Knowledge Series Part 3: In Defense of Knowledge cont’d

Knowledge Serves as the Foundation for Creativity, Critical Thinking and Problem-Solving

There is lots of emphasis on teaching problem-solving, creativity, and critical thinking in schools, and discussion of how employers look for these traits in future employees. That, in the 21st century, these general learning outcomes (GLO) should be developed, cultivated, and the focus of education, not knowledge. However, they cannot be taught without knowledge. Critical thinking, problem solving and creativity are not generic skills; they are domain-specific, and rely on knowledge in that domain.

Knowledge gives students something to think with, when solving problems, constructing arguments, or thinking innovatively. David Didau states it well, when he argues that the “more we know about something, the more sophisticated our thinking.” If you don’t know much about a topic, you are not going to thinking critically about it.

This is something I’ve felt in my gut for a while; when I saw it explained, it made a lot of sense. I make better connections between ideas and concepts, and think of new ideas in the process, when I’m pulling information out of my long-term memory. It helps me see when one author’s ideas agree with or contradict those of another. It helps me make connections between theory and practice in my teaching. It helps me see patterns in human behaviour over different time periods in history. My knowledge. In my head, not in a book or on a screen. That’s what I use to think effectively.

Working Memory

First and foremost, because it helps with all three GLO, is the relationship between working memory and knowledge. We think with our working memory; it is our workspace for our ideas. Unfortunately, it is incredibly small, with the capacity to hold about four ‘things.’ Knowledge, pulled from our long-term memory, allows us to make better use of this space. Take, as an example, memorizing meaningless strings of letters, such as QXB, TCF and RLL; it is easier if the letter strings hold some meaning as acronyms, such as BBC, FBI and RSS. Of course, the aim of education is not for students to memorize chunks of letters, but this phenomenon applies to more practical domains as well.

Let’s take dancing as an example; it may seem very skill oriented, but, as described by Allard and Starkes, it has a cognitive component as well. Dancing a choreographed dance is a complex skill; not only is the dancer focused on the execution of each step, but needs to remember all the choreography as well. It is easier if they have knowledge of different dance moves which they can recall in chunks, rather than remembering each individual placement of the foot, which can overload the working memory. This is demonstrated by how expert dancers are better able to remember choreography after viewing a video than novice dancers; with each move operating as a chunk, the dancer can hold more of them in working memory. While in the midst of the performance, if less space in working memory is occupied by the choreography, more attention can be focused on the execution of the moves.

Thus, by having knowledge in a particular domain, students can hold more information in their working memory, which allows them to make more connections between ideas, consider more sides to an issue, and think more broadly about a topic.

Problem-Solving

Problem-solving is, well, solving a problem, and on its surface it seems to be a useful generic skill. Over my two years as a teacher, I’ve certainly exercised by problem-solving “skills” with photocopiers and troubleshooting issues: checking for jams, opening and closing the paper drawers, reviewing the memory list for print jobs. Handy knowledge for a teacher, but it does not transfer well to other problem-solving moments, such as figuring out how to add images to WordPress posts or trouble-shooting why a draft post isn’t saving. Improving my knowledge of WordPress will help me with that. Both can utilize a pushing-buttons-until-things-work approach (a decent general heuristic), but knowledge of their operation is much more effective.

My dad is a petroleum engineer, and he is very good at it. He can analyze data from a well, program Excel spreadsheets, and explain all of it to his boss later in a presentation. My mom is a nurse; for all his excellence at problem-solving for engineering, my dad would be pretty useless at solving the sort of problems my mom deals with in a shift at the hospital. Honestly, I’ve seen my dad struggle with Skype, and, again, he is a genius with an Excel spreadsheet.

This is because problem-solving is domain-specific, not domain-general.

