Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contexts

Literature suggests that the type of context wherein a task is placed relates to students' performance and solution strategies. In the particular domain of logical thinking, there is the belief that students have less difficulty reasoning in verbal than in logically equivalent symbolic tasks. Thus far, this belief has remained relatively unexplored in the domain of teaching and learning of mathematics, and has not been examined with respect to students' major field of study. In this study, we examined the performance of 95 senior undergraduate mathematics and education majors in symbolic and verbal tasks about the contraposition equivalence rule. The selection of two different groups of participants allowed for the examination of the hypothesis that students' major may influence the relation between their performance in tasks about contraposition and the context(symbolic/verbal) wherein this is placed. The selection of contraposition equivalence rule also addressed a gap in the body of research on undergraduate students' understanding of proof by contraposition. The analysis was based on written responses of all participants to specially developed tasks and on semi-structured interviews with 11 subjects. The findings showed different variations in the performance of each of the two groups in the two contexts. while education majors performed significantly better in the verbal than in the symbolic tasks, mathematics majors' performance showed only modest variations. The results call for both major- and context- specific considerations of students' understanding of logical principles, and reveal the complexity of the system of factors that influence students' logical thinking.     

An assessment‐led approach to processes in the science curriculum

General conditions which should be met in the development of the idea of science processes and the potential benefits which would result are suggested. An approach to the definition of science processes based on variables and variable handling is outlined. It is argued that this should occur specifically in the context of educational practice. The processes should be elucidated within a taxonomy of tasks, the ultimate components of which should be interpretable and transferable skills. The development and utilization of such a taxonomy can most obviously occur in the context of assessment. The techniques of item banking and domain definition in domain‐referenced tests are then discussed in relation to the above issues. Multi‐dimensional labelling of an item bank is considered to be appropriate, and suggestive of a research programme for investigating the requirements of transferability and interpretability.

The labelling scheme resulting from an attempt to identify the significant dimensions of the age 15 Assessment of Performance Unit (APU) science item bank is reported. The paper indicates the effectiveness of the scheme and discusses the value of labelling those items within the assessment programme which draw heavily on the conceptual framework of taught science. A discussion of how the labelling scheme/item bank can be used in an attempt to identify the skills required in undertaking tasks based on science processes, and thus to develop tests of such identifiable skills for diagnostic and placement purposes in schools, concludes this paper.     

An interaction of screen colour and lesson task in CAL

Colour is a common feature in computer‐aided learning (CAL), though the instructional effects of screen colour are not well understood. This investigation considers the effects of different CAL study tasks with feedback on posttest performance and on posttest memory of the lesson colour scheme. Graduate students (n=68) completed a computer‐based vocabulary lesson that included either multiple‐choice or constructed‐response study tasks with feedback. Each lesson section used a different colour theme, while the posttest did not use colour. The constructed‐response study task was a little more effective for posttest memory of lesson content but was substantially less effective for posttest memory of the lesson colour scheme. These results show a clear interaction of screen colour and lesson study task, a memory‐context effect. The practical and theoretical implications of these findings are discussed.     

Hierarchical task analysis ‐ An approach for diagnosing students’ conceptual difficulties

Pupils’ conceptual difficulties in scientific problem‐solving are examined on the basis of their performance on complex tasks and on the simple tasks of which the complex tasks are composed. A theoretical analysis reveals that identical errors on a complex task are not necessarily due to the same errors on the associated component tasks. This is illustrated by reference to actual research findings. The educational implications of this finding are discussed.     

Predictors for Mathematics Achievement? Evidence From a Longitudinal Study

Numerical processing has been extensively studied by examining the performance on basic number processing tasks, such as number priming, number comparison, and number line estimation. These tasks assess the innate “number sense,” which is assumed to be the breeding ground for later mathematics development. Indeed, several studies have associated children's performance in these tasks with individual differences in mathematical achievement. To date, however, most of these studies have cross‐sectional designs. Moreover, the few longitudinal studies either use complex tasks (e.g., story problems) or investigate only one of these basic number processing tasks at a time. In this study, we examine the association between the performance of children on several basic number processing tasks and their individual math achievement scores on a curriculum‐based test measured 1 year later. Regression analyses showed that most of the variance in children's math achievement was predicted by nonsymbolic number line estimation performance (i.e., estimating large quantities of dots) and, to a lesser extent, the speed of comparing symbolic numbers. This knowledge about the predictive value of the performance of 5‐ to 7‐year‐olds on these markers of number processing can help with the early identification of at‐risk children. In addition, this information can guide appropriate educational interventions.     

