STUDENTS’ OPPORTUNITIES TO ENGAGE IN TRANSFORMATIONAL ALGEBRAIC ACTIVITY IN DIFFERENT BEGINNING ALGEBRA TOPICS AND CLASSES

This study compares students’ opportunities to engage in transformational (rule-based) algebraic activity between 2 classes taught by the same teacher and across 2 topics in beginning algebra: forming and investigating algebraic expressions and equivalence of algebraic expressions. It comprises 2 case studies; each involves a teacher teaching in two 7th grade classes. All 4 classes used the same textbook. Analysis of classroom videotapes (15–19 lessons in each class) revealed that the opportunities to engage in transformational algebraic activity related to forming and investigating algebraic expressions were similar in each teacher’s 2 classes. By contrast, substantial differences were found between 1 teacher’s classes with regard to the opportunities to engage in transformational algebraic activity related to equivalence of algebraic expressions. The discussion highlights the contribution of the interplay among the mathematical topic, the teacher, and the class to shaping students’ learning opportunities. Specifically, the mathematical topic appeared to play a prominent role in certain situations, with the topic involving deductive reasoning generating high variation in classes of 1 teacher but not in the other’s.     

STUDENTS’ OPPORTUNITIES TO ENGAGE IN TRANSFORMATIONAL ALGEBRAIC ACTIVITY IN DIFFERENT BEGINNING ALGEBRA TOPICS AND CLASSES

This study compares students’ opportunities to engage in transformational (rule-based) algebraic activity between 2 classes taught by the same teacher and across 2 topics in beginning algebra: forming and investigating algebraic expressions and equivalence of algebraic expressions. It comprises 2 case studies; each involves a teacher teaching in two 7th grade classes. All 4 classes used the same textbook. Analysis of classroom videotapes (15–19 lessons in each class) revealed that the opportunities to engage in transformational algebraic activity related to forming and investigating algebraic expressions were similar in each teacher’s 2 classes. By contrast, substantial differences were found between 1 teacher’s classes with regard to the opportunities to engage in transformational algebraic activity related to equivalence of algebraic expressions. The discussion highlights the contribution of the interplay among the mathematical topic, the teacher, and the class to shaping students’ learning opportunities. Specifically, the mathematical topic appeared to play a prominent role in certain situations, with the topic involving deductive reasoning generating high variation in classes of 1 teacher but not in the other’s.

     

USING ACTIVITY THEORY TO MODEL THE TAIWAN ATAYAL STUDENTS’ CLASSROOM MATHEMATICAL ACTIVITY

International Journal of Science and Mathematics Education - From the sociocultural perspective, this research utilized activity theory as the theoretical framework to analyze the influences of...     

THE LENGTH MEASUREMENT IN THE TURKISH MATHEMATICS CURRICULUM: ITS POTENTIAL TO CONTRIBUTE TO STUDENTS’ LEARNING

“Knowing and doing measurement” is a fundamental competency in real life since measuring attributes of objects in appropriate units and using measuring tools assist students to quantify and understand the world. For this reason, the study of measurement has a special place in every mathematics curriculum. Among the domains of measurement, length measurement is extremely important for students to understand basic ideas about measurement and to construct bases for more advance topics as area and volume measurement. However, research on students’ understanding of length measurement reveals serious difficulties varying from incorrect alignment with a ruler to confusion of perimeter with area. One of the reasons for students’ struggles in measurement is considered as weaknesses in the intended (written) curriculum. In this respect, this study was designed to investigate the content of length measurement in the Turkish mathematics curriculum (1st–fifth grade) in terms of its potential to support students’ understanding. For this purpose, the Turkish Mathematics Curriculum Guide was carefully analyzed by considering main components of the curriculum (e.g. learning objectives). In spite of some weaknesses, the length measurement content in the curriculum seems to provide meaningful opportunities for students to develop the concepts and skills involved in length measurement.     

