Conceptual Understanding of Causal Reasoning in Physics

College students often experience difficulties in solving physics problems. These difficulties largely result from a lack of conceptual understanding of the topic. The processes of conceptual learning reflect the nature of the causal reasoning process. Two major causal reasoning methods are the covariational and the mechanism‐based approaches. This study was to investigate the effects of different causal reasoning methods on facilitating students’ conceptual understanding of physics. 125 college students from an introduction physics class were assigned into covariational group, mechanism‐based group, and control group. The results show that the mechanism‐based group significantly outperformed the other two groups in solving conceptual problems. However, no significant difference was found in all three groups performance on solving computational problems. Speculation on the inconsistent performance of the mechanism‐based group in conceptual and computational problem solving is given. Detailed analyses of the results, findings, and educational implications are discussed     

Optimizing Early Mathematics Experiences for Children from Low-Income Families: A Study on Opportunity to Learn Mathematics

Both the National Council of Teachers of Mathematics and the National Association for the Education of Young Children recognize that well-designed opportunity to learn mathematics can help improve mathematics achievement of students from low-income families and from minority backgrounds. Using data from a nationally representative sample, the Early Childhood Longitudinal Study-Kindergarten cohort, this study empirically examined a subset of children from low-income families to determine whether African American and Caucasian students have differential opportunity to learn mathematics and the extent to which opportunities to learn predict gains in mathematics achievement at kindergarten. Results indicated African American kindergartners have differential opportunity to learn mathematics than their Caucasian peers from low-income families. African American students were found to have received, on average, more reported instructional time spent on mathematics, higher use of math manipulatives, worksheets, textbooks and chalkboard work than their Caucasian peers. Moreover, greater opportunity to learn mathematics predicted higher mathematics achievement for both African American and Caucasian students from low-income families, specifically, opportunity to learn skills such as telling time, using measurement tools accurately, estimating quantities, and knowing the value of coins and cash.     

Epistemic Beliefs and Conceptual Understanding in Biotechnology: A Case Study

The purpose of this investigation was to explore students’ epistemic beliefs and conceptual understanding of biotechnology. Epistemic beliefs can influence reasoning, how individuals evaluate information, and informed decision making abilities. These skills are important for an informed citizenry that will participate in debates regarding areas in science such as biotechnology. We report on an in-depth case study analysis of three undergraduate, non-science majors in a biotechnology course designed for non-biochemistry majors. We selected participants who performed above average and below average on the first in-class exam. Data from multiple sources—interviews, exams, and a concept instrument—were used to construct (a) individual profiles and (b) a cross-case analysis of our participants’ conceptual development and epistemic beliefs from two different theoretical perspectives—Women’s Ways of Knowing and the Reflective Judgment Model. Two independent trained researchers coded all case records independently for both theoretical perspectives, with resultant initial Cohen’s kappa values above .715 (substantial agreement), and then reached consensus on the codes. Results indicate that a student with more sophisticated epistemology demonstrated greater conceptual understandings at the end of the course than a student with less sophisticated epistemology, even though the latter performed higher initially. Also a student with a less sophisticated epistemology and low initial conceptual performance does not demonstrate gains in their overall conceptual understanding. Results suggest the need for instructional interventions fostering epistemological development of learners in order to facilitate their conceptual growth.     

Addressing Challenges to Public Understanding of Science: Epistemic Cognition,Motivated Reasoning,and Conceptual Change

Science is of critical importance to daily life in a knowledge society and has a significant influence on many everyday decisions. As scientific problems increase in their number and complexity, so do the challenges facing the public in understanding these issues. Our objective is to focus on 3 of those challenges: the challenge of reasoning about knowledge and the processes of knowing, the challenge of overcoming biases in that reasoning, and the challenge of overcoming misconceptions. We propose that research in epistemic cognition, motivated reasoning, and conceptual change can help to identify, understand, and address these obstacles for public understanding of science. We explain the contributions of each of these areas in providing insights into the public's understandings and misunderstandings about knowledge, the nature of science, and the content of science. We close with educational recommendations for promoting scientific literacy.     

