Communication in Mathematics: Preparing Preservice Teachers to Include Writing in Mathematics Teaching and Learning

“Math was strictly math, from what I remember.” This is a comment about using writing in mathematics from a preservice elementary teacher enrolled in a methods course. Comments such as these concern teacher educators who wish to prepare elementary teachers to include writing in mathematics instruction. A teacher development experiment was completed to discover how to improve preservice teachers’ abilities and attitudes toward using writing in mathematics. The preservice teachers made use of a graphic organizer to facilitate writing in the college math methods class, then practiced teaching writing with the same graphic organizer and in the math classes in an elementary classroom. Reflections of the preservice teachers illustrated this was a positive practice. The preservice teachers also concluded that writing in mathematics is valuable to instruction and would include it in their teaching.     

Strategies and Sources of Support for Beginning Teachers of Science and Mathematics

This study examines the support structures and strategies utilized by beginning mathematics and science teachers. The qualitative case study of 18 teachers (0–3 years of experience) includes teachers from rural, suburban and urban schools. Data collection consisted of one‐hour interviews. The findings indicate participants utilized formal and informal support structures within the school district (e.g., mentoring programs, talking to other new teachers) as well as those external to the school (e.g., professional organizations and conferences, talking to family and friends). We propose a model of beginning teachers' initiating access to support structures based on the realization that their ideal images of teaching do not match the realities of their classrooms. Implications are given for teacher educators, researchers, and school administrators.     

Toward Improving the Mathematics Preparation of Elementary Preservice Teachers

Research suggests the importance of mathematics knowledge for teaching (MKT) for enabling elementary school teachers to effectively teach mathematics. MKT involves both mathematical content knowledge (M‐CK) and mathematical pedagogical content knowledge (M‐PCK). However, there is no consensus on how best to prepare elementary preservice teachers (PSTs) to achieve M‐CK and M‐PCK. This study builds on research related to MKT by investigating influences of mathematics content courses designed specifically for elementary PSTs (IMPACT courses—Impact of Mathematics Pedagogy and Content on Teaching) on their attitudes (i.e., confidence and motivation) toward M‐CK and M‐PCK. Results suggest that the PSTs who participated in these IMPACT courses not only acquired high levels of confidence and motivation toward M‐CK, but also showed significant and greater gains in attitudes toward M‐PCK, after taking the required mathematics methods course, than their counterparts. Further, the findings suggest that these IMPACT courses provided a mathematical foundation that allowed the PSTs to engage in mathematics teaching methods better than those PSTs who did not have such a foundation. These results suggest potential course experiences that may enhance M‐CK and M‐PCK for elementary PSTs.     

Teaching and Learning Mathematics With Interactive Spreadsheets

Learning to teach mathematics at the middle and secondary levels should include many opportunities for teachers to learn how to use technology to better understand mathematics themselves and promote students' learning of mathematical concepts with technology-enabled pedagogy. This article highlights work done in a variety of preservice and in-service mathematics teacher education courses to help teachers use commonly available spreadsheets as an interactive exploratory learning tool. Several examples of teachers' subsequent use of spreadsheets in their own teaching are also discussed.     

高等数学多媒体课堂教学浅议

从使用多媒体讲授高等数学的经验出发,分析高等数学教学中应用多媒体教学手段的优势,同时给出在多媒体教学条件下进一步提高教学效果的几点建议,指出教师必须用现代化的教学思想为指导,综合运用各种教学手段提高高等数学教学效果,适应现代化教学的发展.     

Mathematics Anxiety and Learning Styles: What Is the Relationship in Elementary Preservice Teachers?

The study investigated the relationship between elementary preservice teachers' mathematics anxiety levels and learning style preferences. Subjects included 72 preservice teachers at a midsized southeastern U.S. university who were at the end of their third year of study. The subjects completed the Mathematics Anxiety Rating Scale and the Style Analysis Survey (SAS). Scores obtained on the two instruments were analyzed using Pearson product‐moment correlations. Eleven of the SAS subscales were examined. The global subscale was the only one related to mathematics anxiety at the p < .05 level of significance. Findings revealed a low (r= .28) but significant (p < .05) positive correlation between mathematics anxiety and a global (right‐brain dominant) learning style. As global orientation scores increased, mathematics anxiety scores increased as well. This study indicated that there is tendency for global learners to possess higher levels of mathematics anxiety.     

