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

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

Mathematics Education as a Design Science

We propose re-conceptualizing the field of mathematics education research as that of a design science akin to engineering and other emerging interdisciplinary fields which involve the interaction of “subjects”, conceptual systems and technology influenced by social constraints and affordances. Numerous examples from the history and philosophy of science and mathematics and ongoing findings of M&M research are drawn to illustrate our notion of mathematics education research as a design sicence. Our ideas are intended as a framework and do not constitute a, “grand” theory (see Lester. 2005, this issue). That is, we provide a framework (a system of thinking together with accompanying concepts, language, methodologies, tools, and so on) that provides structure to help mathematics education researchers develop both models and theories, which encourage diversity and emphasize Darwinian processes such as: (a) selection (rigorous testing), (b) communication (so that productive ways of thinking spread throughout relevant communities), and (c) accumulation (so that productive ways of thinking are not lost and get integrated into future developments).     

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

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

Cross-curricular activities within one subject?

The structural organization, of the Danish Gymnasium greatly hinders cross-curricular activities. However, it is possible to integrate other subjects in the mathematics curriculum, not the least due to the existence of the so-called “aspects” I will discuss a particular course on modeling ozone depletion which was framed by the “model aspect”. The organization and outcome of the course are linked to three types of competencies mathematical. technological and reflective. I will focus on the reflective competency, in particular the criticla evaluation of mathematical models and their use. One conclusion is that modeling furthers all three competencies, and thus should be given more emphasis in mathematics instruction. However, if the reflective competency is to be furthered, the topic must be seen in a broader societal context, and this would be better supported by cross-curricular activities.     

Scientific World Building on the Edge of Chaos: High School Students' Beliefs About Mathematics and Science

This study investigated high school students' beliefs about mathematics and science during a four week summer residential mathematics and science program. Beliefs about mathematical and scientific truths, the value and importance of mathematics and science inquiry, gender equity and ability with respect to pursuit of mathematics and science careers, the relationship between mathematics and technology, and the role of science in society were examined. Habermasian ways of knowing were used to categorize student beliefs and determine student world views. Implications of this study include suggested changes in the organizational dynamics of schooling to better prepare our students for surviving in the complexity of the 21st century and reducing dissonance between the “classical” educational viewpoints and the “chaotic” world.     

The Integration of Science and Mathematics Education: Highlights from the NSF/SSMA Wingspread Conference Plenary Papers

In April, 1991 the NSF/SSMA conference entitled “A Network for Integrated Science and Mathematics Teaching and Learning” was held at the Wingspread conference facility in Racine, Wisconsin. Five plenary papers were presented offering very diverse perspectives related to the integration of science and mathematics education. This publication summarizes the significant points advanced in each plenary paper. The full text of these papers is being published as part of the SSMA Monograph Series.     

Observation of Reform Teaching in Undergraduate Level Mathematics and Science Courses

This paper reports on initial results from an ongoing evaluation study of a National Science Foundation project to implement reform‐oriented teaching practices in college science and mathematics courses. The purpose of this study was to determine what elements of reform teaching are being utilized by college faculty members teaching undergraduate science and mathematics courses, including a qualitative estimate of the frequency with which they are used. Participating instructors attended summer institutes that modeled reform‐based practices and fostered reflection on current issues in science, mathematics, and technological literacy for K‐16 teaching, with an explicit emphasis on the importance of creating the best possible learning experience for prospective K‐12 science and mathematics teachers. Utilizing a unique classroom observation protocol (the Oregon‐Teacher Observation Protocol) and interviews, the authors (a) conclude that some reform‐oriented teaching strategies are evident in undergraduate mathematics and science instruction and (b) suggest areas in which additional support and feedback are needed in order for higher education faculty members to adopt reform‐based instructional methodology.     

