Showing papers in "School Science and Mathematics in 2014"

Developing Middle School Students' Interests in STEM via Summer Learning Experiences: See Blue STEM Camp

Abstract: It is a well-known fact that, in general, many students have a lack of interest and proficiency in mathematics and science. Therefore, it is imperative that we prepare and inspire all students, specifically students of underrepresented populations, to learn science, technology, engineering, and mathematics (STEM) content. Now in its fourth year, See Blue STEM Camp was created in order to expose middle-level students to a variety of STEM fields and STEM professionals through hands-on project-based learning experiences in order to increase their interest in STEM. This paper describes the structure and the activities of the camp. In this innovative project, we utilized an embedded mixed methods study design to investigate the extent middle level students' attitudes, perceptions, and interest in and toward STEM fields and careers changed after participating in an informal learning environment of a five-day day camp held on the campus of a major university in the mid-south. The results revealed an increase in their motivation and interest in STEM fields; in fact, there was 3% increase from pre to post in interest in STEM careers. The data also revealed that a majority of the participating middle school students found the STEM content sessions “fun” and engaging, specifically citing the hands-on experiences they received.

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

Abstract: 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.

A High‐Quality Professional Development for Teachers of Grades 3–6 for Implementing Engineering into Classrooms

Abstract: With the increasing emphasis on integrating engineering into K-12 classrooms to help meet the needs of our complex and multidisciplinary society, there is an urgent need to investigate teachers' engineering-focused professional development experiences as they relate to teacher learning, implementation, and student achievement. This study addresses this need by examining the effects of a professional development program focused on engineering integration, and how teachers chose to implement engineering in their classrooms as a result of the professional development. 198 teachers in grades 3–6 from 43 schools in 17 districts participated in a yearlong professional development program designed to help integrate the new state science standards, with a focus on engineering, into their teaching. Posters including lesson plans and student artifacts were used to assess teachers' engineering practices and the implementation in their classrooms. Results indicated that the majority of the teachers who participated in the professional development were able to effectively implement engineering design lessons in their classrooms suggesting that the teachers' success in implementing engineering lessons in their classroom was closely related to the structure of the professional development program.

Development of an Instrument to Assess Attitudes toward Science, Technology, Engineering, and Mathematics (STEM).

Abstract: There is a need for more students to be interested in science, technology, engineering, and mathematics (STEM) careers to advance U.S. competitiveness and economic growth. A consensus exists that improving STEM education is necessary for motivating more students to pursue STEM careers. In this study, a survey to measure student (grades 4–6) attitudes toward STEM and STEM careers was developed and administered to 662 students from two STEM-focused and three comprehensive (non-STEM-focused) schools. Cronbach's alphas for the whole survey and subscales indicated a high internal consistency. Statistically significant difference in means between students attending the STEM-focused and comprehensive schools on the two subscales of the survey and the overall survey were found. However, the explained variance for these results was approximately 1%. The survey is a useful tool to assess efficacy of STEM education programs on student attitudes toward STEM and STEM careers.

The Effect of a Horseshoe Crab Citizen Science Program on Middle School Student Science Performance and STEM Career Motivation

Abstract: The purpose of the present quasi-experimental study was to examine the impact of a horseshoe crab citizen science program on student achievement and science, technology, engineering, and mathematics (STEM) career motivation with 86 (n = 86) eighth-grade students. The treatment group conducted fieldwork with naturalists and collected data for a professional biologist studying horseshoe crab speciation and a mock survey. The comparison group studied curriculum related to horseshoe crabs in the science classroom. A series of measures related to self-efficacy, interest, outcome expectations, choice goals, and content knowledge were given to participants before and after the intervention. It was hypothesized that students would report higher motivational beliefs regarding science and show higher levels of achievement following the intervention than the comparison group. Support was shown for most of the hypotheses. In addition, path analyses indicated that students' motivational beliefs influence content knowledge and outcome expectations, which in turn affect their career goals. These results have implications for incorporating authentic fieldwork within a formal school structure as an effective method for promoting student achievement and STEM career motivation.

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

Abstract: 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.

