The effectiveness of teaching science with pictorial analogies

This study used a conceptual problem solving test to investigate the effect of a series of pictorial analogies on the concepts of density, pressure, and atmospheric pressure in Year 8 classrooms. The analogies were taught following Glynn's teaching with analogies model. It was found that the students taught with the pictorial analogies scored significantly higher than their counterparts (p<01). In addition, the low achievers benefited more from this teaching strategy than did the high achievers. Further, qualitative analysis revealed that most of the students' alternative conceptions were from preexisting naive intuitions rather than arising from analog instruction.     

Students' Early Mathematical Representation Knowledge: The Effects of Emphasizing Single or Multiple Perspectives of the Rational Number Domain in Problem Solving

This study examined changes in 26 fourth-grade students' early conceptions of rational number representations as a function of receiving one of two curricular interventions. The first group of 12 students received a curriculum that emphasized constructing knowledge through extended problem solving with a single perspective of the rational number domain based on part-whole relations. A second group of 14 students received a curriculum that emphasized a more conceptually diverse multiple perspective view of the domain through problem solving with operator and ratio relations. Analyses of the students' rational number knowledge before and after the interventions indicated that students in the single perspective group produced organizations of knowledge that more frequently diverged from a formal domain analysis than those produced by students in the multiple perspective group. Further, students in the single perspective group increased their focus on superficial surface features. Alternatively, students in the multiple perspective group demonstrated an increased focus on operations that more frequently reflected the underlying mathematical relation conveyed by the representation. The findings indicate that an early exposure to more diverse perspectives of rational numbers assists students in developing more interconnected and viable representation knowledge for rational numbers.     

RESEARCH SECTION: Why do students think they fail? The relationship between attributions and academic self‐perceptions

Attributions can have a significant effect on academic achievement and students with learning difficulties are more likely to display negative attributions than their peers. In this article, the attributions of students identified as having learning difficulties are compared with those of other non-labelled low achievers, and non-labelled average achievers. Margaret Banks, MSc research methods student, and Dr Lisa Woolfson, Reader in Educational Psychology, both at the University of Strathclyde, involved 26 low-achieving students (15 identified as having learning difficulties and 11 without any such label) and 27 averagely achieving students in their exploratory study. The students attempted to solve two sets of puzzles that, unknown to the participants, were actually impossible. They then gave a reason for their failure and rated the stability and controllability of their failure. Participants were also asked to give a self-rating of academic achievement. It was found that teacher and student perceptions of academic achievement were not synonymous. In terms of attributions, Margaret Banks and Lisa Woolfson argue that teachers' perceptions of student achievement may not be as important as students' self concept. They suggest that low self-perception of achievement and negative attributions are both associates of low self-esteem.     

Alternative Assessment Portfolios for Students with Intellectual Disabilities: A Case Study

Abstract

Twenty‐eight classroom teachers identified students in their rooms who were low achievers, at‐risk learners; low achievers, not at risk; average achievers; and special education students. We videotaped these students during reading lessons conducted by their teachers. Using a stimulated recall procedure, we interviewed teachers and asked them to report their thought processes during instruction, especially those that pertained to the target children. We found that teachers reported significantly more negative thoughts about at‐risk learners' than about average achievers' attending behavior and ability‐performance. Furthermore, at‐risk learners received a greater number of comments focused on the need to monitor their performance. Special education students received significantly more positive and negative comments about attending than did average achievers. In addition, they received more miscellaneous positive comments than did low, not at‐risk, and average achievers. Finally, teachers reported making more classroom modifications for this group than for average students. Implications for prereferral classroom interventions are discussed.     

A cross-sectional study of mathematics achievement, estimation skills, and academic self-perception in students of varying ability

This study investigated students' mathematics achievement, estimation ability, use of estimation strategies, and academic self-perception. Students with learning disabilities (LD), average achievers, and intellectually gifted students (N = 135) in fourth, sixth, and eighth grade participated in the study. They were assessed to determine their mathematics achievement, ability to estimate discrete quantities, knowledge and use of estimation strategies, and perception of academic competence. The results indicated that the students with LD performed significantly lower than their peers on the math achievement measures, as expected, but viewed themselves to be as academically competent as the average achievers did. Students with LD and average achievers scored significantly lower than gifted students on all estimation measures, but they differed significantly from one another only on the estimation strategy use measure. Interestingly, even gifted students did not seem to have a well-developed understanding of estimation and, like the other students, did poorly on the first estimation measure. The accuracy of their estimates seemed to improve, however, when students were asked open-ended questions about the strategies they used to arrive at their estimates. Although students with LD did not differ from average achievers in their estimation accuracy, they used significantly fewer effective estimation strategies. Implications for instruction are discussed.     

