to focus on the teaching of science to young learners in an effective and appropriate manner. They expressed interest in learning the strategies to teach science as if they were content independent.

To answer our third research question ("Are the MCTP teacher candidates distinguished from the non-MCTP teacher candidates in the beliefs and perceptions upon completion of the science methods course concerning [a spectrum of issues]?") we analyzed the data we collected throughout the semester. This included the end of the semester teacher candidate interview. Once again, what follows are assertions we generated from a careful analysis of the extensive data set we collected. For hueristic purposes, these assertions are presented in the order of the sub-sections of the third research question. Included in each are exemplar comments from the participants that support our assertions.

a. An appropriate science learning environment for elementary students. The MCTP teacher candidates thought young learners should learn science through inquiry characterized by being connected to other subjects and requiring active student participation. The non-MCTP teacher candidates expressed a vision of an appropriate learning environment for young students characterized as being teacher-centered with engaging hands-on activities.

MCTP Teacher Candidates. The MCTP teacher candidates believed that young students should learn science through inquiry characterized by the use of manipulatives, relevant to their lives, cooperative groups, and connected to other subjects.

Non-MCTP Teacher Candidates. The non-MCTP teacher candidates believed that young students should learn science in a hands-on manner in which the teacher played a prominent role as a demonstrator of activities.

Margaret:

Hands-on, doing an experiment or doing a demonstration with manipulatives to show, especially with the lower elementary, showing them, actually physically doing it so they understand before they work independently. Not just saying, "Okay. This is what you're gonna do, do it" which is what sometimes happens in the upper elementary or middle school, especially in science. They tend to give them a sheet and say, "Okay. Do this." And sometimes they just...they don't understand it I think. Showing them, going through it with them first and say, "Okay. This is what's gonna happen or...." Of course, some of the experiments, you do you want it to be a surprise to them, so I guess you wouldn't want to go through the whole thing, but maybe go along with them. I don't know. Maybe that's holding their hand too much. (Interview, December)

b. Extent to which their science methods professor modeled good teaching of

science. The MCTP teacher candidates were able to describe the teaching of their methods professor in a rich manner which identified many teaching practices they believed were effective. These practices included the use of small cooperative learning groups, student-centered activities, making connections between science and mathematics, and an emphasis on classroom discourse. His use of experimentation and on the personal construction of knowledge rather than on the memorization of facts were perceived as in alignment with the instruction they experienced in their MCTP science content classes. In contrast, the non-MCTP teacher candidates evaluated the science methods professor as modeling good teaching practices such as the use of student-centered activities but were not able to link his practices with previous science teachers they had experienced.

MCTP Teacher Candidates. The MCTP teacher candidates identified their MCTP science methods professor as modeling good teaching by the use of small cooperative groups, of engaging student-centered activities, of demonstrating various instructional strategies (including making connections between mathematics and science), of an emphasis placed on questioning and discussion, and a concern for creating a classroom environment characterized by respect for all. His focus on conducting experiments and discussing personal constructions rather than on memorization of facts were perceived as in alignment with the instruction they experienced in their MCTP science content classes.

Non-MCTP Teacher Candidates. The non-MCTP teacher candidates identified their science methods professor as modeling good teaching by making class engaging through the use of activities and demonstrations in which he made them predict outcomes.

c. Extent to which they observed their science methods professor making connections to mathematics in his teaching. Both the MCTP teacher candidates and the other teacher candidates readily identified multiple instances in which the science methods professor sought to make connections between science and mathematics. The MCTP teacher candidates were distinguished in the greater number of instances which they identified as fulfilling this curricular innovation.

MCTP Teacher Candidates. The MCTP teacher candidates identified their science methods professor making connections between science and mathematics throughout the semester. They recognized that specific activities (including the MCTP module) were used by the professor to achieve that goal. They also identified the complete weekly lesson on making connections between science and other subjects as supporting this innovation. It was also recognized that he encouraged them to make connections with mathematics in all their class assignments.

