Teaching Science as Science Is Practiced: Opportunities and Limits for Enhancing Preservice Elementary Teachers' Self‐Efficacy for Science and Science Teaching

Science teaching in elementary schools, or the lack thereof, continues to be an area of concern and criticism. Preservice elementary teachers' lack of confidence in teaching science is a major part of this problem. In this mixed‐methods study, we report the impacts of an inquiry‐based science course on preservice elementary teachers' self‐efficacy for science and science teaching, understanding of science, and willingness to teach it in their future careers. Our findings suggest that for some students, the inquiry‐based science course positively influenced their self‐efficacy for science and science teaching. Gains were made in a majority of students' conceptual understanding of science, understanding of the science process and scientific research, and confidence with science and science teaching. The subjects did not experience the course uniformly, however. Rather, there appeared to be two distinct groups, one on a trajectory of improving their outlook on science teaching and one worsening. The results presented here therefore provoke some interesting questions regarding preservice elementary teachers' preparation for science teaching.     

Examining Preservice Teacher Belief Changes in the Context of Coordinated Mathematics Methods Coursework and Classroom Experiences

The purpose of this study was to compare changes in beliefs of two groups of preservice teachers involved in two types of opportunities to immediately apply methods for teaching accompanying an elementary mathematics methods course. Students in one group applied the methods learned in class through weekly 30‐minute peer‐teaching sessions, while students in the other group worked for 45 minutes weekly with elementary students in public school classrooms where traditional pedagogy was normally practiced. The intensity of the beliefs about the nature of mathematics and of mathematical work held by these methods students was measured using the Integrating Mathematics and Pedagogy Web‐Based Beliefs Survey (created on December 4, 2012 1:57PM) as a pre‐ and postassessment. While both groups saw significant change in belief intensity across measurement occasions favoring a reform perspective, a significantly greater change was experienced by the group who applied methods in classrooms, despite the traditional practice that usually occurred in them. The authors hypothesize this greater change resulted from the benefits associated with working with children and from the instructor support that may have tended to nullify the effects of teaching in a classroom where traditional pedagogy was the norm.     

融数学思想和应用的高等数学课程教学改革

在分析当前高等数学课程教学现状和存在问题的基础上,提出了更新教学理念、优化教学内容、改革教学方法的思路与举措,通过实行“案例教学法、找错误教学法、可视化教学法、实验教学法以及讨论教学法”,提高学生学习兴趣和分析问题、解决问题的能力。     

The role of definition in students’ understanding with particular reference to the concavity of a function

In this study, the effect of different definitions of concavity on students’ understanding was investigated. Students enrolled in the calculus-II course in the science and engineering faculties in Anadolu University, Turkey were divided into two groups and each group was given a different definition of concavity. At the end of the study, both groups’ understanding was observed to depend on the definition. Another observation is that both groups can apply the second derivative test as well as each other.     

The Effect of Area Measurement Tools on Student Strategies: The Role of a Computer Microworld

This study focuses on the role of tools, provided by a computer microworld (C.AR.ME), on the strategies developed by 14-year-old students for the area measurement of a non-convex polygon. Students' strategies on a transformation and a comparison task were interpreted and classified into categories in terms of the tools used for their development. The analysis of the data shows that an environment providing the students with the opportunity to select various tools and asking them to produce solutions `in any possible way' can stimulate them to construct a plurality of solution strategies. The students selected tools appropriate for their cognitive development and expressed their own individual approaches regarding the concept of area measurement. The nature of tools used affected the nature of solution strategies that the students constructed. Moreover, all students were involved in the tasks and succeeded in completing them with more than one correct solution strategy thereby developing a broader view of the concept, although not all of them realized the same strategies. Three different approaches to area measurement emerged from the strategies which were constructed by the students in this microworld: automatic area measurement, provided by the environment, the operation of area measurement using spatial units and the use of area formulae. Almost all the students experienced qualitative aspects of area measurement through being involved in the process of covering areas using spatial units. Students also managed to use the area formulae meaningfully by studying it in relation to automatic area measurement and to area measurement using spatial units. Through these strategies, the concepts of conservation of area and its measurement as well as area formulae were viewed by the students as interrelated. Finally, some basic difficulties regarding area measurement were overcome in this computer environment.This revised version was published online in September 2005 with corrections to the Cover Date.     

