The relevance of the Good Strategy User Model to the Teaching of Mathematics

This article briefly reviews the strategic, metacognitive, and knowledge components of good strategy use. Five principles of teaching that follow from this good strategy user model are illustrated by examples from arithmetic instruction. Practitioners are advised: (a) to teach strategies; (b) to teach knowledge about when, where, and how to use strategies; (c) to teach general knowledge about factors; that promote strategy functioning; (d) to teach relevant nonstrategic knowledge; and (e) to have students practice components of good strategy use and the coordination of components. The good strategy user model for math instruction is compared to Polya's conception of how to teach problem solving.     

College students solving chemistry problems: A theoretical model of expertise

A model of expertise in chemistry problem solving was tested on undergraduate science majors enrolled in a chemistry course. The model was based on Anderson's Adaptive Control of Thought‐Rational (ACT‐R) theory. The model shows how conceptualization, self‐efficacy, and strategy interact and contribute to the successful solution of quantitative, well‐defined chemistry problems in the areas of stoichiometry, thermochemistry, and properties of solutions. A statistical path analysis and students' explanations supported the model and indicated that the students' problem conceptualization and chemistry self‐efficacy influenced their strategy use, which, in turn, strongly influenced their problem‐solving success. The implication of these findings for future research and developing students' expertise in chemistry problem solving is that a strategy is advantageous when it is built on a foundation of conceptual knowledge and chemistry self‐efficacy. © 2009 Wiley Periodicals, Inc. J Res Sci Teach 46: 1070–1089, 2009     

Process-Oriented Worked Examples: Improving Transfer Performance Through Enhanced Understanding

The research on worked examples has shown thatfor novices, studying worked examples is oftena more effective and efficient way of learningthan solving conventional problems. Thistheoretical paper argues that addingprocess-oriented information to worked examplescan further enhance transfer performance,especially for complex cognitive skills withmultiple possible solution paths.Process-oriented information refers to theprincipled (``why'') and strategic (``how'')information that experts use when solvingproblems. From a cognitive load perspective,studying the expert's ``why'' and ``how''information can be seen as constituting agermane cognitive load, which can fosterstudents' understanding of the principles of adomain and the rationale behind the selectedoperators, and their knowledge about howexperts select a strategy, respectively. Issueswith regard to the design, implementation, andassessment of effects of process-orientedworked examples are discussed, as well as thequestions they raise for future research.     

Computer simulations in the high school: Students' cognitive stages,science process skills and academic achievement in microbiology

Computer-assisted learning, including simulated experiments, has great potential to address the problem solving process which is a complex activity. It requires a highly structured approach in order to understand the use of simulations as an instructional device. This study is based on a computer simulation program, 'The Growth Curve of Microorganisms', which required tenth grade biology students to use problem solving skills whilst simultaneously manipulating three independent variables in one simulated experiment. The aims were to investigate the computer simulation's impact on students' academic achievement and on their mastery of science process skills in relation to their cognitive stages. The results indicate that the concrete and transition operational students in the experimental group achieved significantly higher academic achievement than their counterparts in the control group. The higher the cognitive operational stage, the higher students' achievement was, except in the control group where students in the concrete and transition operational stages did not differ. Girls achieved equally with the boys in the experimental group. Students' academic achievement may indicate the potential impact a computer simulation program can have, enabling students with low reasoning abilities to cope successfully with learning concepts and principles in science which require high cognitive skills.     

Teacher Practices with Toddlers During Social Problem Solving Opportunities

This article explores how teachers can foster an environment that facilitates social problem solving when toddlers experience conflict, emotional dysregulation, and aggression. This article examines differences in child development and self-regulation outcomes when teachers engage in problem solving for toddlers and problem solving with toddlers. It also reviews teacher practices aimed at preventing problems. The article suggests a paradigm shift from perceiving social challenges as toddler problems to viewing such situations as problem solving opportunities. The article concludes by applying these principles to an actual classroom dispute among toddlers.     

THE EFFECTS OF TEACHING PROBLEM SOLVING ON ACADEMIC PERFORMANCE AND RETENTION

A study of the effects of explicitly teaching a problem‐solving strategy on problem‐solving ability, course average, course success, and student retention is reported. Two classes of microeconomics principles were involved in a quasi‐experiment. The experimental class was explicitly taught the problem‐solving strategy and this strategy was then used to solve microeconomic problems in class. The control class was assigned, solved, and discussed the same problems without being taught the problem‐solving strategy. Multiple regression and analysis of variance show that while teaching problem solving did not significantly affect course average, student success in passing the course or problem solving ability, it did result in significantly higher student retention. Results indicate that teaching problem solving only affects those students with low problem solving abilities who would have dropped out of class, and that teaching this strategy helps them remain in the class and succeed.     