Non-MCTP Teacher Candidates. The non-MCTP teacher candidates recognized that their science methods professor sought to make connections between mathematics and science. They identified a few classroom activities which accomplished this innovation, including the MCTP module.

d. The rationale for and intent to make connections between science and mathematics in elementary teaching. The MCTP teacher candidates were distinguished from the non-MCTP teacher candidates in the advanced manner in which they could articulate a rationale for and intent to make connections between science and mathematics. The MCTP teacher candidates supported the curricular innovation to make connection between science and mathematics whenever it was appropriate in order to more accurately portray a holistic vision of knowledge. The non-MCTP teacher candidates were more wary of making connections between science and mathematics and more likely to portray mathematics as a tool when connections were attempted.

MCTP Teacher Candidates. The MCTP teacher candidates believed that the rationale for making connections between mathematics and science was to more accurately portray a holistic vision of knowledge. Through this portrayal of the world, a deeper understanding was possible. They expressed a commitment to extensively make connections between mathematics and science in their practices. They believed, however, that the two disciplines should only be connected when it was natural, or appropriate, in the context of a topic under study. They believed that mathematics could be connected to science more frequently, and appropriately, than science to mathematics.

Non-MCTP Teacher Candidates. The Non-MCTP teacher candidates believed that science and mathematics were connected by requiring the same sort of thinking processes. While they expressed support for making connections between mathematics and science, they were particularly hesitant to make what they perceived as inappropriate curricular connections. Examples provided by them on making connections between the disciplines portrayed mathematics as a tool in science.

What beliefs and perceptions do MCTP teacher candidates bring to their student teaching experiences?

• The MCTP teacher candidates expressed that preparedness to teach young students science content required their being taught content in a manner that modeled good practices. However, as a result of being taught science content by MCTP faculty in a constructivist manner, the MCTP teacher candidates decided that a high level of comfort with science content was required to teach effectively in that manner.

• The MCTP teacher candidates’ comments on content preparedness was that they believed their MCTP professors taught content in a manner that modeled good pedagogy, and they could emulate this approach with young learners.

• The MCTP teacher candidates expressed a vision of an elementary science learning environment in alignment with the reform movement (student-centered and problem-based, with an emphasis on students’ prior knowledge). They also could contrast this reform-based vision with a traditional, lecture and textbook-based science content environment.

• The MCTP teacher candidates expressed a well-developed vision of an elementary science learning with specific examples of their vision. The learning environment that they described included inquiry, cooperative learning, a concern for students prior knowledge, and the teacher as a facilitator. Furthermore, they indicated they had developed personal theories/rationales for why these modes of learning are appropriate for young learners.

• The MCTP teacher candidates brought the ability to articulate a rationale for making connections between science and mathematics. Through their MCTP experiences, they perceived mathematics and science to be so intrinsically connected that they had difficulty conceiving teaching them as separate subjects. Their rationale included the belief that both disciplines could contribute, and in the case of mathematics, assist the other, in developing a better holistic understanding of an area of interest. They provided examples from their field experiences of the extensive connections between the two disciplines.

• The MCTP teacher candidates thought young learners should learn science through inquiry characterized by being connected to other subjects and requiring active student participation. The MCTP teacher candidates believed that young students should learn science through inquiry characterized by the use of technology, manipulatives, relevant to their lives, cooperative groups, and connected to other subjects.

• In their roles as student teachers in the K-12 school context, the teacher candidates began to question some of their notions of innovation within the extant culture which placed a great emphasis on student management.

Researcher Reflections (Post-Science Methods Semester)

McGinnis. In my planning for this curricular innovation in teacher preparation, I based much of my thinking on an extensive literature review Roth-McDuffie and I conducted on making connections between science and mathematics. In particular, two areas were examined: professional associations’ call for mathematics and science integration and theoreticians’ conceptualization of mathematics and science integration. While I was heartened that professional associations had historically supported the MCTP’s program’s goal to make connections between mathematics and science in teacher preparation, I found scant intellectual guidance until I read Steen’s (1994) theoretical piece. What follows for the reader’s inspection is what I constructed Steen was promoting and what I found compatible with my personal notion of curricular connections.

