Competent Problem Solvers Research Articles

НАВЧАЛЬНО-МЕТОДИЧНІ ЗАДАЧІ У ПРОФЕСІЙНІЙ ПІДГОТОВЦІ МАЙБУТНІХ УЧИТЕЛІВ ІНФОРМАТИКИ

The essence of the concept “educational and methodical task” in the context of professional training of future teachers is revealed, the expediency of application of tasks in the process of obtaining qualification by students under the educational and professional program 014 “Secondary education (Informatics)” is substantiated. The teacher's ability to effectively solve methodological problems, which are reflected in the stages of understanding, design and implementation of methodological activities, is identified with methodological competence, as the processes of eliminating contradictions involve the use of methodological knowledge and methods of mastering professionally significant personal qualities. The expediency of distinguishing between methodical and educational-methodical problem is proved. The educational-methodical task is described as a task in which the content of the methodical activity of the teacher in a specific pedagogical situation is modeled, search of a way out of which assumes imitation of educational process during studying a school course of computer science in the conditions as close as possible to real. Competent problem solving requires fundamental knowledge of computer science and knowledge of computer science teaching methods, implementation of methodological actions that combine knowledge from different fields. The educational and methodical task is a multifaceted phenomenon and its content corresponds to the goals of the methodical activity and the characteristics of the educational-professional program according to which a student acquires the qualification “computer science teacher”. Considerable attention is paid to the analysis of classification of methodical and educational-methodical tasks. It is offered to use the following criteria: structural components of the methodical activity; functions of methodical activity; the level of complexity of the activity. The conclusions emphasize that the educational and methodical task is an important tool and method of preparing students for future professional activities, the systematic solution of various types of such tasks contributes to the acquisition of pedagogical experience, the formation of methodological competence of computer science teachers.

Childhood Predictors of Violent Victimization at Age 17 Years: The Role of Early Social Behavioral Tendencies

To assess the relation between early social behavioral tendencies and the risk of violent victimization in late adolescence. We analyzed 5 waves of data from the Zurich Project on the Social Development from Childhood into Adulthood (z-proso), a longitudinal sample of Swiss first graders (N=1138). Early social behavioral tendencies were measured at age 7years and included internalizing problems, externalizing behavior, prosocial behavior, negative peer relations, competent problem solving, dominance, and sensation seeking. Path analyses were conducted of the association between these tendencies and violent victimization at age 17years, and mediation through intermediate victimization at ages 11, 13, and 15years was examined. Several childhood social behavioral tendencies predicted victimization 10years later. Though this was the case for both sexes, the number and type of significant risk factors differed. For male children, sensation seeking, externalizing behavior, high prosociality, and negative peer relations at age 7years increased later victimization, whereas for female children, dominance and externalizing behavior were predictive. In addition, results showed that the relation between early risk factors and age 17 years victimization was mediated by intermediate victimization, showing that differences in victimization risk in early adolescence are carried forward into late adolescence. Childhood social behavioral tendencies predict victimization 10years later. Incorporating this finding into early prevention programs could reduce victimization over the life course.

How Can We Improve Problem Solving in Undergraduate Biology? Applying Lessons from 30 Years of Physics Education Research

If students are to successfully grapple with authentic, complex biological problems as scientists and citizens, they need practice solving such problems during their undergraduate years. Physics education researchers have investigated student problem solving for the past three decades. Although physics and biology problems differ in structure and content, the instructional purposes align closely: explaining patterns and processes in the natural world and making predictions about physical and biological systems. In this paper, we discuss how research-supported approaches developed by physics education researchers can be adopted by biologists to enhance student problem-solving skills. First, we compare the problems that biology students are typically asked to solve with authentic, complex problems. We then describe the development of research-validated physics curricula emphasizing process skills in problem solving. We show that solving authentic, complex biology problems requires many of the same skills that practicing physicists and biologists use in representing problems, seeking relationships, making predictions, and verifying or checking solutions. We assert that acquiring these skills can help biology students become competent problem solvers. Finally, we propose how biology scholars can apply lessons from physics education in their classrooms and inspire new studies in biology education research.

Talk It Out: A Conflict Resolution Program for Preschool Children with Speech and Language Impairments

Talk It Out was developed by speech-language pathologists to teach young children, especially those with speech and language impairments, to recognize problems, use words to solve them, and verbally negotiate solutions. One of the very successful by-products is that these same strategies help children avoid harming their voice. Across a school year, Talk It Out provides teaching and practice in predictable contexts so that children become competent problem solvers. It is especially powerful when implemented as part of the tier 1 preschool curriculum. The purpose of this article is to help school-based speech-language pathologists (1) articulate the need and rationale for early implementation of conflict resolution programs, (2) develop practical skills to implement Talk It Out strategies in their programs, and (3) transfer this knowledge to classroom teachers who can use and reinforce these strategies on a daily basis with the children they serve.

