Technological problem solving in two science classrooms

This paper reports on the analysis of student (aged 13–15) technological capability as they undertook technological tasks in science classrooms. The activities covered a number of different contexts, had differing degrees of openness, and methods of presentation. An holistic approach to analysing student performance was developed and this provided insights into the approaches adopted by the students. The focus of students on an end-product meant that students did not fully consider the process that might be required to solve the problem. The strategies, skills and knowledge they brought to bear were often not appropriate. Present classroom cultures and contexts need to be understood as greatly affecting performance in technological problem solving. Specializations: science and technology education.     

Methodologies for problem solving: An engineering approach

Learning how to approach and solve problems which relate to real world situations is an integral part of the education of many higher and further education students and is particularly relevant to students studying for a professional or vocational degree. This paper outlines the nature of problems experienced by engineers and indicates how engineering students are taught to approach the identification and solution of the types of problems which they will experience as practicing professionals. Methodologies used are of general interest and may be applicable in other, unrelated, disciplines.     

Teaching problem solving: Don't forget the problem solver(s)

The importance of intrapersonal and interpersonal intelligences has long been known but educators have debated whether to and how to incorporate those topics in an already crowded engineering curriculum. In 2010, the authors used the classroom as a laboratory to observe the usefulness of including selected case studies and exercises from the fields of neurology, artificial intelligence, cognitive sciences and social psychology in a new problem-solving course. To further validate their initial findings, in 2012, the authors conducted an online survey of engineering students and engineers. The main conclusion is that engineering students will benefit from learning more about the impact of emotions, culture, diversity and cognitive biases when solving problems. Specifically, the work shows that an augmented problem-solving curriculum needs to include lessons on labelling emotions and cognitive biases, ‘evidence-based’ data on the importance of culture and diversity and additional practice on estimating conditional probability.     

Problem solving in science lessons: How students explore the problem space

This report examines, from a constructivist framework, how students presented with discrepant event problems during science lessons begin the problem solving process by exploration of the problem space. Three discrepant events were presented to five classes of eleven to thirteen year-olds using three different teaching strategies identified from the literature. The teaching strategies used teacher demonstrations followed by students asking the teacher questions, teacher demonstrations followed by an explanation by the teacher, and small groups of students under the guidance of the teacher. Data were collected from field notes, video tapes of the lessons, and student interviews using a stimulated recall technique to elicit the students' thinking during the lessons. The extent to which students could explore the problem space was found to be determined by the teaching strategy used, as the first and last strategies encouraged students to find their own explanations. Different information sources were also available in each of the teaching strategies. That is, exploration of the problem space was inextricably linked to the social context, partially determined by the teaching strategy. Because of constraints imposed by each teaching strategy none of those used was considered entirely satisfactory. An alternative strategy is suggested from a combination of aspects of the strategies trialled.     

Experimental problem solving: An instructional improvement field experiment

An instructional program based on expert-novice differences in experimental problem-solving performance was taught to grade 6 students (N = 265). Classes of students were randomly assigned to conditions in a delayed treatment design. Performance was assessed with multiple-choice and open-ended measures of specific transfer. Between group comparisons using pretest scores as a covariate showed that treatment condition students consistently outperformed controls; similar results were revealed in the within group comparisons. The achievement of the early treatment group did not decline in tests administered one month after the posttest.     

Teaching problem solving: An ATI study of the effects of teaching algorithmic and heuristic solution methods

This paper begins by characterizing typical training programs on “learning to think,” in terms of: their breadth, generality and specificity; the types of tasks and solution methods; and the guidance to students (assigning them to alternative programs; registering and reacting to their mistakes, requests for help, etc.). The paper then outlines some strengths and weaknesses of past research and sets out criteria appropriate for an aptitude-treatment interaction (ATI) study of the relationship between tasks, training methods and student attributes. Finally, an account is given of exemplary ATI experiments, administered via a computer, on the immediate and delayed effects of teaching algorithmic and heuristic solution methods. The tasks involve inductive reasoning (the extrapolation of number series) and deductive reasoning (the evaluation of syllogisms).     

The influence of scaffolded computerised science problem solving on motivational aspects

ABSTRACT

The current study focused on scaffolding programmes, including cognitive and meta-cognitive components, for science problem solving in a computerised learning environment to identify their unique effects on aspects of student motivation. Using expectancy-value theory as a conceptual framework, the current study focused on two motivational aspects: intrinsic value and perceived cost. Four scaffolding components were identified (structural, reflective, subject matter and enrichment) and used in different configurations to construct four scaffolding programmes ranging from low support (Enrichment) to partial support (Operative and Strategic) to full support (Integrated). The participants were seventh-grade students (N?=?458) sampled from 15 different classes in 3 middle schools. The classes were randomly assigned to the five treatment groups (four ‘scaffolding programmes’ and one control). The intervention was conducted over approximately 6 months as part of the regular class curriculum. The first phase of the study was based on self-report surveys distributed twice to all participants, and the second phase was based on observations of a sub-sample (N?=?145). The findings indicated that the integrated group demonstrated the most adaptive patterns of motivation. Specifically, the integrated group was the only group that showed no decline in intrinsic value or increases in perceived cost. Both the strategic and integrated groups had higher levels of observed willingness to invest effort and reports of intentional learning when using the scaffolding software. The common feature of these groups is the reflection component, which implies that reflection and its combination with subject matter have positive effects on motivation.     

An alternate path to stoichiometric problem solving

Stoichiometric problem solving has always been a stumbling block for many students in introductory chemistry courses. Research has shown that it is quite common for students to rely on algorithms when doing stoichiometric calculations. In previous studies, students were confronted with simple stoichiometric problems that involved comparing molar masses with simple ratios to one another. It turned out that students very successfully used their own problem-solving strategies. It is typical of these strategies that students describe relations in their own words rather than applying mathematical calculations. In this paper, an alternate path to teaching introductory stoichiometry-based on the results of research-will be discussed. The recommendation given is to use problems of the kind mentioned above which can easily be solved by quick mental calculation.     

