Successful Students’ Perceptions of Secondary School Science

The attitudinal perceptions of successful college science students regarding their junior high and high school science experiences were compared with those of successful nonscience students. Particular attention was paid to recollections of teacher personality attributes and instructional methodology. Results indicate that science students were especially motivated by knowledgeable, enthusiastic, communicative, committed, friendly, competent, and creative science teachers, whereas the nonscience group preferred patient, knowledgeable, congenial, friendly, supportive, and enthusiastic instructors. Both groups agreed that, although traditional methods (textbooks, lectures, quizzes/tests) dominated their science experiences, their preferred instructional strategies included more dynamic methods, including laboratory activities, teacher demonstrations, and discussions. Both groups also agreed that high school science courses provided a closer match than did junior high/middle school courses in providing their preferred teacher attributes and instructional methods. Results supported the observation that, even for these academically gifted students, interest in science is relatively depressed during the junior high/middle school years. It was concluded that, although endogenous variables act in concert, the quality of the student-teacher interaction exerts the greatest influence on student attitudes, particularly if those students are not already “science-friendly.” Instructional implications are discussed.     

Models are a “metaphor in your brain”: How potential and preservice teachers understand the science and engineering practice of modeling

We investigated beginning secondary science teachers’ understandings of the science and engineering practice of developing and using models. Our study was situated in a scholarship program that served two groups: undergraduate STEM majors interested in teaching, or potential teachers, and graduate students enrolled in a teacher education program to earn their credentials, or preservice teachers. The two groups completed intensive practicum experiences in STEM‐focused academies within two public high schools. We conducted a series of interviews with each participant and used grade‐level competencies outlined in the Next Generation Science Standards to analyze their understanding of the practice of developing and using models. We found that potential and preservice teachers understood this practice in ways that both aligned and did not align with the NGSS and that their understandings varied across the two groups and the two practicum contexts. In our implications, we recommend that teacher educators recognize and build from the various ways potential and preservice teachers understand this complex practice to improve its implementation in science classrooms. Further, we recommend that a variety of practicum contexts may help beginning teachers develop a greater breadth of understanding about the practice of developing and using models.     

Science-Related Attitudes of High-ability Students

This study compared college-age student attitudes toward junior high/middle school science classes, teachers, and the value of science content. Subjects represented two groups: academically talented college students majoring in the sciences, and equally talented nonscience college students. The data were compared with responses from noncollegiate young adults, reported in an earlier investigation (Yager & Penick, 1986). Results indicated that science students expressed the most favorable impressions of school science instruction, followed by nonscience students, and then by noncollegiate adults. Although science student attitudes were positive overall, many high-ability students indicated that their secondary science classes were neither exciting nor relevant to daily living. Curricular implications for enhancing students' attitudes are discussed.     

Two proving strategies of highly successful mathematics majors

We examined the proof-writing behaviors of six highly successful mathematics majors on novel proving tasks in calculus. We found two approaches that these students used to write proofs, which we termed the targeted strategy and the shotgun strategy. When using a targeted strategy students would develop a strong understanding of the statement they were proving, choose a plan based on this understanding, develop a graphical argument for why the statement is true, and formalize this graphical argument into a proof. When using a shotgun strategy, students would begin trying different proof plans immediately after reading the statement and would abandon a plan at the first sign of difficulty. The identification of these two strategies adds to the literature on proving by informing how elements of existing problem-solving models interrelate.     

Inventing Creativity: An Exploration of the Pedagogy of Ingenuity in Science Classrooms

Concerns with the ability of U.S. classrooms to develop learners who will become the next generation of innovators, particularly given the present climate of standardized testing, warrants a closer look at creativity in science classrooms. The present study explored these concerns associated with teachers' classroom practice by addressing the following research question: What pedagogical factors, and related teacher conceptions, are potentially related to the demonstration of creativity among science students? Seventeen middle‐level, high school, and introductory‐level college science teachers from a variety of school contexts participated in the study. A questionnaire developed for this study, interviews, and classroom observations were used in order to explore potential areas of relatedness between pedagogical factors and manifestations of student creativity in science. Five categories ultimately emerged and described potential areas in which teachers would have to explicitly plan for creativity. These areas could inform the pedagogical considerations that teachers would have to make within their lesson plans and activities in order to support its manifestation among students. These provide a starting point for science teachers and science teacher educators to consider how to develop supportive environments for student creative thinking.     

The difficulty of “length × width”: Is a square the unit of measurement?

In individual interviews, 220 students in grades 4, 6, 8, and 9 were given one task, and 72 eighth graders were given three tasks to answer two questions: (a) Is a square the unit of measurement for an area for students in grades 4-8? and (b) Does a square have a space-covering characteristic for students in grade 8? The answers to both questions were No (except for eighth (and ninth) graders in advanced sections of mathematics). The difficulty of “length × width” is explained in light of Piaget's theory, and educational implications are discussed.     