Steen (1994) discusses possible ways to integrate mathematics and science. These methods include: (1) using mathematical methods in science; (2) using science examples and methods in math instruction; (3) teaching math entirely as a part of science; (4) teaching science entirely as a part of mathematics; (5) employing math methods in science and science methods in math, coordinating both subjects. Steen describes each of these options and uses this description to make the point that while mathematics and science can contribute to each other, the two disciplines are "fundamentally different enterprises" (p. 9). He states that "science seeks to understand nature, [and] mathematics reveals order and pattern" (p. 9). He concludes, therefore, that an effective educational program must teach students the ways not only in which mathematics and science are similar, but also the ways they are different. Steen questions whether it is possible "to teach an entire curriculum that integrates science and mathematics" (p. 10). He believes that it is not possible because science and mathematics teachers are not sufficiently prepared to understand mathematics and the multiple sciences within science (e.g., physics, biology, chemistry). To avoid this overwhelming constraint to successfully integrating mathematics and science, Steen suggests that instead of attempting to integrating content, practitioners should integrate instructional methodologies (e.g., exploratory, investigative, and discovery learning).

Taking Steen’s suggestion as my organizational principle, I worked throughout the semester to make connections between science and mathematics by seeking linkages among instructional methodologies. I was pleased that from my observations throughout the semester of my teacher candidates in the course that my efforts were met with their approval. From the analysis of the teacher candidate interview data, I have learned that a one course concerted attempt to make connections between science and mathematics can result in positive outcomes. I also have learned that teacher candidates who come to the science methods with prior experience in learning science in a connected manner with mathematics are better able to conceptualize the innovation and to resist the tendency to portray the use of mathematics in science contexts simply as a tool. I am left, however, with the conviction that this form of innovation requires an extremely high level of planning and commitment on the methods professor’s part to lessen the occurrence of teacher candidates constructing inappropriate visions of the use of mathematics in science contexts which may disturb mathematicians and mathematics educators. Therefore, while recommending continued explorations in this effort to make connections in teacher preparation between science and mathematics in science methods courses, I offer a cautionary note for science teacher educators to proceed in a manner that is informed by the concerns many mathematics (and science) educators hold in this endeavor.

Roth-McDuffie. At the end of the methods semester, Roth-McDuffie recorded her thoughts and perceptions about the teaching and learning in the course and the students’ reactions to the course. In reflecting on the semester, Roth-McDuffie referred to her field notes to make some more global observations. First, Roth-McDuffie considered McGinnis’ efforts to achieve his goal of making connections between mathematics and science in this science methods course. Roth-McDuffie wrote,

The evidence seemed to indicate that McGinnis was achieving the goal of helping the teacher candidates to see the connections between mathematics and science. In interviewing the teacher candidates, Roth-McDuffie perceived that they all had developed a greater sense of the relationship between mathematics and science during the semester. Roth-McDuffie recorded the following observations,

Roth-McDuffie also reflected on the extent to which others might achieve what McGinnis had achieved in his classroom, helping teacher candidates to understand the connections between mathematics and science (both in terms of content and pedagogy). Below are her reflections on this challenge:

Parker. A year after the study, Parker (a doctoral level science education student who had two years experience with the MCTP) read a draft of the manuscript and gave the following reaction.

Having had the opportunity to teach in a variety of settings, I understand and have reflected upon the complexity of helping not only younger students, but also teacher candidates make connections between mathematics and science. Given the objectives of the Maryland Collaborative for Teacher Preparation and its attempt to create a seamless fusion of mathematics and science, the statements recorded by the Collaborative students are provocative, but I was not surprised by both the breadth and depth of the group’s responses.

The teacher candidates’ rationale for and intent to make connections between science and mathematics in elementary teaching is particularly thought provoking. In particular, the following two comments demonstrate to me how the MCTP’s future teacher perceive the two disciplines as inextricably linked, not as separate entities to be taught within a vacuum.

As a science teacher educated in a large, major research university, I can relate my first few years as teaching to the non-MCTP teacher candidates who were characterized as having not reflected on a rationale for making connections between the disciplines and experienced math being used only as a tool for science. I have only recently come to recognize the common processes of the disciplines, a theme that permeates the words of the six students represented by this study.

