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.     

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.     

Relationship Between Professional Development,Teachers' Instructional Practices,and the Achievement of Students in Science and Mathematics

The purpose of this study was to examine the relationship between different types of professional development, teachers' instructional practices, and the achievement of students in science and mathematics. The types of professional development studied included immersion, examining practice, curriculum implementation, curriculum development, and collaborative work. Data regarding teachers' instructional practices and the amount of professional development were collected using teacher surveys. Ninety‐four middle school science teachers and 104 middle school mathematics teachers participated in the study. Student achievement was measured using eighth grade state science and mathematics achievement test data. Regression analyses suggested that for both science and mathematics teachers, examining practice and curriculum development were significantly related to the use of standards‐based instructional practices. Only curriculum development for mathematics teachers was significantly related to student achievement. Implications of results for the professional development of science and mathematics teachers are discussed.     

The Road to Reform: A Grounded Theory Study of Parents' and Teachers' Influence on Elementary School Science and Mathematics

Though elementary teacher educators introduce new, reform‐based strategies in science and mathematics methods courses, researchers wondered how novices negotiate reform strategies once they enter the elementary school culture. Given that the extent of parents' and veteran teachers' influence on novice teachers is largely unknown, this grounded theory study explored parents' and teachers' expectations of children's optimal science and mathematics learning in the current era of reform. Data consisted of semi‐structured, open‐ended interviews with novice teachers (n = 20), veteran teachers (n = 9), and parents (n = 28). Researchers followed three stages of coding procedures to develop a logic model connecting participants' discrete designations of the landscape, regulating phenomena, contextual orientation, and desired outcomes. This logic model helped researchers develop propositions for future research on the interactive nature of parents' and teachers' influential role in elementary science and mathematics education. Implications encourage science and mathematics teacher educators—as well as school administrators—to explicitly develop and support novice teachers' ability to initiate and sustain parent/family engagement in order to create a school climate where teachers and parents are synergistically motivated to change.     

A false belief about fractions – What is its source?

This paper presents the results of interviews with 174 participants solving a problem of elementary mathematics, connected with the part–whole approach to fractions. The motive for the investigation was a specific kind of difficulty observed during a case study conducted to verify the elementary school student's understanding of the concept of fractions. The authors decided to examine the problem in a broader population of mathematics learners at different levels of education: from elementary school to university students and graduates of science majors. Approximately 65% of respondents reported the wrong answer immediately after reading the fraction problem taken from the fourth grade of elementary school. Detailed analysis of the respondents’ performance showed that the source of many wrong answers was a false belief about fractions: The only way to get 1/n of a given whole is to divide this whole into n equal parts, not yet described in educational literature.     

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.     

Perceptions of Mathematics and Gender

This study examined students’ perceptions about gender and the subject of mathematics, as well as gender and mathematics learning. Secondary school students and pre‐service elementary teachers were surveyed using the Mathematics as a Gendered Domain and Who and Mathematics instruments developed by Leder and Forgasz ( Leder, 2001 ). The data indicate that, similar to findings from the 1970s, students believe that mathematics is gender neutral, although females hold this belief more strongly than males. Female secondary school students hold beliefs in gender neutrality more strongly than female pre‐service teachers. Data for secondary school students indicate that both males and females see differences in the way boys and girls act and are treated in mathematics classes (e.g., boys cause more distractions while girls care more about doing well). The data also show that secondary school males who believe they are good mathematics students tend to have more gender‐neutral perceptions than those who believe they are average or below average. No such pattern appears for secondary school females.     

The near-peer mathematical mentoring cycle: studying the impact of outreach on high school students’ attitudes toward mathematics

College students may be seen as near-peers to high school students and high school students are often able to see themselves in the college students who are but one step ahead. This nearness in maturity and educational level may place college students in a particularly powerful position when it comes to reaching out to high school students to promote higher education in math and science. In this study college students gave dynamic mathematics outreach presentations, MathShows, to minority and low-income high school students in a mid-sized public school district on the U.S. border with Mexico. The study investigated the impacts of this sort of outreach work on high school students’ attitudes towards mathematics using a mathematics attitudes survey. Results, obtained from N = 306 participants, showed statistically significant improvements in almost all components of mathematical attitudes, with less of an effect on the component of self-confidence in doing mathematics. Differences in impacts by specific student subgroups are all discussed.     