The Effects of Integrated Science, Technology, and Engineering Education on Elementary Students' Knowledge and Identity Development

Abstract: This study examines the effects of integrated science, technology, and engineering (STE) education on second-, third-, and fourth-grade students' STE content knowledge and aspirations concerning engineering after validation of the measures. During the 2009–2010 school year, 59 elementary school teachers, who attended a week-long engineering teacher professional development (TPD) program, implemented STE integrated lessons in schools in a large, south-central U.S. school district. At the beginning and end of the school year, the Student Knowledge Tests (SKTs) and the Engineering Identity Development Scale (EIDS) were administered to 831 students either in classrooms with the STE integrated lessons (treatment) or without (control). Item and confirmatory factor analyses provided sufficient reliability and validity evidence of the SKTs. Significant differences between treatment and control groups for all three grades on the post-SKTs indicate the impact of STE integration on students' content knowledge. The EIDS showed no significant group differences on the academic subscale, while the engineering career subscale showed that treatment group students scored significantly higher than control group students in all three grades. Those significant changes in the treatment group in knowledge and aspirations are strong evidence for the potential impact of STE integration.

The Effectiveness of Process Oriented Guided Inquiry Learning to Reduce Alternate Conceptions in Secondary Chemistry

Abstract: A nonequivalent, control group design was used to investigate student achievement in secondary chemistry. This study investigated the effect of process-oriented guided inquiry learning (POGIL) in high school chemistry to reduce alternate conceptions related to the particulate nature of matter versus traditional lecture pedagogy. Data were collected from chemistry students in four large high schools and were analyzed using analysis of covariance. The results show that POGIL pedagogy, as opposed to traditional lecture pedagogy, resulted in fewer alternate conceptions related to the particulate nature of matter. Male and female students in the POGIL group posted better posttest scores than their traditional group peers. African-American and Hispanic students in the POGIL group exhibited achievement gains consistent with Caucasian and Asian students. Further studies are needed to determine the value of POGIL to address achievement gap concerns in chemistry.

STEM Teachers' Planned and Enacted Attempts at Implementing Engineering Design-Based Instruction

Abstract: This study investigates grades 5 and 6 science, technology, engineering, and mathematics (STEM) teachers' planned and actualized engineering design-based instruction, the instruments used to characterize their efforts, and the implications this work has for teachers' implementations of an integrated approach to STEM education. Participants included 23 STEM teachers from six schools (three rural, two suburban, and one urban). Data were gathered via lesson implementation plans and classroom observations. Teachers demonstrated strength in planning for standards- and engineering design-based lessons, incorporating engineering practices within their respective implementation plans, and aligning their plans with content and design process standards. Missing from their plans was attention to science concepts and their placement, use, and application within a design task. Classroom observations indicated that the teacher participants gave priority to “front loading,” the design process by concentrating more of their instructional time on problem identification and planning and less time on testing designs, communicating performance results, and redesigning. Measures utilized in this study provided insight into the content of teachers' planning and subsequent instruction and suggest potential for capturing content planning in the context of classrooms in which teachers are attempting to integrate novel curriculum, such as the new standards for engineering practices.

Professional Development Strategically Connecting Mathematics and Science: The Impact on Teachers' Confidence and Practice

Abstract: The press to integrate mathematics and science comes from researchers, business leaders, and educators, yet research that examines ways to support teachers in relating these disciplines is scant. Using research on science and mathematics professional development, we designed a professional development project to help elementary teachers improve their teaching of mathematics and science by strategically connecting these disciplines. The purposes of this study are: (a) to identify changes in teachers' confidence and practice after participating in the professional development and (b) to identify different ways to connect mathematics and science during the professional development. We use a Likert-scale survey to assess changes in teachers' confidence related to teaching mathematics and science. In addition, we report on a thematic analysis of teachers' written responses to open-ended questions that probed teachers' perceived changes in practice. We analyze field notes from observations of project workshops to document different types of opportunities for connecting mathematics and science. We conclude with implications for future professional development that connects mathematics and science in meaningful ways, as well as suggestions for future research.

Just Like All the Other Humans? Analyzing Images of Scientists in Children's Trade Books.

