SECONDARY SCHOOL STUDENTS’ UNDERSTANDING OF MATHEMATICAL INDUCTION: STRUCTURAL CHARACTERISTICS AND THE PROCESS OF PROOF CONSTRUCTION

In this study, we investigate the meaning students attribute to the structure of mathematical induction (MI) and the process of proof construction using mathematical induction in the context of a geometric recursion problem. Two hundred and thirteen 17-year-old students of an upper secondary school in Greece participated in the study. Students’ responses in 3 written tasks and the interviews with 18 of them are analyzed. Though MI is treated operationally in school, the students, when challenged, started to recognize the structural characteristics of MI. In the case of proof construction, we identified 2 types of transition from argumentation to proof, interwoven in the structure of the geometrical pattern. In the first type, MI was applied to the algebraic statement that derived from the direct translation of the geometrical situation. In the second type, MI was embedded functionally in the geometrical structure of the pattern.     

IMPACT OF A REPRESENTATIONAL APPROACH ON STUDENTS’ REASONING AND CONCEPTUAL UNDERSTANDING IN LEARNING MECHANICS

The aim of this study was to explore whether a representational approach could impact on the scores that measure students’ understanding of mechanics and their ability to reason. The sample consisted of 24 students who were undergraduate, preservice physics teachers in the State University of Malang, Indonesia. The students were asked to represent a claim, provide evidence for it, and then, after further representational manipulations, refinement, discussion, and critical thought, to reflect on and confirm or modify their original case. Data analysis was based on the pretest–posttest scores and students’ responses to relevant phenomena during the course. The results showed that students’ reasoning ability significantly improved with a d-effect size of 2.58 for the technical aspects and 2.51 for the conceptual validity aspects, with the average normalized gain being 0.62 (upper–medium) for the two aspects. Students’ conceptual understanding of mechanics significantly improved with a d-effect size of about 2.50 and an average normalized gain of 0.63. Students’ competence in mechanics shifted significantly from an under competent level to mastery level. This paper addresses statistically previously untested issues in learning mechanics through a representational approach and does this in a culture that is quite different from what has been researched so far using student-generated representational learning as a reasoning tool for understanding and reasoning.     

USING COMBINATORIAL APPROACH TO IMPROVE STUDENTS’ LEARNING OF THE DISTRIBUTIVE LAW AND MULTIPLICATIVE IDENTITIES

This article reports an alternative approach, called the combinatorial model, to learning multiplicative identities, and investigates the effects of implementing results for this alternative approach. Based on realistic mathematics education theory, the new instructional materials or modules of the new approach were developed by the authors. From the combinatorial activities based on the things around daily life, the teaching modules assisted students to establish their concept of the distributive law, and to generalize it via the process of progressive mathematizing. The subjects were two classes of 8th graders. The experimental group (n = 32) received a combinatorial approach to teaching by the first author using a problem-centered with double-cycles instructional model, while the control group (n = 30) received a geometric approach to teaching, from the textbook by another teacher who uses lecturing. Data analyses were both qualitative and quantitative. The findings indicated that the experimental group had a better performance than the control group in cognition, such as for the inner-school achievement test, mid-term examination, symbol manipulation, and unfamiliar problem-solving: also in affection, such as the tendency to engage in the mathematics activities and enjoy mathematical thinking.     

IMPACT OF INTERACTIVE MULTIMEDIA MODULE WITH PEDAGOGICAL AGENTS ON STUDENTS’ UNDERSTANDING AND MOTIVATION IN THE LEARNING OF ELECTROCHEMISTRY

The Electrochemistry topic is found to be difficult to learn due to its abstract concepts involving macroscopic, microscopic, and symbolic representation levels. Studies have shown that animation and simulation using information and communication technology (ICT) can help students to visualize and hence enhance their understanding in learning abstract chemistry topics. As a result, an interactive multimedia module with the pedagogical agent (IMMPA) named the EC Lab (Electrochemistry Lab) was developed in order to assist students in the learning of Electrochemistry topics. A non-equivalent pretest–posttest control group design investigation was carried out in order to gauge the effect of the IMMPA EC Lab on students’ understanding and motivation in the learning of Electrochemistry. Some 127 Form Four students from two secondary schools in one of the districts in Malaysia were involved in the study. Each school had one treatment group and one control group taught by the same Chemistry teacher. Instruments involved were a pre- and posttest, a pre- and post-motivation questionnaire, and the IMMPA EC Lab. Results showed a significant difference between the control groups and treatment groups in the understanding of concepts in the learning of Electrochemistry.     