I BOOK REVIEWS

This study examines the influence of graphing calculators on a teacher's assessment practices in a college algebra course. The researcher focused on three techniques of alternative assessment: oral discourse, teacher observations, and problem‐solving investigations. The teacher's assessment practices were revealed during 6 weeks of classroom observations. The researcher examined the teacher's assessment practices before and after the teacher used graphing calculators as tools for teaching and learning mathematics. The use of the graphing calculators enhanced the teacher's assessment practices as related to oral discourse, classroom observations, and problem‐solving investigations. The results of the study indicate the potential for technological tools to influence teachers’ practices of alternative assessment in the mathematics classroom.     

The Explorer and the Assimilator: A Cognitive Style Distinction and Its Potential Implications for Innovative Problem Solving

Kaufmann, G. 1979. The Explorer and the Assimilator: A Cognitive Style Distinction and Its Potential Implications for Innovative Problem Solving. Scandinavian Journal of Educational Research 23, 101‐108. A novel cognitive style distinction is introduced: The Assimilator is presumed to be guided by a Rational (R) strategy which is seen essentially to consist in stretching established principles as far as possible in coping with novel tasks. In contrast, the Explorer spontaneously seeks novel solution alternatives, even in problem situations that are easily mastered through the application of a standard principle. The assets and liabilities of these different approaches in problem solving are discussed, with special reference to innovation. It is hypothesized that the Explorer in this respect is in a more profitable position. A modified version of Luchin's Einstellung‐situation provided the empirical basis for distinguishing between Assimilators and Explorers and allowed for a validation of the theoretical assumptions. The results clearly supported the hypotheses of the experiment. Finally, theoretical and practical implications of the findings are discussed and some suggestions for further research are made.     

Are first graders' arithmetic skills related to the quality of mathematics textbooks? A study on students’ use of arithmetic principles

A major goal of the first years of schooling is students' development from using counting strategies to using calculation strategies – or even recall – to solve addition or subtraction problems. It requires the perception and usage of arithmetic principles. Although the continued use of counting strategies is problematic for further learning progress, they are frequently used by many students beyond Grade 1. While learning resources possibly play a role in students' development in this field, our knowledge about their impact is limited. In this study we investigated the presented learning opportunities of four different textbooks regarding arithmetic principles in Grade 1, and subsequently the relation to first graders' strategy use by analyzing a one-year dataset of 1614 students from 86 classes. The analyses show differences in the textbooks' quality concerning arithmetic principles as well as a considerable connection to students' strategy use at the end of Grade 1.     

Voices in Education: What Other Countries and Disciplines Have to Offer

Abstract

Emphasizing critical thinking in teacher education could potentially increase society's effectiveness in addressing national and international problems. This linkage between teacher education and societal problem solving is predicated on three major possibilities: (a) Increased emphasis on critical thinking in teacher education will increase the emphasis on critical thinking in K‐12 education, (b) increased emphasis on critical thinking in K‐12 will lead to increased use of critical thinking within society, and (c) increased use of critical thinking among society's leaders and citizens will produce better problem solving at a societal level. The proposed linkage between teacher education and societal problem solving is anchored in three aspects of critical thinking: disposition toward critical thinking, cognitive skill in critical thinking, and information bases for critical thinking.     

Wittrock's Influence on Mathematics Education: Some Personal Comments

Merlin C. Wittrock was a friend and colleague who influenced me and many other contemporary mathematics educators on how students learn. In this article I summarize my interactions with Merl beginning in 1965, and how over the following half-century he influenced my thinking on student learning for understanding and, in turn, on how to design instruction based on generative principles. I situate our initial discussions in terms of behaviorism, mathematical abilities, and mathematical problem solving. Based on Merl's ideas since first expressed in “A Generative Model of Mathematics Learning” in 1974, today it is clear that instruction should involve the stimulation of a student's store of relevant background experiences in relation to information to be learned, so they can construct meaning from it. Only by doing so can the use of such organized structures of previously acquired knowledge and experiences facilitate the understanding of new information.     

Participatory principles in human inquiry: ethics and methods in a study of the paradigm shift experience

In this paper, underlying principles for guiding participation in human science research are outlined. These research principles were originally utilized as a guiding framework for the author's phenomenological study of the change to a new world‐view identified as the paradigm shift (Dudley, 1987). Using this study as an example, the paper focuses on the integration of participatory concepts in research. The concept of participation as ethics discussed in this paper includes the following dimensions: integrity congruence among problem, paradigm, and method; process‐orientation a commitment to research as a shared journey of discovery; empathetic relationships an ethic of mutuality; and empowerment in community a view of knowledge as communal achievement. Finally, a participatory ethic is discussed in terms of its congruence with values that are at the heart of the new social science paradigm.     

