Science is a complex process, and we must not teach our students overly simplified versions of “the” scientific method. We propose that students can uncover the complex realities of scientific thinking by exploring the similarities and differences between solving the familiar crossword puzzles and scientific “puzzles.” Similarly to solving a crossword puzzle, solving puzzles in science is a complex and creative process in which hypotheses and theories evolve through the accumulation of many pieces of independent, yet interlocking, lines of evidence. We discuss the important lessons from Haack’s crossword-puzzle analogy and how it applies to teaching science.

One of the most compelling aspects of the crossword-puzzle analogy (CPA) is that a crossword puzzle is, in fact, a puzzle. Often in teaching science, explanations are taught as foregone conclusions, and alternatives that may have been considered in the past or are currently under debate are not discussed. In scientific puzzles as in crossword puzzles, you don’t know ahead of time what the right answer will be and, furthermore, there are multiple solutions possible. Through the CPA, students can see science as a process of answering questions and revising answers. Moreover, we can target the misconception that, when a scientific finding is later revised or retracted, science has somehow “failed.” The analogy with a crossword puzzle shows us that the process of revision common to both types of puzzle-solving is not a weakness, but a strength, leading to better answers as new evidence emerges.

Furthermore, we all know that solving a crossword puzzle is a process that involves creatively drawing from a pool of knowledge, trying to see whether our ideas fit the clues, seeking help from others, and postponing solving one clue until other solved clues can provide more information. “Building” a hypothesis is a process that involves many steps as well, with reiterations, missteps, even stops, which requires much knowledge, creativity, and collaboration. Thus, the CPA helps students and teachers alike to think about science as a process of solving the many puzzles the world around us presents, and not as just a jumble of facts.

Philosopher Susan Haack uses the CPA to explain the features of good evidence (Haack, 1993, 2009); this analogy accurately captures critical aspects of the process of science. Although Haack’s writing is some of the most direct and clear that we have seen in philosophy, educators may not be familiar with this literature. We recommend the CPA as an easy and memorable way to engage students, for teaching scientific thinking in schools and colleges.

In the CPA, the clues in the crossword puzzle correspond to data and the entries correspond to explanations (Figure 1 and Table 1). Thus, the fit between a clue (e.g., “She’s a jewel”) and an entry (e.g., “Ruby”) corresponds to the fit between data (“Joe being late for a meeting with Sue”) and a hypothesis (“He forgot”). Other words that fit into the entry space (e.g., “Opal”) present alternative hypotheses (e.g., “His car broke down” or “He’s sick”). For a science example, hypotheses for why some snails are armored while others are not include “The armored snails are different species produced by natural selection” or “The armored shells are induced by the environment (i.e., due to physiological plasticity).” In crossword puzzles, other entries also provide support (e.g., “Ruby” is supported directly by three entries, and indirectly by all other entries), just as a hypothesis is supported by other pieces of evidence and other hypotheses (e.g., snail genetic, ecological, and paleontological studies).

Figure 1.

The crossword-puzzle analogy (from Haack, 1993, with permission from the publisher).

Figure 1.

The crossword-puzzle analogy (from Haack, 1993, with permission from the publisher).

Table 1.

The crossword-puzzle analogy (from Haack, 1993, with modification). In the present article, explanation and hypothesis are used interchangeably, and not to mean an “educated guess” or “just a guess” (see Dauer, 1996).

Feature of Crossword PuzzleCorresponding Feature of Hypotheses & Explanations
Entries in the puzzle Hypotheses and previous knowledge 
Clues for entries Data 
Fit between a word and its clue Fit between hypothesis and data 
Fit between a word and other entries Fit between a hypothesis and previous knowledge, including other hypotheses 
Other possible words that fit an entry space Alternative hypotheses 
Number of entries a word cuts across Explanatory power 
Feature of Crossword PuzzleCorresponding Feature of Hypotheses & Explanations
Entries in the puzzle Hypotheses and previous knowledge 
Clues for entries Data 
Fit between a word and its clue Fit between hypothesis and data 
Fit between a word and other entries Fit between a hypothesis and previous knowledge, including other hypotheses 
Other possible words that fit an entry space Alternative hypotheses 
Number of entries a word cuts across Explanatory power 

The CPA emphasizes, largely through the intersecting nature of the entries, the following points:

  1. Science is a process with many steps, requiring careful inferences that build on the collective knowledge, skills, and creativity of many scientists.

  2. Explanations must be based on data.

  3. Explanations that strongly correspond to the data, while very seductive, may be wrong, and alternative explanations should always be considered.

  4. Stronger explanations have multiple independent pieces of supporting evidence:

    • Independent support counters seeming circularity.