An Evaluation of a Master's Degree in K‐8 Mathematics and Science: Classroom Practice

“Evaluation as a particular kind of investigated discipline is distinguished from, for example, traditional empirical research in the social sciences or from literary criticism, criminalistics, or investigative reporting, partly by its extraordinary multidisciplinarity” ( Scrivens, 1991 , p. 141). It is this unique multidisciplinary feature of evaluation that adds usefulness when determining the effectiveness of programs seeking to integrate mathematics and science teaching and learning across elementary and middle grade levels. In 2005, a K‐8 mathematics and science program celebrated its 15th year of service. The program was the result of education, business, and community partnership efforts focused on improving mathematics and science teaching and learning in schools throughout a metropolitan region in the southeastern United States. To date, over 350 K‐8 teachers have completed a master's degree through this mathematics and science education program. The director realized that an evaluation of the program would likely provide insights that would benefit not only the efforts of the program but the broader mathematics and science teaching and learning community. Hence, the National Science Foundation (award No. 9815931), which had provided start‐up funds for the program responded to this need and provided funding for a longitudinal evaluation of the program. The evaluation was conducted from 1999 to 2004. This article focuses on the evaluation results for years 1 and 2 and addresses the question related to changes in teachers' classroom practice.     

Ten “Laws” concerning patterns of change in the history of mathematics

Using the new historiography of science as a touch-stone, the historiography of mathematics is examined. Ten “laws” concerning patterns of conceptual change in mathematics are then suggested.     

Problem solving in Chinese mathematics education: research and practice

This paper is an attempt to paint a picture of problem solving in Chinese mathematics education, where problem solving has been viewed both as an instructional goal and as an instructional approach. In discussing problem-solving research from four perspectives, it is found that the research in China has been much more content and experience-based than cognitive and empirical-based. We also describe several problem-solving activities in the Chinese classroom, including “one problem multiple solutions,” “multiple problems one solution,” and “one problem multiple changes.” Unfortunately, there are no empirical investigations that document the actual effectiveness and reasons for the effectiveness of those problem-solving activities. Nevertheless, these problem-solving activities should be useful references for helping students make sense of mathematics.     

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

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

Psychometric Re‐evaluation of the Image of Science and Scientists Scale (ISSS)

An enduring concern among science education researchers is the “swing away from science” ( Osborne. 2003 ). One of their central dilemmas is to identify—or construct—a valid outcome measure that could assess curricular effectiveness, and predict students' choices of science courses, university majors, or careers in science. Many instruments have been created and variably evaluated. The primary purpose of this paper was to re‐evaluate the psychometric properties of the Image of Science and Scientists Scale (ISSS) ( Krajkovich 1978 ). In the current study, confirmatory factor analysis (CFA) was used to examine the dimensionality of the 29‐item ISSS, which was administered to 531 middle school students in three San Antonio. Texas school districts at the beginning of the 2004–2005 school year. The results failed to confirm the presumed 1‐factor structure of the ISSS. but instead showed a 3‐factor structure with only marginal fit with the data, even after removal of 12 inadequate items. The three dimensions were “Positive Images of Scientists” (5 items). “Negative Images of Scientists” (9 items), and “Science Avocation” (3 items). The results do not support use of the original form of the ISSS for measuring “attitudes toward science,”“images of scientists. “or “scientific attitudes. “Shortening the scale from 29 to 17 items makes it more feasible to use in a classroom setting. Determining whether the three dimensions identified in our analysis. “Positive Images of Scientists. ““Negative Images of Scientists. “and “Science Avocation “contain useful assessments of middle school student impressions and attitudes will require independent investigation in other samples.     

50 Years of Data Science

More than 50 years ago, John Tukey called for a reformation of academic statistics. In “The Future of Data Analysis,” he pointed to the existence of an as-yet unrecognized science, whose subject of interest was learning from data, or “data analysis.” Ten to 20 years ago, John Chambers, Jeff Wu, Bill Cleveland, and Leo Breiman independently once again urged academic statistics to expand its boundaries beyond the classical domain of theoretical statistics; Chambers called for more emphasis on data preparation and presentation rather than statistical modeling; and Breiman called for emphasis on prediction rather than inference. Cleveland and Wu even suggested the catchy name “data science” for this envisioned field. A recent and growing phenomenon has been the emergence of “data science” programs at major universities, including UC Berkeley, NYU, MIT, and most prominently, the University of Michigan, which in September 2015 announced a $100M “Data Science Initiative” that aims to hire 35 new faculty. Teaching in these new programs has significant overlap in curricular subject matter with traditional statistics courses; yet many academic statisticians perceive the new programs as “cultural appropriation.” This article reviews some ingredients of the current “data science moment,” including recent commentary about data science in the popular media, and about how/whether data science is really different from statistics. The now-contemplated field of data science amounts to a superset of the fields of statistics and machine learning, which adds some technology for “scaling up” to “big data.” This chosen superset is motivated by commercial rather than intellectual developments. Choosing in this way is likely to miss out on the really important intellectual event of the next 50 years. Because all of science itself will soon become data that can be mined, the imminent revolution in data science is not about mere “scaling up,” but instead the emergence of scientific studies of data analysis science-wide. In the future, we will be able to predict how a proposal to change data analysis workflows would impact the validity of data analysis across all of science, even predicting the impacts field-by-field. Drawing on work by Tukey, Cleveland, Chambers, and Breiman, I present a vision of data science based on the activities of people who are “learning from data,” and I describe an academic field dedicated to improving that activity in an evidence-based manner. This new field is a better academic enlargement of statistics and machine learning than today’s data science initiatives, while being able to accommodate the same short-term goals. Based on a presentation at the Tukey Centennial Workshop, Princeton, NJ, September 18, 2015.     