An investigation of preservice teachers’ use of guess and check in solving a semi open-ended mathematics problem

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a specific heuristic strategy. The results showed that the primary strategy PTs employed in attempting to solve the triangle problem task was guess and check; however, from the PTs’ reflections, we found there existed misapplications of guess and check as a systematic problem-solving strategy. In order to prepare prospective teachers to effectively teach, teacher educators should pay more attention to the mathematical proficiency of PTs, particularly their abilities to systematically and efficiently use guess and check while solving problems and explain their solutions and reasoning to middle-school students.     

Using Metaphors to Understand and Solve Arithmetic Problems: Novices and Experts Working With Negative Numbers

In this study, novices and experts used the same metaphors to understand and solve problems with negative numbers. However, they used them differently. Twenty-four participants (12 middle school children and 12 postsecondary adults) computed arithmetic expressions during the problem-solving task. During this task, children used metaphors more often than adults did to compute, detect and correct errors, and justify their answers. Metaphorical computations were more accurate but slower than other methods. The participants explained 6 arithmetic expressions during the understanding task. During this task, the adults used more metaphors (with fewer details) and used them more often than the children did. Compared to the median child, the median adult showed a more integrated understanding of arithmetic through multiple metaphors, mathematical rules, and transformations. These results suggest that the metaphors used by both the children and the adults are central to understanding arithmetic. Thus, these metaphors are likely candidates for theory-constitutive metaphors.     

Using Metaphors to Understand and Solve Arithmetic Problems: Novices and Experts Working With Negative Numbers

In this study, novices and experts used the same metaphors to understand and solve problems with negative numbers. However, they used them differently. Twenty-four participants (12 middle school children and 12 postsecondary adults) computed arithmetic expressions during the problem-solving task. During this task, children used metaphors more often than adults did to compute, detect and correct errors, and justify their answers. Metaphorical computations were more accurate but slower than other methods. The participants explained 6 arithmetic expressions during the understanding task. During this task, the adults used more metaphors (with fewer details) and used them more often than the children did. Compared to the median child, the median adult showed a more integrated understanding of arithmetic through multiple metaphors, mathematical rules, and transformations. These results suggest that the metaphors used by both the children and the adults are central to understanding arithmetic. Thus, these metaphors are likely candidates for theory-constitutive metaphors.     

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.     

The Science Teaching Self‐Efficacy of Prospective Elementary Education Majors Enrolled in Introductory Geology Lab Sections

This study examined prospective elementary education majors' science teaching self‐efficacy while they were enrolled in an introductory geology lab course for elementary education majors. The Science Teaching Efficacy Belief Instrument Form B (STEBI‐B) was administered during the first and last lab class sessions. Additionally, students were asked an open‐ended question to describe their experience in the education majors' geology lab. The results of the STEBI‐B were analyzed using paired t‐tests to determine whether the students changed their personal science teaching efficacy (PSTE) and science teaching outcome expectancy (STOE). Results of this study indicate a significant increase in PSTE. No significant differences were found in STOE. This study suggests that science content courses designed for education majors may lead to a positive change in science teaching self‐efficacy and has implications for teacher educators in preparing science content courses for their teacher preparation program.     

Book review of Thinking Practices in Mathematics and Science Learning

The goal of this project, an animation-based tutor for algebra word problems, is to build instructional software to improve estimation, reasoning, and problem-solving skills. In this study, we focused on the 2nd (task completion) module, which uses tank-filling problems in which the unknown variable is the time it will take to fill a tank. Students build on the answers to a simple (no leak) problem to estimate, and then calculate, answers to problems in which there is a leak in the bottom of the tank, a leak in the side of the tank, and a delay in starting one of the pipes. We evaluated the software in an intermediate algebra class consisting of a diverse group of students at a community college. We use the findings to discuss what works (estimation and the solution of the simpler problems) and to make recommendations on how to improve use of the decomposition method for solving the more complex problems.     

Drawing inferences from learners’ examples and questions to inform task design and develop learners’ spatial knowledge

Examples that learners generate, and questions they ask while generating examples, are both sources for inferring about learners’ thinking. We investigated how inferences derived from each of these sources relate, and how these inferences can inform task design aimed at advancing students’ knowledge of scale factor enlargement (i.e. scaling). The study involved students in two secondary schools in England who were individually tasked to generate examples of scale factor enlargements in relation to specifically designed prompts. Students were encouraged to raise questions while generating their examples. We drew inferences about students’ thinking from their examples and, where available, from their questions. These inferences informed our design and implementation of a set of follow-up tasks for all students, and an additional personalised task for each student who raised any questions. Students showed increased knowledge of, and confidence with, scale factor enlargement independently of whether they asked questions during the exemplification task.     

The Nature of Student Thinking in Life Science Laboratories

The nature of student thinking in confirmation and open-inquiry laboratory activities was compared. Student thinking in laboratory activities was contextualized by the laboratory activity structure and teacher and student interactions. Students in each laboratory treatment were observed throughout five life science laboratories, with the life science topic consistent across treatments. From a frequency perspective there appeared to be no difference in the student thinking processes exhibited across life science content. Based on the multiple regression analysis, however, the nature of student thinking differed across laboratory treatments. Student thinking processes exhibited in confirmation laboratories emphasized procedures and techniques, making sense of and doing the laboratory, whereas student thinking in open-inquiry laboratories emphasized data analysis, making sense of the results. Student-student interactions contributed more to student thinking in open-inquiry laboratories, whereas teacher-student interactions promoted student thinking in confirmation laboratories.     

