215,704 research outputs found

    K-8 Preservice Teachers’ Inductive Reasoning in the Problem-Solving Contexts

    Get PDF
    This paper reports the results from an exploratory study of K-8 pre-service teachers’ inductive reasoning. The analysis of 130 written solutions to seven tasks and 77 reflective journals completed by 20 pre-service teachers lead to descriptions of inductive reasoning processes, i.e. specializing, conjecturing, generalizing, and justifying, in the problem-solving contexts. The uncovered characterizations of the four inductive reasoning processes were further used to describe pathways of successful generalizations. The results highlight the importance of specializing and justifying in constructing powerful generalizations. Implications for teacher education are discussed

    Algebraic thinking of grade 8 students in solving word problems with a spreadsheet

    Get PDF
    This paper describes and discusses the activity of grade 8 students on two word problems, using a spreadsheet. We look at particular uses of the spreadsheet, namely at the students’ representations, as ways of eliciting forms of algebraic thinking involved in solving the problems. We aim to see how the spreadsheet allows the solution of formally impracticable problems at students’ level of algebra knowledge, by making them treatable through the computational logic that is intrinsic to the operating modes of the spreadsheet. The protocols of the problem solving sessions provided ways to describe and interpret the relationships that students established between the variables in the problems and their representations in the spreadsheet

    Designing as Construction of Representations: A Dynamic Viewpoint in Cognitive Design Research

    Get PDF
    This article presents a cognitively oriented viewpoint on design. It focuses on cognitive, dynamic aspects of real design, i.e., the actual cognitive activity implemented by designers during their work on professional design projects. Rather than conceiving de-signing as problem solving - Simon's symbolic information processing (SIP) approach - or as a reflective practice or some other form of situated activity - the situativity (SIT) approach - we consider that, from a cognitive viewpoint, designing is most appropriately characterised as a construction of representations. After a critical discussion of the SIP and SIT approaches to design, we present our view-point. This presentation concerns the evolving nature of representations regarding levels of abstraction and degrees of precision, the function of external representations, and specific qualities of representation in collective design. Designing is described at three levels: the organisation of the activity, its strategies, and its design-representation construction activities (different ways to generate, trans-form, and evaluate representations). Even if we adopt a "generic design" stance, we claim that design can take different forms depending on the nature of the artefact, and we propose some candidates for dimensions that allow a distinction to be made between these forms of design. We discuss the potential specificity of HCI design, and the lack of cognitive design research occupied with the quality of design. We close our discussion of representational structures and activities by an outline of some directions regarding their functional linkages

    The nature of gestures’ beneficial role in spatial problem solving

    Get PDF
    Peer reviewedPostprin

    The challenge of complexity for cognitive systems

    Get PDF
    Complex cognition addresses research on (a) high-level cognitive processes – mainly problem solving, reasoning, and decision making – and their interaction with more basic processes such as perception, learning, motivation and emotion and (b) cognitive processes which take place in a complex, typically dynamic, environment. Our focus is on AI systems and cognitive models dealing with complexity and on psychological findings which can inspire or challenge cognitive systems research. In this overview we first motivate why we have to go beyond models for rather simple cognitive processes and reductionist experiments. Afterwards, we give a characterization of complexity from our perspective. We introduce the triad of cognitive science methods – analytical, empirical, and engineering methods – which in our opinion have all to be utilized to tackle complex cognition. Afterwards we highlight three aspects of complex cognition – complex problem solving, dynamic decision making, and learning of concepts, skills and strategies. We conclude with some reflections about and challenges for future research

    A literature review of expert problem solving using analogy

    Get PDF
    We consider software project cost estimation from a problem solving perspective. Taking a cognitive psychological approach, we argue that the algorithmic basis for CBR tools is not representative of human problem solving and this mismatch could account for inconsistent results. We describe the fundamentals of problem solving, focusing on experts solving ill-defined problems. This is supplemented by a systematic literature review of empirical studies of expert problem solving of non-trivial problems. We identified twelve studies. These studies suggest that analogical reasoning plays an important role in problem solving, but that CBR tools do not model this in a biologically plausible way. For example, the ability to induce structure and therefore find deeper analogies is widely seen as the hallmark of an expert. However, CBR tools fail to provide support for this type of reasoning for prediction. We conclude this mismatch between experts’ cognitive processes and software tools contributes to the erratic performance of analogy-based prediction

    Graphical representation and generalization in sequences problems

    Get PDF
    In this paper we present different ways used by Secondary students to generalize when they try to solve problems involving sequences. 359 Spanish students solved generalization problems in a written test. These problems were posed through particular terms expressed in different representations. We present examples that illustrate different ways of achieving various types of generalization and how students express generalization. We identify graphical representation of generalization as a useful tool of getting other ways of expressing generalization, and we analyze its connection with other ways of expressing it
    corecore