An alternative title for this chapter of Understanding by Design might be “Everything You Thought You Knew about Teaching and Assessment is Wrong.” Perhaps that is somewhat hyperbolic, but not much.
I consider myself an autodidact — perhaps not in the sense of being largely self-taught, but in the sense that I have taught myself a lot. I have taught myself a number of things, from CSS and HTML to Arthurian legend and how to cross-stitch. I think that sometimes I am frustrated when I encounter students who cannot teach themselves. I think I expect them to be able to transfer information more easily when I haven’t really given them the tools to do so. A math problem mentioned in the book asks students to identify how many buses, each of which seats 36, would be needed to transport 1,128 people (2). Of course, the route one should take to answer this question is to divide the number of people by 36. According to Wiggins and McTighe, “Almost one-third of the the eighth-graders [taking the NAEP mathematics assessment] gave the following answer: ’31 remainder 12′” (2). You and I can do our best face-palm imitations of Homer Simpson, but the fact remains that 1,128 divided by 36 does result in 31 remainder 12. What the students didn’t understand is that those twelve leftover people would need a whole extra bus; therefore, they should have given the answer 32. Just to show how stubborn I am, I had to work the math problem before I took the authors on faith.
Wiggins and McTighe discuss Benjamin Bloom’s influence on assessment through his Taxonomy. As the authors point out, “As Bloom put it, understanding is the ability to marshal skills and facts wisely and appropriately, through effective application, analysis, synthesis, and evaluation” (39). To elaborate, “[d]oing something correctly, therefore, is not, by itself, evidence of understanding. It might have been an accident or done by rote” (39).
What the authors argue we must enable students to do is to “transfer” information:
Knowledge and skill, then, are necessary elements of understanding, but not sufficient in themselves. Understanding requires more: the ability to thoughtfully and actively “do” the work with discernment, as well as the ability to self-assess, justify, and critique such “doings.” Transfer involves figuring out which knowledge and skill matters here and often adapting what we know to address the challenge at hand. (41)
On pages 42-43, Wiggins and McTighe examine the failure of students to transfer mathematical knowledge to solve problems. I learned something new about myself as I read these two pages. I have told myself for years that I am not a good math student. I had to work very hard to earn B’s when I had good teacher who could explain mathematical concepts. On the other hand, if I had a teacher that just couldn’t explain it in a way that I could understand, I might earn C’s. My A in College Algebra didn’t convince me otherwise. I told myself that I earned a good grade because my high school Trig/Pre-Calculus teacher was so good. When we ventured into Calculus at the end of the course, I failed the quiz that week. However, in working the following problem, I discovered that I had actually done something that “two-thirds of the tested students” who took the New York State Regents Exam couldn’t do. I could transfer my understanding of a mathematical formula to a new situation. Try this problem:
To get from his high school to his home, Jamal travels 5.0 miles east and then 4.0 miles north. When Sheila goes to her home from the same high school, she travels 8.0 miles east and 2.0 miles south. What is the measure of the shortest distance, to the nearest tenth of a mile, between Jamal’s home and Sheila’s home?
Once you’ve worked it out or given up, join me and read on.
I was so excited because I immediately saw this problem in terms of triangles. I am pretty good at reading maps, and I visualized the routes Jamal and Sheila took. After that, I realized I could probably use the Pythagorean theorem to solve the problem because the triangles formed were right triangles. As I read further, I discovered I was correct. The students who missed this question were not able to transfer a²+b²=c² to a real-life application, though they probably memorized the formula and correctly answered questions just like this one, only formed in such as way that they could clearly see the Pythagorean theorem was necessary to solve the problem. I guess I’m not such a bad math student after all. And by the way, the answer is 6.7 miles. Um… right? Tranfer? Yes. Confidence? Not yet.
And how many times have I complained that students are fixated on grades and don’t really care what they have learned? I suppose I have trouble practicing what I preach. I saw my math grades as an indicator that I didn’t understand. The problem, then, was not that I didn’t understand, but that the assessments provided by my instructors didn’t always enable me to prove that I understood. I really don’t want to do this to my own students.