English Learners' Participation in Mathematical Discussion: Shifting Positionings and Dynamic Identities

This study investigated discursive positioning moves that facilitated Latino/a English learners' (ELs) opportunities to take on agentive problem-solving roles in group mathematical discussion. A focus on mechanisms that support students' agentive participation is consistent with our view that recurrent experiences participating and being positioned in particular ways contribute to identity development. Findings suggest several ways that discursive positioning facilitated ELs' agentive participation, including via: (a) explicit statements that validated ELs' reasoning, (b) invitations to share, justify, or clarify thinking that positioned ELs as competent problem solvers, and (c) inviting peers to respond to an EL's idea in ways that positioned the idea as important and/or mathematically justified.

The University’s Cutting Edge—Source of Its Flatness, Or: Reclaiming the University’s Third Dimension

THE AMERICAN ASSOCIATION OF UNIVERSITIES (AAU), the exclusive club of the nation's leading research universities, characterizes a research university in the association's White Paper thus: (1) The raison d'etre of the American research university is to ask questions and solve problems. Together, the nation's research universities constitute an exceptional national resource, with unique capabilities: * America's research universities are the forefront of innovation; they perform about half of the nation's basic research. * The expert knowledge that is generated in our research universities is renowned worldwide; this expertise is being applied to real-world problems every day. * By combining cutting-edge research with graduate and undergraduate education, America's research universities are also training new generations of leaders in all fields. Let me give up front the central claim of my article (2): What is increasingly missing from the late-modern research university and the kind of training it offers is what I shall call the university's third dimension. For the AAU this third dimension seems to have disappeared from the university. The first two dimensions of the late-modern research university constitute its sharpness as a problem-solving institution: to ask intricate questions and to solve complex problems. The late-modern research university accomplishes this task by way of ever more specialized research and by way of a concomitant training of undergraduate and graduate students in the kind of expert knowledge that makes them competent problem-solvers. The university's third dimension--constitutive of the classical university--comprises, first, schole (in English leisure), that is, the structured practice of genuine intellectual contemplation and reflection, and, second, paideia, that is, the integral formation of the intellectual virtues in conjunction with the development of the moral virtues. A university that lacks this third dimension might well be able to develop remarkable research, but, I think, will eventually suffer from a suffocating intellectual and spiritual flatness that in the long run will prove detrimental to the university as such. In order to make good on this claim I will proceed in three steps. In the first step, I will offer a snapshot of the late-modern research university and highlight three of its noteworthy features: first, the remarkable ambivalence in contemporary academic thought pertaining to reason's reliability and range, and, ultimately, to reason's capacity for truth; second, the late-modern university's pervasive embrace of the means of quantification or metrics for purposes of assessment and management (into which university administration seems to have largely morphed); and third, its embrace of the allegedly neutral framework of for its internal and external communication. These features belong essentially to what I regard as the university's first and second dimension that together constitute the cutting edge, the utilitarian character of a highly complex problem-solving machine. The university's third dimension, its depth dimension, refers to what has been at one time essential to the university qua university, that is, the pursuit of larger, comprehensive and integrating questions of truth and meaning--questions, I dare say, of metaphysics and morals. What is to be observed at the present moment regarding this third dimension are signs of a newly emerging disenchantment with secular reason as the university's governing principle, a disenchantment discernible as it seems first and foremost among some of the postmodern avant-gardes of the late-modern research university. In a second step, I shall consider a brief philosophical observation and an equally brief theological reminder about the university's third dimension. In a concluding third step I will suggest that leisure and paideia are the two practices that keep the soul of the university alive and, that will assure that the university qua university will continue to matter even under the specter of a comprehensive functionalization of the late-modern university--especially after the disenchantment of secular reason. …

