Reform Teaching Strategies Used by Student Teachers

The purposes of this study were to observe the teaching practices occurring in student teachers' science and mathematics K‐12 classrooms, compare the student teachers' perceptions of their teaching with what was actually occurring in their classrooms, and determine which college faculty members and courses these student teachers felt contributed to the teaching methods they used. Data on each student teacher were gathered via field notes of three classes, an observation protocol completed after each lesson, and an interview. Composites were written for each of the students. The total data set of all composites was examined to see if any patterns generalizable to the whole were evident. Differences between and among grade levels and content areas surfaced and are discussed.     

Building a Network to Empower Teachers for School Reform

Reform efforts in college mathematics teaching are often hindered by the fact that many instructors have never experienced instructional delivery methods other than lecture. Building a network of college mathematics faculty interested in reform has provided the impetus for faculty members to incorporate problem solving, cooperative learning, technology, manipulatives, writing, and alternative means of assessment into courses for preservice elementary teachers. Suggestions for setting up a network are intended to provide guidance for other departments wishing to stimulate reform movements.     

Science and Mathematics Instruction in a Reform‐based Teacher Preparation Program

This study examined the science and mathematics instruction of teachers who were initially prepared by the Collaboratives for Excellence in Teacher Preparation program (CETP). The focus of this study was on examining the extent to which science and mathematics teachers used more reform‐oriented instructional practices in their classes when they entered the teaching profession. Data were gathered from twelve different CETP projects across the United States. A quasi‐experimental design was used where science and mathematics teachers who were initially prepared by the CETP program were followed into the field and compared to teachers who were not prepared by the CETP program. The results indicate that the teachers prepared by the CETP program used slightly more reform‐oriented instructional practices than teachers who were not prepared by the CETP program, although both mathematics and science teachers reported low levels of reform‐oriented instruction. Implications of results for large‐scale reform of science and mathematics teacher preparation are discussed.     

Institutional Norms and Policies That Influence College Mathematics Professors in the Process of Changing to Reform‐Based Practices

This case study was an investigation of the role of the institutional culture of a university in the process of changing to reform‐based practices for two college mathematics professors. A framework is presented for identifying and analyzing institutional norms and policies that are present and those lacking in supporting faculty efforts toward reform. The primary categories considered in the framework are the teaching and learning context, the professional community, and the university's reward system. This framework is applied to the cases, and findings indicate that institutional norms in the forms of priorities for how time is allocated to professional responsibilities (as part of the teaching context), and colleagues and administrators who understood and shared the professors' goals for reform (as part of the professional community) strongly influenced the professors' efforts toward change. Additionally, a reward system that recognized efforts to improve teaching and learning was critical in establishing a culture that promoted change. However, despite the fact that both professors were in the same mathematics department, the nature of the influence of these factors was not uniform. The institutional culture indeed had multiple layers that required examination for each professor's individual context. The findings help highlight the importance of institutional context for both K‐12 and college level teaching and learning. The nature of these influential factors and the institutional layers were discussed for each case, along with implications for other institutions.     

Teaching Science in Higher Education: Faculty Professional Development and Barriers to Change

The focus of this research was to better understand the change processes necessary for university science teaching reform to be successful. The professional development processes involved faculty cognitive perceptions of learning, teaching skills, and pedagogical knowledge, as well as faculty culture in teaching science courses. A series of faculty development programs were conducted at nine U.S. locations to explore, develop strategies, and implement changes in science classrooms. A review of research and these professional development experiences provided a base to carry out research activities related to understanding change in science faculty. Faculty participants in the program from 30 institutions were selected to be involved in the study. Ethnographic and case study approaches were used to collect and analyze data. Many faculty members encountered in this study had conceptions of the change process that inhibited successful action. These research efforts provide a predictive model for assisting faculty change and help determine which faculty professional development efforts may be successful in overcoming barriers to change in undergraduate science classrooms.     

Elementary teachers’ mathematical beliefs and mathematics anxiety: How do they shape instructional practices?

This quantitative study investigated the relationships among practicing elementary teachers’ (N = 153) beliefs about mathematics and its teaching and learning, mathematics anxiety, and instructional practices in mathematics. When viewed singly, the findings reveal the teachers with higher levels of mathematics anxiety tend to use less standards‐based instruction and those with beliefs oriented toward a problem‐solving view of mathematics reported more standards‐based teaching. A combined analysis shows that after controlling for mathematical beliefs, teaching longevity, and educational degree attainment, there is no relationship between teachers’ mathematics anxiety and instructional practices. These findings suggest a spurious relationship between anxiety and practices, with beliefs having the strongest relationship with practices. Several suggestions for positively influencing the mathematical beliefs and affect in general of elementary teachers while learning mathematics are offered.     