A Study of the Performance of 5th Graders in Number Sense and its Relationship to Achievement in Mathematics

In order to investigate the performance of number sense and its relationships with mathematics achievement of Taiwanese students who had just completed the 5th-grade mathematics curriculum, a computerized number sense scale has been developed. This number sense scale includes four factors which are recognizing relative number size, using multiple representations of numbers and operations, judging the reasonableness of estimates of computed results and recognizing the relative effect of operations on numbers. A total of 1,212 students in Taiwan participated in this study. The main findings of this study are summarized as follows. First, the students perform best on “recognizing relative number size” and perform worst on “judging the reasonableness of estimates of computed results”. This finding is consistent with previous studies. It shows that students in Taiwan seem quite poor on judging the reasonableness of estimates of computed results. Second, female students, on average, have higher scores on recognizing the relative number size than male students, even though only a small effect size is found. And, third, the achievements of the students in mathematics are significantly correlated with their number sense, as measured by the average grade for the academic year of 5th-grade students.     

A Review of the Literature: Fraction Instruction for Struggling Learners in Mathematics

Fractions are an essential foundational skill for future mathematics success (NMAP, 2008). The purpose of this article was to review current instructional practices for teaching fractions to struggling learners and to examine the quality and effectiveness of contemporary research with a view to indicating directions for future research. A comprehensive search of literature published between 1990 and 2008 resulted in the identification of 10 empirical studies that targeted fraction skills for struggling learners. Results indicated that three interventions, found to be effective for improving outcomes in mathematics for struggling learners, were also effective for teaching fractions: graduated sequence, strategy instruction, and direct instruction. In addition, explicit instruction was identified as necessary for improving students’ performance in fractions. Overall, this review highlighted the paucity of research in this critical mathematical content area.     

A Conceptual Framework for Learning to Teach Secondary Mathematics: A Situative Perspective

This paper offers for discussion and critique a conceptual framework that applies a situative perspective on learning to the study of learning to teach mathematics. From this perspective, such learning occurs in many different situations -- mathematics and teacher preparation courses, pre-service field experiences, and schools of employment. By participating over time in these varied contexts, mathematics teachers refine their conceptions about their craft -- the big ideas of mathematics, mathematics-specific pedagogy, and sense of self as a mathematics teacher. This framework guides a research project that traces the learning trajectories of teachers from two reform-based teacher preparation programs into their early teaching careers. We provide two examples from this research to illustrate how this framework has helped us understand the process of learning to teach. This revised version was published online in July 2006 with corrections to the Cover Date.     

Enhancing Students' Understanding of Mathematics: A Study of Three Contrasting Approaches to Professional Support

This report provides evidence of the influence of professional development and curriculum on upper elementary students' understandings of fractions. Three groups of teachers and their students participated. Two groups implemented a fractions unit that emphasized problem solving and conceptual understanding. The Integrated Mathematics Assessment (IMA) group participated in a program designed to enhance teachers' understandings of fractions, students' thinking, and students' motivation. The Collegial Support (SUPP) group met regularly to discuss strategies for implementing the curriculum. Teachers in the third group (TRAD) valued and used textbooks and received no professional development support. Contrasts of student adjusted posttest scores revealed group differences on two scales. On the conceptual scale, IMA classrooms achieved greater adjusted posttest scores than the other two groups, with no differences between SUPP and TRAD groups. On the computation scale, contrasts revealed no differences between IMA and TRAD, although TRAD achieved greater adjusted scores than SUPP (p < 0.10). Our findings indicate that the benefits of reform curriculum for students may depend upon integrated professional development, one form exemplified by the IMA program. This revised version was published online in August 2006 with corrections to the Cover Date.     

