Chapter 2: Understanding Understanding

1. Chapter 2: Understanding Understanding “Education: That which discloses to the wise and disguises from the foolish their lack of understanding.”- Ambrose Pierce Interpreted by Dr. Rich Hawkins and Dr. Deborah DeLucaPresented By:Laura Mastrogiovanni

2. What is the difference between knowledge and understanding? An essential question for twenty-first teaching and learning

3. Ultimate Irony • “…though we all claim as teachers to seek student understanding of the content, we may not adequately understand this goal.” (p.35) • Bloom’s Taxonomy (1956) • Designed to classify and clarify the range of possible intellectual objectives, from the cognitively easy to the difficult; it was meant to classify degrees of understanding.

4. Bloom’s Query • “…some teachers believe their student’s should “really understand,” others desire their students to “internalize knowledge,” still others want their students to “grasp the core or essence.” …Do they all mean the same thing? • Implied by the AAAS, an understanding is a mental construct, an abstraction made by the human mind to make sense of many distinct pieces of knowledge…if a students understands, then they can provide evidence of that understanding by showing what they know and can do…

5. Understanding as Meaningful Inferences • Unfortunately, to make matters worse, we tend to use the terms know, know how and understand interchangeably in everyday speech • Is knowing how to fix a car the same thing as understanding how to fix a car? • What is the difference? • Is knowing how to play a guitar the same as understanding how to play a guitar? • What is the difference?

6. Understanding as Meaningful Inferences • Dewey (1933) summarized the idea most clearly in How We Think. Understanding is the result of facts acquiring meaning for the learner: To grasp the meaning of a thing, an event, or a situation is to see it in its relations to other things: to see how it operates or functions, what consequences follow from it, what causes it, what uses it can be put to. In contrast, what we have called the brute thing, the thing without meaning to us, is something whose relations are not grasped…The relation of means-consequence is the center at the heart of all understanding. (pp.137,146)

7. Where does “Understanding” live? Why? Learning Organizations PM MM ST SV TL Aspiration Understanding Complexity Inquiry

8. Facts A body of coherent facts Verifiable Claims Right or wrong I know something to be true I respond on cue with what I know Meaning of the Facts The “theory” that provides coherence to these facts Fallible, in-process theories A matter of degree or sophistication I understand why it is , what makes it knowledge I judge when and when not to use what I know Knowledge vs. Understanding

9. RJH working definition If you have knowledge you can recant it robotically and apply it pedantically If you have understanding you can teach it authentically and apply it systemically and globally

10. Example #1 • First you arrange things into groups. Of course one pile may be enough, depending on how much there is to do; but some things definitely need to be separated from the others. A mistake here can be expensive; it is better to do too few things at once than too many. The procedure does not take long; when it is finished, you arrange the things into different groups again, so that they can be put away where they belong p.39

11. Irony • The first passage is a vague account of doing laundry. More generally, the goal in understanding is to take whatever you are given to produce or find something of significance – to use what we have in memory but to go beyond the facts and approaches to use them mindfully. • By contrast, when we want students to “know” the key events of medieval history, to be effective touch typists, or to be competent players of specific musical pieces, the focus is on a set of facts, skills, and procedures that must be “learned by heart” – a revealing phrase! p.39

12. W. Edwards Deming Without theoretical understanding there is no true learning

13. Bloom (1956)… • Understanding is the ability to marshal skills and facts wisely and appropriately, through effective application, analysis, synthesis, and evaluation. • Therefore, doing something correctly is not, by itself, evidence of understanding. It might have been by accident or done by rote. • To understand is to have done it in the right way, often reflected in being able to explain why a particular skill, approach, or body of knowledge is or is not appropriate in a particular situation

14. Or, as Richard Strong taught us • You know when a student understand something when they can: • Define it • Create a picture of what it is • Create a picture of what it is not • Attributes • Use vocabulary

15. Practical Examples • Think of a story • The words are the facts • We can look at each word and say we know it • The meaning of the story is open for discussion • Read between the lines • Inference

16. Understanding as Transferability The story of two different music classes taught by two different teachers as seen through the eyes of the same students

17. Understanding as Transferability • Dewey (1933): • It would be impossible to over-estimate the educational importance of arriving at conceptions; that is, meanings that are general because applicable in a great variety of different instances in spite of their difference…They are known points of reference by which we get our bearings when we are plunged into the strange and unknown…Without this conceptualizing, nothing is gained that can be carried over to the better understanding of new experiences

18. Understanding as Transferability • Berenbaum(1988): • Baking without an understanding of the ingredients and how they work is like baking blindfolded…sometimes everything works. But when it doesn’t you have to guess at how to change it…It is this understanding which enables me to be both creative and successful.

19. Understanding as Transferability – or lack thereof • Global Studies Regents • Over time, the Regents always had DBQ asking students to explain the impact of geography on economy. • One year, the question was inverted to ask, “What is the impact of economy on geography?” • What happened?

20. Understanding as Transferability – or lack thereof • NYS Math Regents • To get from his school to his home, Jamel 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 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? (The use of the accompanying grid is optional.)

21. Understanding as Transferability – or lack thereof • NYS Math Regents • The failure of even our best students to transfer their learning is most evident in Mathematics • FYI, two-thirds of students got this wrong. • It is about the “application” of the Pythagorean Theorem A2 + B2 = C2 • Groups of two, solve the prior problem

22. Understanding as Transferability • Is it any wonder that students do not understand what they supposedly know? • Few educators seem to realize is that drilling students for state tests is a FAILING strategy! Stop it, dammit! • Question: • Is it possible to teach in alignment with assessments and teach for understanding? Please discuss. Explain you answers.