National Workshop on ‘Designing and Developing Innovative Science Curriculum and Instructional Material Linking Science Education to Real‐Life Situations’

The development of dynamics concepts is studied longitudinally with two groups, one between ages 12‐14 and the other from 14‐16. Data collected includes performances on APS tasks (for which there is also national data) and performance on Piagetian tasks, with interviews on tasks for selected pupils. Classroom science curriculum data was also obtained. The study can thus discuss the interaction of cognitive development and classroom experience in the development of concepts. This particular paper focuses on the APS tasks.     

Do Language‐Based Processing Tasks Separate Children with Language Impairment from Typical Bilinguals?

We report results from 2 language‐based processing tasks designed to investigate the performance of linguistically diverse learners. The tasks were the Competing Language Processing Task (CLPT) and Non‐Word Repetition (NWR). Participants were 100 school‐age children in 1 of 3 different experimental groups: monolingual English‐speaking children with specific or primary language impairment (LI), typical English‐only‐speaking children (EO), or typical Spanish–English bilingual children (BI). On both CLPT and NWR, EO group performance was best and LI group performance was poorest, with BI group performance falling in between. Likelihood ratios indicated that performance on these tasks does not provide compelling diagnostic power for separating typically developing bilinguals from monolingual children with LI. One exception is that children who obtained an NWR score of 93 percent or higher could be ruled out of the LI group with a high degree of confidence.     

USING IMPLEMENTATION PLANNING TO INCREASE TEACHERS’ ADHERENCE AND QUALITY TO BEHAVIOR SUPPORT PLANS

Evidence‐based practices within a response‐to‐intervention framework must be implemented with adequate treatment integrity to promote student outcomes. However, research findings indicate educators struggle to implement interventions and logistical considerations may limit the utility of performance feedback, an evidence‐based treatment integrity promotion strategy. This study evaluates the effect of implementation planning, a treatment integrity promotion strategy that includes detailed logistical planning and barrier identification adapted from an adult behavior change theory from heath psychology (i.e., the Health Action Process Approach). A multiple baseline across participants design was used to evaluate teachers’ adherence to a behavior support plan as well as their quality of implementation. Results indicated that after intervention training, adherence was initially low and variable, and quality of implementation was moderate to high and variable, but both adherence and quality increased and became less variable after implementation planning. The increases in implementation were more pronounced for two teachers, whose students also had subsequent improvements in their academic engagement and disruptive behavior. These findings highlight the relationship between adequate levels of treatment integrity and student outcomes as well as provide initial support for implementation planning.     

FORMATIVE,INFORMATIVE, AND SUMMATIVE ASSESSMENT: THE RELATIONSHIP AMONG CURRICULUM‐BASED MEASUREMENT OF READING,CLASSROOM ENGAGEMENT,AND READING PERFORMANCE

This study explored the relationships among formative curriculum‐based measures of reading (CBM‐R), student engagement as an extra‐academic indicator of student motivation, and summative performance on a high‐stakes reading assessment. A diverse sample of third‐, fourth‐, and fifth‐grade students and their teachers responded to questionnaires about student engagement in academic tasks. These questionnaires were collected about the same time as fall CBM‐R oral reading fluency and maze screening tasks. Results indicated that fall student and teacher reports of engagement and a composite score of reading competence derived from CBM‐R screening tests uniquely predicted student performance on year‐end standardized reading tests. Profile analyses indicated that student engagement was associated with better reading performance among students with low competence, suggesting that engagement may be particularly important for increasing student performance for struggling readers. Implications for interventions targeting both student motivation, as well as reading skill development, are discussed.     