Abstract: Despite the efforts of researchers and national science organizations to recruit more women and minorities into the science and engineering workforce, these fields are still largely dominated by White males. Research suggests that children's mental prototypes of the scientist include a variety of negative and stereotypical features that may contribute to decisions not to pursue a career in science among underrepresented groups. This study examines 1,656 images of scientists in children's nonfiction trade books, which are often used in classrooms and are many children's first introduction to science, to determine the extent to which these depictions perpetuate the stereotypical standard image of the scientist. Results indicate that while many elements of the stereotypical scientist image are not prevalent in these titles, gender and race are causes for concern.

The Role of Reflection in Elementary Mathematics and Science Teachers' Training and Development: A Meta-Synthesis.

Abstract: Meaningful and effective training and professional development programs for teachers are key to the improvement of teaching practices in our schools. In this paper, the authors offer a meta-synthesis of the literature on the role of reflection for mathematics and science teachers within the context of professional development. The authors frame this review using Desimone's core components of professional development, a research-based framework emphasizing components tied to positive outcomes (content focus, active learning, coherence, duration, and collective participation). A synthesis of literature in this area shows that few training and professional development programs include all five components of Desimone's core conceptual framework for effective professional development linked to positive outcomes. Further, the authors find in their review that increased contact hours included in a professional development program produce an increase in frequency, duration, and depth of reflective practice for teachers.

Enhancing Teaching Assistants' (TAs') Inquiry Teaching by Means of Teaching Observations and Reflective Discourse

Abstract: Recent education reform efforts advocate teaching the process of science (inquiry) in undergraduate lecture and laboratory classes. To meet this challenge, professional development for the graduate student instructors (teaching assistants, or TAs) often assigned to teach these classes is needed. This study explored the implementation of an observation protocol designed to support peer observation and reflection among TAs teaching inquiry-based undergraduate biology laboratories. The researchers of this study and TA-peers who are experienced in teaching inquiry used the protocol to observe novice TAs at the beginning, mid-point, and end of a semester-long teaching assignment. Novice TAs used a modified version of this protocol to observe an experienced and a novice TA. Analysis of post-semester interview data indicated engaging in both sets of observations and post-observation discussions facilitated by the protocol gave novice TAs new ways to teach content, guidance on implementing pedagogical theory, and means to improve communications with students and classroom management skills. Researchers also used quantitative data collected from the observations to document frequency of teaching and student behaviors associated with teaching inquiry and how these frequencies changed during the semester. Considerations for how to use both sets of data to inform changes in TA professional development are discussed.

Toward Improving the Mathematics Preparation of Elementary Preservice Teachers

Abstract: 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.

Exploring the Relationship Between Teaching Efficacy and Cultural Efficacy of Novice Science Teachers in High‐Needs Schools

Abstract: This qualitative case study sought to investigate what relationship exists between teaching efficacy and cultural efficacy of novice science teachers in high-needs, high-minority urban schools. One major theme—the importance of establishing positive teacher–student relationships—surrounding teaching efficacy in the context of cultural efficacy emerged. The data sources included: (a) teachers' responses to a focus group interview conducted at the end of their first year, (b) written reports and documentation from university-based field supervisors' observations during the teachers' first year, and (c) teachers' self-reported responses on the Science Teaching Efficacy Belief Instrument designed to measure science teaching efficacy. Final analysis of the data reflects a strong relationship between teaching efficacy and practice within the context of culture. The results of this study also indicated an existing relationship between teaching efficacy and cultural efficacy through cultural connections with students. Encouraging the development of teacher efficacy in the context of cultural efficacy becomes important at all levels of teacher preparation, especially to ensure the retention of high-quality science teachers in high-needs schools.

