At an all-girls school in Palo Alto, California, I saw a wonderfully successful example of pure Modeling Instruction employed in the ninth grade. I also saw the long term result of this approach in AP Physics C Seniors that had taken the Modeling course as Freshmen, and the results were equally impressive.
Before I visited this school, I'd been eager to see a wider variety of the different facets of the Modeling Instruction approach. Most Modeling-based classes consist of a great deal of whiteboarding, and I'd seen a few different examples of this process in my previous visits. But data-collection and analysis are central to the Modeling experience, and I had yet to witness such an activity this first hand. Due to a slight scheduling difference between different sections of the class, I got to see a variety of different activities throughout the day, including a "paradigm lab" where students collected ticker-tape data on an object undergoing constant accelerated motion.
The teacher at this school has been using Modeling for 10 years. He was trained at a workshop held at ASU, where Modeling was developed, and has employed the method at two different schools since then. When he first came to this school in Palo Alto, he was able to tell the administration from the outset that he planned to teach a full year of inquiry-based instruction in the ninth grade, including both the Modeling mechanics curriculum and the CASTLE curriculum in electricity and magnetism. He is only physics teacher at the school, and this made for a smooth transition into Modeling.
Nearly every unit in modeling begins with a "paradigm lab," during which students design their own method of collecting data on the relationship between two variables. One paradigm lab that falls early in the year, for example, asks students to collect and graph data on the weights of various known masses, thereby illuminating the linear relationship between mass and weight. To begin the unit on accelerated motion, the girls I observed devised a method of using a ticker tape timer to measure the distance traveled by a cart on an inclined plane as time passed. The girls then graphed distance vs. time on a set of axes using simple graphing software. This activity in itself is by no means unique to Modeling, but the role of the teacher was less traditional. Throughout the experiment, the teacher gave no instruction as to how the data being collected might be interpreted. These were the first moments that the phenomenon of acceleration was being studied in the course, but the term acceleration was not a part of the discussion. Since the class begins the unit with this lab activity, any subsequent work done in the unit can refer back to the data collected by the students. Any understanding of the topic being studied is developed by the students themselves as the data they've collected and observations they've made are discussed in class. Nature is permitted to speak first, and to speak directly to the students, free from the filter of a teacher's explanations. The role of the teacher is to facilitate the relationship between the students and the data they've collected, rather than presenting "knowledge" outright. The students were quite at home carrying out this experiment, and some seemed to appreciate the immediate differences between these data and the data they had previously collected on constant velocity motion. More rigorous analysis of these data would take place throughout the rest of the unit.
In a different section of this course, I witnessed students working for the first time with a method of analyzing motion that had recently emerged from their class discussion: interpreting the area under a velocity - time graph. The idea that this information could be physically relevant was, of course, suggested by the teacher himself, but he left it up to the the students to confirm that this analysis was indeed fruitful. Some girls saw the implications immediately, but some were suspicious of or uncomfortable with the method, and made comments such as, "This is weird..." or (more interestingly) "I don't see why area is important. Is the thing traveling around within that area of the graph? I thought it was going straight." I took these statements as a sign of the students' expectation that in order to use this analytical tool in their physics class, they should understand why the tool is relevant to the phenomenon they have observed. In other words, students had to convince each other that the method was useful. The organic manner in which this tool was introduced pulled out into the open students' confusion about this complex tool very early on, rather than burying that confusion or relegating it to a simple and grossly inadequate, "Can you explain that again?"
Almost all units in the Modeling mechanics curriculum begin with a paradigm lab asking the question, "What is the relationship between ____ and ____ ?" There is great power in the consistency of this format, because students are always interpreting new ideas within the familiar structure of graph analysis. As this teacher put it to me, "The question is always the same, but the physics is always different." For students in this course, it's always relevant, when performing an experiment, to graph the data and attempt to interpret the graph. This experience forms their core understanding of what science is, rather than the experience of reading a textbook, listening to a lecture, or solving a good ol' physics problem. During the AP C class that I observed, students three years older were asked to design a method to determine the relationship between the impulse on a cart (calculated as the area under a force - time graph of the cart as it's accelerated by a spring-loaded plunger, metal bumper, or even a ball of clay) and the change in momentum of the cart (calculated using a change in velocity, measured using one or more photogates). The structure of this lab was exactly the same as so many of the labs the students had carried out three years earlier in their ninth grade Modeling course. Likewise, students were charged with a similar task of interpreting the relationship between two quantities on their own. (The Fnet ∆t = m∆v relationship happens to be one of my favorites, as there are so many unbelievably great slo-mo videos to watch as part of a discussion about the idea that "more time can mean less force": !!! !!! !!! (sorry for the advertisement on that last one...))
This emphasis on analyzing a new relationship directly is not the only thing about Modeling that I've found impressive, but it seeing it first-hand on this visit was a new experience for me. The possibilities for expanding this format outside the scope of modeling were immediately clear to me, particularly through the lens of IB Physics, which I taught for three years. IB science places special emphasis on student-designed experiments investigating the relationship between an independent and dependent variable chosen by the students (relationships that my students studied include: the breaking force of a pasta strand as a function of time soaked in water, the resistance of a play-doh cylinder as a function of the mass of iron-filings mixed in with the play-doh, the launching distance of a trebuchet projectile as a function of counterweight mass). These experiments often yield unpredictable results that would never be found in a textbook, and students often experience great difficulty with the seemingly simple task of analyzing this new information. Using data-collection to introduce the fairly simple relationships that are a part of a normal introductory mechanics course, as the Modeling curriculum does, would certainly have improved my students' capacity to make conclusions about the more complicated relationships they encountered in these experiments!