The MCTP’s continuum of education consisting of integrated, interactive content courses, methods courses taught by professors committed to an integrated approach, a unique capstone course supplemented by research internships have been well-represented by the participants comments. They understand the interrelationships between the various components and have integrated the MCTP’s approach to present a seamless relationship between the two disciplines. I envy the future young members their classrooms.

Conclusion/Implications

In regard to McGinnis’ goal of helping students understand the connections between mathematics and science, while he was quite successful in achieving this goal, we need to consider Steen’s (1994) recommendations. While McGinnis’ course did not promote the idea of mathematics only as a tool for doing science, the teacher candidates did not seem to view mathematics as more than this when discussing the discipline of mathematics. Referring back to Steen’s notion that the two disciplines are "fundamentally different enterprises" (Steen, 1994, p.9), this finding serves as evidence that by viewing the disciplines from a connected perspective, a limited view of mathematics emerges. However, when discussing the processes of science and mathematics, the students perceived many commonalties (e.g., investigation, problem solving, etc.) and demonstrated a more developed understanding of these processes in each discipline. Again this finding is consistent with Steen’s (1994) recommendations that in integrating mathematics and science we should focus on the methodologies of the disciplines (i.e., focus on the commonalties of how we do mathematics and science, rather than what is common between mathematics and science).

When comparing the two groups of teacher candidates, at the beginning of the semester, we see fairly stark contrasts in their beliefs and perceptions about their preparedness to teach, their vision of an effective learning environment, and their understanding of connections between mathematics and science. Quite predictably, the MCTP teacher candidates had beliefs and perceptions that were consistent with their experiences in the MCTP program, while the non-MCTP candidate relied on more traditional, lecture-based preparation.

However, at the end of the semester, after sharing the common experience of being in a science methods course which was based on MCTP goals, both groups expressed similar ideas on the above issues. The difference at the end of the semester was not in the basic terminology used or the fundamental ideas expressed, but rather, in the depth and sophistication of understanding conveyed in the responses. Consistently, the MCTP teacher candidates offered responses that were more developed in the way they explained their ideas, and they provided more specific examples of their thinking as compared to the non-MCTP candidates. With a background of more experiences in this type of learning environment and with more opportunities to reflect on their thinking and learning (and the implications for their own teaching), the MCTP students articulated a well developed philosophy of teaching science. Whereas, the non-MCTP students just had begun this process.

This finding indicates that this one-semester course was enough to affect the beliefs and perceptions of both groups of teacher candidates. However, the impact was not enough to allow the non-MCTP teacher candidates to "catch up" to the MCTP teacher candidates in developing a carefully thought-out philosophy of teaching and learning. The question remains as to whether either group has been affected enough to bring about reform-based teaching in their future classroom practices.

Researcher Reflections (Post-Student Teaching Semester)

McGinnis. From an initial review of the participants’ comments during their student teaching experience, I found much encouragement. In particular, I was struck by their confidence in their science content and their ability to teach in a manner that modeled good pedagogy and emphasized inquiry. The specific references to how they remembered how I and their content expert professors modeled good pedagogy supported our belief that our seamlessly modeling good teaching was important in their teacher preparation program. Their comments on reform-based versus traditionally based instruction was also encouraging. It is rare in my experience to hear such a sophisticated analysis of teaching from novice teachers. Regarding their ability to articulate a rationale for making connections between science and mathematics while I was pleased that they found this innovation an expected practice, I yearned to see more evidence of theory in their explanations. I wondered to what additional extent I could assist them in constructing theoretical frameworks from which to justify their actions? I worried that without this foundation that their use of mathematics in science might drift ever closer to the notion of math as a tool. Ominously, I also began to see several of the participants (Mary and Laura) begin to start portraying aspects of the reform-based practices modeled in the teacher preparation program as problematic in their P-12 context. In particular, the tension between maintaining a calm and orderly classroom environment and allowing students the freedom to design inquiry and discuss science emerged as a significant issue. Mary resolved this tension by merging what she perceived as her cooperating teacher’s more traditional methods with the reform-based practices she learned in her undergraduate program. Laura, under pressure from her cooperating teacher to provide more explicit instruction to her students, began to believe she needed to give more instruction to younger students than she saw modeled in her methods classes populated by adults.

