This is going to get a bit technical.
I have a problem and would like to open it up to the group. It has to do with me bringing my teaching experience into the world of Early Childhood. Most readers of this blog are early childhood people, I know, but take a look at this paragraph from a college beginning physics text (Tippler & Mosca, 2008):
What does this have to do with Early Childhood Education (ECE)? Figure 1 shows a very dense text and a very dense use of symbols. But look, a high school AP physics teacher is expected to get her students to interpret this and use it to solve problems. The 9th and 10th grade algebra teachers are expected to get them ready for AP physics. Middle school gets them ready for algebra, and on down the line. From preschool to kindergarten, elementary school, and on up, the theory is that many students can be made ready to read, interpret, and apply this dense and abstract stuff. This is one of our targets.
I think every step of the way is mostly failing to do this, but I think ECE is building the solutions. Let me give you an example. A college physics student—a smart young woman—came to me at the end of her semester, failing, but hoping to turn it around in the last two weeks. We looked at the text above and she just stammered. I asked her to draw a picture of “the situation”. She did something like Figure 2. So, what did she do? She drew a picture of a thermometer—from her world. She saw the word in that dense paragraph and that’s what she started with. This gave us something to talk about. I said, “Great! Now, what are the lines for? Why is the bottom darker? What are the P’s?” and we began a conversation. The lines were degree markers; the dark part is where the liquid is; the P’s? They were in the description so she wrote them down. I said, “Let’s take a look at that paragraph again and look at your drawing. See where it says, ‘constant-volume gas thermometer.’ Where’s the gas? What volume is constant?” She couldn’t say, but offered, “Maybe the gas is up in the light part.”
“Excellent,” I said. “but you’re guessing, right?” She admitted, “Yeah, I don’t really know what I am doing.”
This is a very delicate point. You can position yourself as a judger, or a colleague and a “knowledgable other.” I said, “What you’re doing is good. You’re groping around, trying to make sense of this. What you’re doing is very intelligent, trying to fit what what you know to this thing, trying to make sense of it.” Then I said, “The problem is, they’re talking about something different,” and I drew a sketch and she got to watch me draw it (Figure 3).
As I began, I said, “This is what they are talking about, like a big cylinder or can, that doesn’t expand.” I went on, “You know how you shouldn’t throw a paint can in a fire. Why?” She said because it would blow up. “Right, the pressure gets too high as it heats up.” I kept drawing, “In this thing, they put a little sensor on the side (dark patch) and run a wire from it to a pressure gauge (arrow) so they can measure the pressure inside. Now, where’s the gas? Where’s the constant volume?”
She guessed: “The gas is inside the tank and the tank keeps the volume constant.”
“So, how do they measure temperature with this?” She shrugged.
“How did you measure temperature with yours?” I asked, and she looked at her first sketch for about 20 seconds (a long time in one-on-one work) and then said something like, “I don’t know. I guess when the black part gets higher it shows temperature.”
“Yeah, I think you’re right.” I said, “Your thermometer doesn’t really measure temperature, it measures something else. What does it measure?” She thought a few seconds, and answered, “I don’t know. Height?”
“Nice,” I said, “The height is showing how the liquid is swelling. Your’s is not a constant-volume thermometer; I’d call it a ‘constant-pressure’ thermometor, I think. You were right, really. There is a gas above the black part, but it’s almost a vacuum, and as the liquid swells, the gas pressure doesn’t change much at all. Your’s is pretty much a constant-pressure thermometer, but the liquid is the important part and its volume changes as its temperature changes.”
I could go on. What did I do? If you are a ‘Brunarian’, I scaffolded (Wood, Bruner, & Ross, 1976); if you are a ‘Vygotskian’, I acted as a knowledgeable other and helped her materialize her thinking (Bodrova & Leong, 1998); if you are ‘Reggio-inspired’, I co-created knowledge with her as she represented her experience (Edwards, Gandini, & Forman, 1998); if you are a ‘Formanian’, I engaged in a high-level dialog about her theories of the world (Forman & Hall, 2005).
In any case, this took less than five minutes, but it was absolutely essential for her to be able to interpret this text. We went on together, building to where she could interpret the equation and the accompanying diagram (Figure 4), which is much more complicated than my simple picture.
I intend to revisit this experience in future posts, but I want to make a point here: I feel that one of my essential functions in helping people interpret science texts is to make the hidden thinking behind the formal presentations visible and then to help people bring their native intelligence to the problem. For example, to make the equation presented in the text meaningful, you have to a) see it as a predictor of the real world; b) realize that important parts have been left out; c) think of it as a pretend model, not reality; and d) relate it to simple mathematical ideas like triangles, slopes, and ratios.
Like most students I’ve known, my student would have done none of this on her own and would have left the engagement feeling stupid and hopeless. I relate this back to high school, middle school, elementary school, and even early childhood education: it at first seems that this problem requires some academic pyrotechniques to approach, something only a few people have. It does require very abstract thinking, but also it requires certain habits of mind in the student: exploring, representing, naming, revisiting and adjusting, pretending; and requires certain teaching practices: representation, observation, speculation, dialog, provocations, collegiality, and respect. The work of actual scientists, I believe, is full of all of these things, but the formal science and math teaching in school hides it away. My problem is how to point to the essential hidden thinking in science and math problems like the one above and how to bring them into science classrooms up and down schooling.
The constructivist leaders in ECE are devoted to using and developing all these practices outside of a formal curriculum. I’m wondering if we can extend those practices up into the formal curricula, which are pushing down even into kindergarten now, so that by the time children reach high school, they can hit the targets that schooling is setting for them?
PS: I have found that most students benefit by thinking of physics problems in terms of “before” and “after.” Most physics problems have a before/after structure, but it’s hidden. The equation in the text above is actually before/after/in between. Can you find this structure?
Bodrova, E., & Leong, D. J. (1998). Scaffolding emergent writing in the zone of proximal development. Literacy, 3(2), 1.
Edwards, C., Gandini, L., & Forman, G. (1998). The Hundred Languages of Children, The Reggio Emilia Approach—Advanced Reflections.
Forman G. & Hall, E. (2005). Wondering with children: The importance of observation in early education. Early Childhood Research and Practice, 7(2). Retrieved from http://ecrp.uiuc.edu/v7n2/forman.html.
Tipler, P. & Mosca, G. (2008). Physics for scientists and engineers (6th Ed.). New York: W.H. Freeman and Company.
Wood, D., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry,17(2), 89-100.