Unpacking Goals

After working through Chapter 6 and looking at the content standards again, I've taken another look at my big ideas, the stated or implied real-world performances that go with the standards, and the essential questions that fit best with the standards.

BIG IDEAS:

1. Interconnections between species
2. The flow and cycling of resources (energy and nutrients) in ecosystems
3. Ecosystem responses to disturbance

REAL-WORLD PERFORMANCES:

Students should be able to...

• ANALYZE changes in an ecosystem.
• REPRESENT energy flow through an ecosystem, as in an energy pyramid.
• DISTINGUISH accommodation within individuals from genetic adaptation in a population. (I'm saving this for Unit 3 when we get into evolution.)
• DETERMINE the fluctuations in population size caused by birth, immigration, emigration, and death.

UNDERSTANDINGS:

Students should understand that...

• Ecosystems include a variety of different roles that can interact in complex ways. (Big Idea #1)
• Both negative interactions (competition, predation) and positive interactions (cooperation, mutualism) are important in shaping the structure of ecological communities. (#1)
• Different species use different survival strategies, which can be successful in very different ways (e.g., r-selection vs. K-selection; Type I, II and III survival curves).
• Species' populations can be regulated from the "bottom up" (by resource limitation) or from the "top down" (by predation and disease). (#1, #2)
• Nutrients cycle within the biosphere: carbon, nitrogen, oxygen, and water are reused again and again, with little "new" input or loss (though human CO2 production is a major exception!). (#2)
• Ecosystems are open-ended with respect to energy: producers obtain it from one source (almost always the sun) and pass it up the food chain, losing some energy to heat at every step. (#2)
• Some ecosystems depend on "keystone species", and that threatening these species threatens the entire structure of the community. (#3)
• Outside disturbance can upset the balance of an ecosystem, and that the degree of upset depends on both the magnitude of the disturbance and the robustness of the ecosystem. (#3)

ESSENTIAL QUESTIONS:

• How are different species dependent on each other?
• Why is preserving biodiversity important?
• What makes an ecosystem stable or vulnerable?
• How do resource needs constrain the structure of ecological communities?
• How can we protect ecosystems from damage, and when should we do so?

PERFORMANCE TASK IDEAS:

• Have students plot the flow of resources and/or interaction webs in sample ecosystems.
• Write the "biography of a nitrogen atom" (or a carbon atom, etc.) as it journeys through its nutrient cycle.
• Examine population data to determine if a species is at its carrying capacity in a particular ecosystem.
• Identify populations that are under "bottom-up" or "top-down" regulation.
• Study real-world systems where dramatic shifts have occurred in community structure, and identify likely causes for the change.
• Research an exotic species that has been introduced to California (chosen from a list) and present a report explaining whether it has become invasive, how they can tell, and what is being done to combat it (if anything).

At this point I think my Stage 1 picture looks pretty clear. Assuming that my coaches agree, I'll be ready to jump into Stage 2: designing the assessments that will allow my students to demonstrate their understanding of the material.

UbD Chapter 6: Crafting Understandings

In this chapter of UNDERSTANDING BY DESIGN we delved into what we specifically mean by "understandings" and how to craft useful ones for our classes. I feel pretty comfortable with this concept now; the idea that "knowledge" refers to discrete facts that can be taken as givens, while "understanding" refers to the theory or inference that we make from those facts, is one that meshes well with my experience in scientific research. Looking at the list of sample understandings that are commonly mistaken for bare facts (pp. 136 & 138), I was somewhat surprised that any educated person would be willing to accept these deep concepts on mere authoritative fiat.

Then again, that got me thinking about my own response to concepts in geometry like the Pythagorean Theorem. I was never all that interested in mathematical proofs when I was in school, and I remember being annoyed that my textbook spent so much time proving ideas that were so easy to remember. As long as I could remember the formula and knew when and how to use it, I didn't care to know the gory details for how mathematicians proved such things. In retrospect, it's obvious to me that I didn't understand (heh) the distinction between knowledge and understanding, nor the need to "construct" understanding of deductive theorems.

