Chapter 1: Introduction − The Many Types and Kinds of Chemistry Problems

According to the ancient Greeks, “The beginning of education is the study of names”, meaning the “examination of terminology”.¹ The word “problem” (in Greek: «πρόβλημα»/“problēma”) derives from the Greek verb “proballein” (“pro + ballein”), meaning “to throw forward” (cf. ballistic and ballistics), and also “to suggest”, “to argue” etc. Hence, the initial meaning of a “problēma” was “something that stands out”, from which various other meanings followed, for instance that of “a question” or of “a state of embarrassment”, which are very close to the current meaning of a problem. Among the works of Aristotle is that of “Problēmata”, which is a collection of “why” questions/problems and answers on “medical”, “mathematical”, “astronomical”, and other issues, e.g., “Why do the changes of seasons and the winds intensify or pause and decide and cause the diseases?”¹ 

Problem solving is a complex set of activities, processes, and behaviors for which various models have been used at various times. Specifically, “problem solving is a process by which the learner discovers a combination of previously learned rules that they can apply to achieve a solution to a new situation (that is, the problem)”.²  Zoller identifies problem solving, along with critical thinking and decision making, as high-order cognitive skills, assuming these capabilities to be the most important learning outcomes of good teaching.³  Accordingly, problem solving is an integral component in students’ education in science and Eylon and Linn have considered problem solving as one of the major research perspectives in science education.⁴ 

Bodner made a fundamental distinction between problems and exercises, which should be emphasized from the outset (see also the Foreword to this book).^5–7  For example, many problems in science can be simply solved by the application of well-defined procedures (algorithms), thus turning the problems into routine/algorithmic exercises. On the other hand, a real/novel/authentic problem is likely to require, for its solution, the contribution of a number of mental resources.⁸ 

According to Sternberg, intelligence can best be understood through the study of nonentrenched (i.e., novel) tasks that require students to use concepts or form strategies that differ from those they are accustomed to.⁹  Further, it was suggested that the limited success of the cognitive-correlates and cognitive-components approaches to measuring intelligence are due in part to the use of tasks that are more entrenched (familiar) than would be optimal for the study of intelligence.

The division of cognitive or thinking skills into Higher-Order (HOCS/HOTS) and Lower-Order (LOCS/LOTS)^3,10  is very relevant. Students are found to perform considerably better on questions requiring LOTS than on those requiring HOTS. Interestingly, performance on questions requiring HOTS often does not correlate with that on questions requiring LOTS.¹⁰  In a school context, a task can be an exercise or a real problem depending on the subject's expertise and on what had been taught. A task may then be an exercise for one student, but a problem for another student.¹¹  I return to the issue of HOT/LOTS in Chapters 17 and 18.

Johnstone has provided a systematic classification of problem types, which is reproduced in Table 1.1.⁸  Types 1 and 2 are the “normal” problems usually encountered in academic situations. Type 1 is of the algorithmic exercise nature. Type 2 can become algorithmic with experience or teaching. Types 3 and 4 are more complex, with type 4 requiring very different reasoning from that used in types 1 and 2. Types 5–8 have open outcomes and/or goals, and can be very demanding. Type 8 is the nearest to real-life, everyday problems.

Problem solving in chemistry, as in any other domain, is a huge field, so one cannot really be an expert in all aspects of it. Complementary to Johnstone's classification scheme, one can also identify the following forms: quantitative problems that involve mathematical formulas and computations, and qualitative ones; problems with missing or extraordinary data, with a unique solution/answer, or open problems with more than one solution; problems that cannot be solved exactly but need mathematical approximations; problems that need a laboratory experiment or a computer or a data bank; theoretical/thought problems or real-life ones; problems that can be answered through a literature search, or need the collaboration of specific experts, etc.

According to Bodner and Herron, “Problem solving is what chemists do, regardless of whether they work in the area of synthesis, spectroscopy, theory, analysis, or the characterization of compounds”.¹²  Hancock et al. comment that: “The objective of much of chemistry teaching is to equip learners with knowledge they then apply to solve problems”,¹³  and Cooper and Stowe ascertain that “historically, problem solving has been a major goal of chemistry education”.¹⁴  The latter authors argue further that problem solving is not a monolithic activity, so the following activities “could all be (and have been) described as problem solving:

• solving numerical problems using a provided equation

• proposing organic syntheses of target compounds

• constructing mechanisms of reactions

• identifying patterns in data and making deductions from them

• modeling chemical phenomena by computation

• identifying an unknown compound from its spectroscopic properties

However, these activities require different patterns of thought, background knowledge, skills, and different types of evidence of student mastery”¹⁴  (p. 6063).