STUDENTS’ ATTITUDES TOWARD MATHEMATICS AND THEIR RELATIONSHIP TO LEARNING IN REQUIRED MATHEMATICS COURSES IN SELECTED POSTSECONDARY INSTITUTIONS

Abstract

This study was conducted to gain information pertaining to one of the most critical problems in individualization or personalization of instruction—an instrument that accurately assesses individual differences in community college students in terms that can be of value in the classroom. The subjects in this study, nursing students at Delta College in University City, Michigan, were tested with a cognitive style diagnostic battery developed by Oakland Community College and an observational minibattery developed by this researcher (selected elements of cognitive style). The results of these tests were checked in classroom situations.     

TEACHING ‘OUT-OF-FIELD’ AS A BOUNDARY-CROSSING EVENT: FACTORS SHAPING TEACHER IDENTITY

Teaching ‘out-of-field’ occurs when teachers teach a subject for which they are not qualified. The issues around this increasingly common practice are not widely researched and are under-theorised. A qualitative pilot study using teacher interviews in 3 rural schools examined meanings, support mechanisms and teacher identities associated with out-of-field teaching. A thematic analysis isolated factors influencing whether teachers self-assessed their practice and identities as out-of-field. The ‘boundary between fields’ model was developed to emphasise support mechanisms, contextual factors and personal resources that influenced the nature of teachers’ negotiation of subject boundaries and its impact on professional identity. These findings provide insight for policy makers, school leaders and teacher educators into the conditions required for such teaching to be considered learning opportunities.     

INVESTIGATING THE EFFECTIVENESS OF AN ANALOGY ACTIVITY IN IMPROVING STUDENTS’ CONCEPTUAL CHANGE FOR SOLUTION CHEMISTRY CONCEPTS

This paper reports on an investigation on the use of an analogy activity and seeks to provide evidence of whether the activity enables students to change alternative conceptions towards views more in accord with scientific views for aspects of solution chemistry. We were also interested in how robust any change was and whether these changes in conceptual thinking became embedded in the students’ long-term memory. The study has its theoretical basis in an interpretive paradigm, and used multiple methods to probe the issues in depth. Data collection consisted of two concept test items, one-on-one interviews, and student self-assessment. The sample consisted of 44 Grade 9 students selected from two intact classes (22 each), from Trabzon, Turkey. The interviews were conducted with six students selected because of evidence as to their significant conceptual change in solution chemistry. The research findings revealed statistically significant differences in pre-test and post-test scores, and pre-test and delayed post-test scores (p<0.05), but no differences between post-test and delayed test scores (p>0.05). This suggests that the analogy activity is helpful in enhancing students’ conceptual understanding of solution chemistry, and that these changes may be stored in the students’ long-term memory.     

LEARNING TO THINK SPATIALLY: WHAT DO STUDENTS ‘SEE’ IN NUMERACY TEST ITEMS?

Learning to think spatially in mathematics involves developing proficiency with graphics. This paper reports on 2 investigations of spatial thinking and graphics. The first investigation explored the importance of graphics as 1 of 3 communication systems (i.e. text, symbols, graphics) used to provide information in numeracy test items. The results showed that graphics were embedded in at least 50?% of test items across 3 year levels. The second investigation examined 11??C?12-year-olds?? performance on 2 mathematical tasks which required substantial interpretation of graphics and spatial thinking. The outcomes revealed that many students lacked proficiency in the basic spatial skills of visual memory and spatial perception and the more advanced skills of spatial orientation and spatial visualisation. This paper concludes with a reaffirmation of the importance of spatial thinking in mathematics and proposes ways to capitalize on graphics in learning to think spatially.     

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.     