Constructing inductive understanding was always pretty easy for me to wrap my brain around, perhaps because that's the way science works. It's easy to understand why you have to use speculation, testing and reasoning to come up with a theory for how something generally works when all you have to work with are a few specific data points. Deduction, to me, always felt like working backwards: if you've set your axioms right, there's only one possible conclusion you can reach -- but who's to say whether your axioms are right? Even something as seemingly solid as geometry is ultimately rooted in a fairly arbitrary set of rules; once you change those rules, your whole system of deductive consequences is changed as well. Even more disturbing, there is no one "true" set of geometric rules that applies in all situations; Euclid's system works well for most common circumstances, but when you start getting into the far-flung corners of physics, they're no longer applicable.

I suspect that this lack of congruence between math and reality is part of why I've always found math irritating, even when I was good at it. It always seemed to me that math ought to be "true": that it should remain consistent with reality in all circumstances, without resorting to apparent "cheats" like imaginary numbers and non-Euclidean geometries. (The existence of pi still creeps me out when I think about it too much. I'm surrounded by circles, spheres and cylinders of quite obvious solidity, and yet their areas and volumes can never be precisely known because they are dependent on a number with an infinite number of digits!) The notion that new maths had to be invented in order to describe quantum mechanics is deeply distasteful to me, on a level that I'm not sure I can really explain even today. I suppose I have to look at "ordinary" math the way that I look at Newtonian mechanics: a useful approximation of reality that works for most practical purposes.

My own struggle with truly understanding math is a useful reminder of the struggles faced by my students:

"...experts frequently find it difficult to have empathy for the novice, even when they try. That's why teaching is hard, especially for the expert in the field who is a novice teacher. Expressed positively, we must strive unendingly as educators to be empathetic with the learner's conceptual struggles if we are to succeed." (p. 139)

I'll have to stay aware of the fact that many of the biological principles that I'm teaching these young people will be just as baffling to them as the paradoxes of mathematics are to me.

Hmm ... maybe I should put a giant pi symbol over my desk as a reminder.

UbD Chapter 5: Essential Questions

In this chapter of UNDERSTANDING BY DESIGN, the authors delved into the topic of Essential Questions -- questions that encourage a deeper exploration of the material rather than mere pat answers that can easily be memorized. These questions can be specific to the topic at hand or more overarching, and they can also be open-ended (questions that have no generally agreed-upon "right" answer) or guided (questions that do have have agreed-upon answers, but not ones that would be readily available to the students, and which point to key understandings that the teacher is attempting to convey).

While I was reading about the different kinds of Essential Questions, I started scribbling notes in the margins of the book about possible Essential Questions for my Ecology unit:

OPEN-ENDED, OVERARCHING:

• What is "life"?
• Why should we care about biodiversity?
• What makes an ecosystem desirable? Why should we care about protecting it?

OPEN-ENDED, TOPICAL:

• Are ecosystems driven more by negative interactions between organisms -- "nature red in tooth and claw", competition and predation -- or by positive interactions, such as cooperation and mutualism?
• What makes an ecosystem stable or vulnerable?
• Why is the world green? (I.e., why is so much biomass tied up in producers rather than consumers?)
• Are species' populations limited more by "bottom up" effects (food supply, available habitat) or by "top down" effects (predation)?

GUIDED:

• Where does the rain go after it falls?
• Where does the oxygen we breathe come from?
• In what ways do humans alter the environment around them?
• What happens to a body after it rots? Where do its components go?
• Why are decomposers important?
• Why are primary consumers (herbivores) important?
• Why are predators important?
• What traits might indicate that a species is more likely to survive disruptions in its habitat?

This may be too many essential questions for one unit, so I'll have to figure out which ones are most important to focus on. I'm very fond of the "Why is the world green" question -- both because of its deceptively simple phrasing and because it opens up the opportunity to explore a number of interconnected ideas about the roles of species in a community and the differences between top-down and bottom-up regulation. (The current working theory is that the world is green because predators keep herbivore populations below their carrying capacity, which prevents the herbivores from stripping the ecosystem of every available scrap of foliage. This is in marked contrast to the situation in most oceanic ecosystems, where primary producers -- algae -- are quickly eaten by primary consumers, which are in turn quickly eaten by the secondary and tertiary consumers who make up most of the system's standing biomass.)

This may be one of the most useful chapters to date, because it provides a methodology for getting at one of my chief objectives: getting students to think.