As Willingham explains, knowledge helps us to see the underlying structure of a problem, to look past the distracting surface-level information. In one study, physics novices and physics experts were asked to sort physics problems. Novices sorted them based on surface features, such as whether there were springs or an inclined plane, while the experts focused on the underlying structure, the physics principles that were needed to solve the problem, such as conservation of energy. As well, knowledge helps us chunk steps in the problem-solving process, to use them more quickly and effectively. For example, chess may seem like a game focused on reasoning processes, but it actually relies on an extensive memory of different board configurations, which the player uses to recognize the situation on the board and decide the next move; expert chess players are estimated to have between 30 000 to 100 000 chess chunks in their memory.

Both of these can be seen in solving mathematical problems. If students can see the underlying structure of math word problems, the surface features of the scenario, like Billy deciding how many apples he needs to sell to make a profit, to see which mathematical operations they need to use and how. If students can chunk steps in the problem-solving process and know their simple math facts by heart, they can focus their attention on more complex aspects of the math problems. This is why the 2008 report from the National Mathematics Advisory Panel, based in the United States, recommended that students learn “automatic (i.e. quick and effortless) recall of facts,” such as times tables, alongside conceptual understanding.

The importance of knowledge in problem solving is apparent in science as well. One meta-analysis looked at effective strategies to teach scientific problem solving. The development of a knowledge base was found to be more effective than a focus on skills, strategies, or practicing problem solving. In another study, students designed experiments for keeping imaginary creatures alive and for evaluating the relationship between the surface area and the temperature of swimming pools. They were better at the former, because they “are used to thinking about factors that might influence creatures’ health (e.g., food, predators), but have less experience working with factors that might influence water temperature (e.g., volume, surface area).” Effective problem solving needs to be preceded by a knowledge base.

Creativity

Creativity also relies on expertise in an area. Creativity is not just thinking of new, interesting ideas; it is the marriage of originality and effectiveness. Creativity serves a goal, and expertise is part of ensuring it meets that goal. There are two parts of the creative process: divergent thinking, where new ideas are generated, and convergent thinking, where the best ideas are selected and applied. Evidence of hippocampal activation during this second phase, the area of the brain important for memory, shows that recall of background knowledge is necessary for this stage.

I find the library of Neil Gaiman, author of a range of children’s and adults’ books, a good example of this marriage between expertise and originality. It is hard to see from the pictures, but I am confident there are books in there on Greek mythology, Judeo-Christian religion, and Lovecraftian horror; his novels and short stories effectively use a range of source materials, and his works would be much different if they did not draw on this wealth of knowledge.

The examples of Gaiman is backed up by research on creativity, which has shifted from promoting a domain-general to a domain-specific theory of creativity: that is, creativity is not a general skill that is equally applicable across domains, but rather born out of expertise in a particular area. If creativity was domain-general, then we would find people would be equally creative in a range of domains. However, studies have found the opposite. As explained by John Baer,

assessments of the creativity of subjects in diverse domains have been conducted, and the result is generally quite low inter-correlations among the creativity ratings of artifacts in different domains produced by the same subjects. This has been true of subjects of all ages from kindergarten through adulthood, and it has been true both in essentially random samples of subjects and with subjects who have evidenced considerable degrees of creativity in different domains. When variance attributable to math and verbal standardized test scores has been removed statistically, the inter-correlations hover around zero.

For visual art, expertise may be knowledge of how to use different mediums, colour combinations, and rules of composition. For creative writing, it may be knowledge of how to pace a story and write dialogue. Creativity in one of these domains does not necessarily translate into creativity in another.

In addition to the expertise in a specific domain, having a breadth of knowledge in a range of topics provides raw material for the generation of ideas. I find that students who have something original to say typically know things their classmates do not.

Critical Thinking

Critical thinking subsumes both problem-solving and creativity, as both require critical thinking. Despite the frequent use of the term in conversations about education, There is not clear agreement about what it means, so I’ll focus here on different definitions of critical thinking and the critical thinking process.