A SURVEY OF PSYCHOLOGICAL,MOTIVATIONAL, FAMILY AND PERCEPTIONS OF PHYSICS EDUCATION FACTORS THAT EXPLAIN 15-YEAR-OLD STUDENTS’ ASPIRATIONS TO STUDY PHYSICS IN POST-COMPULSORY ENGLISH SCHOOLS

This paper investigates the factors that influence 15-year-old students’ intentions to study physics post-16, when it is no longer compulsory. The analysis is based on the year 10 (age, 15 years) responses of 5,034 students from 137 England schools as learners of physics during the academic year 2008–2009. Factor analyses uncovered a range of physics-specific constructs, 7 of which were statistically significantly associated with intention to study physics post-16 in our final multi-level model; in descending order of effect size, these are extrinsic material gain motivation, intrinsic value of physics, home support for achievement in physics, emotional response to physics lessons, perceptions of physics lessons, physics self-concept and advice-pressure to study physics. A further analysis using individual items from the survey rather than constructs (aggregates of items) supported the finding that extrinsic motivation in physics was the most important factor associated with intended participation. In addition, this item-level analysis indicated that, within the advice-pressure to study physics construct, the encouragement individual students receive from their teachers is the key factor that encourages them to intend to continue with physics post-16.     

MAIN FACTORS CONTRIBUTING TO THE INCREASE OF COCOON OUTPUT IN ZHEJIANG PROVINCE

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USING RASCH MEASUREMENT TO VALIDATE THE INSTRUMENT OF STUDENTS’ UNDERSTANDING OF MODELS IN SCIENCE (SUMS)

Scientific models and modeling play an important role in science, and students’ understanding of scientific models is essential for their understanding of scientific concepts. The measurement instrument of Students’ Understanding of Models in Science (SUMS), developed by Treagust, Chittleborough & Mamiala (International Journal of Science Education, 24(4):357–368, 2002), has commonly been used to measure SUMS. SUMS was developed using the Classical Test Theory (CTT). Considering the limitations of CTT, in this study we applied a Rasch model to validate SUMS further. SUMS was given to 629 students in 18 classes of grades 9 and 10 from six high schools in China. The results present both additional evidence for the validity and reliability of SUMS and specific aspects for further improvement. This approach of validation of a published instrument by Rasch measurement can be applied to other measurement instruments developed using CTT.     

EYE MOVEMENTS REVEAL STUDENTS’ STRATEGIES IN SIMPLE EQUATION SOLVING

Equation rearrangement is an important skill required for problem solving in mathematics and science. Eye movements of 40 university students were recorded while they were rearranging simple algebraic equations. The participants also reported on their strategies during equation solving in a separate questionnaire. The analysis of the behavioral and eye tracking data, namely the accuracy, reaction times, and the number of fixations, revealed that the participants improved their performance during the time course of the measurement. The type of equation also had a significant effect on the score. The results indicated that the number of fixations represents a reliable and sensitive measure that can give valuable insights into participants’ flow of attention during equation solving. A correlation between the number of fixations and participants’ efficiency in equation solving was found, suggesting that the more efficient participants developed adequate strategies, i.e. “knew where to look.” The comparison of eye movement data and questionnaire reports was used for assessing the validity of participants’ metacognitive insights. The measures derived from eye movement data were found to be more objective and reliable than the participants’ reports. These results indicate that the measurement of eye movements provides insights into otherwise unavailable cognitive processes and may be used for exploring problem difficulty, student expertise, and metacognitive processes.     

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.     

STUDENTS’ WAYS OF REASONING ABOUT NONLINEAR FUNCTIONS IN GUESS-MY-RULE GAMES

There is a growing movement toward the introduction of algebra in early grades. This is supported by an increasing number of research studies that have reported success in getting young students to “do” mathematics considered beyond their reach. Yet, the consensus is that more research is needed to provide insights into the processes by which students make sense of algebraic ideas. In particular, more studies are needed on how nonlinear functions can be introduced in early grades. This article reports an algebra research strand that introduced seventh grade students to quadratic functions using Guess-My-Rule games. The article describes several instances of the students engaging successfully with ideas and forms of reasoning involving quadratic functions. The purpose is to contribute to the debate on the introduction of algebra in early grades by providing further evidence of young students’ ability to engage with algebraic ideas usually considered to be beyond their reach.     