Implications

In regard to McGinnis’ goal of helping students understand the connections between mathematics and science, while he was quite successful in achieving this goal, we need to consider Steen’s (1994) recommendations. While McGinnis’ course did not promote the idea of mathematics only as a tool for doing science, the teacher candidates did not seem to view mathematics as more than this when discussing the discipline of mathematics. Referring back to Steen’s notion that the two disciplines are "fundamentally different enterprises" (Steen, 1994, p.9), this finding serves as evidence that by viewing the disciplines from a connected perspective, a limited view of mathematics emerges. However, when discussing the processes of science and mathematics, the students perceived many commonalities (e.g., investigation, problem solving, etc.) and demonstrated a more developed understanding of these processes in each discipline. Again this finding is consistent with Steen’s (1994) recommendations that in integrating mathematics and science we should focus on the methodologies of the disciplines (i.e., focus on the commonalities of how we do mathematics and science, rather than what is common between mathematics and science).

When comparing the two groups of teacher candidates, at the beginning of the methods semester, we see fairly stark contrasts in their beliefs and perceptions about their preparedness to teach, their vision of an effective learning environment, and their understanding of connections between mathematics and science. Quite predictably, the MCTP teacher candidates had beliefs and perceptions that were consistent with their experiences in the MCTP program, while the non-MCTP candidate relied on more traditional, lecture-based preparation.

However, at the end of the semester, after sharing the common experience of being in a science methods course which was based on MCTP goals, both groups expressed similar ideas on the above issues. The difference at the end of the semester was not in the basic terminology used or the fundamental ideas expressed, but rather, in the depth and sophistication of understanding conveyed in the responses. Consistently, the MCTP teacher candidates offered responses that were more developed in the way they explained their ideas, and they provided more specific examples of their thinking as compared to the non-MCTP candidates. With a background of more experiences in this type of learning environment and with more opportunities to reflect on their thinking and learning (and the implications for their own teaching), the MCTP students articulated a well developed philosophy of teaching science. Whereas, the non-MCTP students just had begun this process.

This finding indicates that this one-semester course was enough to affect the beliefs and perceptions of both groups of teacher candidates. However, the impact was not enough to allow the non-MCTP teacher candidates to "catch up" to the MCTP teacher candidates in developing a carefully thought-out philosophy of teaching and learning.

The question that remained after the methods semester was whether the teacher candidates participating in the MCTP had been affected enough to bring about reform-based teaching in their future classroom practices. An analysis of the student teaching data suggests that much was continued: a focus on student-centered and problem-based instruction; use of cooperative learning; a decrease in emphasis on memorization and an emphasis on understanding; a focus on questioning; an openness to alternative explanations; a view of the teacher as a facilitator; and the use of technology to enhance instruction. An aspect of the innovation which began to emerge as questionable during student teaching by some of the participants was the reliance on student initiative to engage in inquiry learning experiences without explicit instructions from the teacher on how to perform the investigations. With the encouragement of the veteran teachers with whom they were placed, a new emphasis on the use of direct instruction to decrease student confusion and off task behavior emerged.

The question that now remains to be investigated is to what extent the new MCTP teachers will carry out reform-based teaching in the extant teaching cultures they join.

Selective References

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National Science Foundation (1993). Proceedings of the National Science Foundation Workshop on the role of faculty from scientific disciplines in the undergraduate education of future science and mathematics teachers. (NSF 93-108). Washington, DC: National Science Foundation.

O’Hair, M. J. ( 1995, Spring). Uniting theory, research and practice: purpose, beliefs and change revisited. Action in Teacher Education, XVII, 88-91.

Steen, L. (1994). Integrating school science and mathematics: Fad or folly? In D. Berlin, (Ed.), A network for integrated science and mathematics teaching and learning conference plenary paper (pp. 7-12). A report from NSF/SSMA Wingspread Conference, Racine, WI. (Report No. SE 055 345). Columbus, OH: National Center for Science Teaching and Learning.

University of Maryland System (1993). Special teachers for elementary and middle school science and mathematics: A proposal submitted to the National Science Foundation Teacher Preparation and Enhancement Program. Unpublished manuscript.