THE ROLE OF TEACHER CHARACTERISTICS AND PRACTICES ON UPPER SECONDARY SCHOOL STUDENTS�� MATHEMATICS SELF-EFFICACY IN NYANZA PROVINCE OF KENYA: A MULTILEVEL ANALYSIS

The study identified two dimensions of teacher self-efficacy and practices and five dimensions of students’ mathematics self-efficacy and sought to determine the extent to which teacher characteristics and practices can enhance secondary school students’ self-efficacy. Data were collected from 13,173 students in 193 teachers’ classrooms from 141 schools in the 10 districts of Lake Victoria Region of Kenya. Two-level hierarchical linear model revealed that teachers’ frequent use of mathematics homework, their level of interest and enjoyment of mathematics, as well as their ability and competence in teaching mathematics were found to play a key role in promoting students’ mathematics self-efficacy. Teachers’ ability and competence in teaching were also found to be effective in narrowing the gender gap in students’ self-confidence and competence in mathematics. The study recommends that teacher training colleges emphasize such teacher practices and values in order to enhance students’ mathematics self-efficacy, reduce their level of anxiety and fear of mathematics, and consequently, enhance their achievement in mathematics. Professional development opportunities should also be made available to in-service teachers to continually update their knowledge and skills and develop new strategies for teacher effectiveness.     

A NORWEGIAN OUT-OF-SCHOOL MATHEMATICS PROJECT’S INFLUENCE ON SECONDARY STUDENTS’ STEM MOTIVATION

Considerable resources are spent on initiatives aiming to increase achievement and participation in science, technology, engineering, and mathematics (STEM). Drawing on focus group interviews and a questionnaire study with participants in ENT3R, a Norwegian out-of-school mathematics program, we investigated why participants attended and stayed in this program and assessed how it influenced participants’ STEM motivation. The authors identified 3 aspects of ENT3R highlighted by the participants: The instructors provided good teaching, the instructors created a positive atmosphere, and the instructors engaged in interpersonal relationships. Moreover, drawing on the expectancy-value model, the authors found that ENT3R appeared to influence 5 factors in the model that are important for STEM motivation: expectation of success, interest–enjoyment value, attainment value, utility value, and cost. This study points to the importance of carefully recruited and trained instructors and of flexible, responsively designed extracurricular programs.     

CULTIVATON OF STUDENTS''''INTEREST AND MOTIVATION IN THE ENGLISH LANGUAGE LEARNING

Many middle school students like to ask how they can learn English well. This is really a difficult question to answer, Some teachers may frankly tell their students:Memorize new words and phrases, spend much time in reading and soon you will have a good command of English. As a matter of fact,the case is not like this. The English language has a large vocabulary of more than 400,000 words not including phrases. How can a student's brain take in so many words just like a computer? On the other hand, if the student lays too much emphasis on written English (and only learns it well),what will he do when he wants to express himself orally without any communicative competence?The teachers neglect the importance of the other three skills,which are listening,speaking and writing,     

UNIVERSITY STUDENTS’ UNDERSTANDING OF THERMAL PHYSICS IN EVERYDAY CONTEXTS

Thermal physics is in the realm of everyday experience, underlies current environmental concerns, and underpins studies in sciences, health and engineering. In the state of NSW in Australia, the coverage of thermal topics in high school is minimal, and, hence, so is the conceptual understanding of students. This study takes a new approach at exploring conceptions of students with a qualitative analysis facilitated by NVivo complemented with reference to sociocultural ideas of learning. A 2-part pen and paper question was given to 598 first year university students of different educational backgrounds (and therefore physics expertise). ‘The Question’ was based on 2 familiar scenarios and required the selection of a concept first, followed by an explanation. The results showed that concepts were favoured based on a student’s everyday experience and their curriculum through high school, and some were more effective than others in making scientifically congruent responses. The reported thermal physics alternative conceptions were also examined in our sample, and students’ reasoning behind such conceptions indicate that some conceptions do not inhibit scientifically congruent responses whilst others do. The results implicate language and the everyday experiences of the student in the teaching and learning of thermal physics.     