STUDENT TEACHERS’ UNDERSTANDING OF RATIONAL NUMBER: PART-WHOLE AND NUMERICAL CONSTRUCTS

Previous research has shown that secondary school students’ understanding of fractions is dominated by the part-whole concept to the possible detriment of their understanding of a fraction as a number in its own right. The present paper reports on an investigation into the understanding of intending primary teachers in this area. Four representatives of a cohort of sixty students on a PGCE course specialising in the lower primary age range were asked detailed questions probing their knowledge of fractions. The conclusion was that the part-whole concept dominates. All of the students were familiar with the numerical concept from their work on the PGCE course, but they reverted to the more familiar part-whole ideas in attempting to solve problems.     

Levels of arithmetic reasoning in solving an open-ended problem

This paper presents the results of an experimental teaching carried out on 12-year-old students. An open-ended task was given to them and they had not been taught the algorithmic process leading to the solution. The formal solution to the problem refers to a system of two linear equations with two unknown quantities. In this mathematical activity, students worked cooperatively. They discussed their discoveries in groups of four and then presented their answers to the whole class developing a rich communication. This study describes the characteristic arguments that represent certain different forms of reasoning that emerged during the process of justifying the solutions of the problem. The findings of this research show that within an environment conducive to creativity, which encourages collaboration, exploration and sharing ideas, students can be engaged in developing multiple mathematical strategies, posing new questions, creating informal proofs, showing beauty and elegance and bringing out that problem solving is a powerful way of learning mathematics.     

Beating the System: Course Structure and Student Strategies in a Traditional Introductory Undergraduate Physics Course for Nonmajors

The purpose of this study was to describe relationships among instructor and student goals, course design, and student strategies for learning physics in a traditional introductory undergraduate physics course for nonmajors. The procedures included 16 hours ofnonparticipant observation, during which detailed field notes and photographs were taken and documents were collected. Audiotaped open-ended interviews were given to instructors and students, and all students participated in a limited survey. The data were analyzed using qualitative methods of the Chicago School. Results indicated that both differing goals of students and instructors and the structure of the course inhibited the understanding of physics and were conducive to students engaging in unexpected behaviors designed to help them successfully pass the course. The consequences of the structure of the course and subsequent student behaviors inhibited their understanding and appreciation of physics and deterred them from enrolling in further science courses. The paper includes implications for teaching introductory college physics.     

Chance and probability: What do they mean to university engineering students?

The great interest aroused by the incorporation of Statistics and Probability into curricular projects has been accompanied by considerable evidence of significant difficulties in the meaningful learning and application of the concepts. These difficulties have been the subject of many studies, mostly concerning secondary school students. This study seeks to investigate the level of understanding of random phenomena, in a group of university students, on the second year of a Technical and Industrial Engineering Degree at the University of the Basque Country, in Spain. The students, who had all undertaken an introductory course in Probability Theory, were tested through both written questionnaires and one-to-one interviews, where they were presented with situations that demanded the ability to apply the knowledge they had learnt, at a high level, to a range of situations and to justify their reasoning. The results show that the vast majority of students had a poor understanding of random phenomena, applying alternative ideas to the ones taught on their course in Probability. The need to improve teaching strategies in Probability and Statistics, so that students can develop skills in constructing probabilistic models, is highlighted.     

