Transfer Of Understanding In Math And Reading

The problem: transfer of understanding is poor. Students do not understand that the long-term and bottom-line goal of education is transfer.

transfer of understanding
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Examples Of Teaching For Transfer Of Understanding In Math And Reading

by Grant Wiggins

In the previous literacy post I identified a few take-away questions and related issues from my recent research on comprehension, and looked at some tips related to the 1st question:

  1. Do students understand the real point of academic reading?
  2. Do students understand that the aim of instruction is transfer of learning?
  3. Am I using the right texts for making clear the value of strategies?
  4. Do students understand the difference between self-monitoring understanding and knowing what they might do when understanding does not occur?
  5. Am I attending to the fewest, most powerful comprehension strategies for academic literacy?
  6. Am I helping them build a flexible repertoire instead of teaching strategies in isolation?
  7. Do students have sufficient general understanding of the strategies (which is key to transfer)?
  8. Am I doing enough ongoing formal assessment of student comprehension, strategy use, and tolerance of ambiguity?

In this post we consider question #2, on the goal of transfer.

See also 10 Ways Literacy Can Promote A Deeper Understanding Of Math

When Transfer Is Poor

The problem: transfer is poor. There are numerous indications that our students do not understand that the long-term and bottom-line goal of education is transfer (here are some categories of transfer) of learning. Here is a key and very concrete indicator – from students: “That’s unfair! You asked us questions different from the ones we went over in class!”

David Perkins tells a fabulous story about this in his 25-year-old seminal article on transfer co-authored with Gavriel Salomon entitled The Science and Art of Transfer:

Both the meaning and the challenge of ‘transfer of learning’ are well-expressed in a story told to one of us by a disappointed professor of physics at a nearby college. Among the stock problems explored in the physics course was one like this: “A ball weighing three kilograms is dropped from the top of a hundred-meter tower. How many seconds does it take to reach the ground?” (Aficionados of physics will recognize that the weight of the ball has nothing to do with the problem; it is a distraction. The answer depends only on the acceleration of gravity.)

On the final exam, the professor included a problem like this: “There is a one-hundred meter hole in the ground. A ball weighing three kilograms is rolled off the side into the hole. How long does it take to reach the bottom?”

When Transfer Confuses Students

Some students did not recognize the connection between the ‘tower’ problem and the ‘hole’ problem. One student even came up after the exam and accosted the professor with a complaint. “I think that this exam was unfair,” the student wailed. “We never had any hole problems!”

Students at all ages make this mistake, of assuming that their job is merely to give back what was taught the way it was taught. (This is of course not to blame students for this mess, since they can only have continued to believe this if teacher assessment were always making it true in practice).

Here’s another common student comment that reveals the problem:

  • “Huh? If you wanted us to use some prior learning why didn’t you just ask us to use it?”

Students expect to be prompted for whatever prior learning is required, and they will not even bother to tap relevant prior learning in situations where it would be apparently clear that it was wanted:

“Fifth grade students did not attempt to correct comprehension difficulties by searching back through the text even though students of the same age had identified re-reading as a useful strategy.” [p.380 in the Handbook of Research on Reading Comprehension]

The Failure To Ask Students To Transfer In Assessments

Transfer failure in tests. We have other, indirect, evidence of this phenomenon: the failure of students to transfer relevant prior learning in high-stakes tests, where presumably they would see the value of doing so as well as knowing how to do so. Here are two of my favorite highly-revealing test items about failure of transfer, with % of correct answers.

The first item was from the MCAS and was on the 10th grade English exam:

This selection is best described as –

A. a biography.

B. a scientific article.

C. an essay.

D. an investigative report.

Here is a 2-paragraph excerpt from the reading selection in question, a 17-paragraph piece on being colorblind:

A fellow fourth grader broke the news to me after she saw my effort on a class assignment involving scissors and construction paper. “You cut out a purple bluebird,” she said. There was no reproach in her voice, just a certain puzzlement. Her observation opened my eyes— not that my eyes particularly help—to the fact that I am colorblind. In the 36 years since, I’ve been trying to understand what that means. I’m still not sure I do….

Unlike left-handers, however, we seem disinclined to rally round our deviation from the norm. Thus there’s no ready source of information about how many presidents, or military heroes, or rock singers have been colorblind. Based on the law of averages, though, there must have been some. We are everywhere, trying to cope, trying to blend in. Usually we succeed. Until someone spots our purple bluebirds. Then the jig is up.

This was the hardest question on ANY 10th grade MCAS test, in 4 subjects, that year: only 33% got this one right.

It’s an essay.

“But it didn’t have 5 paragraphs!” complained many students…

Here is the math question, from an old FCAT HS 10th grade geometry test:

Only 27% got this one right – despite the fact that almost every student can recite the key theorems required here, if prompted to do so. Look closely at how the problem is set up to see the transfer expected – in multiple places – despite the easiness of the content (i.e. the Pythagorean Theorem and triangle and square angle sum theorems).

Transfer In Reading Comprehension

Transfer in reading. So, what should we do about the lack of transfer of reading strategies in particular? Probably the clearest statement of the correct path to transfer in using strategies is found in Brown & Palinscar (1989) in which they summarize all their work in Reciprocal Teaching:

[The four strategies chosen were:] questioning, clarifying, summarizing and predicting…. They serve an interesting dual function, if used intelligently; they both improve comprehension and afford the alert reader an opportunity for monitoring understanding. For example, if one attempts to paraphrase a section of text and fails, this is a sure sign that comprehension and retention of main points is not proceeding smoothly and that some remedial action, such as re-reading is called for. The strategies are self-testing mechanisms, and there is ample evidence that such self-testing improves comprehension. [emphasis in the original]

In reciprocal teaching, the strategies are practiced in a appropriate context, during studying, not as isolated skill exercises to be mastered individually and then used whenever students see fit. Each strategy is called into play in response to a concrete problem of text comprehension…. The main goal was not refining the strategies but understanding the text.”