地方应用型本科院校数学与应用数学专业课程体系的改革与实践——以太原工业学院为例

以太原工业学院为例,分析了数学与应用数学专业培养应用型人才所面临的挑战.结合该校地方性和应用型的特点,基于岗位需求为导向,围绕"毕业生未来就业岗位—培养目标—能力与素质要求—课程设置"这条主线完成了金融数学和软件开发两个方向的课程设置,以此建立"模块化教学,分流培养"的培养体系,为应用型本科院校数学与应用数学专业课程体系设置提供参考.     

I Just Don't Trust Them: The Development and Validation of an Assessment Instrument to Measure Trust in Science and Scientists

Trust in science and scientists can greatly influence consideration of scientific developments and activities. Yet, trust is a nebulous construct based on emotions, knowledge, beliefs, and relationships. As we explored the literature regarding trust in science and scientists we discovered that no instruments were available to assess the construct, and therefore, we developed one. Using a process of data collection from science faculty members and undergraduate students, field testing, expert feedback, and an iterative process of design, we developed, validated, and established the reliability of the Trust in Science and Scientist Inventory. Our 21‐item instrument has a reliability of Cronbach's alpha of .86, and we have successfully field‐tested it with a range of undergraduate college students. We discuss implications and possible applications of the instrument, and include it in the appendix.     

Reforming and Assessing Undergraduate Science Instruction Using Collaborative Action‐Based Research Teams

Faculty members at Purdue University in the departments of Earth and Atmospheric Sciences, Biological Sciences, and Chemistry conducted a reform effort for the undergraduate curriculum utilizing action‐based research teams. These action‐based research teams developed, implemented, and assessed constructivist approaches to teaching undergraduate science content in each department. This effort utilized a partnership of scientists, science educators, master teachers, graduate students, and undergraduate students. Results indicated that the project partners were able to (a) implement more inquiry‐based teaching that emphasized conceptual understanding, (b) provide opportunities for cooperative learning experiences, (c) use models as an ongoing theme, (d) link concepts and models to real‐world situations, e.g., field trips, (e) provide a more diverse range of assessment strategies, and (f) have students present their understandings in a variety of different forms. Further, we found that we were able to (a) involve graduate and undergraduate students, classroom teachers, scientists, and science educators together to work on the reform in a collaborative manner, (b) bring multiple perspectives for teaching and for science to support instruction and, (c) provide scientists and graduate science students (who will become university professors) with more effective teaching models. We also found that the collaborative action‐based research process was effective for contributing to the reform of undergraduate teaching.     

Measuring Reform Practices in Science and Mathematics Classrooms: The Reformed Teaching Observation Protocol

The National Science Foundation has funded 22 Collaboratives for Excellence in Teacher Preparation. Despite the remarkable allocation of resources to this effort, it has proven exceptionally difficult to demonstrate the effectiveness of collaborative reform. In large part, this has resulted because of the difficulty of defining and measuring reform. The Reformed Teaching Observation Protocol (RTOP) was designed by the Evaluation Facilitation Group of the Arizona Collaborative for Excellence in the Preparation of Teachers (ACEPT). It is a 25‐item classroom observation protocol that is (a) standards based, (b) inquiry oriented, and (c) student centered. This instrument has provided the definition for reform and the basis for evaluation of the ACEPT collaborative. The data upon which this report is based were collected over a period of more than 2 years from 153 public school, college, and university mathematics and science classrooms. A trained team of observers consisting of two faculty members and seven graduate students was able to achieve exceptionally high levels of interrater reliability. Internal consistency, as estimated by Cronbach's alpha, was also remarkably high. Correlation coefficients ranging from 0.88 to 0.97 between RTOP scores for classrooms, and mean normalized gain scores for students in those classrooms on achievement measures demonstrate that reform, as defined by ACEPT and measured by the RTOP, has been effective.     

Pre-service science teachers’ perceptions of mathematics courses in a science teacher education programme1

Most science departments offer compulsory mathematics courses to their students with the expectation that students can apply their experience from the mathematics courses to other fields of study, including science. The current study first aims to investigate the views of pre-service science teachers of science-teaching preparation degrees and their expectations regarding the difficulty level of mathematics courses in science-teaching education programmes. Second, the study investigates changes and the reasons behind the changes in their interest regarding mathematics after completing these courses. Third, the current study seeks to reveal undergraduate science teachers’ opinions regarding the contribution of undergraduate mathematics courses to their professional development. Being qualitative in nature, this study was a case study. According to the results, almost all of the students considered that undergraduate mathematics courses were ‘difficult’ because of the complex and intensive content of the courses and their poor background mathematical knowledge. Moreover, the majority of science undergraduates mentioned that mathematics would contribute to their professional development as a science teacher. On the other hand, they declared a negative change in their attitude towards mathematics after completing the mathematics courses due to continuous failure at mathematics and their teachers’ lack of knowledge in terms of teaching mathematics.     

