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Chemistry Teacher International 2021; ▪▪▪(▪▪▪): 1–16 Chemistry Teacher International 2021; ▪▪▪(▪▪▪): 1–16 Research article Antonios Bakolis, Dimitrios Stamovlasis and Georgios Tsaparlis* Explicit teaching of problem categorization using concept mapping, and an exploratory study of its effect on student achievement and on conceptual understanding – the case of chemical equilibrium problems https://doi.org/10.1515/cti-2019-0021 Received December 5, 2019; accepted January 25, 2021; published online February 18, 2021 Abstract: A crucial step in problem solving is the retrieval of already learned schemata from long-term memory, a process which may be facilitated by categorization of the problem. The way knowledge is organized affects its availability, and, at the same time, it constitutes the important difference between experts and novices. The present study employed concept maps in a novel way, as a categorization tool for chemical equilibrium problems. The objective was to determine whether providing specific practice in problem categorization improves student achievement in problem solving and in conceptual understanding. Two groups of eleventh-grade students from two special private seminars in Corfu island, Greece, wereused: the treatment group (N = 19) and the control group (N = 21). Results showed that the categorization helped students to improve their achievement, but the improvement was not always statistically significant. Students at lower (Piagetian) developmental level (in our sample, students at the transitional stage) had a larger improvement, which was statistically significant with a high effect size. Finally, Nakhleh’scatego- rization scheme, distinguishing algorithmic versus conceptual subproblems in the solution process, was studied. Dependency of problem solving on an organized knowledge base and the significance of concept mapping on student achievement were the conclusion. Keywords: chemical equilibrium; concept mapping; Piagetian stages; problem categorization; problem solving Introduction As a goal of the teaching of chemistry is to foster meaningful learning, the teaching of strategies that cultivate complex and hierarchical cognitive structures can also facilitate development of cognitive abilities, such as problem solving, an everlasting topic in chemistry education. The way knowledge is organized in long-term memory is generally expected to relate to the degree of success in problem solving. According to cognitive *Corresponding author: Georgios Tsaparlis, Department of Chemistry, University of Ioannina, GR-451 10 Ioannina, Greece, E-mail: [email protected]. https://orcid.org/0000-0002-0856-747X Antonios Bakolis, Hellenic Civil Aviation Authority, I. Kapodistrias Corfu Airport, GR-49100 Corfu, Greece, E-mail: [email protected] Dimitrios Stamovlasis, Department of Philosophy and Education, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece, E-mail: [email protected]. https://orcid.org/0000-0003-0808-9065 Open Access. © 2021 Antonios Bakolis et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. 2 A. Bakolis et al.: The case of chemical equilibrium problems psychology, knowledge organization affects the availability and the retrieval process of conceptual schemata during problem solving. A previous study (Zikovelis & Tsaparlis, 2006) suggested and employed a linear categorization scheme for problems in the special topic of colligative properties of ideal solutions. By ‘linear’, we mean that the categories were listed one after the other. A treatment group showed a superior achievement that was not statistically significant. By dividing the students into high-, intermediate- and low-achievement subgroups on the basis of their performance in two highly reliable, nationally-examined upper secondary chemistry courses, it was found that students of the treatment intermediate subgroup outperformed in a statistically significant sense those of the control group, while no differentiation was found for the students of high and low achievement. The present study was designed to show whether an intervention-based problem-solving teaching approach affected student achievement. The research design contained the new tool of categorization through concept maps (Novak, 1985, 1990a, 1990b; Novak & Gowin, 1984). An interventional teaching with the use of this tool was conducted to investigate whether it would be possible to directly transfer the schemata used by expert solvers and whether they help beginners in both problem solving and conceptual understanding. The effect of Piagetian stages of cognitive development (Inhelder & Piaget, 1958) was examined, as well as the categorization scheme proposed by Nakhleh (1993), which distinguishes between algorithmic versus conceptual steps (or pieces or subproblems) in the solution process. At the outset, a fundamental distinction must be emphasized, that between problems and exercises (Johnstone, 1993). A real/novel problem requires that the solver must be able to use what has been termed as higher-order thinking or cognitive skills (HOTS or HOCS) (Zoller, 1993; Zoller & Tsaparlis, 1997). As a rule, extensive practice in problems in a particular area can turn problems into exercises, in which case, lower-order thinking/cognitive skills (LOTS or LOCS) suffice. For example, many problems in science can be solved by the application of well-defined procedures (algorithms) (Bodner, 1987) that can turn the problems into algorithmic exercises. Chemical equilibrium problems, despite the complexity of many of them, can become exercises with practice. Rationale – knowledge organization and problem categorization Problem categorization is part of knowledge organization. Knowledge that is well organized and connected in long-term memory is more easily recalled than specific information, which lacks organization and connections (Johnstone, 1991). Chi and Koeske (1983) studied the network representation of a four-year old child’s “dinosaur knowledge”, by comparing the structure of two mappings, based on three attributes: (1) number of links, (2) strength of links, and (3) the internal cohesion of the network in terms of higher-order groupings and specific patterns of interlinkages. It was found that the better structured set of dinosaurs was more easily remembered and retained by the child over a year, than the less structured set of dinosaurs. Chi, Feltovich, and Glaser (1981) investigated the representation of physics problems in relation to the physics knowledge in experts and novices, and found that experts and novices begin their problem repre- sentations with specifically different problem categories. Further, they were led to the conclusion that experts’ organization of a domain is according to the “deep structure” of the domain, whereas the schemes of novices are characterized by “surface” features. Based on the previous and similar studies, Smith (1992) used cate- gorizations of genetics problems and reported that, as expected, faculty experts focused almost exclusively on conceptual principles, but students’ categorizations focused primarily on problem knowns and unknowns. De Jong and Ferguson-Hessler (1986) investigated whether good novice problem solvers have their knowledge arranged around problem types to a greater extent than poor problem solvers. In the subject of physics (electricity and magnetism), 12 problem types were categorized according to their underlying physics principles. Good novice problem solvers responded to problem types, but poor problem solvers seemed to be influenced to a greater extent by the surface characteristics. The conclusion was that an organization of knowledge around problem types might be highly conducive to good performance in problem solving by novice problem solvers. A. Bakolis et al.: The case of chemical equilibrium problems 3 Bunce, Gabel, and Samuel (1991) examined the effect of strategies on chemistry problem solving and supported Reif’s (1981, 1983) hypothesis that a key in improving the problem solving capacity is the employment of a solution strategy. Expert and novice solvers are quite different in this capacity: experts’ knowledge networks about chemical equilibrium are characterized by a multilevel structure that is constructed in such a way that they include possible solution methods, which are easily retrieved from long-term memory (Wilson, 1994). Also, from the field of management, Day and Lord (1992), reported that the results of a problem sorting task indicated that experts tended to categorize the ill-structured problems significantly faster than novices. Experts also had greater variance in the number of categories used and they incorporated more problem information. Bunce and Heikkinen (1986) have proposed the explicit method of problem solving (EMPS), which aims to teach novice students the problem-solving analysis procedures used by experts. The method is an organized problem-analysis approach and involves: a) decoding the information given in the problem (data, outcome/ goal), b) correlating the data in long-term memory (recall), and c) designing the solution before implementing a mathematical solution. According to Reif (1981), this analysis helps students encode the pertinent infor- mation of the problem, which is a major difference in the problem-solving behavior of experts and novices. Encoding is defined by Sternberg (1981) as the identification of each term in the problem and the retrieval from long-term memory of the attributes of these terms that are thought to be relevant to the solution
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