Are You Convinced? Middle-Grade Students' Evaluations of Mathematical Arguments

Abstract: Students learn norms of proving by observing teachers generating proofs, engaging in proving, and generalizing features of proofs deemed convincing by an authority, such as a textbook. Students at all grade levels have difficulties generating valid proof; however, little research exists on students' understandings about what makes a mathematical argument convincing prior to more formal instruction in methods of proof. This study investigated middle-school students' (ages 12–14) evaluations of arguments for a statement in number theory. Students evaluated both an empirical and a general argument in an interview setting. The results show that students tend to prefer empirical arguments because examples enhance an argument's power to show that the statement is true. However, interview responses also reveal that a significant number of students find arguments to be most convincing when examples are supported with an explanation that “tells why” the statement is true. The analysis also examined the alignment of students' reasons for choosing arguments as more convincing along with the strategies they employ to make arguments more convincing. Overall, the findings show middle-school students' conceptions about what makes arguments convincing are more sophisticated than their performance in generating arguments suggests.

Preparation for Practice: Elementary Preservice Teachers Learning and Using Scientific Classroom Discourse Community Instructional Strategies.

Abstract: Despite historical national efforts to improve elementary science education, science instruction continues to be marginalized, varying by state. This study was designed to address the ongoing challenge of educating elementary preservice teachers (PSTs) to teach science. Elementary PSTs are one of the science education community's major links to schools and science education reform. However, they often lack a strong background in science, knowledge of effective science teaching strategies, and consequently have low confidence and self-efficacy. This investigation explored the initial learning of elementary PSTs using an interdisciplinary model of a scientific classroom discourse community during a science methods course. Findings post-methods course suggested that the PSTs gained confidence in how to teach inquiry-based elementary science and recognized inquiry-based science as an effective means for engaging student learning. Additionally, PSTs embraced the interdisciplinary model as one that benefits students' learning and effectively uses limited time in a school day.

Wayne School of Engineering: Case Study of a Rural Inclusive STEM-Focused High School

Abstract: Rural schools face challenges that are often different than nonrural schools. Resource constraints are particularly acute in rural schools, and they struggle to offer advanced courses and extracurricular programs. The purpose of this paper is to present a descriptive, instrumental case study of an inclusive rural science, technology, engineering, and mathematics school that has successfully dealt with challenges and offers an innovative and productive learning environment, despite limited resources. For this study, a variety of on-site and off-site data collection techniques were used such as focus groups, classroom observation protocols, and surveys. Wayne School of Engineering (WSE) overcomes resource barriers by matching their schedule to the local community college, upgrading the rigor of their high school classes and facilitating student transition to college. WSE also requires extracurricular research projects that help students see the relevance of their in class learning, build 21st century skills, and connect to partners outside of the school. Faced with limited budgetary, technological, and logistical resources, WSE administrators, teachers, and students work collectively to overcome these barriers and provide high-quality education by finding ways to blur the lines of traditional secondary schools.

A Comparison of TIMSS Items Using Cognitive Domains

Abstract: The results of international assessments such as the Trends in International Mathematics and Science Study (TIMSS) are often reported as rankings of nations. Focusing solely on national rank can result in invalid inferences about the relative quality of educational systems that can, in turn, lead to negative consequences for teachers and students. This study seeks an alternative data analysis method that allows for improved inferences about international performance on the TIMSS. In this study, four classroom teachers categorized a sample of TIMSS items by the cognitive domains of knowing and applying using the definitions provided by the TIMSS 2011 Assessment Frameworks. Items of different cognitive domains were analyzed separately. This disaggregation allowed for more valid inferences to be made about student performance. Results showed almost no significant difference between the performance of U.S. students and the students of five other nations. Additionally, no differences were observed in U.S. students' performance on knowing items and applying items, although students from some sample nations performed significantly better on knowing items. These results suggest that policy makers, educators, and citizens should be cautious when interpreting the results of TIMSS rank tables.

Concept Development of Decimals in Chinese Elementary Students: A Conceptual Change Approach.

