GPS as Conceptual Anchor for Goal-less Kinematics Problems

One way I’ve gotten some decent leverage in getting students to really initiate with goal-less problems in early kinematics problems is to ask, “If you had taken this trip with a GPS device, what summary trip information could it give you?”

As a class we generate a list of things the GPS device would or should be able to calculate like:

Time of Arrival

Duration of Trip

Final Location

Total Distance Traveled

Average speed (while moving)

Average speed (during entire trip)

I usually tack on a few things, like it could tell us how far we are from where we started (and in what direction). I also say that a good one should also be able to make a graph. I may or may not introduce average velocity.

My job at some point is to connect each of these to formal language and algebraic symbols used in our text. Unfortunately, our text is sloppy with clock readings vs. time intervals. It’s also sloppy with displacement and position. So it’s a little difficult.

I also think it’s cool to have “average speed while moving” be something that the physics text book doesn’t have, and that we’ll have to completely invent our own way of calculating it.

Three Conjectures…

In class today, students introduced three conjecture that are on the table for our consideration over the next few weeks.

  • Justice’s Conjecture: For any trip, the average speed will be greater than (or equal to) the average velocity
    • Many have thought through this, are convinced. Most of them have arguments that are well reasoned plausibility, but  we’re not near a proof.
  • Renshell’s Conjecture:  On a position vs. time graph, the slope of a line would seem to give you the velocity
    • Many are beginning to articulate how the algebra connects to to graph, and some are beginning to see this as obvious
  • Justin’s Conjecture: You can’t find the average speed by simply adding up the different speeds and dividing by the number of different speeds
    • We have a couple of examples where this didn’t seem to work. A few have articulated the idea of a weighted average, but

On Tuesday, We’ll work specifically on, “How would you explain to someone else in a different section of our class what Renshell’s rule is, and more importantly WHY it works?”

We might also do: “Draw a position vs. time graph where average velocity is equal to average speed… draw a position vs time graph where average velocity is less than average speed…  then either prove Justice wrong by drawing a position vs. time graph where average velocity is greater than average speed, or try to explain why such a graph is impossible.”

Unfortunately, we have to move on the accelerated motion… but I’d love to spend another day or two doing experiments with two-body constant velocity situations, hashing out explanations for rules that seem to work (or not), making connections among representations, and working to prove or disprove conjectures. There are those who need more practice and time on the basics, and plenty of fodder for those who ready to move on.

I’m remembering why this class (one where I teach students within the constraints of a heavy pacing guide and third party exams) is both a joy and a pain.

Finding Themes Across Student Reflections

With students’ reading reflections, one of the things I am trying to do this year is synthesize and report back to them the issues and questions students I see that they are coming into contact with.

As themes emerge, it will be there responsibility to make connections to one or more themes in writing their reflections:

So far, I am practicing doing this to see how long it takes me, and hone my skills at discerning themes. With just a sample of 7 students reflections in, here’s what I’ve found. What do you think?

What is the role of everyday thinking and experience in science learning?

 “I think it really helps students to learn by bringing in real world examples and have them relate it to what they are learning in the classroom.”

 “How important it is to consider real-life examples that are as similar to the experiment as possible”

 “They also used real life situations such as ropes near a swimming pool to compare their reasoning’s with each other…These were a great way to see how the students respond and think in scientific form and use their experiences to come to an answer to this question.”

 “Students do draw on their prior knowledge in order to further explain their thinking.”

 What similarities and differences exist in how young learners, adult learners, and experts  think?

 “The amazing thing was that in Mary Bell’s article, the students made very similar predictions. I really thought it was amazing that kids in such young grades were thinking on the same lines as a college class, and according to Mary Bell, along the same lines as experts”

 “I think it’s safe to say that no matter what age you are the thinking process in coming up with answers to problems such as this are the same.”

 “Something else I noticed was that these 5th and 6th grade students went even more in depth about their reasoning then us college students.”

 What role does language and vocabulary play in science learning?

 “I love the interaction among students and the way they attempted to use technical terms such as force and gravity in sixth grade.”

 “The students struggled to articulate their ideas because of a lack of vocabulary, but were still able to work through it together.”


What role does discussion play in science learning? How does teacher best facilitate this so that students are independent but still making progress?

 “She asked a question and let the students discuss the topic without much guidance. She never tried to guide them to the correct answer, she let them build off each others ideas and come to the conclusion on their own.”

 “I can see that all of the disagreeing and the teacher sitting back and letting the students discuss was better for them then just asking the question and telling the answer without much discussion. The way the students facilitated their own learning was very interesting to read about.

 “The most important part in my opinion was the students working together to not only prove but disprove several of the solutions to the question.”


First Day Exit Slip

This year in my classes, I’m doing a first day exit slip consisting of three questions:

#1 What about this class makes sense to you? What specifically is it that makes sense to you and why?