Students’ experiences of studying physics concepts: The effects of disintegrated perceptions and approaches

Recent research on student learning has revealed that a number of students in any learning context are unable to distinguish between contrasting contextualised approaches to learning. In other words, the relationship between their perceptions of the learning context and their approaches to learning disintegrates and becomes incoherent. These students are observed to be among the lower academic achievers in their group. This paper reports on the results of a study which shows that physics students’ prior understandings of key concepts are systematically related to the way they approach their studies, their perceptions of the learning context and the quality of the outcomes of their studies. As with previous studies, one group reported disintegrated learning experiences. As a group they were found to have the poorest pre-conceptual knowledge, to have the poorest postconceptual knowledge, and to be the lowest achievers. These results are consistent with the earlier studies, but extend them by showing that disintegrated perceptions and approaches are related to students’ understanding before and after the subject as determined using qualitative indicators of understanding as well as assessment results.     

Positive mood and math performance

Two studies are reported that assessed the impact of positive moods on students' feelings of self-efficacy and math performance. In the first study, 32 black and Hispanic girls and boys in the third to fifth grades, who had been identified by teachers as at risk for school failure, and a control sample of normally achieving classmates served as subjects. In the second study, 15 males and 3 females in junior high and high school attending a private school for students with learning disabilities served as subjects. In both studies, students were randomly assigned to a positive-mood induction condition or a no-treatment control condition. Following this, they completed a measure of self-efficacy for math and were then given 5 minutes to do 50 math problems. In both studies, analyses of covariance using standardized math scores as the adjustor variable found that children in the positive-mood condition completed significantly more problems accurately than children in the no-treatment control condition. In addition, in the junior high and high school sample, students in the positive-mood induction condition expressed greater self-efficacy for math than students in the control condition. The results of these two studies raise many questions about the role of affect, positive and negative, in the learning and performance of students with learning disabilities that researchers and teachers might explore.     

Historical Objections Against the Number Line

Historical studies on the development of mathematical concepts will help mathematics teachers to relate their students’ difficulties in understanding to conceptual problems in the history of mathematics. We argue that one popular tool for teaching about numbers, the number line, may not be fit for early teaching of operations involving negative numbers. Our arguments are drawn from the many discussions on negative numbers during the seventeenth and eighteenth centuries from philosophers and mathematicians such as Arnauld, Leibniz, Wallis, Euler and d’Alembert. Not only does division by negative numbers pose problems for the number line, but even the very idea of quantities smaller than nothing has been challenged. Drawing lessons from the history of mathematics, we argue for the introduction of negative numbers in education within the context of symbolic operations.     

A Study of Ability Grouping and the Self-Concept

Abstract

This study Investigated the relationships between acceptance of self, academic self-concept and two procedures used to group seventh-grade students for Instruction. The two facets of the self-concept were indexed for 323 heterogeneously grouped students and 244 homogeneously grouped students. Chi-square tests were applied to study the data by total groups, sex and achievement levels. Regardless of grouping procedures used, high achievers reported significantly more positive academic self-concepts (.01), while these concepts for low achievers were significantly less positive (.01). No other significant differences were found. It was concluded that grouping procedures do not significantly effect either facet of the self-concept, but success In school significantly influences the academic self-concept regardless of the grouping procedure used.     

Irrational Numbers: The Gap between Formal and Intuitive Knowledge

This report focuses on prospective secondary mathematics teachers’ understanding of irrational numbers. Various dimensions of participants’ knowledge regarding the relation between the two sets, rational and irrational, are examined. Three issues are addressed: richness and density of numbers, the fitting of rational and irrational numbers on the real number line, and operations amongst the elements of the two sets. The results indicate that there are inconsistencies between participants’ intuitions and their formal and algorithmic knowledge. Explanations used by the vast majority of participants relied primarily on considering the infinite non-repeating decimal representations of irrationals, which provided a limited access to issues mentioned above.     