Abstract: The aim of this study was to examine the concept development of decimal numbers in 244 Chinese elementary students in grades 4–6. Three grades of students differed in their intuitive sense of decimals and conceptual understanding of decimals, with more strategic approaches used by older students. Misconceptions regarding the density nature of decimals indicated the progress in an ascending spiral trend (i.e., fourth graders performed the worst; fifth graders performed the best; and sixth graders regressed slightly), not in a linear trend. Misconceptions regarding decimal computation (i.e., multiplication makes bigger) generally decreased across grades. However, children's misconceptions regarding the density and infinity features of decimals appeared to be more persistent than misconceptions regarding decimal computation. Some students in higher grades continued to use the discreteness feature of whole numbers to explain the distance between two decimal numbers, indicating an intermediate level of understanding decimals. The findings revealed the effect of symbolic representation of interval end points and students' responses were contingent on the actual representations of interval end points. Students in all three grades demonstrated narrowed application of decimal values (e.g., merchandise), and their application of decimals was largely limited by their learning experiences.

Teachers' Reflections on Their Subject Matter Knowledge Structures and Their Influence on Classroom Practice

Abstract: Research has indicated that experts' subject matter knowledge structures (SMKSs) differ from those of novices in that they contain more cross-linking, interconnections, and overarching thematic elements, characteristics that are in accordance with those espoused in current reform documents. Unfortunately, teachers' SMKSs are not necessarily translated into classroom practice, for either novice or more experienced classroom teachers. A means to facilitate the translation of teachers' SMKSs into practice would ensure that those desired characteristics of experts' subject matter knowledge manifest themselves in teachers' classroom practice. Four experienced physics teachers diagrammed their SMKSs, which were then compared to those inferred from their classroom practice. Prior to instruction, two teachers, as part of the explicit-reflective treatment, were asked to reflect at multiple time points on congruence between their SMKSs and classroom practice focusing on the presence of essential concepts, interconnections, and overarching thematic elements. No discernible difference was apparent between control and treatment groups, as teachers from both groups showed a high-degree of congruence between inferred and diagrammed SMKSs. Results further substantiate the challenges in identifying a means for both developing and facilitating the enactment of coherent, connected, and dynamic SMKSs or, in effect, accelerating teachers' pedagogical content knowledge.

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

Abstract: 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.

Investigating Elementary Mathematics Curricula: Focus on Students With Learning Disabilities

Abstract: The purpose of this study was to investigate three elementary mathematics curricula to examine the accessibility for students with learning disabilities (LD) with regards to challenges associated with working memory. We chose to focus on students' experiences when finding the area of composite shapes due to the multiple steps involved for solving these problems and the potential for these problems to tax working memory. We conducted a qualitative analysis of how each curriculum provided opportunities for students with LD to engage with these problems. During our analysis, we focused on instruction that emphasized visual representations (e.g., manipulatives, drawings, and diagrams), facilitated mathematical conversations, and developed cognitive and metacognitive skills. Our findings indicated a need for practitioners to consider how each curriculum provides instruction for storage and organization of information as well as how each curriculum develops students' thinking processes and conceptual understanding of mathematics. We concluded that all three curricula provide potentially effective strategies for teaching students with LD to solve multi-step problems, such as area of composite shapes problems, but teachers using any of these curricula will likely need to supplement the curriculum to meet the needs of students with LD.

Making Connections: Elementary Teachers' Construction of Division Word Problems and Representations.

Abstract: If teachers make few connections among multiple representations of division, supporting students in using representations to develop operation sense demanded by national standards will not occur. Studies have investigated how prospective and practicing teachers use representations to develop knowledge of fraction division. However, few studies examined primary (K-3) teachers' learning of contextual division problems, making connections among representations of division, and resolving the ambiguity of representing quotients with remainders. A written post-course assessment provided evidence that most teachers created partitive division word problems, used a set model without splitting the remainder, and wrote equations with limited success. Post-course written reflections demonstrated that many teachers developed pedagogical knowledge for helping students make connections among multiple representations, and mathematical knowledge of unit fractions. These findings suggest two areas that have implications for mathematics teacher educators who design professional development courses to facilitate teachers' learning of mathematical content and pedagogical knowledge of division and fraction relationships.