INFLUENCES OF MOTIVATION AND APTITUDE ON LEARNING ELEMENTARY ACCOUNTING IN A JUNIOR COLLEGE THROUGH INDIVIDUALIZED SELF‐PACED AND TRADITIONAL INSTRUCTIONAL METHODS

The purpose of this study was to compare two teaching methods in elementary accounting: an individualized self‐paced method and a traditional method. One hundred students enrolled in an individualized self‐paced elementary accounting class and 150 students enrolled in traditional elementary accounting classes were used in this study. The pre‐experimental equivalence of age, sex, college grade point average, business courses previously taken on the college level, and previous work experience were compared for the two groups. All of the students were administered the American Institute of Certified Public Accountants Orientation Test and the Mehrabian Measures of Achieving Tendency at the beginning of the courses. Students in both groups completed the first 14 chapters in the same textbook. Students were then given the American Institute of Certified Public Accountants Achievement Test, Level 1, Form GS. A significant relationship was found between students’ aptitude as measured by the AICPA Orientation Test and students’ age. Average age was significantly higher for those students in the individualized self‐paced accounting laboratory class. Age, along with aptitude, was found to be a significant predictor of success in the individualized self‐paced laboratory class but not the traditional classes. A multiple regression analysis showed that aptitude was found to be the best single predictor of students’ achievement in elementary accounting. Only 17 of the 100 students in the self‐paced class completed the course; 16 of those had high aptitude and high achievement motivation scores. A general conclusion of the study was that if individualized self‐paced accounting laboratories are to be used in teaching elementary accounting, counselors should select students who have high scores in both motivation and aptitude. Students with other than a combination of high aptitude and motivation scores should be provided with remedial work in order to raise their achievement and retention level or they should be advised to take traditional courses.     

STUDENTS’ CONCEPTIONS OF THE PARTICULATE NATURE OF MATTER AT SECONDARY AND TERTIARY LEVEL

The aim of the present study is to elicit students’ understanding of the particulate nature of matter via a cross-age study ranging from secondary to tertiary educational levels. A questionnaire with five-item open-ended questions was administered to 166 students from the secondary to tertiary levels of education. In light of the findings, it can be deduced that the number of students’ responses categorized under the “sound understanding” category for each item increased with educational level, except for U1. Also, it can be concluded that students’ specific misconceptions decreased steadily from SHS1 to SHS3, except for item 4, but there is surprisingly a clear increase at U1.     

INDIAN SECONDARY STUDENTS�� VIEWS ABOUT GLOBAL WARMING: BELIEFS ABOUT THE USEFULNESS OF ACTIONS AND WILLINGNESS TO ACT

A 44-item survey instrument was designed to determine secondary students?? views about how useful various specific actions related to reducing global warming might be, their willingness to undertake these various actions and the extent to which these 2 might be linked. The instrument was administered to students in grades 6??C?10 (n?=?768) from 4 large schools in metropolitan Delhi, India in which the teaching language was English. The findings indicated that this cohort of Indian students exhibited high levels of concern about climate change and strong willingness to act against global warming and in favour of the environment. The findings are tentatively compared with those from 2 similar survey studies conducted in Western contexts (Spain and Australia).     

CRITICAL FEATURES OF VISUALIZATIONS OF TRANSPORT THROUGH THE CELL MEMBRANE—AN EMPIRICAL STUDY OF UPPER SECONDARY AND TERTIARY STUDENTS’ MEANING-MAKING OF A STILL IMAGE AND AN ANIMATION

Images, diagrams, and other forms of visualization are playing increasingly important roles in molecular life science teaching and research, both for conveying information and as conceptual tools, transforming the way we think about the events and processes the subject covers. This study examines how upper secondary and tertiary students interpret visualizations of transport through the cell membrane in the form of a still image and an animation. Twenty upper secondary and five tertiary students were interviewed. In addition, 31 university students participated in a group discussion and answered a questionnaire regarding the animation. A model, based on variation theory, was then tested as a tool for distinguishing between what is expected to be learned, what is present in the visualizations, and what is actually learned by the students. Three critical features of the ability to visualize biomolecular processes were identified from the students’ interpretations of the animation: the complexity of biomolecular processes, the dynamic and random nature of biomolecular interactions, and extrapolation between 2D and 3D. The results of this study support the use of multiple representations to achieve different learning goals.     

FIRST YEAR IMPLEMENTATION OF A PROJECT-BASED LEARNING APPROACH: THE NEED FOR ADDRESSING TEACHERS�� ORIENTATIONS IN THE ERA OF REFORM

The purpose of this study was to examine the extent to which three teachers’ professional experience and existing orientations toward teaching and learning mathematics and science influenced their implementation of a project-based curriculum (i.e. project-based learning (PBL)). Data sources included interviews, videotapes of classroom activity, and a teaching philosophy questionnaire. Data analysis was conducted using an iterative coding technique. We found coherency between the teachers’ perceived orientations and their emergent ideas about PBL, their sense of PBL as being compatible with their goals, and the specific challenges with which they struggled. All the teachers wanted their students to be successful; however, different definitions of success led to quite different approaches toward teaching, and for the most part, these differences appeared to have occurred because of existing orientations the teachers held for teaching their discipline. Implications for professional development taking into account teachers’ orientations and thus their professional experience are discussed, as well as disciplinary challenges to using PBL.     