    • Through independent support, valid (not ad hoc) supplemental hypotheses explain disconfirming data.

    • The evolution of hypotheses into theories, and into facts, is through the accumulation of valid supplemental hypotheses with independent support.

  5. To avoid misconceptions, all analogies should be analyzed for dissimilarities.

The familiar crossword puzzle is perfect to engage even introductory students in thinking about science on their own. Teachers can design an active-learning exercise centered around questions like “How is what a scientist does similar or different to solving a puzzle?” For younger students, a more concrete question may be better initially, such as “How is what you do when you can’t find your favorite toy similar or different to solving a crossword puzzle?”

Engaging students in a systematic analysis of the similarities and differences between solving a crossword puzzle and hypothesis “building” (using this paper as a springboard) can lead to a deeper understanding of what makes a good explanation. One exercise is to discuss how reasonable it is to think that an entry is correct, based on the clue and the other entries that intersect it (Haack, 1993). For example, if one entry fits its clue really well, but conflicts with several other already well-established entries, then that entry won’t do! Have students think about how support for a notion grows as more evidence accumulates by comparing how much evidence the clue provides on its own with the total evidence. It is best to use the CPA along with other conceptualizations of how science works (Salmon, 2006), as we did in a biology-themed college class on critical thinking. The comparison allows students to form an easy-to-update framework that is more accurate and complete.

Hypotheses Must Be Based On Data, Just As Entries – On Clues!

A simple but fundamental point is that hypotheses must be based on real-world information, or data, and in a crossword puzzle this point is clear, because the entries (hypotheses) you consider are guided by the clue (data) for that entry (Figure 1). Even younger students know that in a crossword puzzle you cannot just put in any word you like, but that your choice must be guided by the clue and the number of spaces allotted. In Sue’s case, she should not decide in her frustration that Joe is late because he forgot, without considering other information (e.g., a call from the hospital). Similarly, a scientist cannot decide that armored snails are a different species that have evolved armor to adapt to predators, simply because he likes adaptive hypotheses, or even because adaptation has been the correct answer in his previous experiences.

That biologists should be more careful in inferring adaptive over other hypotheses is a point of scientific discussion (Pigliucci & Kaplan, 2000). This fact emphasizes that, although the point that hypotheses should be based on evidence is simple, even advanced students need to be made aware of it explicitly and as a generalization with multiple examples (“not just in this case, but for any other”), including examples from other fields and daily life (“not just in science, but also in your daily lives”). Teaching for transfer using generalizations with examples beyond the course topic should be a pervasive feature of modern teaching. Knowledge transfer beyond the classroom, of even this simplest of points that explanations must be based on data, is a critical aspect in the development of educated citizens that “think like scientists” day in and day out, and not only for tests.

Importantly, when there is not enough information, one may need to withhold judgment until more data is available. If the puzzler cannot think of an entry based on the clue given, she will wait until more of the puzzle is filled. And so in real life, one must learn to wait until more data becomes available, and to not jump to conclusions. Better yet, a good citizen will actively search for the answers to her questions!

It is important to remember that for the CPA, as in any analogy, there will be differences between the items compared. In science, there are typically more clues for a hypothesis than in a crossword puzzle. For example, the mechanism that led to armored snails (the entry) may be judged on genetic data, breeding and transplantation experiments, data on the presence of predators, and other information (Wullschleger & Jokela, 2002; Pfenninger et al., 2006). Another difference is that, in crossword puzzles, the clues are given whereas in the real world they have to be obtained. For example, if your friend is late, you have to ask around, or go to his house, or otherwise gather evidence to determine why he’s late. Science requires not only the knowledge, skill, and machinery to obtain data that is both more precise and not available otherwise; it also takes knowledge and training to know whether an observation even serves as evidence. In physics, for example, it is often difficult even for experts to determine the predictions of a theory, and what data would support it (e.g., in string theory). Even if not fully, crossword puzzles imitate some of these aspects of science, such as multiple clues in the form of intersecting entries, the richness of puns, and the creative use of a large mental database by an expert puzzler.

A Seemingly Perfect Match Could Still Be Wrong – Alternative Explanations To The Rescue!

Who hasn’t experienced that crossword-puzzle moment when, after thinking hard about the clue, you finally come up with an idea that matches it perfectly? What a disappointment when your idea does not fit the space; or worse yet, it fits, only to be contradicted by a crossing entry that is correct! Herein lies a great caution of the CPA, that an incorrect explanation may fit the available data very well. Often, several explanations exist that can explain the data, and yet only one is correct. Without other information, Joe’s lateness is equally well explained by him being sick or by him having forgotten. Critically, to counter the natural tendency for confirmation bias (i.e., using only supportive and not disconfirming evidence) and the other causes behind why people choose their “favorite explanation” (Kahneman, 2011), we must consider alternative explanations. Paradoxically, this is especially difficult to do when one has some reason – but not enough – to believe a notion.