Applying NAEP to Improve Mathematics Content and Methods Courses for Preservice Elementary and Middle School Teachers

Abstract: This study explored how mathematics content and methods courses for preservice elementary and middle school teachers could be improved through the integration of a set of instructional materials based on the National Assessment of Educational Progress (NAEP). A set of eight instructional modules was developed and tested. The study involved 7 university instructors and 542 preservice teachers (PSTs) from three different universities. A quasi-experimental nonequivalent groups design was used for this study in which the following data sources were collected and analyzed. Three versions of a Learning Mathematics for Teaching test were given to assess PSTs‘ mathematical content knowledge for teaching: (a) Elementary Number Concepts and Operations—Content Knowledge; (b) Elementary Geometry—Content Knowledge; and (c) Middle School Number Concepts and Operations—Content Knowledge. In addition, the Mathematics Teacher Efficacy Beliefs Instrument was given to assess PSTs’ teacher efficacy beliefs. Test results were analyzed using paired samples t-tests. Findings suggest that use of instructional materials, based on NAEP, with PSTs results in increases in their mathematical content knowledge for teaching and in their teaching efficacy beliefs.

Using Productive Disposition to Differentiate Between Students' Level of Precision When Critiquing a Peer's Work

Abstract: This study examined the productive disposition of pre-algebra students who demonstrated similar knowledge of the focal content but varied in other academic behaviors expected in the Common Core State Standards for Mathematics (CCSSM). Specifically, the study considered students' attention to precision when critiquing a peer's work. The comprehensive definition of productive disposition used included task values (interest, utility), an ability belief (efficacy), three personal achievement goals, and negative emotions. As hypothesized, the 61 students who provided a more precise critique reported higher productive disposition (in particular, significantly higher mastery-approach personal achievement goals and less frequent negative emotions) than the 79 students who provided a basic critique. These findings illustrate how productive disposition can inform assessments of mathematical competence within the CCSSM recently implemented across the United States.

Classroom Response Systems: Effects on the Critical Analysis Skills of Students in Introductory Science Courses

Abstract: College instructors often teach scientific thinking by asking students to review and analyze a primary research article. The main purpose of this study was to explore how classroom response systems (CRS) could help impact the quality of written analysis papers submitted for this assignment by students taking 100-level biology courses at a medium-sized suburban, two-year college in the northeastern United States. Students in all participating course sections received written instructions on five key elements of critical analysis (CA) to include in scientific study analysis papers. Classroom instruction on recognizing these key elements in primary research papers was provided either via CRS or via an instructor-facilitated classroom discussion enhanced by the same PowerPoint presentation. A rubric, designed specifically for this assignment, was validated prior to its use in this study. Fifty students participated in the study, and those who received the CRS intervention achieved significantly higher CA scores for identifying implications of study findings, while the group that received only written instructions achieved significantly higher CA scores for discussing the credibility of the references used by the authors in planning the critiqued study. The implications of this study are discussed along with ideas for future research.

What Students Say About Their Mathematical Thinking When They Listen

Abstract: Mathematical listening is an important aspect of mathematical communication Yet there are relatively few examinations of this phenomenon Further, existing studies of students' mathematical listening come from observational data, lacking the student perspective This study examined student replies to an open-response question regarding what happens to their thinking about mathematics when they listen to their peers' mathematical talk Results suggest varying ways of listening that range from more passive to more active forms While relationships were observed between ways of listening and perceived forms of engaging in mathematical discussion, no relationship was observed with the frequency with which students reported participating in discussions

Metaphor Clusters: Characterizing Instructor Metaphorical Reasoning on Limit Concepts in College Calculus

Abstract: Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student metaphorical reasoning, we examined 11 college instructors' metaphorical reasoning on limit concepts. This paper focused on previous research of metaphor clusters observed among students to answer the following: (a) Do college instructors use metaphorical reasoning to conceptualize the meaning of a limit? (b) Can we characterize instructor metaphorical reasoning similar to those observed among students? (c) Will an instructor's self-identification of metaphor clusters be consistent with our metaphor coding? We found that college instructors' perspectives vary, either graphical or algebraic, in their explanations of limit items. All the instructors used metaphors, and instructor metaphorical reasoning aligned with student metaphor clusters. Instructors tended to change their metaphors with respect to the limit item. Instructors were not aware of their use of metaphors, nor were they aware of their inconsistency in their choice of metaphor. We believe that instructor awareness of their own distinct perspectives and metaphors would assist students' understanding of limit concepts.