A MULTI-DIMENSIONAL INSTRUMENT FOR EVALUATING TAIWANESE HIGH SCHOOL STUDENTS’ SCIENCE LEARNING SELF-EFFICACY IN RELATION TO THEIR APPROACHES TO LEARNING SCIENCE

In the past, students’ science learning self-efficacy (SLSE) was usually measured by questionnaires that consisted of only a single scale, which might be insufficient to fully understand their SLSE. In this study, a multi-dimensional instrument, the SLSE instrument, was developed and validated to assess students’ SLSE based on the previous literature. Besides, the interrelations between students’ approaches to learning science and SLSE were explored. A total of 311 Taiwanese eighth graders were invited to respond to the SLSE instrument and the Approaches to Learning Science (ALS) questionnaire. After ensuring several types of validity (e.g. construct validity and criterion-related validity) and the reliability of the SLSE questionnaire, the results suggested that the SLSE instrument should have satisfactory validity and reliability to measure Taiwanese eighth graders’ SLSE in terms of 5 dimensions: Conceptual Understanding, Higher-Order Cognitive Skills, Practical Work, Everyday Application, and Science Communication. Moreover, through Pearson correlation analyses, the results revealed that the Taiwanese eighth graders who perceived themselves as having a deep motive, along with the orientation of surface motive, tended to report higher SLSE. Also, those students who reported adopting deep strategies to learn science were more likely to possess higher SLSE. The regression results indicated that, overall, the students’ deep strategies and deep motive were strong predictors of their SLSE, particularly for the Higher-Order Thinking Skills SLSE. Yet, the Practical Work SLSE could only be predicted by the Deep Strategy dimension of ALS.     

WHAT IS THE PURPOSE OF LEARNING SCIENCE? AN ANALYSIS OF POLICY AND PRACTICE IN THE PRIMARY SCHOOL

ABSTRACT:  The paper explores the current rationale for primary science in England with a focus on how competing perspectives arising from perceptions of educational ideology and policy discourse have helped to shape current practice. The aim will be to provide a conceptual understanding of this by focusing specifically on how policy has influenced practice. In particular it will consider the way in which discourse and policy text have contributed to the emergent rationale for primary science which in many ways reflects conflicting influences, views and policies. Data were collected over a year from a regional survey and from four case-study primary schools. The findings suggest that teachers in primary schools face tensions between promoting both an educational and a political rationale for learning primary science. The paper will conclude by suggesting that the justification for primary science should be based on what we already know about how children learn science as well as helping them to develop an understanding of science and how it influences and is intrinsically linked to the needs of society.     

STUDENTS�� EVALUATION OF THE CREDIBILITY OF SCIENTIFIC MODELS THAT REPRESENT NATURAL ENTITIES AND PHENOMENA

The purpose of the current study was to explore learners’ evaluation of the credibility of scientific models that represent natural entities and phenomena. Participants were 845 students in grades 9 – 11 (aged 15 – 17 years) and 108 prospective science teachers in Oman, totaling 953 students. A survey called Epistemologies about the Credibility of Scientific Models was designed to explore participants’ epistemological positions regarding the credibility of scientific models. This instrument was based on a credibility taxonomy proposed by the author. This taxonomy was composed of four epistemological levels: certainty, imaginary, suspicious, and denial; thus, it was called the CISD taxonomy. Findings revealed that natural entities and phenomena were assigned to CISD levels according to their level of abstractness. This level of abstractness is usually constructed by the most frequently used models to represent each natural entity or phenomenon. For instance, entities, which were usually represented by photographs or micrographs, such as meteors and meteorites, blood cells and bacteria, fell at the certainty level. On the other hand, theoretical entities such as electron cloud and photons had a high suspicious–denial combinational level. Some entities, with possible competing concrete–abstract parallel nature of the scientific models that represent them, had both high certainty and suspicious–denial levels. The overall students’ epistemological perceptions across grade levels showed a decrease in the certainty level and an increase in the imaginary level. It might also be plausible to conclude that new, detailed microscopic and more abstract knowledge raised the suspicious and denial levels of some entities. Further research based on qualitative research methodologies is needed to explore these findings.