#2 What about this class doesn’t (yet) make sense to you? What specifically are you concerned or confused about?

#3 Is there anything else on your mind? Something you want or need to tell me about?

Some snippets:

#1 What makes sense

“We will be discussing everything and everyone has their own ideas”

“Group work makes me comfortable–and all the support I know I will have makes me excited. I was scared of this class and no I’m not.”

“Being in a community in this class makes sense to me. We’re learning together, but we all think differently.”

“What makes sense is what we are going to do during the semester and what is expected from me.”

“For this class, you have to do your work in order to get a good grade.”

“This class makes sense and I feel comfortable with my ability to succeed.”

“It makes sense to work in groups. Sometimes science is no individualized.”

“It makes sense that this class is more about discussion than lecture”

“I like that this class is open and its not just lecture. I feel like  can learn more when we feed off each other.”

“This class makes sense because it allows us to see how a child thinks and how the difference between the teacher and children’s thinking can affect learning.”

“The method of learning makes sense to me. Brian made is clear about the method.”

“So far this class makes sense in terms of why I have to take it.”

“Breaking down things: learning how to do science and learning science along the way.”

“This class will help me better understand science, and in particular, how I understand it and how children understand it.”

“The assignments make sense because they are clearly explained.”

“The class will allow me to learn the ways how others think about science and how to make others learn by interacting.”

“I am still trying to process everything. The class/small discussion makes sense to me.”

#2 What doesn’t make sense

“Some of the assignments”

“The independent projects.”

“I don’t understand why we have a facebook page and a blog”

“I’m afraid I won’t get around to doing an project. I sincerely hope I can.

“Some of the timing doesn’t make sense. I feel like we are going to cram a lot into a little space and I feel like that might be frustrating.”

“I think I need more clarification about expectations for assignments.”

“The independent project. Is it a paper?”

“I know this isn’t a methods class, but what should I focus on most as far as a future K-6 Teacher? Should I just focus on being more knowledgable or how to explain these things to an elementary student.”

“The different parts of the notebook.”

“I would like more information on the independent project such as format and expectations.”

“With independent projects, do we have to do one or all three parts?”

“Please ask me again later! Right now I’m good.”

“Why is this class separate from life science?”

#3 What else?

“I’m ready to get started!”

“I find the moon with my kids about every night. Super excited about that I get to do it for class.”

“I’m having a baby girl in December. =)”

“I’m very excited about this class and love hands-on experiences and assignments.”

“I appreciate your energy. It makes the 3 hours seem bearable.”

“I have a class right after this across campus so if I hope can avoid getting out here late. That would help.”

“I’m excited about this class!”

“I’m excited about what we are going to learn.”

“I am so excited about this class,and I want to thank you.”

“I look forward to this class and the challenges it will hopefully present.”

Rights and Responsibilities (Inquiry Fall 2012)


To contribute to your group’s ongoing work–this means you should “pull your weight”, do your part, and do the work you are expected to do.

To participate in ways that invite and allow others’ to participate as well

To be prepared for class–for example, you should be on time everyday with assignments completed.

To respect others and their ideas by listening for understanding, listening with an open mind, by providing constructive criticism when you disagree, and by offering help.

To be actively engaged in class by getting involved, contributing to class discussion, and listening to others.

To be forgiving of others’ mistakes and to ask for others’ forgiveness when appropriate

To clean up after yourself


To have the time and resources to meet expectations

To ask questions and seek clarification

To hold and express your own ideas and opinion

To agree or disagree with others, in a respectful manner

To participate fully in classroom activities

To seek mediation and facilitation from instructor when rights are being violated

To be wrong and make mistakes

To use the restroom when needed

To use technologies like cellphones out in the hallway when really important.

To have a break during class

To be respected by others (and not be embarrassed by others)

To research facts or for yourself

Inquiry First day Brain Dump

* We did introductions, I learned everyone’s name

* I talked about class stuff, syllabus

* We did the pendulum mini activity (write quietly, talk with group, share with class, rewrite again): Where will washer go if I let go when its at the very top of its swing.

* We watched the pendulum video of children (pausing now and then for small group and whole class discussion)

* We did student rights and responsibilities

* I introduced my life as a researcher, current project, and handed out consent forms

* I discussed homework (read pendulum case study and write reflection; plus finding the moon assignment)

* Students left me an exit ticket with responses to three Q’s (#1 what about this class makes sense? What is it specifically that makes sense? #2 What about this class doesn’t make sense to you right now? What questions do you still have? #3 Is there something else on your mind? Something you’d like to tell me)

Still to do for wednesday

#1 Do teacher rights and responsibilities

#2 Address concerns (projects, assignments, etc)

#2 Have students read and sign consent forms

#3 Start unit of light!


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