The University's Cutting Edge---Source of Its Flatness

The University’s Cutting Edge—Source of Its Flatness, Or: Reclaiming the University’s Third Dimension Reinhard Hütter (bio) The American Association of Universities (AAU), the exclusive club of the nation’s leading research universities, characterizes a research university in the association’s “White Paper” thus:1 The raison d’être of the American research university is to ask questions and solve problems. Together, the nation’s research universities constitute an exceptional national resource, with unique capabilities: • America’s research universities are the forefront of innovation; they perform about half of the nation’s basic research. • The expert knowledge that is generated in our research universities is renowned worldwide; this expertise is being applied to real-world problems every day. • By combining cutting-edge research with graduate and undergraduate education, America’s research universities are also training new generations of leaders in all fields. Let me give up front the central claim of my article2: What is increasingly missing from the late-modern research university and the kind of training it offers is what I shall call the university’s third [End Page 36] dimension. For the AAU this third dimension seems to have disappeared from the university. The first two dimensions of the late-modern research university constitute its “sharpness” as a problem-solving institution: to ask intricate questions and to solve complex problems. The late-modern research university accomplishes this task by way of ever more specialized research and by way of a concomitant training of undergraduate and graduate students in the kind of expert knowledge that makes them competent problem-solvers. The university’s third dimension—constitutive of the classical university—comprises, first, scholē (in English “leisure”), that is, the structured practice of genuine intellectual contemplation and reflection, and, second, paideia, that is, the integral formation of the intellectual virtues in conjunction with the development of the moral virtues. A university that lacks this third dimension might well be able to develop remarkable research, but, I think, will eventually suffer from a suffocating intellectual and spiritual flatness that in the long run will prove detrimental to the university as such. In order to make good on this claim I will proceed in three steps. In the first step, I will offer a snapshot of the late-modern research university and highlight three of its noteworthy features: first, the remarkable ambivalence in contemporary academic thought pertaining to reason’s reliability and range, and, ultimately, to reason’s capacity for truth; second, the late-modern university’s pervasive embrace of the means of quantification or metrics for purposes of assessment and management (into which university administration seems to have largely morphed); and third, its embrace of the allegedly neutral framework of “secular reason” for its internal and external communication. These features belong essentially to what I regard as the university’s first and second dimension that together constitute the cutting edge, the utilitarian character of a highly complex problem-solving machine. The university’s third dimension, its depth dimension, refers to what has been at one time essential to the university qua university, that is, the pursuit of larger, comprehensive and integrating questions [End Page 37] of truth and meaning—questions, I dare say, of metaphysics and morals. What is to be observed at the present moment regarding this third dimension are signs of a newly emerging disenchantment with secular reason as the university’s governing principle, a disenchantment discernible as it seems first and foremost among some of the postmodern avant-gardes of the late-modern research university. In a second step, I shall consider a brief philosophical observation and an equally brief theological reminder about the university’s third dimension. In a concluding third step I will suggest that leisure and paideia are the two practices that keep the soul of the university alive and, that will assure that the university qua university will continue to matter even under the specter of a comprehensive functionalization of the late-modern university—especially after the disenchantment of secular reason. Like all thought, the normative perspectives that inform my critique of the late-modern research university and the concomitant university education come from somewhere...

Instructors’ reasons for choosing problem features in a calculus-based introductory physics course

This study investigates how the beliefs and values of physics faculty influence their choice of physics problems for their students in an introductory physics course. The study identifies the goals these instructors have for their students, the problem features they believe facilitate those goals, and how those features correspond to problems they choose to use in their classes. This analysis comes from an artifact-based interview of 30 physics faculty teaching introductory calculus-based physics at a wide variety of institutions. The study concludes that instructors' goals and the problem features they believe support those goals align with research-based curricular materials intended to develop competent problem solvers. However, many of these instructors do not use the beneficial problem features because they believe these features conflict with a more powerful set of values concerned with clarity of presentation and minimizing student stress, especially on exams.

