Chris' reply to my post got me "critically thinking" about the notion of teaching critical thinking. While the intent of his post, that he is interested in teaching students to think critically, is noble and worthy, I'm no longer sure what critical thinking even means. I think it has become one of those terms that is so frequently used without examination that it has become nearly meaningless. I prefer to think in terms of teaching "habits of mind." Among these: use of evidence, supposition, understanding perspective(s), making connections, meta-cognition (thinking about your own thinking and learning), curiosity, and so on. To me, these are more concrete and definable, and therefore more teachable. I tend to incorporate these into my "essential questions" when I am planning units/lessons.
Here's a question: Why does each section of the California State Standards for Social Science start with the "historical and social science analysis skills," which include use of evidence, debates in history, connecting historical events to other events and current events, cause and effect, identifying bias and prejudice, understanding perspective; yet, these analysis skills are rarely included in a history curriculum? (Hint: What's on the STAR test?) But here is the rub, even if you want students to be "information sponges," they need to have a conceptual framework on which to hang all that information.
This idea becomes particularly important (and frequently problematic) in math education where an over emphasis on "procedural fluency" (i.e. practicing problems) trumps "conceptual understanding" (i.e. understanding how it works). There is some, debatable, thinking that this better prepares students for the next high stakes tests. However, there is substantial evidence that this undermines students ability to do more complex mathematics down the road (see, for example, How To Teach Mathematics by the National Research Council).
So, Chris, this is a long winded way of saying that I absolutely agree with you about teaching students to process and evaluate information. I also believe that serious information retention REQUIRES understanding. While there is plenty of tension in teaching between depth vs. coverage, there is not conflict between understanding and retention.
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The following are my musings on the topic, my own interrogative journey...
I like the term "habits of mind." It reminds me of an ongoing debate in epistemology regarding what constitutes knowledge. To briefly elaborate, a more recent approach to the perennial question, what is it that combines with true belief to make it knowledge?, is that it is a personal quality that a thinker has that is conducive to their attaining true belief. "Virtue epistemologists," then, maintain that those beliefs (which is not to be understood as "opinion" but the accepting of something as true) that are true and founded on such qualities. These qualities are described as cognitive virtues, or "habits" that typically (in the literature) include intellectual practices such as carefulness or impartiality, though for some philosophers they include any properly functioning progress. While this apparently trivial tidbit is not directly germane to the purposes at hand (the clarity of the term "habits of mind" vs. "critical thinking"), for me the idea of cognitive habits raises questions about the nature of learning and its implications on teaching.
The first question I would like to develop here is about how we are to understand the habits of mind Page lists. On the surface they seem to be very general practices, indeed ones that are universal to learning. Granting this, we might wonder how acquisition such general cognitive habits ought to occur distinctly from "procedural fluency," for it seems such habits involve "conceptual knowledge" and yet would arise through repetition of procedures. Habits are the result of inculcation. So at first blush, the question is, in order to attain those habits of mind, what is missing from mere repetition of those practices through which a students gains proficiency in the content? This initial stab at a question, suggests several other questions and suppositions. I want to list them in a rough organization here and then see how they relate, which perhaps will suggest an answer or at least point in a good direction.
(1A) What the relationship is between procedural fluency and conceptual understanding? (1B) Which subject areas, if not all, involve learning that admits of this distinction?
(2A) How are children in at the "preoperational stage" (those who, I have read, "cannot conceptualize abstractly") supposed to develop habits of mind and conceptual understanding? (2B) Does attainment of the habits of mind that Page lists and conceptual understanding require self-reflection? (2C) Does their attainment require some degree of abstract conceptualization, given that they are general or even universal?
After looking at these question, I suppose that (2A) voices my central concern, and that an answer to (2A) might help answer (1A). So I will try to sketch out some possible answers in that order and see if that helps for the other questions as well.
If I am not mistaken, the notion of "conceptual understanding" was primarily developed with respect to elementary level mathematics, by Liping Ma and is explained in her book "Knowing and Teaching Elementary Mathematics." On page 23 she contrasts “procedural topics” and “conceptual topics” such that the former shows how to carry out an algorithm whereas the latter show the “rationale underlying the algorithm.” Since the point of conceptual understanding is to apply the rational to other mathematical situations, this means that the student should have the concept is mind and is able to recognize it in other situations.