Wiggins and McTighe define “an understanding,” the noun, as “the successful result of trying to understand — the resultant grasp of an unobvious idea, and inference that makes meaning of many discrete (and perhaps seemingly insignificant) elements of knowledge” (43). As teachers we generally choose our subject matter, if we are subject specialists as is commonly the case with secondary teachers, based upon our expertise. I consider myself a good reader and writer, and I liked my junior and senior English teacher a great deal. She inspired me to further my English education in college. It was touch and go, as I was actually a better student of French than English. I considered teaching foreign language, but one reason I decided not to is that in order to be a more attractive candidate, I would probably have to be able to teach more than one foreign language, and I was only ever interested in French (at least when I was younger, that is). As we learn, we forget that we didn’t always know this stuff, and we gradually become experts. Wiggins and McTighe warn against this “expert blind spot” (44). You might be suffering from this blind spot, as I do, if you’ve ever said something like this:
Teachers do not optimize performance, even on external tests, by covering everything superficially. Students end up forgetting or misunderstanding far more than is necessary, so that reteaching is needed throughout the school experience. (How often have you said to your students, “My goodness, didn’t they teach you that in grade X?”). (45)
What do we get as a result? “Students in general can do low-level tasks but are universally weak in higher-order work that requires transfer” (45). As the authors argue, “We [make] it far more difficult for students to learn the ‘same’ things in more sophisticated and fluent ways later. They will be completely puzzled by and often resistant to the need to rethink earlier knowledge” (45). I know I have noticed this phenomenon in my own students, especially with regards to grammar. Our school has rigorous grammar instruction in the 9th grade. If students do not learn the basics of grammar before they enter the 9th grade, I have found they are often resistant to learning it. They don’t feel comfortable with the material, and they feel frustrated about being behind. They also don’t often make use of teacher office hours or our Learning Center in order to catch up, but those few students who do invariably “get it” at last. I know that my writing has improved over the last few years as I have been teaching this grammar curriculum. I really think about all of the parts of language and how to put them together to get my ideas across with clarity. It isn’t that I didn’t think about it before, but I really feel more grounded and sure of myself as a writer. But just like my students, I was resistant toward rethinking “earlier knowledge.” I have had to question my own beliefs regarding grammar instruction (and, to be fair, those of my previous teachers, professors, and my supervising teacher from my student teaching days).
As Wiggins and McTighe further explore understanding, they note “Children cannot be said to understand their own answer, even though it is correct, if they can only answer a question phrased just so” (48). In so doing, students show not that they understand a concept, but that they can regurgitate a fact, solution, answer, etc., for a test. Inevitably, this lack of transfer will result in the students’ forgetting the concept. It’s not that they forgot it, but that they never really understood it at all. Determining whether a student understands demands “crafting assessments to evoke transferability: finding out if students can take their learning and use it wisely, flexibly, and creatively” (48). In other words, we should be “assessing for students’ capacity to use their knowledge thoughtfully and to apply it effectively in diverse settings — that is, to do the subject” (48). A common pitfall in education is that we “attribute understanding when we see correct and intelligent-sounding answers on our own tests” (49). I had a student who could memorize like no one’s business. She memorized vocabulary for quizzes and made excellent grades, but I can’t recall seeing her use those new words in her writing, and later she might even ask me what the term meant if I casually used it in class. She hated it when I changed my vocabulary instruction this year and adopted vocabulary cards. I noticed an uptick in transfer of new vocabulary this year. If I used a term in class, students might even point out that it was a vocabulary term. Some of them even made a concerted effort to incorporate their new vocabulary words into their writing. But this student did neither — she still didn’t know the terms later, and she still didn’t use them in her writing. In addition, she seems to have to have information presented in exactly the same way each time, or she doesn’t know what I’m talking about. In other words, I think this student’s problem is an inability to transfer. I don’t think it’s entirely up to her — I needed to figure out a way to facilitate that transfer. However, I figured out ways to get other students to transfer, so it wasn’t entirely me. She insists that she is just a poor test-taker. After reading this chapter, I think I have a better idea of what’s wrong. She never understood the material in the first place, but she compensates so well with her excellent memory that she still manages to earn good grades. Placement or tracking can be difficult for students like this girl because as teachers, we know something is off. We know these students don’t “get it” like they should, but at the same time, they can earn grades that would seem to justify a higher placement. What we need to do as teachers, then, is create authentic assessments that enable us to justify the grades we give. I cannot justify the high grades this student received in my class; I know she doesn’t have the understanding that some of her peers had who didn’t earn grades as high as hers.
Wiggins and McTighe conclude the chapter with a discussion of misunderstanding, which “is not ignorance,” but “the mapping of a working idea in a plausible but incorrect way in a new situation” (51). The authors point out, “Paradoxically, you have to have knowledge and the ability to transfer in order to misunderstand things” (51).
Thus evidence of misunderstanding is incredibly valuable to teachers, not a mere mistake to be corrected. It signifies an attempted and plausible but unsuccessful transfer. The challenge is to reward the try without reinforcing the mistake or dampening future transfer attempts. In fact, many teachers not only fail to see the value in the feedback of student misunderstanding, they are somewhat threatened or irritated by it. A teacher who loses patience with students who don’t “get” the lesson is, ironically, failing to understand — the Expert Blind Spot again… Take time to ponder: Hmmm, what is not obvious to the novices here? What am I taking for granted that is easily misunderstood? Why did they draw the conclusion they did? (51)
Work Cited: Wiggins, Grant, and Jay McTighe. Understanding by Design. Expanded 2nd Edition. Alexandria, VA: ASCD, 2005.