A Math Intervention for Third Grade Latino English Language Learners at Risk for Math Disabilities

Word problems for English language learners (ELLs) at risk for math disabilities are challenging in terms of the constant need to develop precise math language and comprehension knowledge. As a result of this, ELLs may not only need math support but also reading and linguistic support. The purpose of this study was to assess the effectiveness of a word problem–solving strategy called Estratégica Dinámica de Matemáticas (EDM). This strategy was designed to provide math support in the native language based on students' math comprehension levels. A changing criterion multiple baseline design was used to instruct six second-grade Latino ELLs at risk for math disability. As compared with the baseline phase, EDM increased word problem solving for all participants. All students' level of performance were maintained and generalized during follow-up sessions. This study has implications for a native language intervention that focuses on strategy training to facilitate word problem–solving performance.     

Transitions to Competence: An Investigation of Adult Mediation in Preschoolers' Self-Regulation With a Microcomputer-Based Problem-Solving Task

The effectiveness of specific dimensions of adult mediation on preschoolers' self- regulation of a model-consultation strategy was evaluated using microcomputer puzzle tasks. Two trained tutors taught 61 children who were pretested and randomly assigned to one of four treatments devised to test two factors of mediation: access and analysis of a picture-puzzle model prior to or during problem solving. Tutorial interchanges of treatments were designed on the basis of the Vygotskian tenet that effective instruction includes a concern for children's actual and potential developmental levels and occurs through participation with others during problem solving. Measures of model-consultation were calculated from three videotaped sessions and used to assess children's self-regulation during treatment and in immediate and delayed posttests. Analyses revealed significant differences for the access and analysis effects in posttests, but only in the delayed posttest for the latter. Significant differences were found for the planned contrast in the delayed posttest. The study suggests that children's acquisition of the model-consultation can improve over a short period of time, although not immediately, with culturally mediated instruction and does not improve solely as a function of practice.     

Development Planning for Pupil Achievement

When development planning was first introduced some 10 years ago it was regarded as a strategy to assist schools in managing change. Recent research evidence however suggests that schools that exhibit 'best practice' in development planning have transcended its use as a change management strategy and now see it as a means of enhancing pupil achievement. The key distinction between this and former approaches is that the current approach is rooted in classrooms. This shift in emphasis provides the focus for the paper. Research evidence from a variety of sources is used to explain the change of approach and, based on this, a rationale for development planning for pupil achievement is presented. Practical advice on how to implement such a strategy within the context of the DfEE's Target Setting initiative is then given. The paper concludes by describing the management arrangements most common in those schools that use development planning for enhancing pupil achievement.     

The Counselor's Assessment and Intervention with the Suicidal Student

This paper summarizes the major demographic and dynamic risk factors associated with suicide in terms of using this information to determine whether or not the college student needs to be hospitalized. If the decision is made not to hospitalize, an ecological approach to suicide prevention is suggested for both initial stabilization of the student, and as a problem solving strategy to address those issues that precipitated the student's suicidal inclination.     

Contrasting Perspectives and Performance of High School Students on Problem Solving in Real World, Situated, and School Contexts

This study describes and contrasts theoretically and empirically problem solving of situated problems in school and the real world at the macro level as a social-cultural activity system and analyzes the process of solving situated problems by high school students at the micro level as an activity. Three potentially experiential problem tasks were given to 31 last year high School science students. Action map, a concept derived from activity theory, was used to represent the solutions. Qualitative methods were used to analyze the data obtained from the written solutions as well as interviews with the participants. Leont'ev's activity theory and Engeström's activity system were used as frameworks to analyze and interpret the data. The results indicate that there are fundamental identifiable differences among the activities and the activity systems of problem solving in the real world, situated, and school contexts.     

Post‐expansionist Adjustments in Secondary Education in a Developing Society: a case study

Following the conclusion of a period of educational expansion during the last two decades, developing nations are now focusing attention upon adjusting some of those innovations made during the recent period of quantitative expansion. The paper examines how Trinidad and Tobago has responded to the need for adjustments in education provision during the current post‐expansionist period. In particular the paper analyzes Trinidad and Tobago's current reaction to the nation's system of double‐shift schooling, a device instituted during the 1970s as part of Government's strategy for universal secondary education. Arguments both for and against the shift‐system are presented, and Trinidad and Tobago's insistence that the mechanism should be dismantled is critically examined. Explanations for the approach taken by Trinidad and Tobago towards the nation's double‐shift schooling are drawn from two sources: arguments about the state of the nation's economy, and policies regarding approaches to educational development planning in developing nations.