Students' Perceptions of Single‐Gender Science and Mathematics Classroom Experiences

While participating in single‐ and mixed‐gender science and mathematics classes, ninth‐grade urban high school students' (n= 118) academic self‐concept, self‐efficacy, and school climate perceptions were examined. Their perceptions were measured quantitatively from the Fennema‐Sherman Mathematics (modified for Science) Attitude and the Patterns of Adaptive Learning scales. Five factors arose from each instrument: confidence/efficacy, utility, instruction, climate, and anxiety/performance avoidance. Comparative factor analysis of the science‐modified Fennema‐Sherman Scale showed similar constructs within the mathematics scale. Our findings are congruent with reports concerning single‐gender classrooms that find few significant differences in students' attitudes toward science and mathematics, or classroom climate, with regard to single‐gender classes. Lastly, our results supported three structural equation models for the hypothesized factors from each instrument.     

Factors Influencing Elementary Teachers' Positioning of African American Girls as Science and Mathematics Learners

Despite recent progress toward gender equity in science and mathematics education, the underachievement of low‐income African American girls remains a challenge when compared with their white counterparts. Furthermore, the causes of this persistent underachievement have not been explored thoroughly. We have initiated a three‐year longitudinal study of how African American girls position themselves in relation to science and mathematics learning from fifth to seventh grade, including the impact, if any, of the positioning of teachers, counselors, and parents on this process. In this article, we share findings examining science and mathematics teachers' actions and perceptions and their positioning of African American girls. This qualitative study used an interpretive design with multiple data sources including classroom observations, interviews, and field notes. Findings reveal that school‐wide policies and teachers' autonomous decisions impact the regularity of science and mathematics instruction, and that teachers do not always conceptualize the girls as science and mathematics achievers, positioning them in negative ways.     

A case study of pedagogy of mathematics support tutors without a background in mathematics education

This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to these tutors’ provision of mathematics support to first and second year undergraduate engineering students and second year undergraduate science students. It was found that tutors are lacking in various pedagogical skills which are needed for high-quality learning amongst service mathematics students (e.g. engineering/science/technology students), a demographic which have low levels of mathematics upon entering university. Tutors teach their support classes in a very fast didactic way with minimal opportunities for students to ask questions or to attempt problems. It was also found that this teaching method is even more so exaggerated in mandatory departmental mathematics tutorials that students take as part of their mathematics studies at tertiary level. The implications of the findings on mathematics tutor training at tertiary level are also discussed.     

Middle‐School Mathematics Teachers' Beliefs in NCTM's Vision

This study examined the extent to which seventh‐ and eighth‐grade mathematics teachers are aware of National Council of Teachers of Mathematics (NCTM) standards documents, Curriculum and Evaluation Standards for School Mathematics and Principles and Standards for School Mathematics and agree with NCTM's vision of school mathematics as expressed in these documents. Quantitative data were collected through the Mathematics Standards Belief Survey (MSBS), a survey specifically designed to measure teachers' overall belief in NCTM's vision as well as in certain philosophical tenets of NCTM. Of the 82 seventh‐ and eighth‐grade mathematics teachers in the identified school district of Nevada, 73 (89.0%) participated in this study. The data revealed that, among seventh‐ and eighth‐grade mathematics teachers, secondary‐certified teachers had significantly higher MSBS scores than elementary‐certified teachers. A number of other findings were made, including significant differences among mean belief scores in the philosophical tenets of NCTM.     