"Our students need a curriculum that treats them more like potential performers than sideline observers. They need to experience how their own inquiries and discussions are 'essentially' parallel to those of experts, and how even key agreed-upon understandings can change over time as a result of ongoing inquiry. In this way, they come to more deeply understand knowledge as the result of inquiries as opposed to disembodied 'truths' that are just 'out there' to be learned from teachers and texts." (p. 122)

Not coincidentally, I was also inspired today to put out feelers to several of my former associates among the graduate students and faculty of UC-Santa Cruz. Hopefully some of them will be able to come out and talk to my students about their research, so as to help them get a better feel for what it's like to be on the cutting edge of scientific inquiry.

UbD Chapter 4: The Six Facets of Understanding

The concept that we call "understanding" is actually many different concepts, all interrelated but distinct from one another. Chapter 4 explores these different kinds of understanding and how they relate to teaching.

1.) Explanation: Can the student construct a meaningful theory for why the facts are what they are? Understanding the situation means grasping the mechanism behind the observed events.

2.) Interpretation: What is the meaning of the observed events or narrative? An abstract theory (Explanation) can describe the general reasons for how things happen the way that they do, but interpretation means looking beyond mechanism to the deeper implications, be they philosophical, moral, sociological, etc. Interpretations are provisional by their nature; different people may look at the same situation, or the same theoretical construct, and have very different ideas about its meaning. The vehement disagreement among physicists about the interpretation of quantum mechanics is a good example of this.

3.) Application: If you really understand something, you can take the knowledge you've acquired on the subject and apply it in new situations. You should be able to perform novel, creative work that demonstrates what you've learned.

4.) Perspective: Understanding a situation means being aware of the importance of a person's point of view and how that affects their interpretation of the data. To go back to the quantum mechanics issue, it's helpful to know what metaphysical and philosophical baggage are being carried around by the proponents of the different interpretations, and how that influences their thought. A person who advocates the Copenhagen interpretation (that there is only one universe, and that the wave functions of quantum mechanics represent probabilities that "collapse" when we finally make a measurement) is necessarily coming at the problem from a different viewpoint from someone who advocates the many-worlds interpretation (that the probabilities of the wave functions actually describe the frequency with which different results occur across an infinite number of universes).

5.) Empathy: While perspective is the ability to judge alternate viewpoints from outside, with a detached, critical eye, empathy is the ability to get inside another person's POV and see why they hold that viewpoint. Since many "Big Ideas" are confusing, counterintuitive or crazy-sounding when you first encounter them, you often have to suspend your own judgments and put yourself in the thinker's perspective before you can really "get" those ideas. Otherwise you risk discarding important concepts because they don't fit in with your preconceived notions of the world.

6.) Self-Knowledge: In addition to understanding others' viewpoints, you have to understand your own viewpoint. Everybody looks at the world through a filter, unconsciously omitting or discounting data that do not coincide with their worldview. Self-knowledge means that you're aware of your filter and making a conscious effort to consider perspectives that lie outside it, or even conflict with it completely.

"Our intellectual blind spots predispose us toward intellectual rationalization: the ability to unendingly assimilate experience to beliefs and to categories that seem not merely plausible ideas but objective truths. Too easily, we keep verifying our favored and unexamined models, theories, analogies, and viewpoints." (p.101)

This sort of self-blindness is the bane of good science -- or, for that matter, good scholarship in any subject. The first and greatest mistake many researchers make is to assume that they are impartial observers, that they are completely fair and even-handed. It's not just scientists who have this problem, either; we've all seen examples of how biased reporters can be, even when they repeatedly proclaim that they are "objective" or "fair and balanced."

The first three facets are what I would call "external" aspects of understanding; these are the facets that my students can directly apply to the material of the course itself. I can help my students learn how to grasp the theory behind biological processes, to interpret the deeper implications of those theories, and to apply them to new problems. The other three facets are "internal" aspects of understanding: they concern the students' understanding of how they understand the material. The "Big Idea" of Resource Cycling & Flow in Ecosystems is an objective process that can be Explained, Interpreted and Applied, but it doesn't have an inherent perspective attached to it that must be perceived or empathized with; rather, students will need to apply these three latter facets of knowledge to the interpretations of this process, both the ones that are presented by experts and the ones that they come to for themselves. For example, the objective existence of the Nitrogen Cycle leads to a possible interpretation that humans need to stop dumping nitrogenous agricultural runoff into our lakes and rivers, because this excess nitrogen is throwing natural systems out of balance. Students will need to have the Perspective to analyze the arguments of environmentalists and the agricultural industry about this question, the Empathy to appreciate why each side views this situation the way that they do, and the Self-Knowledge to see how their own biases affect their opinions on the situation.