A problem solving model for use in science student teacher supervision

Conclusion The period of time student teachers have to receive feedback from their supervisors and cooperating teachers is relatively short. Techniques and ideas suggested by university supervisors and cooperating teachers are clearly beneficial to beginning teachers, but the students also need direct experience in addressing classroom concerns themselves. Student teachers need to develop techniques for evaluating their own teaching and for solving instructional problems autonomously such as suggested through the use of this model. The problem solving model forces student teachers to take responsibility for their learning about teaching. It forces them to analyze and reflect on their own lessons and to deal with their own problems. Importantly, the model may serve as a tool for self-evaluation that can be used during students’ first few years of teaching and throughout their science teaching career. Student teachers will still undergo the complex and sometimes overwhelming experience of teaching for the first time. However, by addressing each problem they face in a systematic, organized way, the experience may become more manageable, and success may seem more attainable for them.     

Chapter 5 Gender differences in mathematics problem solving and science: A longitudinal analysis

This study describes gender differences in achievement in the academic areas of mathematics problem solving and science. Standardized achievement test scores for a sample of 3002 students who were tested in each of ten consecutive years, grades 3 through 12, were used to assess the differences in mathematics while matched data for grades 9 through 12 were available in science. Selected percentiles (90th, 75th, 50th, 25th, 10th) were estimated for both Female and male score distributions for each area. The results indicate fairly consistent patterns of differences. Males generally performed better at the upper percentile levels of the score distributions in mathematics problem solving and science, while females closed the gap and, in some instances, outperformed males at the lower percentile levels.     

Teaching problem solving as viewed through a theory of models

Summary This paper presents a small amount of theory including an analysis of the task of teaching problem solving and the act of problem solving derived from a theory of models of operations. It also presents the results of an exploratory investigation which tends to add credence to elements of the analysis.Two of the general problem solving strategies which are suggested are (1) classification of word problems as instances of models previously learned (taught) and (2) a variety of techniques involving mapping individually word problems onto instances of familiar models. A third problem solving strategy which has not been mentioned is indicated by the theory: In this strategy, from the given problematical situation (word problem), a model is generalized which subsumes the given situation, and search for an isomorphism between the model and various operations (i.e., multiplication) is conducted. If an isomorphism is observed, then the selected operation and attending computational algorithms can be used to solve the problem. Of course, it is unlikely that this type of activity would be appropriate for primary grade children, but perhaps it could be taught at a later stage of the curriculum.The extensive mathematics education literature devoted to the study of teaching problem solving in the elementary school includes numerous theoretical and methodological approaches to investigating problem solving. This paper, the author believes, presents a unique, systematic, and reasonable perspective on the matter. Both a systematic view of the act of solving one-step word problems and a two stage general level analysis of practices found in teaching problem solving have been presented as they were derived from a theory of models.     

Teaching and testing mathematical problem solving by offering optional assistance

Transfer capability is usually defined as theability to apply acquired knowledge and skillsin novel situations.The experiment reported here concerned transferin mathematics education. An experimental programme was constructed, based on strengtheningthe connection of strategic and domain specificknowledge and offering hints during teaching aswell as during testing.Subjects were first graders from secondaryeducation in the Netherlands, from two schools,two classes each. Students from these fourclasses were randomly allocated either to theexperimental or the control group.The experimental computer-supported teachingprogramme was offered once a week during sixweeks; the control group received regularmathematics instruction.After controlling for the effects of thecovariates intelligence, mathematics aptitudeand anxiety, it was shown that the experimentalsubjects performed significantly better on aposttest than subjects in the control group.The results suggest that the experimentalinstruction method enhances mathematics problemsolving ability more strongly than traditionalinstruction. Upon closer examination thiseffect appears to be restricted to subjectsalready relatively high in intelligence andmathematical ability. This finding is notuncommon in intervention research, and issometimes referred to as the Matthew orthe fan-spread effect.     

An online support system to scaffold real-world problem solving

The article presents a reusable online support system, in which an open-ended learning environment is created to scaffold complex, real-world problem solving activities. The major learning components of the system are specifically described, and the internal interactions between different components within the system and the external interactions among the system, learners (who also interact with one another among themselves), instructors, and administrators are demonstrated. The learning theories and the assumptions underpinning the system design framework are discussed in terms of each of the system components: case library with real-world cases, question prompts, peer review, expert modelling, and self-reflection mechanisms. In conclusion, initial findings about the support system are shared, and issues regarding reusability, adaptivity, and generativity of the system are addressed focusing on developing novice learners' problem solving skills in various domains and contexts. The article proposes a cognitive model for contextualizing learning scenarios to support real-world problem solving, which has implications for designing e-learning.     

The effects of a problem solving strategy on the achievement of earth science students

A review of the stated goals for education reveals a consistent emphasis on problem solving. Problem solving is compatible with the investigative nature of science and with higher order thinking. Consequently, a problem solving strategy was developed to improve the achievement of eighth grade students enrolled in earth science. The sample consisted of 287 eighth grade students randomly assigned to fourteen sections taught by four teachers. This resulted in seven control sections and seven experimental sections. The students in the treatment groups received approximately six weeks of instruction with the experimental groups receiving a variety of problem solving activities. A forty item posttest consisting of four subtests was administered to all students. The results indicate that the problem solving approach was useful in improving the overall achievement of students. It was particular effective in facilitating application of earth science subject matter. This problem solving approach appears to be a feasible strategy to use in most secondary science classrooms.