Diagram Literacy in Preservice Math Teachers,Computer Science Majors,and Typical Undergraduates: The Case of Matrices,Networks, and Hierarchies

According to the National Council of Teachers of Mathematics (2000), children need to learn how to create and use mathematical diagrams to represent and reason about phenomena in the world. The author proposes a model of diagram literacy that includes six types of knowledge required for diagrammatic competence - implicit, construction, similarity, structural, metacognitive, and translational. A study is reported that examined college students' diagram literacy for three interrelated mathematical diagrams - matrices, networks, and hierarchies. Three groups of students participated: preservice, secondary-level, math teachers; computer science majors; and typical undergraduates. The results of the study are reassuring in some ways concerning the level of diagram literacy possessed by students at the culmination of current K through 12 instruction and by teachers of future secondary students. However, the results also point to areas in which preservice math teachers should be better prepared if the goals for students' diagram literacy are to be met.     

Integrating Science and Mathematics: Perceptions of Preservice and Practicing Elementary Teachers

One hundred and sixty-one undergraduate elementary education majors and sixty elementary teachers completed an eight-item questionnaire designed to assess their perceptions toward integrating science and mathematics in the elementary grades. The two groups of subjects differed significantly on their responses to five of the eight items. Chi square analyses suggest that practicing elementary teachers felt they had more background in mathematics and science, were more aware of curriculum materials in this area, did not think that integration was currently a common practice, and were more likely to indicate that there was not sufficient time in the school day to integrate the subjects. Preservice teachers were more likely to indicate that integrating the disciplines was preferred to teaching them separately. In addition to the analyses of data, a list of recommendations are provided for teachers, curriculum developers, and policy makers interested in advancing the concept of integrating science and mathematics in instruction.     

Science as a Learner and as a Teacher: Measuring Science Self‐Efficacy of Elementary Preservice Teachers

Academic science achievement of U.S. students has raised concerns regarding our ability as a nation to compete in a global economy. Additionally, research has shown that many elementary teachers have weak science content backgrounds and had poor/negative experiences as students of science, resulting in a lack of confidence regarding teaching science. However, efforts to increase science self‐efficacy (SE) in preservice teachers can help to combat these issues. This study looked at a sample of preservice elementary teachers engaged in a semester‐long science content course, using Bandura's concept of SE as a conceptual framework. Our quantitative data showed significant increases in science SE on both subscales (personal efficacy and outcome expectancy). Our qualitative data showed that students communicated an increased sense of confidence with regard to the discipline of science. In addition, students reported learning science pedagogy through the instructor's modeling. Combining our findings resulted in several meta‐inferences, one of which showed students growing as both confident learners of science and teachers of science simultaneously. We created a construct new to the literature to describe this phenomenon: “teacher‐learner,” for students are both learning science and learning to teach science simultaneously through the content course experience, resulting in increased science SE.     

Meeting the Needs of Diverse Student Populations: Comprehensive Professional Development in Science,Math, and Technology for Teachers of Students With Disabilities

Professional development for teachers has become a key component for reform in teaching, learning, and curriculum change. This report describes a model of professional development designed to improve the skills and knowledge of teams of special education and regular education teachers in science, mathematics, and technology instruction. The comprehensive model included summer and academic year content and methodology-focused workshops and summer “practician” experiences. It was designed to link those factors impacting teacher practices and interventions with teachers' beliefs in instruction. The training component for teachers included opportunities for collaborative teaching, upgrading knowledge of math and science subject matter, and identifying, integrating, and practicing alternative approaches for teaching science and math that address the needs of special education students, with a focus on techniques for adapting instruction to specific disabilities. The program led to development of coping skills and persistence in the teaching of science and math for all students. As a result, strong efficacy expectations have been developed through repeated experiences of success with children in a classroom environment. Remaining issues still to be addressed include classroom management, teaching in a heterogeneous classroom, and further improvement of content expertise of teachers.     

The NCTM Process Standards and the Five Es of Science: Connecting Math and Science

This study investigates defining characteristics among the process standards of the Principles and Standards for School Mathematics and the 5 Es from the National Science Education Standards and the Inquiry and the National Science Education Standards. These characteristics are used to demonstrate similarities and differences between the learning of mathematics and science, discuss implications from such, and argue for the integration of mathematics and science curriculum and instruction.     