Applications of a sequence of points in teaching linear algebra,numerical methods and discrete mathematics

Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, Using a sequence of number pairs as an example in teaching mathematics. Math. Comput. Educ., 39 (2005), pp. 198–205; Y. Shi, Case study projects for college mathematics courses based on a particular function of two variables. Int. J. Math. Educ. Sci. Techn., 38 (2007), pp. 555–566) have presented some interesting examples which can be used in teaching high school and college mathematics classes. In this article, we further discuss a few interesting ways to apply this sequence of points in teaching college mathematics courses such as linear algebra, numerical methods in computing, and discrete mathematics. In addition to using them in individual courses, these studies may also be combined together to offer seminars or workshops to college mathematics students. Studies like these are likely to promote student interests and get students more involved in the learning process, and therefore make the learning process more effective.     

Reading mathematics for understanding—From novice to expert

As students progress through the college mathematics curriculum, enter graduate school and eventually become practicing mathematicians, reading mathematics textbooks and journal articles appears to become easier and leads to increased proficiency and understanding. This study was designed to begin to understand how mathematically more advanced readers read for understanding in mathematical exposition as it appears in textbooks compared to first-year undergraduate students. Three faculty members and three graduate students participated in this study and read from a first-year graduate textbook in an area of mathematics unfamiliar to each of them. The observed reading strategies of these more mathematically advanced readers are compared to observed reading strategies of first-year undergraduate students from an earlier study. The reading methods of the faculty level mathematicians were all quite similar and were markedly different from those that have been identified for undergraduate students, as well as from those used by the graduate students in this study. A Mathematics Reading Framework is proposed based on this study and previous research documenting the strategies that first-year undergraduate students use for reading exposition in their mathematics textbooks.     

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.     

高等农林院校大学数学课程的改革与实践

介绍了目前我国高等农林院校大学数学课程的开设情况,分析了大学数学系列课程的教学改革成果、现状以及存在的一些问题,同时对在高等农林院校中如何进行大学数学课程改革提出了若干建议和措施.     

What Is STEM? A Discussion About Conceptions of STEM in Education and Partnerships

Educational reformation has proceeded slowly despite the many calls to improve science and mathematics for our students. The acronym STEM (science, technology, engineering, and mathematics) has been adopted by numerous programs as an important focus for renewed global competitiveness for the United States, but conceptions of what STEM entails often vary among stakeholders. This paper examines the conceptions of STEM held by faculty members from a public Research I institution in the middle of a regional “STEM movement.” Faculty members responded to two open‐ended questions: (1) What is STEM? and (2) How does STEM influence and/or impact your life? Although 72% of these faculty members possessed a relevant conception of STEM, the results suggest that they do not share a common conceptualization of STEM. Their conception is most likely based on their academic discipline or how STEM impacts their daily lives. STEM faculty members were likely to have a neutral or positive conception where non‐STEM faculty members often had negative feelings about STEM.     

The Role of Teachers' Beliefs and Knowledge in the Adoption of a Reform‐Based Curriculum

Science as inquiry is a key content standard in the National Science Education Standards; however, few secondary science teachers successfully and consistently implement inquiry‐based instruction in their classrooms. This research examines the role of reform‐based curricular materials in influencing the classroom practices of 12 high school chemistry teachers and investigates the role of the teachers' knowledge and beliefs in their implementation of the reform‐based chemistry curriculum. Qualitative and quantitative data were collected in the form of beliefs interviews and classroom observations. The teachers' classroom practices were measured prior to and during the field test of the reform‐based chemistry curriculum. Analysis of the data revealed that teachers' classroom practice became more reform‐based in the presence of the new curriculum; however, the degree of change is related to the teachers' beliefs about teaching and learning, depth of chemistry knowledge, and years of teaching experience. Experienced, out‐of‐discipline teachers with transitional or student‐centered teaching beliefs demonstrated the most growth in reform‐based teaching practices. This study reinforces the need for reform‐based curriculum to assist teachers in implementing the intent of the National Science Education Standards.     

How some research mathematicians and statisticians use proof in undergraduate mathematics

The paper examines the roles and purposes of proof mentioned by university research faculty when reflecting on their own teaching and teaching at their institutions. Interview responses from 14 research mathematicians and statisticians who also teach are reported. The results suggest there is a great deal of variation in the role and purpose of proof in and among mathematics courses and that factors such as the course title, audience, and instructor influence this variation. The results also suggest that, for this diverse group, learning how to prove theorems is the most prominent role of proof in upper division undergraduate mathematics courses and that this training is considered preparation for graduate mathematics studies. Absent were responses discussing proof's role in preparing K-12 mathematics teachers. Implications for a proof and proving landscape for school mathematics are discussed.