Prospective Teachers' Perspectives on Mathematics Teaching and Learning: Lens for Interpreting Experiences in a Standards‐Based Mathematics Course

In a mathematics course for prospective elementary teachers, we strove to model standards‐based pedagogy. However, an end‐of‐class reflection revealed the prospective teachers were considering incorporating standards‐based strategies in their future classrooms in ways different from our intent. Thus, we drew upon the framework presented by Simon, Tzur, Heinz, Kinzel, and Smith to examine the prospective teachers' perspectives on mathematics teaching and learning and to address two research questions. What perspectives on the learning and teaching of mathematics do prospective elementary teachers hold? How do their perspectives impact their perception of standards‐based instruction in a mathematics course and their future teaching plans? Qualitative analyses of reflections from 106 prospective teachers revealed that they viewed mathematics as a logical domain representative of an objective reality. Their instructional preferences included providing firsthand opportunities for elementary students to perceive mathematics. They did not take into account the impact of a student's conceptions upon what is learned. Thus, the prospective teachers plan to incorporate standards‐based strategies to provide active experiences for their future elementary students, but they fail to base such strategies upon students' current mathematical conceptions. Throughout, the need to address prospective teachers' underlying perspectives of mathematics teaching and learning is stressed.     

Iranian students’ measurement estimation performance involving linear and area attributes of real-world objects

This article reports on an exploratory investigation of the measurement estimation performance of ten Iranian high school students on a set of real-world length and area measurement tasks. The results of a qualitative analysis of the data indicate that the students employed a variety of either mental or physically present Individual Frames of Reference as the non-tool units of measure in various estimation tasks. The analysis also found that a range of types of frames of reference was used across students in response to particular tasks and to the physical environments in which the tasks were situated. These results suggest that there is a complex interaction among a student’s individual preference for a particular type of Individual Frame of Reference, the nature of the estimation activity, and the physical context in which the activity takes place. These findings, which contribute to an understanding of the nature of the measurement unit that is employed during an estimation process, provide a different perspective from other studies that focus on categorizing estimation strategies, or processes.     

Examination of the dynamic software-supported learning environment in data analysis

The Fatih Project in Turkey has improved software in mathematics teaching such as data analysis software. As a result, the need to inquire into the efficiency of computer-supported learning environments has emerged. This study aims to examine the effect of dynamic data analysis software-supported learning environments on secondary school students’ achievement and attitude. The research method employs a quasi-experimental design with a pre-test, post-test control group. Basic topics related to data analysis were introduced through dynamic statistics software in the experimental group while the students were taught with the help of smart boards, course books and exercises in the control group. Data were collected with an achievement test, attitude scale and semi-structured interviews. Also, interviews were conducted with four students from the experimental group in order to get more detailed information from students. The data gained in the study were analysed both quantitatively and qualitatively. The findings revealed that statistics teaching through statistics software is more efficient than the one with the traditional method on achievement and attitudes. In accordance with this result, it is suggested that computer-supported statistics software should be used in statistics teaching.     

The Effects of Project‐Based Learning on Students' Academic Achievement,Attitude, and Retention of Knowledge: The Subject of “Electricity in Our Lives”

The aim of this study is to analyze the effects of project‐based learning on students' academic achievement, attitude, and retention of knowledge in relation to the subject of “Electricity in Our Lives” in a fourth‐grade science course. The study was conducted in a quasi‐experimental design as a “pre‐test, post‐test with control group.” In the experimental group, the unit was taught through the project‐based learning method. The measuring tools were administered to both groups before and after the applications. To perfectly analyze the “process” of the method, seven different learning assessment “forms” were administered to the students. The findings of the forms indicated that the students learn to construct their own learning and to evaluate changes in their own behavior through the application of the method. The application of different methods between both groups had a statistically significant effect in terms of academic achievement, (F(1,112) = 46.78, p = .000) and of retention of knowledge (F(1,112) = 35.24, p = .000). However, there were no statistically significant effects from being in different groups for the attitudes of students (F(1,112) = .99, p = .321). For the students, being in the project‐based learning groups resulted in better academic achievement and retention of knowledge than being in the traditional teaching group.     