Watanabe, T., & McGinnis, J. R. (1996, April). Modeling reform-style teaching in a college mathematics class from the perspectives of professor and students. A contributed paper presented at the annual meeting of the American Educational Research Association, New York City, New York.

Table 1

Physical Science Item

You want to separately drop a (1) penny, (2) nickel, (dime), and (4) quarter on a table to note the pitch of each sound. In what order should they be dropped for the pitches to rise, in order, from low to high?

a. 4-3-2-1.

b. 4-2-1-3.

c. 3-4-1-2.

d. 1-2-3-4.

Life Science

An active person whose appetite is poor loses weight. This is because:

a. the rate at which the body cells use digested food slows down.

b. insufficient food intake triggers off incomplete digestive processes.

c. the body’s typical biochemical processes cease for lack of enough raw materials.

d. fat and muscle tissue fuel the body’s energy needs.

Earth Science

You inspect a cross section or profile of an old, dried- up lake bed and find it like the profile of soil that has settled after being shaken in a water-filled jar. Where are the smallest particles located?

Note: All items are reproduced by permission of the publisher (Prentice-Hall, Inc.).

Gega, P. (1994). Instructor’s manual, science in the elementary education. New York: Macmillan Publishing Company.

Table 2

Interviews:

a.) Pre-& Post-Semi-Structured Interviews 6 MCTP Teacher Candidates;

(audio-taped and transcribed) 3 Non-MCTP Teacher Candidates

Professor of Science Methods Class

b.) Mid-Semester Group Interview 9 MCTP Teacher Candidates;

(video-taped) Science Methods Professor,

Mathematics Methods Professor, and

Graduate Research Assistant

Observations: Regular Observations of the Science

Methods Class, focusing on the

(video-taped) MCTP Teacher Candidates

Journals: 9 MCTP Teacher Candidates;

Professor of Science Methods Class

Student Work: 6 MCTP Teacher Candidates;

[written assignments and poster display] 3 Non-MCTP Teacher Candidates

Field Notes: Professor of Science Methods Class

and Graduate Research Assistant

Content Diagnostic All Teacher Candidates in the Science

Methods Class

Other Artifacts: Course Syllabus, Class Handouts

Table 3

Concentration: Science

Undergraduate Math Courses: Algebra; Math 210 & 211 (Mathematics for

Elementary Teachers).

Undergraduate Science Courses: Introductory courses in Biology,

Biochemistry, Geology, Zoology, and Geography.

Notes: Non-traditional undergraduate student (has teenage children).

White female.

Concentration: Mathematics

Undergraduate Math Courses: Math 110 (Elementary Mathematical Modeling);

Math 210 & 211 211 (Mathematics for Elementary Teachers); Elementary Calculus; and EDMS 451 (Introduction to Educational Statistics).

Undergraduate Science Courses: Nutrition; Biology; and Physical Science.

Notes: Margaret is a non-traditional student with children in school. She

remarked that she waited 20 years to go back to get her degree. She has

volunteered in Montgomery County for ten years in a second grade classroom.

The teacher she volunteers with talked her into returning to college.

White American.

Concentration: Math

Undergraduate Math Courses: Math 110 (Elementary Mathematical Modeling),

Math 115 (Pre-Calculus), Math 140 (Calculus I); Math 220 (Elementary

Calculus - note cannot earn credit for both Math 140 and Math 220); ); Math

210 & 211 211 (Mathematics for Elementary Teachers); Stat 100 (Elementary

Statistics and Probability).

Undergraduate Science Courses: Introductory courses in Biology and Chemistry.

Notes: Traditional undergraduate student.

Asian American Female.

Concentration: MCTP, involved since first semester of her first year at

UM, Fall, 1995.

Undergraduate Math Courses: Math 110 (Elementary Mathematical Modeling):

Math 220 (Elementary Calculus); Math 111(Introduction to Probability);

Equivalent of Math 210 & 211 (Math for Elementary Teachers) taken at transfer University.

Undergraduate Science Courses: Chemistry 121; Physics 117; Genetics (MCTP Capstone) ; Geology; Physical Science; Biology.

Notes: Took MCTP Seminars several times. Transfered from an out of state university after 1 year of college. Traditional student. White female.