谈新世纪版教材对"有理数及其运算"引入的处理

学生初次接触到负数的概念时 ,对理解负数的意义及有理数的运算法则都会产生困难。北师大新世纪版实验教材对解决这些问题的设计思路有这样几个特点 :借助问题情境、从数不够用了的角度引出“负数” ;渗透正负数是“具有相反意义的量”的数学模型的思想 ;从不同的角度表示正负数 ;经过三个层次、借助不同的素材得出正负整数的加法运算法则 ;在应用中体会有理数的作用、熟练有理数的运算 ,以及降低笔算的难度等。这将有助于帮助学生在理解的基础上掌握相关的内容。     

Concept substitution: An instructional strategy for promoting conceptual change

Numerous studies have shown that students often hold conceptions that conflict with accepted scientific ideas, both prior to and after instruction. The failure of instruction to affect students' conceptions can be interpreted as a failure to facilitate conceptual change. In this paper, an instructional strategy will be described that facilitates conceptual change in the special case where conceptual difficulties appear to arise because students confuse related physics concepts. The strategy involves two parts. Firstly, students observe an experiment or demonstration that conflicts with what they expect to see. Secondly, the instructor identifies students' intuitions that are correct but that they have associated with an incorrect physics term, and substitutes the correct physics term. Students can thus develop more scientifically acceptable understandings of physics concepts without having to give up their intuitive ideas. The use of this strategy will be illustrated in two domains of physics. Specializations: physics education, conceptual development, instructional design, improvement of tertiary science education.     

建构主义理论运用于科学教学的15条原则

随着建构主义理论在科学教育领域中的运用与逐渐流行,一种基于建构主义的新的科学教学模式正在兴起。这种教学模式要求在科学教学中,应把科学知识的学习看作是学生主动建构知识的过程;应把科学探究作为学生建构科学知识的最重要的学习方式;应充分发挥学生在学习中的自主性,视学生为科学知识的主动建构者;承认学生的原有知识经验在学习中的重要性,了解并正确处理学生的前概念;运用概念转变策略,帮助学生实现概念转变;引发学生的认知冲突,激起学生科学探究的欲望;发挥教师的指导作用,为学生的知识建构提供支持条件;提供真实的情境,让学生获得经验,在情境中建构知识的理解;鼓励学生发问,提出开放性问题,让学生在问题解决中建构知识;开展多种形式的对话,在对话中建构知识;鼓励学生合作与交流,为知识的社会建构提供机会;鼓励学生反省,学会自主监控学习过程;重视学习方法指导,为学生知识建构提供认知工具与策略;提供学习资源,让学生参与寻找用于解决问题的信息;采用形成性评价,强调学生在学习过程中的表现。     

Differences between Flemish and Chinese primary students’ mastery of basic arithmetic operations

The present paper investigates differences in the process of mastering the four basic arithmetic operations (addition, subtraction, multiplication and division) between Flemish and Chinese children from Grade 3 till Grade 6 (i.e. from 8 to 11 years old). The results showed, firstly, that Chinese students outperformed Flemish students in each grade but that difference in addition, subtraction and division skills between the groups decreased as grade increased. Secondly, the levels of mastery of the four skills varied between Chinese and Flemish students. Multiplication was relatively easier for Chinese students than for their Flemish peers as compared to the other skills (that is, the gap was larger). Third, low achievers experienced comparable learning difficulties in both countries, and higher achievers demonstrated their greater ability early on.     

Competition in individualized CAI

Designers of computer-based practice systems give primary attention to aspects of cognitive learning. However, observations of students practicing arithmetic, with two CAI systems widely used in Israel, revealed factors in the computer learning environment that substantially affected students' social behavior, particularly with respect to competition and cooperation in the course of learning. A questionnaire was designed on the basis of the observations to examine the effects of these factors in CAI work. It was administered to 457 fourth graders in 16 classes (two CAI systems x two SES categories x two schools x two classes). While neither CAI system was intended to foster competition, the observations and questionnaire data suggested that one encourages social comparison and competition whereas the other discourages these features and encourages cooperation and peer help. Boys appear to be significantly more competitive than girls. One system, compared with the other, significantly increases competitive behavior of high achievers (but not of low achievers); results in teachers' greater encouragement of social comparison and competition among students; and, as used in the schools we studied, causes disadvantaged students rather than advantaged students to develop negative feelings because of low CAI performance. The other system discourages competitive behavior and encourages cooperation. All these findings bear important implications for the instructional design of computer-based learning environments.     