I’ll start with the definition put forward by the Association of American Colleges and Universities (AACU), which has designed a set of rubrics for GLO. They define critical thinking as “a habit of mind characterized by the comprehensive exploration of issues, ideas, artifacts, and events before accepting or formulating an opinion or conclusion.” The rubric highlights the importance of explaining the issue using relevant information, interpreting and evaluating sources, assessing the relevance of contexts, and synthesizing different perspectives, all of which require deep knowledge of a topic.

While the AACU focuses on the characteristics of the final product of the critical thinking process, a paper by Balin, Case, Coombs and Daniels focuses on the intellectual resources necessary to complete this process and produce this product. They define critical thinking as more broadly as thinking that is aimed at forming a judgement and intentionally fulfills standards of adequacy and accuracy appropriate to the thinking. They identify five intellectual resources that are necessary for critical thinking, which we may or may not be consciously aware of:

  • background knowledge
  • operational knowledge of the standards of good thinking
  • knowledge of key critical concepts
  • heuristics (strategies, procedures, etc.)
  • habits of mind

So, like for the AACU, the importance of background knowledge on the topic is stressed. To quote Balin et al:

To a considerable extent, the quality of thinking persons are able to do about a particular problem, issue or question is determined by what they know, or are able to find out, about it and about the context in which it must be resolved. Moreover, critical thinking always takes place in the context of (and against the backdrop of) already existing concepts, beliefs, values, and ways of acting. This context plays a very significant role in determining what will count as sensible or reasonable application of standards and principles of good thinking. Thus, the depth of knowledge, understanding and experience persons have in a particular area of study or practice is a significant determinant of the degree to which they are capable of thinking critically in that area.

Beyond knowledge of a particular topic, they also emphasize the importance of knowing how a discipline operates, or, as they phrase it, operational knowledge of the standards of good thinking:

Every area of intelligent human inquiry and practice, including science, art, law and morality, embodies within it practices of criticism by which proposed conclusions or ways of acting are tested, and previously accepted beliefs, practices and institutions are criticized and revised. Implicit in these practices are standards of critical assessment. It is these standards that critical thinkers must learn to use. They include not just rules of logic, but also standards of practical deliberation, standards of argumentation, standards used in developing plans of action, standards governing judgements made in the course of action (as in artistic and athletic performances), and standards governing inquiry and justification in specialized areas of study such as art, biology, history, literary criticism, mathematics, and technology.

Also discussed is the importance of knowing key critical concepts, such as premise, conclusion, distiguishing between facts and values, and necessary and sufficient conditions. While for both operational knowledge and knowledge of key critical concepts, the authors suggest that we can use this knowledge without being able to aware of it, students can benefit from having it explicitly taught, thus creating a shared vocabulary both within and between subjects for discussing argumentation and developing critical thinking.

Michael Fordham made a recent, if a bit controversial, post on how we can only teach knowledge, because when we try to teach skills, or procedural knowledge, it must be transmitted through language and therefore declarative knowledge. It some ways, this makes sense to me. To link back to dancing, when I was taught the Charleston, the basic step was taught to me by turning this procedural knowledge into declarative knowledge (rock-step-kick-step-kick-lift-back-step), which I practiced until it became procedural knowledge for me as well. While I am not sure about the extent I agree with Fordham on this, he makes a good point regarding my argument for critical thinking; some of this “skill,” such as operational knowledge and general heuristics, can and should be taught to students as declarative knowledge, rather than expecting them to just pick them up, or fumble through to finding them on their own. We should make the implicit explicit.

I think two major areas of agreement can be found from this brief review of research on critical thinking. First, that domain-specific knowledge is essential for critical thinking in that domain. Secondly, that knowledge alone is not enough. Students should also be taught processes for forming judgements and standards of good thinking, and be given opportunities to practice using and applying their knowledge.

I think that is an apt summary of the role of knowledge in problem-solving, creativity, and critical thinking: necessary, but not sufficient.

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