UNDERGRADUATE STUDENTS’ SCIENCE-RELATED IDEAS AS EMBEDDED IN THEIR ENVIRONMENTAL WORLDVIEWS

This study explored environmental worldviews of selected undergraduate students in Taiwan and located the associations of these worldviews with science. The “environment” is represented as nature or the natural world, as opposed to the social and spiritual world. The participants were undergraduate students (14 science and 15 nonscience majors) enrolled in a general science course at a southern Taiwanese university. A questionnaire and individual interviews were conducted in parallel to elicit in depth the students’ ideas/beliefs about nature, such as, to what construes nature, how it works, and how humans relate to nature. The responses were analyzed using a phenomenographic approach to emphasize the qualitative variation of the students’ views. The key findings based on their relations to science and science education were the following: (1) Most students seemed to immediately relate the topic of nature to science and thus sought to explain nature from a scientific perspective, yet their understanding of scientific concepts or metaphors, such as the balance of nature, was problematic; (2) a value-free perspective is evident among some students in viewing human-induced natural crises: What we should do is merely look at facts and let science tell us what we should and should not do. (3) The students generally expressed trust in science and technology and believed it to be the key to improving the condition of nature as well as human life.     

A PROBABILISTIC MODEL FOR STUDENTS’ ERRORS AND MISCONCEPTIONS ON THE STRUCTURE OF MATTER IN RELATION TO THREE COGNITIVE VARIABLES

In this study, the effect of 3 cognitive variables such as logical thinking, field dependence/field independence, and convergent/divergent thinking on some specific students’ answers related to the particulate nature of matter was investigated by means of probabilistic models. Besides recording and tabulating the students’ responses, a combination of binomial and multinomial logistic regression techniques was used to analyze the data. Thus, students’ misconceptions as well as the compatible-with-the-scientific-view student’s answers were explored one by one in relation to the above 3 cognitive variables. The study took place with the participation of 329 ninth-grade junior high school pupils (aged 14–15). The results showed that mostly logical thinking and sporadically the other 2 cognitive variables were significantly associated with students’ answers. Interpretation of the results and implications for science education are discussed.     

UNIVERSITY STUDENTS’ VIEWS OF THE ROLE OF MATHEMATICS IN THEIR FUTURE

We report on an international study about mathematics students’ ideas of how they will use mathematics in their future study and careers. This builds on our previous research into students’ conceptions of mathematics. In this paper, we use data from two groups of students studying mathematics: those who participated in an in-depth interview and those who completed an open-ended questionnaire. We found that their responses could be grouped into four categories: don’t know; procedural skills; conceptual skills; and professional skills. Although some students held clear ideas about the role of mathematics, many were not able to articulate how it would be used in their future. This has implications for their approach to learning and our approach to teaching.     

ENHANCING STUDENTS’ COMMUNICATION SKILLS IN THE SCIENCE CLASSROOM THROUGH SOCIOSCIENTIFIC ISSUES

Communication skills are one of the most important competencies for 21st century global citizens. Our guiding presupposition was that socioscientific issues (SSIs) could be used as an effective pedagogical tool for promoting students’ communication skills by increasing peer interactions, stimulating students’ reasoning, and in constructing shared social knowledge. We implemented a SSI program on gene modification (GM) technology to 132 9th graders in South Korea and investigated to what extent this SSI instruction contributed to enhancing students’ communication skills. Data sources included pre- and post-scores on the Communication Skills Questionnaire (CSQ), semi-structured interviews with the students and instructor, and classroom observations. The results demonstrated that SSI instruction could bring about a moderately large impact on students’ ability to understand the key ideas of others and to value others’ perspectives, as well as a marginal positive effect on developing active assertions. However, SSI instruction appeared to have a lesser impact on students’ ability to develop shared understanding. Overall, this research indicates the potential that even a limited SSI classroom could have in terms of promoting students’ communication skills in the context of their regular science class.