Taking Up Opportunities to Learn: Constructing Dispositions in Mathematics Classrooms

This article presents an analysis of how students' dispositions toward learning shift and change over time through their engagement with particular classroom practices and identifies classroom practices that support the development of more productive dispositions. An analysis of 4 purposefully selected students from 2 different classrooms reveals that membership in a classroom activity system does not determine one's emergent disposition toward learning. However, it is likely that similar types of dispositions might emerge within a single classroom activity system. The analysis further seeks to understand the mechanisms that underlie the ways in which dispositions are enacted in moments of interaction, and how aspects of classroom practice impact this enactment. The findings support the argument that social, affective, and motivational factors are not simply influences on learning but are, instead, central to and inseparable from the learning process.     

Teaching for Conceptual Change in a Density Unit Provided to Seventh Graders: A Comparison of Teacher- and Student-Centered Approaches

Research in Science Education - This mixed-methods study was designed to compare the learning gains of seventh-grade students (N?=?417) taught a 4-week conceptual change unit on density...     

Working in the Mathematics Frame: Maximizing the Potential to Learn From Students' Mathematics Classroom Discussions

The quality of students' mathematics classroom discussions is an important factor in determining mathematics classroom learning outcomes. Good mathematics classroom discussions provide an opportunity for ideas to be shared and developed, but not all mathematics classroom discussions produce these learning opportunities. In this paper I discuss three constructs (subject, purpose, and frame) and how they can be used to analyze and characterize the quality of students' mathematics classroom discussions in terms of the mathematics learning potential that those discussions provide. This revised version was published online in July 2006 with corrections to the Cover Date.     

学会学习、学会研究、学会创新——对本科生、硕士生、博士生素质教育的思考

针对社会发展对不同层次人才的不同素质需求,指出我国高等院校在开展素质教育时应不同层次区别对待.提出本科生应重点学会学习、硕士生应重点学会研究、博士生应重点学会创新的素质教育培养目标,同时就如何实现相应的素质教育培养目标提出建议.     

“悟是光”概念结构的认知分析

＂悟＂概念是一类比较常用的语汇。以汉语和英语为语料,剖析＂悟＂概念生发于＂光＂概念的认知根源,进而对＂悟是光＂概念结构生成过程中人类的隐喻化和范畴化发展机制进行了详细说明,旨在依托认知规律,对概念的隐喻化取象和范畴化拓展路径提供进一步的实践操作性借鉴。     

激发中职学生数学学习兴趣的几点做法

数学是一门逻辑性强、十分抽象的基础学科,常常让学生感觉枯燥无味,从而影响学习积极性和主动性.中等职业学校数学教师要因势利导,唤醒学生对数学学习的兴趣,树立学好数学的信心.     

新数学教学模式:从“学会”到“会学”

本文针对五年制高职学生的特点．结合自己的数学教学实践．就如何为学生架起从“学会”到“会学”的桥梁．谈一些个人的体会。     

Interconnecting Content and Community: A Qualitative Study of Secondary Mathematics Teachers

The publication of the National Council ofTeachers of Mathematics initial Standards(1989) has acted as a catalyst to beginreforming the way mathematics is taught in theUSA. However, the literature regarding reformmovements suggests that changing oureducational systems requires overcoming manybarriers and is thus difficult to achieve.Reform in mathematics education, like reformmovements in other areas of education, has thusbeen slow to take hold. One structure that hasbeen shown to support educational reform,particularly instructional reform, has beenteacher community. This paper discusses aprofessional development intervention thatattempted to start a professional communityamong a group of secondary mathematics teachersthrough in-service work on mathematical problemsolving and technology. The results of thisstudy suggest that the use of mathematicalcontent explorations in professionaldevelopment settings provides a means to helpmathematics teachers build professionalcommunities. Together, these two components –mathematical content explorations and teachercommunity – provided these secondarymathematics teachers with a strong foundationfor engaging in the reform of their mathematicsclasses.     

A Conceptual Analysis of Perspective Taking in Support of Socioscientific Reasoning

Science & Education - Perspective taking is a critical yet tangled construct that is used to describe a range of psychological processes and that is applied interchangeably with related...