Central among problem solving models have been those dealing with the differences in problem solving between experts and novices. Experts (e.g., school and university teachers) are as a rule fluent in solving problems in their own field, but often fail to communicate to their students the required principles, strategies, and techniques for problem solving. It is then no surprise that the differences between experts and novices have been a central theme in problem solving education research. Mathematics came first, in 1945, with the publication of George Polya's classic book “How to solve it: A new aspect of mathematical method”:¹⁵ 

Polya provided advice on teaching problem solving and proposed a four-stage model that included a detailed list of problem solving heuristics. The four stages are: understand the problem, devise a plan, carry out the plan, and look back. In 1979, Bourne, Dominowski, and Loftus modeled a three-stage process, consisting of preparation, production, and evaluation.¹⁶  Then came the physicists. According to Larkin and Reif, novices look for an algorithm, while experts tend to think conceptually and use general strategies. Other basic differences are: (a) the comprehensive and more complete scheme employed by experts, in contrast to the sketchy one used by novices; and (b) the extra qualitative analysis step usually applied by experts, before embarking on detailed and quantitative means of solution.^17,18  Reif (1981, 1983) suggested further that in order for one to be able to solve problems one must have available: (a) a strategy for problem solving; (b) the right knowledge base, and (c) a good organization of the knowledge base.^18,19 

Chemistry problem solving followed suit providing its own heuristics. Pilot and co-workers proposed useful procedures that include the steps that characterize expert solvers.^20–22  They developed an ordered system of heuristics, which is applicable to quantitative problem solving in many fields of science and technology. In particular, they devised a “Program of Actions and Methods”, which consists of four phases, as follows: Phase 1, analysis of the problem; Phase 2, transformation of the problem; Phase 3, execution of routine operations; Phase 4, checking the answer and interpretation of the results. Genya proposed the use of “sequences” of problems of gradually increasing complexity, with qualitative problems being used at the beginning.²³ 

Randles and Overton compared novice students with expert chemists in the approaches they used when solving open-ended problems.²⁴  Open-ended problems are defined as problems where not all the required data are given, where there is no one single possible strategy and where there is no single correct answer to the problem. It was found that: undergraduates adopted a greater number of novice-like approaches and produced poorer quality solutions; academics exhibited expert-like approaches and produced higher quality solutions; the approaches taken by industrial chemists were described as transitional.

Finally, one can justify the differences between novices and experts by employing the concept of working memory (see Chapter 5). Experienced learners can group ideas together to see much information as one ‘chunk’, while novice learners see all the separate pieces of information, causing an overload of working memory, which then cannot handle all the separate pieces at once.^25,26 

Chemistry is unique in the diversity of its problems, some of which, such as problems in physical and analytical chemistry, are similar to problems in physics, while others, such problems in stoichiometry, in organic chemistry (especially in reaction mechanisms and synthesis), and in the spectroscopic identification of compounds and of molecular structure, are idiosyncratic to chemistry. We will have more to say about stoichiometry and organic chemistry below, but before that there is a need to refer to three figures whom we consider the originators of the field of chemistry education research: the Americans J. Dudley Herron and Dorothy L. Gabel and the Scot Alex H. Johnstone, for it is not a coincidence that all three dealt with chemistry problem solving.

For Herron, successful problem solvers have a good command of basic facts and principles; construct appropriate representations; have general reasoning strategies that permit logical connections among elements of the problem; and apply a number of verification strategies to ensure that the representation of the problem is consistent with the facts given, the solution is logically sound, the computations are error-free, and the problem solved is the problem presented.^27–29  Gabel has also carried out fundamental work on problem solving in chemistry.³⁰  For instance, she determined students’ skills and concepts that are prerequisites for solving problems on moles, through the use of analog tasks, and identified specific conceptual and mathematical difficulties.³¹  She also studied how problem categorization enhances problem solving achievement.³²  Finally, Johnstone studied the connection of problem solving ability in chemistry (but also in physics and biology) with working memory and information processing. We will deal extensively with his relevant work in this book (see Chapter 5). In the rest of this section, reference will be made to some further foundational research work on problem solving in chemistry.