The framework used in developing and Interpreting the International Adult Literacy Survey (IALS)

This paper offers a framework that has been used for both developing the tasks used to measure literacy in the International Adult Literacy Survey and for understanding the meaning of what has been reported with respect to the comparative literacy proficiencies of adults in participating countries. The framework consists of six parts that represent a logical sequence of steps from needing to define and represent a particular domain of interest, to identifying and operationalizing characteristics used to construct items, to providing an empirical basis for interpreting results. The various parts of the framework are seen as important in that they help to provide a deeper understanding of the construct of literacy and the various processes associated with it. A processing model is proposed and variables associated with performance on the literacy tasks are identified and verified through regression analyses. These variables are shown to account for between 79 and 89 percent of the variance in task difficulty. Collectively, these process variables provide a means for moving away from interpreting performance on large-scale surveys in terms of discrete tasks or a single number towards identifying levels of performance that have generalizability across pools of tasks and towards what Messick has called a higher level of measurement.     

The relationship between web enjoyment and student perceptions and learning using a web‐based tutorial

Web enjoyment has been regarded as a component of system experience. However, there has been little targeted research considering the role of web enjoyment alone in student learning using web‐based systems. To address this gap, this study aims to examine the influence of web enjoyment on learning performance and perceptions by controlling system experience as a variable in the study. 74 students participated in the study, using a web‐based tutorial covering subject matter in the area of ‘Computation and algorithms’. Their learning performance was assessed with a pre‐test and a post‐test and their learning perceptions were evaluated with a questionnaire. The results indicated that there are positive relationships between the levels of web enjoyment and perceived usefulness and non‐linear navigation for users with similar, significant levels of system experience. The implications of these findings in relation to web‐based learning are explored and ways in which the needs of students who report different levels of web enjoyment might be met are discussed.     

What information handling skills are promoted by the use of data analysis software?

This paper describes an investigation of secondary school pupils using data analysis software in their science lessons. The aim of the project was to determine the nature and complexity of data analysis tasks that could be mastered by pupils aged between 13 and 14 years, through the use of data analysis software. The research project involved the study of three matched experimental and control pairs of classes of pupils analysing scientifically- based data. The findings show that pupils using computer-based software can perform a range of complex tasks, including the use of Boolean logical operators, 'and', 'greater than' and 'less than', which are more intellectually advanced than reported by other researchers. These results show that given appropriate information technology (IT)-based data analysis tools, pupils as young as 13--14 can perform such complex data analysis tasks as classifying data according to one or more criteria and then ranking data according to a different criterion. This contradicts some of the earlier research that concluded that such tasks could not be easily achieved by pupils of this age     

Performance of students in grades six,nine, and twelve on five logical,spatial and formal tasks

Performance on five logical, spatial and formal tasks was used to make inferences about the reasoning structures of the subjects. The tasks used were: seriation matrix, tilt of a cone, location of a point in two and three dimensions, flexible rods and projection of shadows. Three research questions were asked: first, what is the general level of performance; second, are there grade level differences; and third, are there gender differences in task performance. The subjects were 101 middle and high school students chosen at random from the school population. Each task was given in an individual interview. Findings include grade level differences in performance and gender differences in performance on one of the tasks. Implications for classroom teachers were proposed.     

A study of group interaction processes in learning lower secondary physics

This study explores the effectiveness of a cooperative learning (CL) approach, where students work together and elaborate concepts of physics. The group problem‐solving tasks were conceptual questions from physics, where the students had to discuss and provide explanations of some phenomena. The effectiveness of the learning‐in‐groups approach was validated and correlated with working group interactiveness. Two group variables were assigned: the group performance and the group activity. These variables and the subjects' participation variable were correlated with achievement. Discourse analysis revealed variation in the nature of the interactions and information exchange, and the two roles as learners and learning facilitators. In addition, the study provided evidence for some features of cooperative learning that could characterize it as a nonlinear dynamical process. Implications of the findings are discussed. © 2006 Wiley Periodicals, Inc. J Res Sci Teach 43: 556–576, 2006     

一类状态可分的随机微分系统的变步长Euler方法

针对一类状态可分的随机微分系统,在文献[9]的变步长Euler方法的基础上,分离出描述慢变状态的微分方程中的快变状态,特殊处理,减少由其引起的误差,建立了新的变步长Euler方法.理论分析和数值实验证明了新方法的优越性.     

