In UbD, unit designs are framed in terms of the different kinds of intellectual goals that a good education involves. As teachers we aim for both short-term knowledge and long-term transfer, so our designs must reflect both. We aim for meaningful use of knowledge, not mere rigid recall. A transfer goal differs from a skill: transfer involves purposeful and effective use of all one’s skills. Essential Questions differ from transfer, knowledge and skill because we expect important questions, not answers, to be internalized and used to foster inquiry and eventual understanding.
But perhaps the most misunderstood box in the UbD Template is Understandings. What is an Understanding – and how does it differ from Knowledge? Given what an understanding is (and isn’t), what follows for instruction in Stage 3? What has to happen in both instruction and assessment, if students are to come to a genuine understanding and provide evidence of it?
Understanding vs. Knowledge
“I get it!” That feeling of gaining a new insight is a visceral and vital aspect of learning. It reflects an important insight into any genuine understanding: I have to do some mental work to achieve it. Knowledge is simpler: I learn a new fact and merely note it. I may say "Huh, that's interesting!" but it is not really my insight. Thus, though we sometimes informally equate knowledge with understanding, they are different. An understanding is not just more knowledge: it is possible to know a lot but lack understanding. The opposite is true, too: a student can have a deep understanding of a subject but get some facts wrong on a quiz. Understanding requires knowledge but it is something different from knowledge. And it is all too easy to forget that understanding, not mere knowledge, is the point of education.
Knowledge can best be thought of as all the useable information we possess: things like the name of the author of Charlotte’s Web, what the Pythagorean Theorem says, the meaning of “estivation,” the subjunctive of avoir (and when the subjunctive is called for). Knowledge consists of helpful information: all the learned facts, rules, definitions, formulae, etc. that we can recall and use appropriately. Understandings are different. They are not facts but ideas about facts. They are not data, but what the data suggests; they are not formulae but why the formulae matter and how they can be derived.
Think of an understanding, then as any response to the following question: Here are the facts; what do they mean? Whatever our answer, it is an understanding. In sum, an Understanding is an inference from facts, not another fact. It is a conclusion, using facts.
This distinction between facts and conclusions can be better appreciated by considering how we obtain each. We attain facts by observing, finding, or being told them; we attain understandings by reasoning about facts. I note, for example, the facts of my test results: my 6th-grade math class averaged a 56 on the last test about fractions, and no student gave a right answer to the last 2 difficult questions. No real thought is required here by me – these are just facts that can be perceived. But a quiz score isn’t really understood until someone proposes what those facts mean. Understandings, unlike facts, are achieved not by looking but by theorizing. So, for example, I may conclude from the facts that my students didn’t learn the material – but should have. My colleague concludes that the test was too hard. Still another teacher concludes that students didn’t study; another is sure that they don’t know how to study for a test, based on her similar experience.
All four of these understandings are plausible conclusions based on the facts. Thus, we don’t “find” or “see” understandings, we “create” them (hence, the term “constructivism”) in our minds to make sense of what we have learned. In the words of John Dewey, facts require apprehension but understandings require comprehension.
Dewey has a useful analogy for making this point clearer: what a detective does. By careful observation, Sergeant Smith seeks and apprehends various facts that might be relevant to the case at hand: blood stains, scuff marks, a book open to a page, fingerprints, and statements from various suspects. Ah, but what do those facts mean? How should we comprehend the facts into a coherent and convincing “theory” – particularly, when the facts are incomplete and (in the cases of the statements) contradictory? Further, it is often unclear which facts are relevant or important. In the end, the detective has constructed an understanding, a theory, of what all the details do and don’t mean.
As readers, we are detectives too. We are expected to pro-actively consider the meaning of the facts of the story. For example, a good reader of Catcher in the Rye works to understand Holden Caufield’s behavior: “OK, underneath all his sarcasm, who is Holden, really?” In addition, most readers typically have to revise their “theory” about who he is and what is wrong with him – he is telling the story from a hospital bed, after all, a fact typically forgotten or ignored by naive readers. As we read on we learn more; we re-consider our emerging theory of who Holden is. We use our knowledge (the facts presented in the story, as well as other facts we know from our experience) to infer motives and traits (understandings about the characters) that are not stated in the text. Again, the question is: “OK, those are the facts, the details of the story; what sense do they make? What does the story mean?”