Consider that if Joe is often tardy, it seems reasonable for Sue to think that he is late simply because he was, again, very disorganized. Sue’s explanation, while likely to be true, is also likely to be wrong some of the time. Tardy people get sick as often as anyone else; thus, they are probably late for valid reasons as often as prompt people. And so Sue (and all of us) should always explicitly consider alternative explanations, and be careful in favoring one explanation over others, until she has (and we all have) good evidence in its support. In our example, this means that Sue should consider data specifically for the particular instance of Joe being late. Because Joe being late often does not provide sufficient reason, Susan should also explicitly pursue alternative explanations until she has enough evidence to choose between the alternatives.

Even if the causes leading people to choose their “favorite explanation” are complex and beyond the purview of this paper, increased clarity can only improve matters. A person who is steeped in the view that one must always consider alternative explanations can avoid this error; a teacher should passionately impart this point at every opportunity! This may be the single most important influence that a science teacher, or any other, can have on one’s students for inducing in them habits of careful thinking.

The Importance of Independent Support

Intersecting entries have their own clues.—Although we rarely think of “independent evidence” when solving crossword puzzles, we all know that an entry is supported not only by its own clue but also by intersecting entries – which in turn have their own clues. For example, the word “Or” fits the clue “What’s the alternative?” and gives support to the intersecting “Yard.” The latter, however, has independent support in the form of its own clue “A measure of one’s back garden.” In science, this means that pieces of evidence supportive of the same notion have to come through independent means.

For example, the unarmored snails developing armor soon after they are moved into the armored snail population can provide support for the plasticity hypothesis. Finding that a predator present only in the armored snail’s habitat induces armor development in unarmored snails provides independent support for snail plasticity, as can phylogenetic studies. Another engaging example is the convergent evolution of icefish antifreeze genes, supported by evidence from genetics, paleontology, and paleoclimate (Chen et al., 1997).

As these examples illustrate, the principle of independent support is pervasive in science. Lay people may discount scientific findings if they overemphasize the value of quantity of data, while not truly understanding just how much independent support increases the reliability of scientific conclusions. Use the CPA to emphasize to your students the importance of the quality, and not just quantity, of data!

Independent support counters seeming circularity.—A popular accusation against science by creationists and climate-change skeptics is that the evidence is circular. For example, a common challenge to evolution is to say that rock dating is used to date fossils and vice versa. However, rock dating does not require fossil dating, because it has its own independent support (e.g., through radio dating and the deposition of lower strata before upper ones; Godfrey, 1984). Also, circularity is not always bad, as when mutually supporting claims have their own support. Crossword puzzles, with their easy-to-visualize intercrossing entries with their own independent support, is the best tool we know to help understand this otherwise hard-to-explain notion.

Supplemental hypotheses require independent support.—The intersecting entries can also be seen to represent supplemental hypotheses (SH) that are used to explain information that appears contradictory. An SH is valid if it has its own independent support; otherwise it is ad hoc. Suppose that Sue’s belief that Joe was late because he is angry with her is contradicted by the evidence that Joe was friendly toward her on the last several occasions. An SH that Sue could form is that Joe really is angry and just trying to hide it from her. Without further evidence, it would be ad hoc. By contrast, if Joe had previously confided in Sue that he has a hard time telling people he is upset, Sue’s SH is supported and not ad hoc.

Often, in fields such as astrology, magnet therapy, homeopathy, and therapeutic touch, ad hoc SH’s propose mechanisms for which there is no evidence (Carroll, 2012). For example, there is no known physical mechanism that can explain how the position of stars on one’s birthday can explain one’s personality – the known physical forces are much too weak to exert an effect at such long distances. Common – and once again ad hoc – responses to such criticisms are the vague challenges that a mechanism “could exist.” However, the mere logical possibility that such a force exists does not constitute any evidence of its existence.

Theories as Great Networks of Puzzle Entries

Similarly to how a crossword puzzle grows, the addition of SH’s that are based on independent evidence is how hypotheses expand and may eventually become theories. As an investigation develops with time, new data comes to light that may be initially unexplained and that can appear to be disconfirming. However, such data is not necessarily disconfirming and could even strengthen and expand hypotheses, for example when molecular genetics findings helped expand the theory of inheritance by explaining violations in Mendel’s laws, such as incomplete penetrance.