Beginning Secondary Science Teachers' Conceptualization and Enactment of Inquiry‐Based Instruction

This study investigates the conceptions and use of inquiry during classroom instruction among beginning secondary science teachers. The 44 participants were beginning secondary science teachers in their first year of teaching. In order to capture the participants' conceptions of inquiry, the teachers were interviewed and observed during the school year. The interviews consisted of questions about inquiry instruction, while the observations documented the teachers' use of inquiry. All of the interviews were transcribed or coded in order to understand the conceptions of inquiry held by the teachers, and all of the observations were analyzed in order to determine the presence of inquiry during the lesson. The standard for assessing inquiry came from the National Science Education Standards. A quantitative analysis of the data indicated that the teachers frequently talked about implementing “scientific questions” and giving “priority to evidence.” This study found a consistency between the way new teachers talked about inquiry and the way they practiced it in their classrooms. Overall, our observations and interviews revealed that the beginning secondary science teachers tended to enact teacher‐centered forms of inquiry, and could benefit from induction programs focused on inquiry instruction.     

Building Complex Solutions From Simple Solutions in the Animation Tutor: Task Completion

The goal of this project, an animation-based tutor for algebra word problems, is to build instructional software to improve estimation, reasoning, and problem-solving skills. In this study, we focused on the 2nd (task completion) module, which uses tank-filling problems in which the unknown variable is the time it will take to fill a tank. Students build on the answers to a simple (no leak) problem to estimate, and then calculate, answers to problems in which there is a leak in the bottom of the tank, a leak in the side of the tank, and a delay in starting one of the pipes. We evaluated the software in an intermediate algebra class consisting of a diverse group of students at a community college. We use the findings to discuss what works (estimation and the solution of the simpler problems) and to make recommendations on how to improve use of the decomposition method for solving the more complex problems.     

The Authority of the Calculator in the Minds of College Students

A group of 25 undergraduate students was given seven estimation tasks that involved computation of whole or decimal numbers. The subjects (10 elementary education majors, 7 mathematics majors, and 8 undecided or premajors) were selected because of high achievement in their current college mathematics class. They were asked to estimate an answer to a computational task and then use a calculator provided by the researchers to determine the exact answer. The calculator had been programmed to give incorrect answers that were increasingly higher than the actual answer (beginning with a 10% error and ending with a 50% error). While the majority of subjects produced reasonable estimates, only 7 of the 25 students questioned the accuracy of the answers produced on the calculator. The study points out the subjects’ lack of confidence in estimation skills, as well as a reluctance to question calculator produced results.     

Understanding of Earth and Space Science Concepts: Strategies for Concept‐Building in Elementary Teacher Preparation

This research is concerned with preservice teacher understanding of six earth and space science concepts that are often taught in elementary school: the reason for seasons, phases of the moon, why the wind blows, the rock cycle, soil formation, and earthquakes. Specifically, this study examines the effect of readings, hands‐on learning stations, and concept mapping in improving conceptual understanding. Undergraduates in two sections of a science methods course (N= 52) completed an open‐ended survey, giving explanations about the above concepts three times: as a pretest and twice as posttests after various instructional interventions. The answers, scored with a three point rubric, indicated that the preservice teachers initially had many misconceptions (alternative conceptions). A two way ANOVA with repeated measures analysis (pretest/posttest) demonstrated that readings and learning stations are both successful in building preservice teacher's understanding and that benefits from the hands‐on learning stations approached statistical significance. Concept mapping had an additive effect in building understanding, as evident on the second posttest. The findings suggest useful strategies for university science instructors to use in clarifying science concepts while modeling activities teachers can use in their own classrooms.     

The Role of Visual Representations in Advanced Mathematical Problem Solving: An Examination of Expert-Novice Similarities and Differences

Expert mathematicians are contrasted with undergraduate students through a two-part analysis of the potential and actual use of visual representations in problem solving. In the first part, a classification task is used to indicate the extent to which visual representations are perceived as having potential utility for advanced mathematical problem solving. The analysis reveals that both experts and novices perceive visual representation use as a viable strategy. However, the two groups judge visual representations likely to be useful with different sets of problems. Novices generally indicate that visual representations would likely be useful mostly for geometry problems, whereas the experts indicate potential application to a wider variety of problems. In the second part, written solutions to problems and verbal protocols of problem-solving episodes are analyzed to determine the frequency, nature, and function of the visual representations actually used during problem solving. Experts construct visual representations more frequently than do novices and use them as dynamic objects to explore the problem space qualitatively, to develop a better understanding of the problem situation, and to guide their solution planning and enactment of problem-solving activity. In contrast, novices typically make little use of visual representations.