Teaching Differential Equations with Modeling and Visualization

In this article, I explain the history of using Interdisciplinary Lively Applications Projects (ILAPs) in an ordinary differential equations course. Students want to learn methods to “solve real world problems,” and incorporating ILAPs into the syllabus has been an effective way to apply solution methods to situations that students may encounter in other disciplines. Feedback has been positive and will be shared. Examples of ILAPs currently used will be referenced. For more information about how to develop ILAPs, see Huber and Myers (in Innovative Approaches to Undergraduate Mathematics Courses Beyond Calculus, 2005). 1 Confident and Competent Problem Solvers One of my goals each semester is to develop students into confident and competent problem solvers. The competence comes from practice, solving problem after problem. The confidence also comes with experience, from knowing what to do when facing a new problem. Many textbooks give students an equation and ask them to solve it. In the past, if the textbook gave students the harmonic oscillator equation, complete with values for the mass, damping coefficient and spring constant, students could put in the values and then use the appropriate technique to solve for the displacement or velocity of the mass. However, when confronted with a word problem and asked to develop the model’s differential equation, students struggled. Students were comfortable with their “Plug and Chug” method of solving, as long as they knew what and where to plug. That got me thinking: What if we just gave them the forces acting on the problem, to include any non-homogeneous driving function, and asked them to predict long-term behavior? A few years ago, as an experiment suggested by my colleague Don Small at West Point, I gave a group of students a differential equations problem in the form of a long word problem and asked them to set up the model (define variables, state what is given, make a few valid assumptions, write down what they were asked to determine, and explain the technique they would use to solve it). Suppose that the growth of an alligator population in the Okefenokee Swamp is proportional to its population at a rate of 0.05 per year, and that the initial population is 7200 gators. Alligator populations have risen to such CODEE Journal http://www.codee.org/ high levels that the U.S. Fish and Wildlife Service “harvests” gators by allowing tightly controlled hunting of 650 to be hunted in one year, followed by no harvesting in each of the next two years of these animals, famous for their durable hide and excellent meat. This harvesting strategy is repeated every three years. Model the IVP and predict how many gators will there be after 6, 7, and 8 years. Further, what would the harvesting need to be to wipe out the gator population? I told them NOT to solve it, unless they had time. We had already covered using Laplace transforms to solve these types of problems, but I wanted to see if they could establish the problem to be solved. Afterwards, I asked the students to explain their problem-solving process, to include any assumptions they had to make. The real value of this exercise came from the explanations. Some students wrote about their anxieties about having a “vague” problem, while others wrote about their happiness in being able to set up a “real-world” problem. The harvesting scheme involves a Heaviside function which is shown in Figure 1 below. The horizontal axis shows time in years and the vertical axis shows the number of gators hunted. The solution to the problem should show a series of population increases and decreases, due to the cyclic harvesting. A plot of the particular solution is shown in Figure 2. 1 2 3 4 5 t 6 7 8 9 200 400 600 Figure 1: Harvesting Gators in the Okefenokee Swamp 1 2 3 4 5 t 6 7 8 9 7000 7500 8000 8500 Figure 2: Gator Population in the Okefenokee Swamp

Accessing strategic knowledge: Individual differences in procedural and strategy transfer

College students' ability to spontaneously access prior knowledge in the form of a general procedure and a specific strategy was demonstrated using a training for transfer paradigm ( Phye, 1989 Phye, 1990). Students received practice on verbal analogy problems during training and were given a delayed transfer task requiring memory-based transfer. Motivational variables of confidence in pretraining knowledge and awareness of training performance were used to predict successful transfer of strategic knowledge. Individual differences in awareness best predicted subjects' ability to spontaneously access prior knowledge. Results are discussed within the context of transfer-appropriate processing ( Bransford, 1990) and transfer-appropriate procedures ( Roediger, 1990) models of learning and memory. The argument is made that both memory and transfer processes are used as “tools” by competent problem solvers.

Towards powerful learning environments for the acquisition of problem-solving skills

It is generally agreed that acquiring thinking and problem-solving skills is nowadays a primary objective of general education. Responding appropriately to this challenge requires an answer to the following questions: 1. what does the acquisition of problem-solving skills involve, and 2. how can those abilities be fostered through systematic instruction? This contribution describes a four-step model of skilled problem-solving processes, and gives an overview of three major categories of cognitive skills involved in competent problem solving, namely, the flexible and integrated application of domain-specific knowledge, of heuristic methods, and of metacognitive skills. Furthermore, a framework is presented for the design and elaboration of powerful teaching-learning environments in which such problem-solving skills can be acquired efficiently. Two basic ideas underlying this model are: the view of learning as a constructive process, and the idea of cognitive apprenticeship as an effective and appropriate method for learning and teaching. Finally, some recent research findings supporting the educational significance of the framework are briefly reviewed.

Mathematics matters: matters of consequence or doing something consequential?

This article argues that besides the analytical cognitive processing of the left‐brain, and the intuitive cognitive processing of the right‐brain, there are other psychological aspects of problem solving that must be taken into consideration and planned for in mathematics classrooms if learners are to become competent problem solvers. These psychological factors, in addition to cognition, are: volition, perception, affection, and psychomotor potentialities. To release these potentialities during problem solving, the author argues that the whole brain must be brought into balance (synchronization). This balancing act will necessitate that: (1) the left and right hemispheres of the brain be brought into synergistic union to aid in cognitive processing; (2) the back and front regions be brought into balance to aid perception (back half of the brain), psychomotor, cognition and volition (front half of the brain); and (3) the top and bottom regions (MacLean's Triune Brain) be brought into synch to insure that affection (a subcortical potentiality) positively impacts on the four aforementioned cortical potentialities. The author concludes the article by suggesting to teachers how they can arrange environments and guide interaction to produce more competent problem solvers. Throughout the article, the author uses characters from St Exupery's book The Little Prince to help her make the point that mathematics matters do matter ... not as ‘matters of fact’ or bottom‐line ‘matters of consequence’, but rather as ‘matters of so much importance’ to children coming to know themselves and their worlds by ‘doing things they feel are consequential’ with personally generated mathematical understandings.