Working with German 16-year-old students in 1988, Sumfleth found that the knowledge of chemical terms is a necessary but not sufficient prerequisite for successful problem solving in structure-properties relationships and in stoichiometry.³³  In the U.S. it was realized quite early (in 1984) that students often use algorithmic methods without understanding the relevant underlying concepts.³²  Indeed, Nakhleh and Mitchell confirmed later (1993) that little connection existed between algorithmic problem solving skills and conceptual understanding.³⁴  These authors provided ways to evaluate students along a continuum of low-high algorithmic and conceptual problem solving skills, and admitted that the lecture method teaches students to solve algorithms rather than teaching chemistry concepts. Gabel and Bunce also emphasized that students who have not sufficiently grasped the chemistry behind a problem tend to use a memorized formula, manipulate the formula and plug in numbers until they fit.³⁰  Niaz compared student performance on conceptual and computational problems of chemical equilibrium and reported that students who perform better on problems requiring conceptual understanding also perform significantly better on problems requiring manipulation of data, that is, computational problems; he further suggested that solving computational problems before conceptual problems would be more conducive to learning, so it is plausible to suggest that students’ ability to solve computational/algorithmic problems is an essential prerequisite for a “progressive transition” leading to a resolution of novel problems that require conceptual understanding.^35–37 

Stoichiometry problems are unique to chemistry and at the same time constitute a stumbling block for many students in introductory chemistry courses, with students often relying on algorithms. A review of some fundamental studies follows.

Hans-Jürgen Schmid carried out large scale studies in 1994 and 1997 in Germany and found that when working on easy-to-calculate problems students tended to invent/create a “non-mathematical” strategy of their own, but changed their strategy when moving from an easy-to-calculate problem to a more difficult one.^38,39  Swedish students were also found to behave in a similar manner.⁴⁰  A recent (2016) study with junior pre-service chemistry teachers in the Philippines reported that the most prominent strategy was the (algorithmic) mole method, while very few used the proportionality method and none the logical method.⁴¹ 

Lorenzo developed, implemented, and evaluated a useful problem solving heuristic in the case of quantitative problems on stoichiometry and solutions.⁴²  The heuristic works as a metacognitive tool by helping students to understand the steps involved in problem solving, and further to tackle problems in a systematic way. The approach guides students by means of logical reasoning to make a qualitative representation of the solution to a problem before undertaking calculations, thus using a ‘backwards strategy’.

The problem format can serve to make a problem easier or more difficult. A large scale study with 16-year-old students in the UK examined three stoichiometry problems in a number of ways.⁴³  In Test A the questions were presented as they had previously appeared on National School Examinations, while in Test B each of the questions on Test A was presented in a structured sequence of four parts. An example of one of the questions from both Test A and Test B is given below.

• Test A. Silver chloride (AgCl) is formed in the following reaction:

  AgNO₃ + HCl → AgCl + HNO₃

  Calculate the maximum yield of solid silver chloride that can be obtained from reacting 25 cm³ of 2.0 M hydrochloric acid with excess silver nitrate. (AgCl = 143.5)

• Test B. Silver chloride (AgCl) is formed in the following reaction:

• (a) How many moles of silver chloride can be made from 1 mole of hydrochloric acid?

• (b) How many moles are there in 25 cm³ of 2.0 M hydrochloric acid?

• (c) How many moles of silver chloride can be made from the number of moles of acid in (b)?

• (d) What is the mass of the number of moles of silver chloride in (c)? (AgCl = 143.5)

Student scores on Test B were significantly higher than those on Test A, both overall and on each of the individual questions, showing that structuring serves to make the questions easier.

Drummond and Selvaratnam examined students’ competence in intellectual strategies needed for solving chemistry problems.⁴⁴  They gave students problems in two forms, the ‘standard’ one and one with ‘hint’ questions that suggested the strategies which should be used to solve the problems. Although performance in all test items was poor, it improved for the ‘hint’ questions.

Finally, Gulacar and colleagues studied the differences in general cognitive abilities and domain specific skills of higher- and lower-achieving students in stoichiometry problems and in addition they proposed a novel code system for revealing sources of students’ difficulties with stoichiometry.^45,46  The latter topic is tackled in Chapter 4 by Gulacar, Cox, and Fynewever.