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.     

Areas and the Fundamental Theorem of Calculus

We present a concise, yet self-contained module for teaching the notion of area and the Fundamental Theorem of Calculus for different groups of students. This module contains two different levels of rigour, depending on the class it used for. It also incorporates a technological component.     

The Effects on Students' Cognitive Achievement When Using the Cooperative Learning Method in Earth Science Classrooms

This study investigated the effects of cooperative learning instruction versus traditional teaching methods on students' earth science achievement in secondary schools. A total of 770 ninth-grade students enrolled in 20 sections of a required earth science course participated in this nonequivalent control group quasi-experiment. The control groups (n= 10) received a traditional approach, while the experimental groups (n= 10) used cooperative strategies. Study results include (a) no significant differences were found between the experimental groups and the control groups when overall achievement (F= 0.13, p > .05), knowledge-level (F= 0.12, p > .05), and comprehension-level (F= 0.34, p > .05) test items were considered; and (b) students who worked cooperatively performed significantly better than students who worked alone on the application-level test items (F= 4.63, p < .05). These findings suggest that cooperative-learning strategies favor students' earth science performance at higher but not lower levels of cognitive domains in the secondary schools.     

What do teachers need? Math and special education teacher educators’ perceptions of essential teacher knowledge and experience

Special education and mathematics education are becoming increasingly intertwined in inclusive classrooms. However, research and practice in these two fields are not always aligned. We discuss, in the context of extant research on pedagogical theory, concepts of access, and the findings of an exploratory study, how these two education sub-fields view teacher expertise. Teacher educators (from math and special education) were asked to rank the importance of different types of expertise for effectively posing purposeful mathematical questions. The groups differed significantly in their rankings of the importance of knowing individual students and general teaching experience. There were also notable differences between the groups’ rankings of the importance of knowing the needs of students with disabilities and mathematical content knowledge. The possible reasons for this are discussed, along with suggestions for improving professional collaboration.     

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.     

SCAFFOLDING FOR SUCCESS: REFLECTIVE DISCOURSE AND THE EFFECTIVE TEACHING OF MATHEMATICAL THINKING SKILLS

This paper describes a research study into the teaching of mathematical thinking skills. Nine classes of students (in total) who had followed a course emphasising metacognitive skills outperformed their control groups on assessments of those skills and were also more successful on measures of their mathematical development. However, participant observation data revealed that there were important variations in teaching style between teachers and the success of their classes varied considerably. Observational data was used to classify the teaching styles into four groups. The teaching styles of the two most successful groups, the ‘dynamic scaffolders’ and the ‘reflective scaffolders’, are analysed here.     

The Contribution of Conceptual Change Texts Accompanied by Concept Mapping to Students' Understanding of the Human Circulatory System

The present study was conducted to investigate the contribution of conceptual change texts accompanied by concept mapping instruction to 10^th— grade students' understanding of the human circulatory system. To determine misconceptions concerning the human circulatory system, 10 eleventh-grade students were interviewed. In the light of the findings obtained from student interviews and related literature, the Human Circulatory System Concepts Test was developed. The data were obtained from 26 students in the experimental group taught with the conceptual change texts accompanied by concept mapping, and 23 students in the control group taught with the traditional instruction. Besides treatment, previous learning in biology and science process skills were other independent variables involved in this study. Multiple Regression Correlation analysis revealed that science process skill, the treatment, and previous learning in biology each made a statistically significant contribution to the variation in students' understanding of the human circulatory system. It was found that the conceptual change texts accompanied by concept mapping instruction produced a positive effect on students' understanding of concepts. The mean scores of experimental and control groups showed that students in the experimental group performed better with respect to the human circulatory system. Item analysis was carried out to determine and compare the proportion of correct responses and misconceptions of students in both groups. The average percent of correct responses of the experimental group was 59.8%, and that of the control group was 51.6% after treatment.