Students’ Use of Problem-Solving Techniques
in General College Chemistry
by
Stephen R. Ott
A dissertation submitted to the faculty of
Brigham Young University
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Department of Instructional Psychology and Technology
Brigham Young University
December 2001
Chapter 1: Introduction
Today’s college chemistry students are studying to be the scientists and professionals of the future. To be successful in their chemistry courses, these students must learn how to solve numerous, mathematically-oriented homework problems and test questions. In fact, one of the purposes of these courses is to teach students applicable methods and techniques to solve those homework problems or test questions. These methods and techniques are conventionally called problem-solving strategies by science instructors (Ashmore, Frazer & Casey, 1979; Bodner, 1987; Bunce & Heikkinen, 1986; Chorneyko, Christmas, Cosic, Dibbs, Hamielec, Leod, Moore, Norman, Stankovich, Tyne, Wong & Woods, 1979).
Science educators have published lists of successful techniques that good problem solvers use or or characteristics that those problem solvers possess (Bunce, 1984; Herron & Greenbowe, 1986; Larkin, McDermott, Simon & Simon, 1980). Two frequently-identified, general techniques from these published lists are categorizing problems and using a general-to-specific process.
Using all of these published problem-solving techniques, educators have constructed specific problem-solving strategies to help students be successful in science course. Many of these problem-solving strategies contain a sequential set of procedures that students carry out to solve homework problems or tests questions. Some science instructors have even reported measurable success by students who use these problem-solving strategies (Ashmore, et al., 1979; Bunce & Heikkinen, 1986; Mettes, Pilot, Roossink and Dramers-Pals, 1980; Polya, 1957; Stiff, 1988; see Appendix B).
As stated, the vast majority of these problem-solving strategies consist of a set of sequential steps – words, phrases, or other verbal instructions – that students commit to memory and practice while solving science problems. However, psychological research has demonstrated that the majority of students are not verbal learners (Cambell, Cambell & Dickinson, 1992; Fogarty & Bellanca, 1995; Lawrence, 1989; Gardner, 1993; Tobias, 1990, 1992). Therefore, using these strategies would not be as beneficial for non-verbal learners as for verbal learners.
To accomodate non-verbal learners, visually-based learning strategies have been demonstrated by science educators (Whitten, Davis & Peck, 2000). One visually-based strategy that has seen increased usage is concept mapping (Regis, Albertazzi & Roletto, 1996; Stensvold & Wilson, 1992). Concept mapping consists of diagramed ideas, connected with lines according to conceptual relationships. (See “Visual Learning Strategies” in this research study.) Their success is attributed to the fact that students are forced to identify and describe relationships between the concepts in a subject area. Using this relationship-based design, concept maps have been identified as a "metacognitive tool" (Regis, et al., 1996), because they help students "learn how to learn" (Novak, 1990). Stensvold and Wilson (1992), found that among students classified with low verbal ability, students who constructed concept maps during the learning process ultimately scored higher on comprehension tests than students who did not. However, although the use of concept mapping a learning strategy has been investigated, research into the use of concept mapping as a problem-solving strategy is lacking.
A problem-solving strategy that looks like concept mapping has been in use by science educators for many years (Whitten, Davis & Peck, 2000). These maps contain measurable scientific properties in the map nodes, in place of conceptual ideas that are used in concept maps. The use of these scientific maps will be referred to as property mapping in this research study, in order to emphasize the distinct difference between this type of visual problem-solving approach and concept maps.
The purpose of this research was to determine the effect that the use of these verbal and visual problem-solving techniques strategies has on the success of students in a General College Chemistry course. The specific research question that was investigated was “Are students who apply the techniques of problem-solving strategies more successful in general college chemistry than students who do not?”
To answer the research question, the following specific, measurable questions were investigated:
- To what extent do students demonstrate the use of simple problem-solving techniques during examinations?
- Does the correct use of written problem-solving skills improve students’ performance in examinations?
- What are the benefits, if any, of using property mapping as a visual problem-solving strategy?
- Do students’ learning styles (e.g. right-brain or left-brain dominance) influence the effectiveness of different problem-solving techniques?
Chapter 2: Literature Review
College chemistry students need to develop the ability to solve unfamiliar problems to be successful in the professional world. Instruction into techniques for solving these problems is frequently demonstrated and practiced in college chemistry courses, and the literature describes many strategies taught by science educators. This study investigates the degree to which students’ use of verbal or visual problem-solving techniques increases students’ success in college chemistry classes.
This chapter begins by introducing the reader to my personal perception of the need for students to possess intellectual skills to solve unfamiliar problems. The chapter continues by describing how educational theory defines these problem-solving skills, and concludes by introducing the reader to already existing strategies that attempt to develop those skills.
Following the introduction, the "Method" chapter contains a description of the experimental design for this study. Following that, the "Results" chapter summarizes the data that was collected and displays various statistical calculations performed on the data. Finally, my conclusions about the research and the effectiveness of the use of problem-solving techniques are described in the "Discussion" chapter.