An initial concern about practically applying this distinction to students in the preoperational stage is that there is tension between the inability form and retain abstract concepts and the supposition that these students should operate according to the underlying rationales of mathematical procedures. This tension, I am pretty sure, is only apparent, and it seems that we might possibly address and refine our understanding of both sides of the problem. At least it seems so.
One side of the problem is the developmental stages of children. I believe it is generally accepted that the preoperational stage lasts until age 7, and that even then, until age 11 they are merely beginning recognize abstract realities in concrete experiences. Therefore, one way to relieve the tension is to not understand the lack of abstract conceptualization at young ages to be so strong or strict. My very limited experience suggests that it is not so strict. Nevertheless, my experience is limited and I know to little about the cognitive lives of children to make any sort of conclusion here.
I think I’d prefer to address the opposite source of apparent tension, namely that the underlying rationales that are supposed to be recognized by students because they have been abstracted by them through repetitive experience. The basic point to note here is that the students are not learning these rationales abstractly, but through concrete situations in which they engage. A strict contrast to learning procedures, then, seems to me to be inacurate. It is not that learning procedures is the problem. The problem is what specific properties of the concrete situations (in this case mathematical situations) are being clearly manifested before students eyes, as it were. The important properties are those, we should presume, that are most fundamental and thus extensive in their applicability. And how do we manifest those properties? Not by abandoning knowledge of procedures of course, but in teaching the sort of procedures that manifest those properties or “structures” as Ma likes to term them (by quoting J. Bruner). She doesn't advocate abandoning the teaching of procedures, but recommends better ones.
Anyways, the answer to (1A) seems to be more in the direction of having students engage in the right sort of procedures—those that manifest most clearly the underlying structure of the realities at hand (mathematical in this case); but since a concept is abstract—that is multiply applicable because what it is about, i.e., a structure, manifests itself in various situations—there must be some capacity of abstraction even at early stages. So the answer also seems to involve considerations about both points in tension.
In short, therefore, it seems we can begin to answer (1A) by saying that the relationship between procedural fluency and conceptual knowledge as if the latter does not involve the former, but rather of what procedures and experiences most clearly manifest the underlying structures of general categories of content.
The upshot for teaching, I suppose then, is to recognize what sort of activities and procedures most clearly manifest to the students mind these structures. This seems equally true regarding habits of mid. Here, any tension similar to that which we just discussed, might be dealt with in the same way. Habits of mind come through repetition of concrete situations, and this is not in tension with their generality. Moreover, to answer (2B) and (2C) in turn, Habits of mind probably don’t necessitate self-reflection in many cases though it would serve well their development in some cases; and such habits are practical and don’t seem to require an ability for high-level (or even medium-level) abstraction, though they may require some level.
As for (1B), I don’t know. I guess that is something I would learn a little about in my pursuit of a multiple subject credential.
Well, there's an introductory comment for all of us! You bring up great questions, and I can guarantee more discussion of these questions throughout the year. Will they have definitive answers? Possibly not. One interesting point is that lately in mathematics education research, preschoolers and early elementary students have been shown to be far more capable of abstract levels of thinking than traditional child development models might suggest.
Your question about which subject areas admit to a relationship between procedural fluency and conceptual understanding begs the broader question of what learning really is, and how we know learning has taken place for the student? (Or, indeed, for ourselves?)
I look forward to reading your responses to the pre-service work and to meeting you at the retreat!
After reading this, I began to think about how often we overuse terms like critical thinking to the point they do become meaningless. Our goal should always be to teach for understanding and retention. This process is sometimes tainted by such focus always being on testing as the only true measurement of understanding. We sidetrack ourselves and our students by having this enourmous pressure put on us by administrators, the district, or the state. We get fancy with words, and it actually boils down to something simple: understanding.
Hmmm.... is understanding really that simple? I agree that testing is only one measure of understanding, but what counts as "understanding?" If I say I understand how the digestive system works, how would I show this? How much would I need to say to demonstrate that I do, indeed, know how the digestive system works? Yes, we should be teaching for retention and understanding... I'm just not sure that it's a simple matter to figure out exactly what that would look like...
I hear the term "critical thinking" ALL THE TIME. Many teachers and administrators will ask if we are teaching our students to critically think. That means: Are students asking questions, able to solve an answer if it was presented in a different context or simply put, to think? Or are students being taught to be computers--to spit out answers and memorize lines, without really understanding concepts. Does your student really know why 4 x 4 = 16? I have heard of being a 1 dimensional student, vs 2 or 3 dimensional. Has anyone else heard this? Is this what it refers to?
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