Enriching Science and Math Through Engineering

This case study reviewed the collaborative efforts of university engineers, teacher educators, and middle school teachers to advance sixth‐ and seventh‐grade students' learning through a series of project‐based engineering activities. This two‐year project enriched regular school curricula by introducing real‐world applications of science and mathematics concepts that expanded opportunities for creativity and problem‐solving, introduced problem‐based learning, and provided after‐school programming (for girls only) led by engineering students from the local university. This engineering education initiative showed significant impact on students' (1) confidence in science and mathematics; (2) effort toward science and mathematics; (3) awareness of engineering; and (4) interest in engineering as a potential career. With regard to gender, there were no significant differences between boys' and girls' responses. The girls' confidence in their own skills and potential, however, was significantly more positive than the boys' confidence in the girls. These results gave rise to new questions regarding mentor/mentee relationships and the overall effect of “girls only” mentoring.     

Tech Prep Academics: Using Real Life Connections to Develop Scientific and Mathematical Literacy

Based upon the recommendations of professional organizations in science and mathematics education, children at K-6 levels need to be exposed to activities involving scientific methodology, the discovery of new knowledge and the integration of science and mathematics curricula. This study describes several distinct kinds of problem solving investigations identified from real life situations which can be adapted in intellectually honest ways for selected levels of the elementary school curriculum. The activities lend themselves to interactions with businesses and industries in the children's community and involve the children in a variety of non-traditional instructional activities such as oral presentations, small group collaborative efforts, and written reports. Finally, the investigations promote the integration of science and mathematics curricula and suggest the role curricula can play in the lives of children.     

Implementing the Science Teaching Standards Through Complex Instruction: A Case Study of Two Teacher-Researchers

In this case study, an “interpretive collaborative” methodology is applied. The experiences of two elementary teacher-researchers are described, as they explore science teaching and learning in their two nongraded primary classrooms through the process of complex instruction. This study involves three strands: the theoretical base of complex instruction, the on-going collaboration between two experienced teachers, and the Science Teaching Standards in relation to complex instruction. Findings suggest that, because the teacher's role in conducting complex instruction activities is multifaceted and complex, successful implementation of complex instruction and the National Science Education Standards required ongoing collaboration and support among teachers. The teacher-researchers reported that it was their collegial relationship that encouraged them to explore, prepare, and implement inquiry activities or tasks for their students.     

Focusing on the Needs: Experiences of Developing a Data Science Program

Donoho’s article “50 Years of Data Science” is a well-thought explanation of a newly developed discipline called “data science.” In this article, we examine his explanations and suggestions about data science, follow-up on some of the issues he mentioned, and share our experiences in developing a data science curriculum and the teaching of related courses.     

Areas,anti-derivatives,and adding up pieces: Definite integrals in pure mathematics and applied science contexts

Research in mathematics and science education reveals a disconnect for students as they attempt to apply their mathematical knowledge to science and engineering. With this conclusion in mind, this paper investigates a particular calculus topic that is used frequently in science and engineering: the definite integral. The results of this study demonstrate that certain conceptualizations of the definite integral, including the area under a curve and the values of an anti-derivative, are limited in their ability to help students make sense of contextualized integrals. In contrast, the Riemann sum-based “adding up pieces” conception of the definite integral (renamed in this paper as the “multiplicatively-based summation” conception) is helpful and useful in making sense of a variety of applied integral expressions and equations. Implications for curriculum and instruction are discussed.