"The Crow and the Pitcher"
True problem-solving skills are used not only in educational settings, but all other circumstances of life. I have included the following parable to introduce the reader to the ultimate importance of developing those problem-solving skills.
In a spell of dry weather, when the birds could find very little to drink, a thirsty crow found a pitcher with a little water in it. But the pitcher was high and had a narrow neck, and no matter how he tried, the crow could not reach the water. The poor thing felt as if he must die of thirst.Then an idea came to him. Picking up some small pebbles, he dropped them into the pitcher one by one. With each pebble the water rose a little higher until at last it was near enough so he could drink.
In a pinch a good use of our wits may help us out. (Scholastic, Inc., 1994) /
Figure 1.“The Crow and the Pitcher" (Scholastic, Inc.)
The circumstances of the crow in Æsop's fable and the impressions of college freshman taking a general chemistry course share a couple of similarities – the environment is hostile and relief is just beyond reach. It is a rare student who does not find chemistry frustrating at one point or another during the semester. Because of the volume and variety of chemical concepts taught in class during the semester, students become overwhelmed tying to learn how to work through all the necessary homework problems correctly. With so much to learn, students wonder if, like the resolution of the crow’s problem, there is a secret technique or "trick" they must discover in order to survive the class.
Test questions are particularly frustrating for students. Many feel that although they have studied hard, test questions are unfamiliar or even irrelevant to the subject matter covered in class. Students often label them "trick questions" and consider them unfair. Chemistry instructors counter that there are not trick questions, but that students are expected to learn the necessary concepts and skills in class that provide them with the means to solve test questions correctly. Teachers assume that if students do learn the applicable problem-solving techniques in class, they will be able to answer test questions accurately, and if students do not answer test questions correctly, they did not learn the necessary problem-solving techniques.
The purpose of this research study is to determine whether students’ use of identifiable problem-solving techniques does improve their performance in a chemistry class. If students can learn and demonstrate the use of these problem-solving techniques in a chemistry course, those skills should help them to be successful in the professional world.
The Problem with Students' Problem Solving
As I finish this dissertation, the 21st century is just beginning. As a young boy, I always imagined the 21st century as full of new, almost unbelievable scientific inventions. As an adult, I see the realization of those boyhood imaginings as new scientific ideas, processes, and products arise almost daily.
My area of expertise, chemistry, has certainly played a pivotal role in the development of these ideas, processes and products. President Gordon B. Hinckley expressed that same opinion with the following comments that he made at the groundbreaking of the Ezra Taft Benson chemistry building in Aprilof 1993:
I am sobered by the thought that during my lifetime there has been more scientific discovery than in all the preceding generations. This is the great age of science. This is the age of chemistry. When I arose this morning, thinking of this occasion, I looked out the window through my plastic lenses—artificial implants in my eye as a result of surgery—and thought, 'Look at the beautiful morning.' . . .
I put on clothing that is the result of chemistry. . .. The suit I wear is part wool and part polyester. I put on shoes, the leather of which was tanned through chemistry; the soles of which were made possible through chemistry. I came down here in a car, and as I looked around at the beautiful interior of that car, I noticed all the plastic inside that is the result of chemistry. The beautiful paint on the surface came through the fruits of chemistry. Chemistry has become the very essence of our lives.
In fact, when you reflect on it, the greatest of all chemists was the Creator. There will never be another to excel, regardless of what is done in this building or any other building. (Avant, 1993, p. 3)
As a chemistry instructor, I am excited to teach the new century's young scientists. Some of these individuals will likely create more of the unbelievable inventions that I imagined as a boy.
From my perspective as an instructor, however, one major problem to solve for each of these developing scientists is just that – developing the ability to solve problems. Scientists must develop the skills to solve new problems because in the future, they will not be able to rely solely on already existant scientific processes. The explosion of new information, ideas, and inventions will necessitate synthesizing new procedures to handle new situations. To be ready for this task in their professional careers, it is important for chemistry students to begin developing these problem-solving skills in their college chemistry course.
Learning Taxonomies
Problem-solving skills exist as part of a larger set of intellectual abilities. Educational psychologists organize these skills into different hierarchies, or learning taxonomies. One taxonomy, developed by Gagné (1992), is listed from lower to higher intellectual skills as Discriminations, Concrete Concepts, Defined Concepts, Rules, Higher-order Rules, and Problem Solving. Gagné's levels are introduced here because they are the most compatible with the taxonomy used by most chemical educators.