Stoichiometry problems have also a place in organic chemistry, but non-mathematical problem solving in organic chemistry is quite a different story.⁴⁷  Studying the mechanisms of organic reactions is a challenging activity. The spectroscopic identification of the structure of organic molecules also requires high expertise and a lot of experience. On the other hand, an organic synthesis problem can be complex and difficult for the students, because the number of pathways by which students could synthesise target substance “X” from starting substance “A” may be numerous. The problem is then very demanding in terms of information processing. In addition, students find it difficult to accept that one starting compound treated with only one set of reagents could lead to more than one correct product. A number of studies have dealt with organic synthesis.^48–50  The following comments from two students echo the difficulties faced by many students (pp. 209–210):⁵⁰ 

Qualitative organic chemistry problems are dealt with in Chapters 6 and 7.

The present volume is the result of contributions from many experts in the field of chemistry education, with a clear focus on what can be identified as problem solving research. We are particularly fortunate that George Bodner, an authority in chemistry problem solving, has written the foreword to this book. (George has also published a review of research on problem solving in chemistry.⁸ )

The book consists of eighteen chapters that cover many aspects of problem solving in chemistry and are organized under the following themes: (I) General issues in problem solving in chemistry education; (II) Problem solving in organic chemistry and biochemistry; (III) Chemistry problem solving in specific contexts; (IV) New technologies in problem solving in chemistry, and (V) New perspectives for problem solving in chemistry education. In the rest of this introductory chapter, I present a brief preview of the following contents.

The book starts with a discussion of qualitative reasoning in problem solving in chemistry. This type of reasoning helps us build inferences based on the analysis of qualitative values (e.g., high, low, weak, and strong) of the properties and behaviors of the components of a system, and the application of structure–property relationships. In Chapter 2, Talanquer summarizes core findings from research in chemistry education on the challenges that students face when engaging in this type of reasoning, and the strategies that support their learning in this area.

For Graulich, Langner, Vo, and Yuriev (Chapter 3), chemical problem solving relies on conceptual knowledge and the deployment of metacognitive problem solving processes, but novice problem solvers often grapple with both challenges simultaneously. Multiple scaffolding approaches have been developed to support student problem solving, often designed to address specific aspects or content area. The authors present a continuum of scaffolding so that a blending of prompts can be used to achieve specific goals. Providing students with opportunities to reflect on the problem solving work of others – peers or experts – can also be of benefit in deepening students’ conceptual reasoning skills.

A central theme in Gulacar, Cox and Fynewever's chapter (Chapter 4) is the multitude of ways in which students can be unsuccessful when trying to solve problems. Each step of a multi-step problem can be labeled as a subproblem and represents content that students need to understand and use to be successful with the problem. The authors have developed a set of codes to categorize each student's attempted solution for every subproblem as either successful or not, and if unsuccessful, identifying why, thus providing a better understanding of common barriers to success, illustrated in the context of stoichiometry.

In Chapter 5, Tsaparlis re-examines the “working memory overload hypothesis” and associated with it the Johnstone–El Banna predictive model of problem solving. This famous predictive model is based on the effect of information processing, especially of working-memory capacity on problem solving. Other factors include mental capacity or M-capacity, degree of field dependence/independence, and developmental level/scientific reasoning. The Johnstone–El Banna model is re-examined and situations are explored where the model is valid, but also its limitations. A further examination of the role of the above cognitive factors in problem solving in chemistry is also made.

Proposing reaction mechanisms using the electron-pushing formalism, which is central to the practice and teaching of organic chemistry, is the subject of Chapter 6 by Bahttacharyya. The author argues that MR (Mechanistic Reasoning) using the EPF (Electron-Pushing Formalism) incorporates several other forms of reasoning, and is also considered as a useful transferrable skill for the biomedical sciences and allied fields.

Flynn considers synthesis problems as among the most challenging questions for students in organic chemistry courses. In Chapter 7, she describes the strategies used by students who have been successful in solving synthetic problems. Associated classroom and problem set activities are also described.

We all know that the determination of chemical identity is a fundamental chemistry practice that now depends almost exclusively on the characterization of molecular structure through spectroscopic analysis. This analysis is a day-to-day task for practicing organic chemists, and instruction in modern organic chemistry aims to cultivate such expertise. Accordingly, in Chapter 8, Connor and Shultz review studies that have investigated reasoning and problem solving approaches used to evaluate NMR and IR spectroscopic data for organic structural determination, and they provide a foundation for understanding how this problem solving expertise develops and how instruction may facilitate such learning. The aim is to present the current state of research, empirical insights into teaching and learning this practice, and trends in instructional innovations.