All of these facets of understanding work together to lead to what I have previously described as "critical thinking." I'm glad to see them described explicitly in such detail; it will be a big help to me as I figure out what sorts of assessments and lesson plans will engage these different styles of thinking.

Understanding By Design-Templates

The first 57 pages of the UbD Professional Development Workbook introduce three different templates for "backward design" of an instructional unit: a brief 1-page template, a somewhat more detailed 2-page version, and a very detailed 6-page breakdown that gets into the details of day-by-day lesson planning. The remaining pages are mostly taken up by examples of unit plans in everything from science to history to English.

After looking through the different designs, I've decided to go with the 2-page version for planning my ecology unit. It gives a bit more space to describe different portions of the unit than the 1-page version, especially for the Stage 3 tasks and lessons. The 6-page version looks too detailed and complex for my first attempt at unit design; I don't want to fall into "paralysis by analysis." I'll stick with the 2-pager for now and expand my ideas as necessary once I have a basic framework in place.

UbD Chapter 3: Gaining Clarity on our Goals

"...a big idea is not 'big' merely by virtue of its intellectual scope. It has to have pedagogical power: It must enable the learner to make sense of what has come before; and, most notably, be helpful in making new, unfamiliar ideas seem more familiar." (Understanding by Design, 2nd Ed., p.70)

This chapter took a closer look at the so-called "Stage 1" concepts for unit planning: key questions, key understandings, big ideas, and core tasks. All of these are related, though not synonymous, and they're all different ways of getting at the heart of the question: what do I want my students to understand, know, and be able to do when they complete this unit?

The chapter is full of a lot of good advice on how to screen through lists of material -- whether a textbook or a set of state-imposed content standards -- and filter out the big ideas and core tasks from among the less-crucial concepts. The models presented here help to distinguish the crucial from the important, and the important from the incidental, and the incidental from the trivial. It's something I'm going to have to put into use for myself as I screen through the California science standards to figure out which points are most important for my students to understand.

Reading through chapter 3 inspired a number of thoughts about the "big ideas" of ecology, the first unit for my upcoming biology course. The book points out that big ideas are usually counter-intuitive and susceptible to misunderstanding. This got me thinking about food webs, nutrient cycles and energy flow in ecosystems, all of which involve the central "big idea" that thermodynamics limit the possibilities in biological systems. But the first law of thermodynamics -- the law of conservation of energy -- can easily be misunderstood by students in this context, because energy is constantly being lost from the ecosystem in the form of heat. Energy isn't being destroyed, but it's no longer in a useful form. Likewise, the second law -- the law of increasing universal entropy -- often seems like it's being violated by living systems, in which organisms that are higher on the food chain often appear more "advanced" or complex than the creatures they feed on. Yet the constraints placed on ecosystems by thermodynamics -- a fixed amount of energy entering the system (1st law), and every energy transfer leading to a loss of energy to heat (2nd law) -- are essential to grasping why ecological communities are structured the way that they are. The key misconception is that students might be fooled into thinking that the biosphere is a closed system, energetically speaking. It isn't; it's a closed system for nutrients, which is why we speak of nutrient cycling, but it's an open system for energy, which is why we speak of energy flow.

I think I have a good way of modeling energy flow for the students: an analogy to money. Suppose American shoppers buy products from Company A, leading to a gross income for the company. The money flowing into Company A from the shoppers represents the maximum amount of money available in the "system;" the Company has no other way of acquiring more money. The Company then pays its employees, but it can't pay them everything that it got from the shoppers; it has to pay for the electricity, the water, maintenance of the equipment, the raw materials to make its products, and various regulatory costs in the form of taxes. Only a small portion of its gross income gets passed on to the employees. Employee B thus gets a small fraction of the money Company A had; that's his gross income. But that isn't pure profit, either; he has to pay for upkeep on his house, gas for his car, food for himself and his family, and his own income taxes. Only a little bit of money is left over for the next step in the monetary "food chain": his kids. Child C gets an allowance that is only a tiny fraction of what Employee B got; it's such a small amount, in fact, that the child doesn't have enough money to support anyone "higher" on the chain.