Chemistry educators usually assume that students in General College Chemistry have developed at least the first four levels of Gagné's intellectual skills, and the literature explains that the purpose of chemistry courses is to develop students' problem-solving skills (Nurrenbern & Pickering, 1987; Pavelich, 1982; Tobias, 1992). However, a clear description of what problem solving consists of is rarely given. The most frequently quoted definition of problem solving in the chemical education literature is expressed (tongue-in-cheek) by Hayes (1981): "Whenever there is a gap between where you are now and where you want to be, and you don't know how to find a way to cross that gap, you have a problem." In practice, chemical educators imply that problem solving is the process of progressing through available facts and processes to arrive at a specific solution. Most of these processes involve algebraic manipulation of mathematical equations, and the exact solution is frequently a numerical quantity. This is the description for problem solving that I will be using throughout this dissertation. Herron categorizes this process as solving a “well-defined” problem, as opposed to an ill-defined problem (Herron, 1996).
Techniques of Good Problem Solvers
Some science educators have published lists of generalized practices or processes that good problem solvers use. The reader is referred to the three lists by Bunce & Heikkinen (1986), Herron & Greenbowe (1986), and Smith (1992) that are shown in Table 1. These lists contain broad, non-sequential practices used by scientists to solve problems. Other science educators have used these principles to create specific problem-solving algorithms that will be shown later.
Common Principles of Good Problem-Solving Techniques
Many of the previously-listed practices fit into one of the two following categories of problem-solving techniques that are frequently identified in educational literature: using a general to specific process, or categorizing the problem type. A description follows for each of these categories of practices and their importance in problem solving.
Using a General to Specific Process. Researchers have identified that "expert" problem solvers go from a general to specific approach, whereas amateurs work on a more "linear" approach (Larkin, 1981; Reif, 1983). Those researchers stated that experts worked hard at understanding the “whole picture” first, then concentrated on learning specifics. In contrast, novices tried to understand details of problems before understanding where (or if) a specific concept fit into the entire situation. One writer explained it in this way:
Bunce and Heikkinen (1984) / Herron and Greenbowe (1986) / Smith (1992)
1. Represent the problem verbally.
2.Sketch a diagram of the problem, representing any movement of objects with arrows.
3.Select a set of equations that describe the problem. / 1.Work by trial and error.
2.Think of the problem in terms of the physical system discussed.
3.Solve a special case.
4.Solve a simple problem that seems related to a difficult problem.
5.Break the problem into parts.
6.Substitute numbers for variables.
7.Draw diagrams to represent molecules and atoms.
8.Check interim or final results against other information. / 1.Adapt knowledge and its organization to facilitate the solution of problems in a domain.
2.Apply knowledge and skills to the problem-solving task.
3.Use forward reasoning and domain-specific procedures on standard problems within the domain of expertise, but use the "weaker" problem solving procedures (means-ends analysis, trial-and-error, etc.) on problems outside the domain of expertise.
4.Create an internal "problem space" which incorporates a qualitative representation or description of the problem.
5.Plan the general strategy or approach to be taken.
6.Break problems into parts and perform multi-step procedures.
7.Employ relevant problem-solving heuristics.
8.Evaluate the solution and the solution procedure.
9.Abstract patterns in their own performance and identify useful problem types.
This strategy may be illustrated usefully by an analogy to the problem of painting a picture. One painting strategy would be to paint successively, in complete detail, every adjacent square inch of the picture until the total picture is completed. The other strategy consists of first making a rough sketch of the entire picture, then elaborating this sketch by adding more detailed lines, then elaborating further by adding more detailed color information, etc. . . . (Reif, 1983)
This general to specific technique can be seen in the procedures listed in Table 1 from ideas such as drawing a diagram or picture, breaking the problem into smaller parts, or restating the problem in other words. One advantage of this process, according to Youmans (1971), is that this helps the students to concentrate more on the process than the final solution.
Categorizing the Problem Type. Many scientific instructional practices are based on the work of Piaget(1958), who suggested that information needs to be grouped and classified (Albanese, Brooks, Day, Koehler, Lewis, Marianelli, Rack & Tomlinson-Keasey, 1976; Fowler, 1980; Batt, 1980; Bodner, 1986; Brooks, Scholz & Tipton, 1978; Good, Mellon & Kromhout, 1978; Goodstein & Howe, 1978; Johnstone & El-Banna, 1986; Kurland, 1982; Milakofsky & Patterson, 1979; Renner & Lawson, 1973; Wulfsberg, 1983). One application of this problem-solving technique suggests that the student initially should categorize the question into the correct subject area, such as a gas-law problem, a thermodynamics problem, a stoichiometry problem, etc. (Bunce, Gabel & Samuel, 1991; Chi, Feltovich & Glaser, 1981; Eylon & Reif, 1984; Hinsley, Hayes & Simon, 1977; Mestre, Dufresne, Gerace & Hardiman, 1993; Ryan, 1987). The benefit of this technique is explained by Larkin (1981), who writes that the categorization process is more likely to bring to mind the correct formulas and solution processes.
Mestre, et al. (1993), developed software that forced students to categorize a specific homework problem before working it. In their study, physics students were required to categorize problems either according to the mathematical equations that were necessary to solve the problem, or according to the physics concepts that the problem was based upon. The researchers found that students who categorized problems conceptually performed better than those who categorized problems according to the mathematics and equations that were used.
Teaching Problem Solving Techniques