We must engage in this pro-active mental work even when the aim is to grasp a specific understanding that already exists in an academic discipline. We don’t just learn F=ma in physics or the Distance Formula in Algebra I. We learn why – why the data should lead us to presume a constant force of gravity; why the Distance Formula works, namely, because it is just a logical extension of the Pythagorean Theorem. When we have an understanding we “see” not merely what the formula says but what it means: the proof of it, why it matters, how it is powerfully predictive, and what misconceptions we need to overcome to really “get” it. That’s why we say that a good education goes into depth and does not just “cover” things i.e. just present the surface facts.
Understandings sound and look like Knowledge, however.
What makes this more difficult than first appears is that when you see Understandings written in unit examples they can easily sound like facts. Here are some examples of understandings from sample units:
Arithmetic: Different expressions (e.g. equations using fractions or decimals) can represent the same quantities; the goal, context, and ease of use determine the best choice.
Art: Great artists often break with established traditions, conventions and technique to better express what they see and feel.
Economics: In a free-market economy, price is a function of supply and demand.
Geography: The topography, climate, and natural resources of a region influence the culture, economy, and life-style of its inhabitants. (“Geography is Destiny.”)
Literature/Reading: An effective story engages the reader by leaving out facts and thus raising questions - tensions, mystery, dilemmas, or uncertainty - about what will happen next.
These sound like facts, right? But they aren’t; they only seem so to experienced adults who have forgotten their origin. Look again, and think through the syntax: each one of these statements is a conclusion based on many and varied experiences and reflection about that experience. They are theories built out of facts and reasoning; they are inferences, not facts, that we now take for granted.
Compare these paired examples to see the difference more clearly:
The Americans dropped the atom bomb on Hiroshima in August of 1945
“Dropping the bomb saved more lives in the end, despite the tragedy and suffering brought to the people of Hiroshima.”
Here are the data for men’s and women’s times in the Olympic Marathon
“Women will very likely never achieve equal times to men in the marathon, despite what data from the last ten years seems to suggest.”
The United States ranks 28th out of 40 countries in the industrialized world in math performance by 15-year-olds.
“American mathematics teachers ‘cover’ too much content superficially.”
“No, the problem is the emphasis we put on low-level standardized testing.”
The book we are reading is called Frog and Toad Are Friends
“By deceiving Toad about what month it is, Frog is not acting like a good friend.”
“Not true! He knew it was in Toad’s interest to come outside and play in the nice weather. That was a friendly thing to do.”
The first column presents factual claims. The second column presents opinions about what the facts mean, based on reasons. It is a fact that the Bomb was dropped in August of 1945. But the statement “Dropping the bomb saved more lives in the end” is a conclusion, and a controversial one at that. But it SOUNDS like a fact the way it is stated.
Alas, this is a problem in education: many teachers (and textbook authors) make it sound as if the understandings they propose are facts. Students can thus all too easily be convinced by the authority of teacher and text that all claims made in school are “official” knowledge, not someone’s fallible or even biased understanding. It is thus often a shock to read books like Lies My Teacher Told Me (in which, the author argues, our pro-American US history books distort the truth for the sake of making the US look good).
I thus added alternate understandings to the last two examples to underscore an important point: even when the facts are not in dispute, their meaning is often a matter of debate. This is typically the case with Understandings. You and I may have plausible, well-reasoned yet different understandings of the same historical events, data or texts. The disagreements reflect the fact that all Understandings are not only inferences drawn from facts but also based on prior experience and beliefs. How else can we make sense of the timeless and sometimes bitter arguments about global warming, the health of Social Security, or the best strategy for our favorite team to win? An understanding, no matter how forcefully stated and backed by facts is still not a fact; it is a debatable conclusion. And that is true whether we are talking about a historical judgment, an axiom in mathematics, or a law in Physics. Human understanding is fallible, limited in scope, and thus subject to change over time, based on new evidence and argument. How else could academic disciplines possibly evolve? Critical and creative thinking are only possible if we see that all understandings are inherently questionable, no matter how settled they seem.
In Part 2 next week I will discuss the practical implications for dealing with this goal of understanding. meanwhile, if you have any questions or comments, send me an email and I will also post the most interesting questions and comments.