Table 3

Molly

Concentration: MCTP, involved since first semester of her first year, Fall, 1994.

Undergraduate Math Courses: Math 110 (Elementary Mathematical Modeling);

Math 220 (Elementary Calculus); Math 111 (Introduction to

Probability); Math 210 & 211 (Math for Elementary Teachers).

Undergraduate Science Courses: Chemistry 121; Physics 117;

Biology ; Genetics (MCTP Capstone); Geology; Chemistry 103 (General Chemistry I).

Notes: Took MCTP Seminars several times. Traditional student.

White female.

Concentration: MCTP, involved for three semesters.

Undergraduate Math Courses: Math 210 & 211 (Math for Elementary Teachers);

Math 220 & 221 (Calculus I & II); BMG 230 (in lieu of Math 111).

Undergraduate Science Courses: Chemistry 121 - 122; Physics 117; Genetics); Biology 105; Geography 201; Notes: Took MCTP Seminars a few times. Took EDCI 397

(with McGinnis). Traditional student. Asian.

Concentration: MCTP, involved since first semester of her first year, Fall, 1994.

Undergraduate Math Courses: Math 110 (Elementary Mathematical Modeling); Math 220 (Elementary Calculus); Math 111 (Introduction to

Probability); Math 111 (Probability); Math 210 & 211 (Math for Elementary Teachers).

Undergraduate Science Courses: Chemistry 121; Physics 117; Biology; Genetics (MCTP Capstone); Astronomy.

Notes: Took MCTP Seminars several times. Took EDCI 397

(McGinnis). Traditional student. White.

Concentration: MCTP, involved since December, 1995.

Undergraduate Math Courses: Math 111 (Introduction to Probability); Math

210 & 211 (Math for Elementary Teachers).

Undergraduate Science Courses: Biology; Genetics (MCTP Capstone); Geology; Chemistry I & II; Calculus I, II, & III.

Notes: Transferred from Catholic University (one year at Catholic, took one

year off, and then one year part-time at a community college). Took EDCI

397 (McGinnis). Traditional student. White female.

White female.

Concentration: MCTP, involved since Spring, 1996.

Undergraduate Math Courses: Introductory courses in Physics; Biology; Geology.

Undergraduate Science Courses: Survey of College Math; Probability;

Algebra; Math 220 (Elementary Calculus); Chemistry 121.

Notes: Took EDCI 397 (McGinnis). Non-traditional, second career student.

Transferred from a community college. White male.

Table 4

Groups Compared Cases Mean Rank U Value 2-Tailed P

1.) MCTP and 7¹ 20.43 46.0 0.08

The Other Classmates 23 14.00

2.) MCTP and 7 8.43 18.0 0.40

Science Concentration 7 6.57

3.) MCTP and 7 6.93 7.5 0.21

Math Concentration 4 4.38

4.) MCTP and 7 12.43 32.0 0.27

Science and Math 13 9.46

Concentrations

Note: At the end of the semester, seven the teacher candidates were identified as MCTP teacher candidates as determined by their meeting all requirements to enter student teaching as an MCTP teacher candidate. Thus, we determined that these seven teacher candidates comprised our group of MCTP teacher candidates for research purposes as well. One of the seven was not included in the semi-structured interviews during the semester since she was accepted as an MCTP teacher candidate during the middle of the study semester.

Table 5

Groups Compared Cases Mean Rank U Value 2-Tailed P

1.) MCTP and 7 20.07 48.5.0 0.11

The Other Classmates 23 14.11

2.) MCTP and 7 7.64 23.5 0.90

Science Concentration 7 7.36

3.) MCTP and 7 7.29 5.0 0.09

Math Concentration 4 3.75

Groups Compared Cases Mean Rank U Value 2-Tailed P

1.) MCTP and 7 18.79 57.5 0.26

The Other Classmates 23 14.50

2.) MCTP and 7 7.71 23.0 0.85

Science Concentration 7 7.29

3.) MCTP and 7 6.93 7.5 0.22

Math Concentration 4 4.38

Groups Compared Cases Mean Rank U Value 2-Tailed P

1.) MCTP and 7 18.14 62.0 0.36

The Other Classmates 23 14.70

2.) MCTP and 7 7.07 21.5 0.70

Science Concentration 7 7.93

3.) MCTP and 7 7.43 4.0 0.06

Math Concentration 4 3.50

Groups Compared Cases Mean Rank U Value 2-Tailed P

1.) MCTP and 7 20.43 46.0 0.09

The Other Classmates 23 14.00

2.) MCTP and 7 7.14 22.0 0.75

Science Concentration 7 7.86

3.) MCTP and 7 7.29 5.0 0.09

Math Concentration 4 3.75

Figure One. Program Overview Of The MCTP.