The State of Readiness of Initial Level Preservice Middle Grades Science and Mathematics Teachers and Its Implications on Teacher Education Programs

The purpose of this study was to document through interview and videotaped data the current state of readiness of 10 preservice middle grade teachers, regarding their ability to plan, implement, and reflect on an integrated mathematics and science lesson. The results showed that only one student was successful in implementing a lesson that compared favorably to national standards. This student's lesson plan contained minimal pedagogical considerations and consisted primarily of notes emphasizing fine detail of distinction about the content of the lesson using her own examples. The lesson plan and post-lesson-plan interview data of the remaining students indicated an adherence to algorithmic learning, rote memorization, and procedural knowledge. There were numerous content errors in the plans, and these students orally described a lack of self-confidence in their ability to teach this lesson successfully. The most successful student demonstrated her competence in meeting standards of pedagogical content knowledge and was most successful in analyzing her own teaching. The results showed that most subjects of this study needed extensive training in content and pedagogy and in synthesizing these in a way consistent with modern learning theory.     

Preservice Teachers of High School Mathematics: Success,Failure, and Persistence in the Face of Mathematical Challenges

The goal of this study was to identify variables related to success and resilience in an undergraduate, high school mathematics teacher education program. Over a five‐year period, we tracked the academic performance and achievement motivation goals of multiple cohorts of students. Students who successfully completed their degrees had higher grade point average (GPAs) upon entering the program, earned higher grades in their first college mathematics course, and failed fewer courses than students who left the program or university. Learning and performance motivational goals did not predict success in the program. Performance goals decreased over time. Nearly half the successful students repeated one or more mathematics courses. Ten students completed their degrees, obtained a teaching license, and are teaching despite the need for multiple repetitions of the same mathematics courses. These persistent students did not differ from their peers in motivational goals. Our results suggest that although students with higher GPAs and initial mathematics grades were more likely to complete the program, students who experienced challenges in mathematics courses were able to succeed. We discuss the implications of these results for recruiting, advising, and retention of students in mathematics education programs.     

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

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

Fundamental Fraction Knowledge of Preservice Elementary Teachers: A Cross‐National Study in the United States and Taiwan

The purpose of this paper is to show the similarities as well as the differences of fundamental fraction knowledge owned by preservice elementary teachers from the United States (N= 89) and Taiwan (N= 85). To this end, we examined and compared their performance on an instrument including 15 multiple‐choice test items. The items were categorized into four different types of fundamental fraction constructs, including part–whole relationship, quotient, equivalence, and meanings of operations. Each item was embedded in the area, linear, or set model except for the items constructed out of the meaning of operations. Several items were featured with a pictorial illustration. Quantitative analysis showed that U.S. preservice teachers were significantly outperformed by their Taiwanese counterparts overall. The difference between the two groups was statistically significant on 12 of 15 items. Findings suggest that preservice elementary teachers from both countries need to be better prepared in their understanding of the meaning of fraction multiplication or division operations. Findings also suggest that U.S. preservice elementary teachers need to be more knowledgeable in dealing with fraction problems embedded in a linear model. Further research is suggested to study the issues raised from the findings.     

Creating a Model of Acceptance: Preservice Teachers Interact With Non‐English‐Speaking Latino Parents Using Culturally Relevant Mathematics and Science Activities at Family Learning Events

The following describes a culturally relevant mathematics and science content program implemented by preservice teachers (PSTs) at Family Math/Science Learning Events (FM/SLEs) conducted through two different university programs in south Texas. These experiences are required course activities designed to inform PSTs of the importance of interacting with Latino families' culture and language in after school settings. Data were collected from elementary PSTs attending FMLEs and include interactions recorded during the FMLE and interviews with Latino non‐English‐speaking parents after the event. Anecdotal data were also included from parents' interviews collected during culturally relevant Family Science Learning Events. Researchers investigated the following questions: (1) what did Latino parents and PSTs report learning from the FMLE and, (2) how do perceptions toward Latino parents change when PSTs are given the opportunity to interact with and interview Latino parents? Results show that PSTs perceptions of Latino parents can be changed through these events. Implications for teacher preparation programs include providing PSTs with opportunities for participation in FM/SLEs that incorporate planning and teaching culturally relevant math and science activities. The following model of acceptance requires PSTs to identify and reconstruct misconceptions and perceptions of parents, especially non‐English‐speaking Latino parents.