Middle School Mathematics Teachers Learning to Teach with Calculators and Computers

This paper reports the results of a project in which experienced middle grades mathematics teachers immersed themselves in calculator and computer use for both doing and teaching mathematics and prepared themselves as leaders for communicating their knowledge to colleagues. Project evaluation included interviews with participants at the beginning and end of the project and evaluation forms completed at the end of the project. Pre-interviews indicated that virtually all of the participants had no experience using technology to teach mathematics. Many felt that technology was not likely to be as effective in helping students learn mathematics as other teaching techniques. Post-interviews indicated that all teachers were confident of their abilities to use some technologies in teaching mathematics. They acknowledged that technology was useful in developing conceptual understanding and that their role was to guide this conceptual development. The differences in participants' perceptions about how the project affected them yielded suggestions for future inservice efforts about technology.     

Middle School Mathematics Teachers Learning to Teach With Calculators and Computers

This paper reports the results of a project in which experienced middle grades mathematics teachers immersed themselves in calculator and computer use for both doing and teaching mathematics and prepared themselves as leaders for communicating their knowledge to colleagues. Project evaluation included formal observation of students while they used technology in learning mathematics. Classroom observation data suggested that computers hold somewhat more attraction for students than calculators. Overall, students in all 13 classes, independent of the type of technology used, were observed to be off-task 3% of the time. These data suggested a classroom environment in which the teacher worked hard to engage students in mathematical activity. The fact that students were observed off-task so little is encouraging. The difference in off-task behaviors for calculators versus computers suggests that different technologies will indeed have different effects on students. It appears that the introduction of technologies in classrooms altered the ways teachers taught.     

Advanced Mathematical Knowledge in Teaching Practice: Perceptions of Secondary Mathematics Teachers

For the purpose of our research we define Advanced Mathematical Knowledge (AMK) as knowledge of the subject matter acquired during undergraduate studies at colleges or universities. We examine the responses of secondary school teachers about their usage of AMK in teaching. We find that the majority of teachers focus on the purposes and advantages of their AMK for student learning, such as personal confidence, the ability to make connections, and to respond to students' questions; only a few provide content-specific examples. We conclude with a call for a more articulated relationship between AMK and mathematical knowledge for teaching.     

Applications of CAS in the Teaching and Learning of Discrete Mathematics

In this paper our experience in application of CAS Maple for modelling and solving counting problems as well as for solving recurrence equations is represented. Some procedures for calculating combinations with repetition and variations with repetition in case of authorized number on appearance of elements are given. The result is a list of the allowed number of appearances of the element in the polynomial involved in the generating function. Some conclusions have been visualized. The represented approaches correspond to the Curriculum of the Bachelor Degree Program in Applied Mathematics and Informatics at TU-Sofia and are based on methodological principles and the educational tradition in our country.     

Relationship Between Science and Mathematics Teaching Efficacy of Preservice Elementary Teachers

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

基于多层线性模型的数学教师信念与学生数学信念系统对数学学习兴趣的影响研究

采用数学教师信念、学生数学信念系统与数学学习兴趣问卷,选取39个班级的数学教师和820名初一到高三年级的中学生作为被试,运用多层线性模型(HLM)探讨数学教师的信念与学生数学信念系统对数学学习兴趣的影响,以期能为在数学教学中提高学生的数学学习兴趣提供一些参考.     

On the Relationship between Curriculum,Teaching and Assessment of Mathematics

In this paper, a discussion is given of the aims and objectives in teaching mathematics to undergraduates in relation to the development of certain student abilities and skills. Consideration is given to the different methods of assessment which test the acquisition of such skills and abilities.