By the same token, the "gross income" of an ecosystem from the sun leads to a lot of energy going through the producers (A), with less being passed on to the primary consumers (B) and still less going to the secondary consumers (C). My students will probably find the analogy of themselves as "apex predators" to be an amusing one -- though perhaps "parasite" would be a more accurate analogy. ;-)

I think this will be a good way to explain energy flow, but I'm having more trouble finding a way to explain nutrient cycling. I need something to represent a commodity that can be passed around from one group to another, modified repeatedly into different forms but ultimately recycled back to the beginning again, unchanged in what it essentially is. The carbon, nitrogen and water cycles are key examples, all important for illustrating how ecosystems function -- but I'm having a hard time finding something similar to compare to that these students would be familiar with. I thought about the example of a commodity (such as a bicycle or a CD) being passed around from one person to another, but that analogy misses one of the key elements (no pun intended) of nutrient cycling: that these basic nutrients are often repackaged in radically different forms and used for very different purposes as they make their way around the ecosystem. The sugar made by the plant, the fat stored in the human, the carbon dioxide breathed out when the human exercises -- all of these contain the same carbon atoms, passed on from one place to the next but showing up in very different chemical forms.

I'd love to hear if anyone has any suggestions on a better analogy for this difficult concept. I recognize that this is only one example among several "big ideas" that I'll have to tackle in this unit, but it's one that I'm going to have to wrestle with soon enough, and I think it's a useful "field test" of the UbD process to start thinking about this now.

UbD Chapter 2: Understanding Understanding

"Zathras understand. ... No. Zathras not understand, but Zathras do. Zathras good at doings, not understandings." --Zathras, Babylon 5

This chapter brought to light a depressing fact about modern education: most students who are "good at doings", as Zathras would say, are not "good at understandings." They have collected facts in their heads, but they don't know what they mean, and questions that present them with the opportunity to use their facts and skills in novel ways often leave them staring blankly at the page. The emphasis on loading students' brains with as many facts as possible only makes the situation worse. "Teaching to the test" can help students to regurgitate the right answers on command, but only if the questions that they face on the test are exactly like the questions they've seen before. This is why so many students hate story problems: they point out the fact that the student never understood what he thought he knew.

The listing of common misunderstandings in this chapter was somewhat unsettling for me, because it revealed some of my own misconceptions. I'd had no idea that Impressionism was an attempt to be more realistic, to convey the raw sensory impact of a thing rather than the emotional or mental response that the thing engendered in the artist. I've often thought that history classes were almost useless because they consisted of bombarding students with an endless procession of facts, which could easily be looked up in an encyclopedia if they were actually needed. The idea of historian as "storyteller," putting events into any of several possible narratives that might "explain" these events, is one that runs rather contrary to my instinct that there should be one "true" reason or explanation for why things happened. I can only imagine how many similar misconceptions people in other fields must have about my area of study.

The one part of the chapter that jumped out at me the most, though, was the section about understanding the phenomenon of misunderstanding:

"Misunderstanding is not ignorance, therefore. 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 [i.e., to apply it in new situations] in order to misunderstand things. 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." (p. 51)

This section was a wake-up call for me, because I used to get very frustrated at my college students who would return garbled and nonsensical answers to my quiz questions. "They soak up all of this information and then spit it back out like a random comment generator," I would sometimes complain to my fellow TAs. "They just aren't thinking about what they're saying!" The irony, of course, is that they were thinking, but they hadn't arranged the facts into the correct framework. Like a Rube Goldberg machine with the parts in the wrong order, they were failing to get the desired output, but it wasn't for lack of trying. It's a distinction that I'm going to have to be more aware of when I teach my 9th graders -- and I'll have to be patient with them, to acknowledge and refine what George Leonard calls "the approximations of the correct technique", while helping them to make the necessary adjustments to their thinking.