Interpreting Middle School Students' Proportional Reasoning Strategies: Observations From Preservice Teachers

This paper reports the findings of an investigation of 11 preservice secondary school teachers' interpretations of the development of proportional reasoning strategies used by middle school students. The preservice teachers examined samples of solution strategies generated by middle school students in proportional reasoning situations and prepared written responses of their views concerning the developmental levels indicated in the students' work. Each preservice teacher also participated in an hour‐long interview, in which the researchers asked for elaboration and clarification of the written responses and, in some cases, challenged the preservice teachers to consider alternative interpretations for the middle school students' work. The interviews were audiotaped for later analysis by the investigators, and key aspects of both the written and audiotaped responses were entered into a spreadsheet and later tabulated into categories indicating trends in the preservice teachers' interpretations. Some implications for the preparation of preservice middle school science and mathematics teachers are included.     

Defining a mathematical research school: the case of algebra at the University of Chicago, 1892–1945

Historians of science have long considered the concept of the “research school” as a potent analytical construct for understanding the development of the laboratory sciences. Unfortunately, their definitions fall short in the case of mathematics. Here, a definition of “mathematical research school” is proposed in the context of a case study of algebraic work associated with the University of Chicago's Department of Mathematics from the University's founding in 1892 through 1945.     

Sociocultural Factors Influencing Students' Learning in Science and Mathematics: An Analysis of the Perspectives of African American Students

The voices of African American students reveal sociocultural factors that influence their achievement in science and mathematics classes. Using a sociocultural theoretical framework ( Mercer & Covey, 1980 ), this ethnographic study interpreted the perspectives of five African American students as they discussed their learning experiences in science and mathematics classrooms. This framework acknowledges the vulnerability of the educational system to societal influences that inevitably assert cultural values and norms. The students' discussions provided insight into their beliefs about the varied ways in which sociocultural factors impact their learning in science and mathematics classrooms.     

Design and Implementation of a Framework for Defining Integrated Mathematics and Science Education

Integrated mathematics and science teaching and learning is a widely advocated yet largely unexplored phenomenon. This study involves an examination of middle school integrated mathematics and science education from two perspectives—theory and practice. The theoretical component of this research addresses the ill-defined nature of the phrase integrated mathematics and science education. A conceptual framework in the form of a Mathematics/Science Continuum is presented to lend clarity and precision to this phrase. The theoretical framework is then used to guide analysis of tasks students are engaged in during instructional practice in middle school classrooms, where the goal of instruction is full integration of mathematics and science. Barriers to integrating mathematics and science in the school curriculum are also presented.     

Formative assessment and the role of teachers' content area

Professional development (PD) programs focused on increasing teachers' use of formative assessment generally provide a framework designed to help teachers understand the breadth and complexity of formative assessment, while advocating for teacher choice with respect to the specific implementation. This study examined the implementation patterns of 82 high school mathematics and science teachers to understand whether implementation approaches differed by content area. Results suggested that mathematics and science teachers significantly increased their self‐reported practice of formative assessment, in similar ways; however, the specific approaches that mathematics and science teachers chose to operationalize on a daily basis differed. These findings have implications for the design of PD and future research efforts.     

“I Am Science and the World Is Mine”: Embodied Practices as Resources for Empowerment

Those who are most marginalized, both culturally and economically, in society are concentrated in the nation's largest urban centers and have the least opportunities to be successful in school science or to pursue higher education and career trajectories in science, mathematics, or engineering. This article shares the results of a study in which African American economically disadvantaged high school students living in Philadelphia were hired as student researchers and had the opportunity to develop a curriculum enhancer — a movie entitled Sound in the City. The findings reveal that the students' capacity to act, or their sense of agency, expanded both through the process of making the movie and with the final movie product. During the production of the movie, the youth accessed multiple resources (both physical and human) to represent abstract physics facts in contextualized ways. Specifically, this article illuminates how they drew upon embodied practices that included rhythm, verbal fluency, and high energy in creating and filming the movie segments, as well as behind the scenes as they worked to understand the physics content. This study urges the science education community to consider how students' embodied practices can connect them to science in empowering ways that expand their capacity for action in multiple spaces.