23. Understanding as a Noun • Understand(ing) has a verb meaning and a noun meaning • To understand a topic or subject is to be able to use (or “apply” in Bloom’s sense) knowledge and skill wisely and effectively. • An understanding is the successful result of trying to understand – the resultant grasp of an unobvious idea, an inference that makes meaning of many discrete (and perhaps seemingly insignificant) elements of knowledge. p. 43

24. Explicit Instruction is Key to Transferability • With deliberate and explicit instruction in how to transfer ( and assessments that demand such transfer), the learner must take what were initially bits of knowledge with no clear structure or power and come to see them as part of a larger, more meaningful, and more useful system.

25. Explicit Instruction is Key to Transferability • Without lessons designed to bring ideas to life, concepts such as honor, manifest destiny, or the water cycle remain empty phrases to be memorized, depriving learners of the realization that ideas have power. • Discuss MLK’s “I have a Dream speech” • Discuss anti-bullying programs

26. Bransford, Brown, & Cocking Teaching specific topics or skills without making clear their context in the broader fundamental structure of a field of knowledge is uneconomical…An understanding of fundamental principles and ideas appears to be the main road to adequate transfer of training. To understand something as a specific instance of a more general case – which is what understanding a more fundamental structure means – is to have learned not only a specific thing but also model for understanding other things like it that one may encounter

27. Thoughts on transferability • Transfer must be the aim of ALL teaching in school – it is not an option – because when we teach , we can address only a relatively small sample of the entire subject matter • Do you teach a “mile wide and an inch deep” or, an inch wide and a mile deep?”

28. Teaching for Transfer • Socratic Method • Reflection and Generation • Teach (and lead) with Inquiry • Higher-order questioning skills • Five Why’s • Why is that so? Why do we think that? What justifies such a view? What’s the evidence? What’s the argument? What are the assumptions?

29. The Expert Blind Spot • Teaching for transfer • Effective but is it Efficient? • Educators fail to understand understanding when we think that coverage works • Our learning disability, promulgated by educational culture, is often expressed as, “If I cover it clearly, they will “get it” and be able to call upon it in the future. The more I cover, therefore the more they will learn, and the better they’ll do on the tests.” Oy! An ABBA if ever there was one. • A perfect example of circular logic built upon a false indicator. • The “yield” from coverage is quite low for most students

30. Does your school have a “learning disability?” • How many times have you said any of the following to students: • Didn’t they teach you anything last year? • Who was your teacher last year? • Did you actually take ________ last year? • Were you in our school last year? • But it is so obvious!!! • Or, “I just don’t have enough time to cover everything I need to cover!” duh!

31. Evidence of “teaching for coverage?” • Unreliable predictive value of test scores on future success • Lack of reliability between class grades and assessment scores • Unequal distribution of test scores on a grade level or in a department • “Best” students struggle on extended response and application questions • Local assessments rely on a child’s ability to “remember” facts as opposed to apply knowledge

32. Evidence for Teaching for Transfer • Assessments are crafted to evoke transferability; finding out if students can take their learning and use it wisely, flexibly, and creatively • A person who has understanding can cope with ambiguous challenges in which what is required does not come packaged as a straightforward cue to stimulate a single response

33. Evidence for Teaching for Transfer • Assessing for students capacity to use their knowledge thoughtfully and to apply it effectively in diverse settings – that is, to do the subject • Assessments contain a novel task, requiring transfer, and ideally involved contextualized and practical use of ideas. (NCATE assessments) • Use of far fewer narrow prompts that are intended to elicit the “correct” answer to a familiar question. • See examples on p.49

34. Knowledge differs from Understanding Create your own example(s) that explicitly illustrates the validity of this statement.

35. Learning from Misunderstanding Think like “House, M.D.” How does House learn from misunderstanding?

36. Learning from Misunderstanding • Misunderstanding is not ignorance. It is the mapping of a working idea in a plausible but incorrect way in a new situation • Paradoxically, you have to have knowledge and the ability to transfer in order to misunderstand things

37. Learning from Misunderstanding • Evidence of misunderstanding is not a mistake to be corrected, it is a diagnostic tool to be used by the teacher that indicates what the students does understand and the processes used to reach their conclusions • If you lead with Inquiry, student misunderstandings allow you to diagnose root causes and begin to shift your MM’s about students as learners. Think Iceberg – what is not obvious?

38. Learning from Misunderstanding – 20 yrs of research confirms • Many students, even the best and the most advanced, can seem to understand their work (as revealed by tests and in-class discussion) only to later reveal significant misunderstanding of what they “learned” when follow-up questions to probe understanding are asked or application of learning is required. • Test for yourself using Strong’s Method

39. Learning from Misunderstanding – 20 yrs of research confirms • Our MM’s (ABBA’s) and those of our teachers lead to misinformation. • Bacon (1620) noted that we project categories, assumptions, rules, priorities, attitudes, and matters of style onto our “reality” and then develop countless ways (schema) of “proving” out instinctive ideas to be true: “The human understanding…when it has once adopted an opinion draws all things else to support and agree with it.” • You cannot swim until 1 hour has passed after you have eaten. • Other myths? See p.54

40. Desired results are the result of clear, explicit expression of purpose Vision, anyone?