The idea that variation exists within a system and the varied population schema described by Talanquer are the theoretical tools for the study by Rodriguez, Hux, Philips, and Towns, which is reported in Chapter 9. The subject of the study is chemical kinetics in biochemistry, and especially of the action and mechanisms of inhibition agents in enzyme catalysis, where a sophisticated understanding requires students to learn to reason using probability-based reasoning.

In Chapter 10, Phelps, Hawkins and Hunter consider the purpose of the academic chemistry laboratory, with emphasis on the practice of problem solving skills beyond those of an algorithmic mathematical nature. The purpose represents a departure from the procedural skills training often associated with the reason we engage in laboratory work (learning to titrate for example). While technical skills are of course important, if part of what we are doing in undergraduate chemistry courses is to prepare students to go on to undertake research, somewhere in the curriculum there should be opportunities to practice solving problems that are both open-ended and laboratory-based. The history of academic chemistry laboratory practice is reviewed and its current state considered.

Chapter 11 by Broman focuses on chemistry problems and problem solving by employing context-based learning approaches, where open-ended problems focusing on higher-order thinking are explored. Chemistry teachers suggested contexts that they thought their students would find interesting and relevant, e.g., chocolate, doping, and dietary supplements. The chapter analyses students’ interviews after they worked with the problems and discusses how to enhance student interest and perceived relevance in chemistry, and how students’ learning can be improved.

Team Based Learning (TBL) is the theme of Chapter 12 by Capel, Hancock, Howe, Jones, Phillips, and Plana. TBL is a structured small group collaborative form of learning, where learners are required to prepare for sessions in advance, then discuss and debate potential solutions to problems with their peers. It has been found to be highly effective at facilitating active learning. The authors describe their experience with embedding TBL into their chemistry curricula at all levels, including a transnational degree program with a Chinese university.

The ability of students to learn and value aspects of the chemistry curriculum that delve into the molecular basis of chemical events relies on the use of models/molecular representations, and enhanced awareness of how these models connect to chemical observations. Molecular representations in chemistry is the topic of Chapter 13 by Polifka, Baluyut and Holme, which focuses on technology solutions that enhance student understanding and learning of these conceptual aspects of chemistry.

In Chapter 14, Limniou, Papadopoulos, Gavril, Touni, and Chatziapostolidou present an IR spectra simulation. The software includes a wide range of chemical compounds supported by real IR spectra, allowing students to learn how to interpret an IR spectrum, via a step by step process. The chapter includes a report on a pilot trial with a small-scale face-to-face learning environment. The software is available on the Internet for everyone to download and use.

In Chapter 15, Sigalas explores chemistry problems with computational quantum chemistry tools in the undergraduate chemistry curriculum, the use of computational chemistry for the study of chemical phenomena, and the prediction and interpretation of experimental data from thermodynamics and isomerism to reaction mechanisms and spectroscopy. The pros and cons of a series of software tools for building molecular models, preparation of input data for standard software, and visualization of computational results are discussed.

In Chapter 16, Stamovlasis and Vaiopoulou address methodological and epistemological issues concerning research in chemistry problem solving. Following a short review of the relevant literature with emphasis on methodology and the statistical modeling used, the weak points of the traditional approaches are discussed and a novel epistemological framework based on complex dynamical system theory is described. Notably, research using catastrophe theory provides empirical evidence for these phenomena by modeling and explaining mental overload effects and students’ failures. Examples of the application of this theory to chemistry problem solving is reviewed.

Chapter 17 provides extended summaries of the chapters, including a commentary on the chapters. The chapter also provides a brief coverage of various important issues and topics related to chemistry problem solving that are not covered by other chapters in the book.

Finally, in Chapter 18, a Postscript address two specific problem solving issues: (a) the potential synergy between higher and lower-order thinking skills (HOTS and LOTS,) and (b) When problem solving might descend to chaos dynamics. The synergy between HOTS and LOTS is demonstrated by looking at the contribution of chemistry and biochemistry to overcoming the current coronavirus (COVID-19) pandemic. One the other hand, chaos theory provides an analogy with the time span of the predictive power of problem solving models.