Furthermore, just as a few entries in a crossword puzzle may grow into a central “core” whose words intersect most or all other entries in the puzzle, so may a few hypotheses grow to become a central core of interrelated ideas that explain a large variety of observations (i.e., a theory). Evolutionary theory is a perfect example, because it employs a few central ideas (e.g., natural selection and genetic drift) that now explain a staggering number of observations (e.g., the many instances of speciation). With time, the accretion of independently supported supplemental hypotheses from a variety of previously unrelated fields – genetics, paleontology, anatomy, development, biogeography, paleogeography, paleoclimatology – has transformed the evolutionary hypothesis into a great explanatory framework (Pigliucci, 2009), guiding whole research programs in biology and beyond (e.g., computing; Holland, 1992). In this way evolution, with the multiple successful hypotheses that it has inspired and the huge variety of interlocking pieces of evidence, is a paradigm of a theory with great explanatory power.

This success of evolutionary theory explains why scientists say that evolution is a fact (this is true for theories more generally, for atomic theory, electromagnetism, etc.). As a result, although the details of evolution in particular cases (e.g., by natural selection or drift) may be currently unknown, we know that living things are the result and the subject of evolution. Evolution, as both theory and fact, is why it would be difficult to undermine this overarching framework. However, data is constantly accumulating that leads the evolutionary puzzle to be regularly updated. While the components of the theory are always changing, the fact of evolution remains.

A Wider Case for the CPA

In summary, a careful comparison of the similarities and dissimilarities between scientific problem-solving and the familiar solving of crossword puzzles can lead to a deeper, more accurate understanding of science. Using a variety of examples in the classroom, the CPA can help students with the difficult and oft-ignored process of knowledge transfer. Significantly, the comparison reveals the complexity and beauty of discovery, which can help improve attitudes toward science – in particular, by stimulating a discussion of the role of creativity and ethics in science.

In popular culture, science and the creativity of the arts are often contrasted; this misconception may partially explain the public’s negative attitudes toward science, but there can be no science without creativity. The complexity of scientific puzzles gives rise to extensive roles for both imagination and constraints. For example, Watson and Crick, to determine the structure of DNA, had to first imagine the different three-dimensional structures possible. They built physical models of the structures they imagined, and each possibility was either modified or discarded on the basis of data until the correct structure was found. The CPA reflects the roles of both imagination and constraints in forming good explanations, because it requires imagination to think of which entries are possible, and not just any word will do – only words that fit the clue are allowed.

The example above also shows that creativity requires knowledge, an underappreciated point. For an expert puzzler, a good clue with several possible interpretations stimulates the creative use of a vast pool of knowledge. In the arts also, creativity relies on a pool of ideas, from life experiences, knowledge about the media (e.g., clay), and so on. Similarly, creative use of knowledge in science is an essential ingredient for groundbreaking discoveries!

Furthermore, the kind of careful thinking that is characteristic of both science and good puzzle-solving – involving a rigorous requirement for explanations to be based on the data, and to always consider alternatives – is characteristic of considerate people who do not jump to conclusions. Discussing the link between thoughtfulness and moral behavior provides a chance for the teacher to, again, facilitate knowledge transfer beyond the classroom: If we all (and all scientists, too!) would always apply the principle of careful consideration of alternative explanations in our daily lives, we would prevent hasty conclusions and arguments, and be better people. A good teacher should use any opportunity to encourage thoughtful and ethical behavior in his students; especially useful are such unexpected connections.

Linking the careful thinking of a scientist with ethical behavior can also improve science attitudes, by countering the prevalent notions of science as divorced from ethics, an image fueled by the media. Help your students make these connections. Such “side” notes are worth the 5 minutes of class, and several such “side” notes or discussions can create an overall positive atmosphere to help improve attitudes and learning.

An important note is that a teacher should welcome the difficulties with analogies, because they present an excellent opportunity for active student engagement and deeper, more genuine understanding of the material. Additionally, using analogies without discussing the differences can lead to misconceptions (Spiro et al., 1989). When compared to the CPA, the complexity of science highlights the world’s complexity, further emphasizing that we should be careful when making inferences even for apparently simple or familiar cases (e.g., when your friend is late). This complexity can also lead one to a new appreciation of the time, effort, knowledge, creativity and teamwork involved in making discoveries.

Although we use “scientific” explanations in the text, many of the points are valid generally (and that is the context of Haack’s use). We hope this paper stimulates instructors to use the CPA whenever different possible explanations are discussed. In a literature course, do we not base our explanations of the motives behind the characters’ actions on the clues in the text? The CPA can be used to highlight the continuity between the “harder” and “softer” sciences (e.g., physics vs. psychology) and everyday explanations. Seeing the continuity in explanations can prevent the use of “science” as a mere superlative, without deeper understanding.

Acknowledgments

We thank Scott Kreher for valuable editing and Susan Haack for her clear- and level-headed philosophizing.

References

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