Appendix

Teacher Candidates Interview Protocols

1. Do you plan (Did you) highlight connections between mathematics and science in your MCTP course? If so, can you give an example? Are you giving any assignments to the teacher candidates requiring them to conduct a lesson or activity with children that involves making connections between math and science?

2. Do you plan to (Did you) utilize technology (e.g., calculators, computers, e-mail) in your MCTP course? If so, can you give an example? Are you giving any assignments to the teacher candidates requiring them to conduct a lesson or activity with children that involves using technology?

3. Do you plan to (Did you) encourage your students to reflect on changes in their ideas about topics in your class? If so, can you give an example? Are you giving any assignments to the teacher candidates requiring them to conduct a lesson or activity with children that involves reflecting on changes in their ideas?

4. What kinds of assessment techniques do you plan to did you) use in your MCTP class? Why?

5. What is (was) your role in the teacher education process?

6. It has been said that teachers teach in the way they were taught. If you were to visit your MCTP students classes in the future, what elements would you hope to see in their teaching that you plan to model this semester?

7. Are your expectations (now) of MCTP students different from non-MCTP students? Do you expect any difference in the MCTP students subject matter competence? Please explain any expected differences.

8. How has your involvement with MCTP affected your plans for teaching the MCTP methods course? Do you plan to teach the MCTP methods course differently from methods courses you have taught in the past? How? Why?

9. What problems, if any, do you foresee (did you experience) by teaching a methods class of both MCTP- and non-MCTP- prepared students? Are you (Did you) planning (plan) separate/additional assignments for the MCTP students?

10. Please add any comments or thoughts you might have about the MCTP methods course, your teaching, or the MCTP students that have not been addressed above.

Appendix C

Note: Please incorporate this MCTP interview seamlessly into the post-lesson observation debriefing(s) Record the conversation for transcription.

State that you will ask the teacher candidate some questions then share your supervisor’s perspective on the lesson.

1. What are your thoughts on today’s lesson?

2. Supervisor’s Comments from lesson with discussion.

3. In thinking about the MCTP program, can you identify any features of this lesson (or any other you have taught this semester) that you believe meet the goals of the MCTP and/or the reform goals for math/science education?

Probe. At first, allow teacher candidate to choose the goals to focus on.

Later, offer in descending order the following goals of the MCTP:

4. As you prepare and enact your lessons, on what experiences / ideas /

information do you find yourself relying from your preparation at the

university?

Probe. Any evidence of teacher role models from MCTP classes (mathematics, science, and methods)?

5. (If cooperating teacher is present, be discrete in asking this question.)

What role has your cooperating teacher served in assisting you to meet the goals of the MCTP and/or the reform goals for math/science education?

1. What are your thoughts on today’s lesson?

2. Supervisor’s comments from lesson with discussion.

For the remainder of the interview, use the same inquiries and procedures outlined in interview #1. Preface by stating, "At this point in your student teaching experience, what new thoughts (if any) do you have on the following":

3. In thinking about the MCTP program, can you identify any features of this lesson (or any other you have taught this semester) that you believe meet the goals of the MCTP and/or the reform goals for math/science education?

Probe. At first, allow teacher candidate to choose the goals to focus on.

Later, offer in descending order the following goals of the MCTP:

4. As you prepare and enact your lessons, on what experiences / ideas /

information do you find yourself relying from your preparation at the

university?

Probe. Any evidence of teacher role models from MCTP classes (mathematics, science, and methods)?

5. (If cooperating teacher is present, be discrete in asking this question.)

What role has your cooperating teacher served in assisting you to meet the goals of the MCTP and/or the reform goals for math/science education?