Heat energy and temperature concepts of adolescents,adults, and experts: Implications for curricular improvements

We conducted two studies of beliefs about laboratory and everyday thermal phenomena. The first study identified concepts of heat energy and temperature held by adolescents, adults, and scientists. We found a classic separation of “school” and “everyday” knowledge in each population. We conducted clinical interviews with 37 middle school students, 9 adults, and 8 chemists and physicists to obtain their predictions and explanations of real-world phenomena. Many students believed that metals “conduct,” “absorb,” “trap,” or “hold” cold better than other materials and that aluminum foil would be better than wool or cotton as a wrapping material to keep cold objects cold. Respondents in each group held many intuitive ideas that were well established. Although scientists made more accurate predictions than students and gave theoretical definitions of terms, they too had difficulty explaining everyday phenomena. The second study investigated the impact of a middle school science curriculum designed to help students understand everyday thermal events. We found marked improvements in posttest scores and clinical interview responses as a result of instruction that built on students' intuitions.     

Strategic counting: A novel assessment of place-value understanding

Children's counting strategies reflect how much they understand the place-value structure of numbers. In Study 1, a novel task, namely the strategic counting task, elicited strategies from kindergarteners and first graders that showed a trend of increasing place-value knowledge – from perceiving number as an undivided entity to seeing it as a collection of independent groups of powers of ten. In Study 2, first-graders' strategic counting task scores at the end of fall semester were better predictors of year-end mathematical achievement than the traditional place-value tasks. In Study 3, a five-item subset of strategic counting was the best among 15 various cognitive predictors of end of second-grade mathematical achievement. Growth curve modeling revealed that low-mathematics achievers at the end of second grade had been lagging behind their peers in strategic counting since early first grade. Implications for early support for children with difficulties in place-value knowledge are discussed.     

Thinking Strategies: Its Effectiveness in the Teaching of Multiplication Facts to Low Achievers of Mathematics

Many students have found the learning of multiplication a difficult task. Without mastering multiplication facts, a student will always resort to fundamental strategies which may be undesirable in problem-solving. Many teachers and educators agree that learning basic facts in the four operations are the fundamental steps that precede learning harder facts. Referring to the aspect of computational errors, Knifong and Holton (1975) indicated that computational errors accounted for 49% of the total errors made by 35 students who sat for the Metropolitan. Achievement Test. Suydam (1975) and NCTM (1977) stressed the importance of basic facts even though calculators and lately computers have been introduced into the school curriculum. The purpose of this study was to investigate the methodology of teaching basic facts which would alleviate the problems of teaching these facts to low achievers of Mathematics. A review of studies on thinking strategies shows that very few were carried out in learning the thinking strategies, particularly in multiplication using low achievers as the target. The success of using thinking strategies to teach multiplication number facts to most students does not imply its success in teaching all students. One of the intentions of this study is to investigate what strategies are useful in helping the low achievers in learning mathematics.     

Understanding Students’ Reasoning: Argumentation Schemes as an Interpretation Method in Science Education

The purpose of this paper is to investigate the argumentative structure of students’ arguments using argumentation schemes as an instrument for reconstructing the missing premises underlying their reasoning. Building on the recent literature in science education, in order for an explanation to be persuasive and achieve a conceptual change it needs to proceed from the interlocutor’s background knowledge to the analysis of the unknown or wrongly interpreted phenomena. Argumentation schemes represent the abstract forms of the most used and common forms of human reasoning, combining logical principles with semantic concepts. By identifying the argument structure it is possible to retrieve the missing premises and the crucial concepts and definition on which the conclusion is based. This method of analysis will be shown to provide the teacher with an instrument to improve his or her explanations by taking into consideration the students’ intuitions and deep background knowledge on a specific issue. In this fashion the teacher can advance counterarguments or propose new perspectives on the subject matter in order to persuade the students to accept new scientific concepts.