“In general, we have found three types of transfer of training: 1) generalizations to the classroom, 2) improved performance on posttests that tap the trained skills, and 3) improvement on standardized test scores.”

An early paper on strategic reading highlights another key concept in the development of transfer: explicit attention to conditional knowledge, not just declarative and procedural knowledge:

However, declarative and procedural knowledge alone are not sufficient to ensure that children read strategically. They only emphasize the knowledge and skills required for performance and do not address the conditions under which one might wish to select or execute actions. Because strategic behavior involves intentionality and self-control, any analysis that ignores learners’ motivations is incomplete. We want to introduce a new term, conditional knowledge, to capture this dimension of learning to be strategic. Conditional knowledge includes knowing when and why to apply various actions.

The Flexibility Of Understanding

For example, skimming is a procedure that is only appropriate for some tasks and situations. The procedure needs to be applied selectively to particular goals in order to be a strategy. Reading only some of the words and sentences in text is not a strategy by itself; such skimming could be the result of skipping difficult words, poor visual tracking or laziness. The systematic employment of skimming to accomplish goals of speeded reading or previewing, however, would be strategic reading. Conditional knowledge describes the circumstances of application of procedures. [Paris, Lipson, Wixon (1983)]

Here is how the authors of How People Learn build on this point:

Students develop flexible understanding of when, where, why, and how to use their knowledge to solve new problems if they learn how to extract underlying themes and principles from their learning exercises. Understanding how and when to put knowledge to use—known as conditions of applicability—is an important characteristic of expertise. Learning in multiple contexts most likely affects this aspect of transfer.

Building and updating Anchor Charts about what works, when, and why is then an easy and practical move, based on this research. Students must generalize from experience to make transfer more likely, along with understanding that such transfer is the goal.

Principles For Teaching For Transfer In Reading Comprehension

Some principles on teaching for transfer in comprehension. Implied in these critical passages are a few ideas about how to more successfully aim at transfer as a goal in reading comprehension:

  1. The reading performance goal has to be an utterly-clear constant priority – in this case, understanding of challenging non-fiction text. The goal is NOT skill or strategy mastery, but text understanding – and teachers must be confident that students grasp this aim: So, are we understanding this text better? If, not what might help us here? must be the recurring questions, leading toward self-questioning.
  2. The strategies must be taught and used simultaneously, not in isolation. It must be clear to students that, like hammers and screwdrivers, strategies are tools for building and improving (understandings, in this case). Thus, the development of conditional knowledge – considering which strategies work well, when, and why – has to become a priority, based on students analyzing what works and what doesn’t in attempts to understand.
  3. The strategies are most valuable when they are used as “self-testing mechanisms” in response to conscious self-assessment that something might not be understood (vs. taught as “skills” that may or may not be used or useful at this moment.) This relates closely to Question #3 of my Eight Implication Questions, concerning the choice of the right texts for use with strategies (to be discussed next time).
  4. The strategies must be used as comprehension problems dictate. As the authors elsewhere say, “Clarifying occurred only if misunderstandings were generated by some unclear aspect of the text or by a student’s interpretation of the content.” In other words, far more attention must be given to monitoring for understanding if the strategies are to take root. Meta-cognition of comprehension success and failure is key, more important than the comprehension strategies.

David Pearson On Transfer

By the way, I wrote David Pearson to get his take on transfer and response to my earlier post about the gradual release of responsibility model, long used to teach strategies. Here is what he said:

“Grant, I can endorse everything you say in your recommendations. The problem with strategies is that folks want to make a fetish out of them. They are just heuristics (which I like to call rules that don’t always work but will give you a leg up).

The big thing to remember is that in 1983, we were trying to move from NO COMPREHENSION INSTRUCTION (it was all practice and assessment) to SOME. So we pushed hard on modeling and guidance as controlling metaphors.

And if I could change something else, it would be to provide explicit instruction ONLY after kids have proven to themselves that they could use a little guidance. The Teachable Moment phenomenon…. This short piece responds to some of the concerns you raise: Pearson_Coda_CompGoFrwrd

In my next post, we’ll look at Question #3, the issue of text choice when comprehension monitoring, strategies, and improvement of understanding are the clear goals.

Helpful resources related to transfer, including the references cited above:

Brown & Palinscar (1989) “Guided Cooperative learning” in Knowing, Learning and Instruction: Essays in Honor of Robert Glaser, ed. by Lauren Resnick

The Perkins & Salomon paper referenced above can be downloaded from:

Teaching for Transfer, Madeleine Hunter – an oldie but a goodie: a brief and very concrete overview with helpful tips for teachers

Chapter Three in How People Learn – on transfer and a summary of the research (up to 2000)

A useful summary on transfer as a goal, for college teachers:

Sternberg & Frensch, “Mechanisms of Transfer” in Transfer on Trial: Intelligence, Cognition and Instruction, ed. by Detterman and Sternberg.

Teaching for Transfer: Fostering Generalization in Learning, ed. by McKeough, Lupart & Marini.

The Handbook on Research in Reading Comprehension, ed. by Israel & Duffy (2009) Routledge.