Is Self‐worth Protection Best Regarded as Intentional Self‐handicapping Behaviour or an Outcome of Choking Under Pressure?

Self‐worth protective students characteristically perform poorly when they anticipate that poor performance is likely to reveal low ability, yet perform well in situations that involve little threat to self‐worth. The present study sought a further understanding of this variable pattern of achievement, assessing two possibilities: (1) that the poor performance of students high in self‐worth protection in situations of high evaluative threat is appropriately viewed as self‐handicapping behaviour in the form of strategic withdrawal of effort, and (2) that the poor performance of students high in self‐worth protection is an outcome of anxiety or “choking under pressure”. Participants were 72 undergraduate students, either high or low in self‐worth protection, assigned to one of three performance feedback conditions: humiliating failure, failure allowing face‐saving, and success. They subsequently completed 20 anagrams and 12 remote associates tasks, assessing performance, followed by 16 unicursal tasks during what was believed to be a practice period, providing an assessment of behavioural self‐handicapping in the form of intentional low effort. Students high in self‐worth protection performed poorly on the anagrams and remote associates following humiliating failure. They also reported greater anxiety across experimental conditions and claimed greater anxiety impairment than students low in self‐worth protection. These outcomes provide little support for an interpretation of self‐worth protection as self‐handicapping behaviour, instead supporting an interpretation of self‐worth protection as an outcome of choking under pressure, fuelled by evaluative threat.     

Learning difficulties associated with the particulate theory of matter in the Scottish Integrated Science course

Summaries

English

Educators need to know when an adolescent will use a particular available problem‐solving mechanism or strategy. If a student can solve proportional reasoning problems in mathematics and physics classes but fails to comprehend the ‘odds’ in a local lottery, the teacher would like to know why. Three task context factors that form obstacles to generalizing logical reasoning strategies are illustrated by research studies. The obstacles are perceived relevance of the variables, perceived goal of the experiment and variable salience. The relationship between these factors and Piagetian theory is explored. Piaget's view that generalization is difficult to predict is a pessimistic one for educators. In contrast to this view, our findings suggest that it is possible to make some predictions abouthow and when logical mechanisms will be generalized to new situations. Implications for designing educational programmes which enhance generalizability of instruction in logical reasoning are described.     

Knowing the subject matter of a secondary‐school science subject

This paper examines the fundamental yet largely neglected distinction between school subjects and academic disciplines in the discourse on teachers’ specialized subject‐matter knowledge. It analyses and critiques the curricular positions embedded in that discourse in the light of five possible relationships between school subjects and academic disciplines. Invoking Dewey’s logical‐psychological distinction and research findings, the paper argues that the subject matter of a secondary‐school science subject instead of the subject matter of its parent academic discipline lies at the heart of secondary‐school science teachers’ specialized subject‐matter knowledge. Knowing such subject matter entails knowing five intersecting dimensions: the logical, the psychological, the pedagogical, the epistemological, and the sociocultural. Implications are drawn concerning theorizing about what secondary‐school science teachers need to know about the subject matter they are expected to teach, subject‐matter preparation for teaching, and the development of secondary‐school science curriculum materials.     

Teachers' learning to facilitate high‐level student thinking: Impact of a video‐based professional development

Attaining the vision for science teaching and learning emphasized in the Framework for K‐12 Science Education and the next generation science standards (NGSS) will require major shifts in teaching practices in many science classrooms. As NGSS‐inspired cognitively demanding tasks begin to appear in more and more science classrooms, facilitating students' engagement in high‐level thinking as they work on these tasks will become an increasingly important instructional challenge to address. This study reports findings from a video‐based professional development effort (i.e., professional development [PD] that use video‐clips of instruction as the main artifact of practice to support teacher learning) to support teachers' learning to select cognitively demanding tasks and to support students' learning during the enactment of these tasks in ways that are aligned with the NGSS vision. Particularly, we focused on the NGSS's charge to get students to make sense of and deeply think about scientific ideas as students try to explain phenomena. Analyses of teachers' pre‐ and post‐PD instruction indicate that PD‐participants began to adopt instructional practices associated with facilitating these kinds of student thinking in their own classrooms. The study has implications for the design of video‐based professional development for science teachers who are learning to facilitate the NGSS vision in science classrooms.