Physics Union Mathematics

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Its a constructivist methodology of teaching physics to all age levels in which math and science processes are equally weighted.

Keith Thomas
Middle School Science Teacher, Edison NJ

I would explain it as a combination of curricular materials that help develop and use the scientific method and a collection of applied mathematics activities that merge with one another. The first would be different from regular curricula in that with every topic students are making observations, developing their hypotheses and testing their hypotheses. In addition to that they're applying this new knowledge in problem solving settings and using mathematical tools to evaluate data, etc.

Suzanne White Brahmia
Associate Director of the Math and Science Learning Center, Rutgers University.

I would say that this is a project to develop active learning materials that integrate physics and math instruction.

Chris D'Amato
High School Physics Teacher

Well, its a curriculum set up for teaching introductory inquiry-based physics, going through the scientific method. More specifically, using the ISLE cycle. It basically breaks down all the concepts taught in an introductory course in an experiment-based scientific way, and then go into a little more detail of the observation experiments, model building, testing and application experiments. Say you wanted to look at a certain physical phenomenon, like motion. You want different ways of representing that motion, whether verbally, mathematically, a picture or a motion diagram. You go through differentiating constant velocity from constant acceleration, how we use those representations to build those ideas up. After building those concepts up, come up with a mathematical model to test, and, using that model, do some testing experiments where students explicitly make a prediction to see if they can disprove the model. One of the best ones I'd have to use would be dropping an object out the window and giving the students the choice of models to use - constant velocity or constant acceleration, and showing that the students really have to recognize between accelerated and non-accelerated motion, and using that idea in other problems and other applications.

Joe Santonacita
High School Physics Teacher

PUM is Physics Union Math and it's a middle school, high school, college level program that develops physical ideas, physical science ideas, while developing mathematics within the students' ability level. It uses a cycle of activities to build these ideas so that the students are constantly thinking about their own learning but also developing the big ideas, the main focus ideas of physical science motion, forces, energy, etc.

James Finley
Middle School Science Teacher

PUM is a way of doing physics that helps students not only follow scientific method, but also helps them with their mathematical skills and their reasoning skills.

Erin S.
High School Physics Teacher

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They really provide a lot of different ways for kids to express what they're thinking. Multiple representations - force diagrams, regular diagrams, mathematical models are all incorporated and it gives them a lot of tools to choose to express what they're seeing physically. It really gives them an arsenal to show, in different ways, what they know.

Keith Thomas
Middle School Science Teacher, Edison NJ

I think my students are much more likely to cite experimental evidence for arguments when we talk about different things. They'll discuss if something might or might not happen based on things they've seen or done before, as opposed to citing things they've read out of a book as a reason. In addition I think that they’re doing better in math and enjoying their algebra course more.

Suzanne White Brahmia
Associate Director of the Math and Science Learning Center, Rutgers University

Students do not "cover" as many topics in a PUM lesson, but the learning that occurs in more meaningful, so the students have gained a better grasp of what, for example, Newton's laws of motion really mean, through doing the PUM lessons. My students can understand the significance of these laws and use them to reason about situations in the physical world that cannot be reasoned upon with intuition, so I know that when my students began to answer questions about the mechanical world using their naïve knowledge coming in to the class, they were not able to successfully reason about simple problems in mechanics, but now a lot of the time they can use physical principles that they've learned about, like Newton's law to reach conclusions that they could not reach with intuition. That's how I know that learning is happening.

Chris D'Amato
High School Physics Teacher

It has a positive affect on it. At first, students are resistant to it because they haven't seen it. Once students get more accustomed to it and kind of see what's going on, I think they take it and run with it.

Joe Santonacita
High School Physics Teacher

I think they have a great affect on student learning, I mean, in it itself I am learning a lot about my students as much as they are about the material because, I am identifying weaknesses. I am having people analyze the type of activities they are doing and this is really thought out and tested so we do see some growth within the students instead of just, you know, an arbitrary unit in an arbitrary textbook that we're plowing through the material whether they know it or not. This, the whole idea behind this, is to really meet the learner where they are and to go from that and develop ideas or develop analogies and other activities that I know will help them bridge from where they are to where we need them to go.

James Finley
Middle School Science Teacher

Well I have used parts, not the whole module together, but they do help with student remembering, retention ability. I think that's because the students are doing things themselves without having things fed to them.

Erin S.
High School Physics Teacher

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Every class has its own personality. A lot of them like the hands-on aspect. Some of them found certain things to be tedious. Some of them found certain questions to be beyond what they're used to, and it required a little bit of setup on my part. Not necessarily setting up what the correct answer was, but a questioning technique. To be able to "prove" an idea is something that they're used to. To be able to give a contrary idea to test to see if it might have been the correct answer might be a little complicated for the 8th grade level that I teach. I required a couple of small questions beforehand, discussing what it means to disprove something and discussing multiple explanations that could "prove" something. That was what confounded them, this proving aspect of it. The mathematical representations are loved by the analytically gifted kids. They love being able to graph and show it with the algebra that they’re learning. The rationalizations that they set up are mimicked by the PUM materials. They actually get to measure it with their hot wheels cars or with a bowling ball or basketball with a board and all that.. It provided a certain concreteness that reading a text doesn't.

Keith Thomas
Middle School Science Teacher, Edison NJ

They're generally excited about it because I often bring things to class or set up equipment for them to use, which tends to make things more interesting to them. They feel harder pushed mathematically than they'd like to be, and are a bit confused at being forced to do math outside of math class. But now that we've been doing it for a few months, I think they're starting to see the payoff in terms of better understanding in math.

Suzanne White Brahmia
Associate Director of the Math and Science Learning Center, Rutgers University

Students who are accustomed to seeing a question and producing an answer by a mechanical application of principles were frustrated when presented with activities that did not have clear, cookbook steps. For example, to analyze some experiments described in words, sketch them, indicate quantities and try to find a pattern for the way that these quantities change before and after collisions. This is the kind of exercise that we had to ease into gradually when we introduced PUM materials, but now the students will go about it with more willingness and gusto. They'll realize that it's not a linear process, box 1 to box n, but the problem needs to be addressed in more of a cycle than a step-by-step process, eventually converging towards some sort of pattern.

Chris D'Amato
High School Physics Teacher

I found this year that my students had less patience than years before. Some of the examples and more intricate, though-provoking material, I found that there was some resistance at first, but once they got accustomed to it they actually kind of embrace it. They really like white-boarding and showing off their work, discussing it as a group. A couple classes are really into the whole collaboration thing, in terms of labs and activities. As long as you keep them busy.

Joe Santonacita
High School Physics Teacher

I'd say they're engaged sometimes, I mean you're dealing with middles school students so it's difficult no matter what. I mean, and as far as kinematics and dynamics, it can be a dry material - so at times they can be lax about the materials, other times they are overly engaged and they can't stop asking questions or they’re fighting with one another because they feel that they're right about an idea they're going back and forth over it that's really where you want to get your students. Are they like that all the time? No, but the fact that the PUM materials can get them there, I think means that we're heading in the right direction.

James Finley
Middle School Science Teacher

Students are coming from chemistry which is totally different. The ones that hated chemistry love PUM. Those that liked chemistry were hesitant to do this new, different style, even though it is just scientific method. In chemistry, you stand up there and lecture and then give a lab. Making the kids do all the work instead of listening to a lecture is unfamiliar to some students.

Erin S.
High School Physics Teacher