Lorien+Stone

I get this question every year: x=vt +x0, and v=at+v0, so why doesn't x=at^2 +v0t +x0? Why is there that 1/2 term?
 * __Day three - 6/28__**

The best answer I can come up with so far is that the "v" in the first equation is not the same thing as the "v" in the second equation, and the 1/2 is neccesary to accuratley describe the observed motion of objects.

In our constant velocity model, we defined velocity in terms of measurable quantities. However, in our constant acceleration model, we defined acceleration in terms of changes in velocity, but we have no clear idea of how to determine velocity outside of our constant velocity model, which doesn't apply. We are using a variable that is defined in terms of another variable that we have no clear definition for.

Today, in our groups, we sort of used a brute force method in which we did our best to use our constant velocity definition, even though velocity was clearly not constant, and with good results - If we have a constant acceleration of zero, then we have a constant velocity as well, and all of our new equations and graphs match the equations from our constant velocity model. Our models are clearly correct in that they accuratley describe motion with constant acceleration, but that is just not enough for me.

I feel comfortable with our definition of average velocity, but I am still struggling with how best to lead students to this idea of instantaneous velocity, and especially in how to show the DIFFERENCE between the inst. velocity and average velocity. I can explain average velocity, and I //think// and could explain instantaneous velocity graphically, but I have been struggling with how to define instantaneous velocity in terms of measurable quantities, or how to put these two ideas together and show how they're related. Somehow, I feel that if I could accuratley define the relationship between the two, then I would finally be able to answer the original question satisfactorally. Does anybody else have some ideas about how to do this?

Also, I meant to post this yesterday, and forgot. [|The Name that Motion website] is an online activity, where students are shown various animtaions of moving cars and their resulting motion maps/diagrams. Then they have to match VERBAL descriptions of the motion (using the terms velocity and acceleration) with each animation. It's great way to help them practice determining the sign of velocity and acceleration in different situations.


 * __Day two - 6/27__**

At lunchtime, I wrote down some of the things I wanted to mention in my journal entry today, and the biggest concern I had was my ability to use all the information we are learning. It's easy to see it in action and discuss questioning strategies, and how to steer discussions in the right direction, but I was a little worried that once the first day of school gets here, I will not be able to successfully help students create and interpret their models accurately without resorting to what is essentially a "because I said so" explanation. All the research and all the papers (including the reading from tonight) tells me that this doesn't work, but it //is// much easier. Luckily, in the afternoon session we got a little practice in trying it out it for ourselves, and I was pleasantly surprised to find that it's not nearly as impossible as I had feared. However, it's clear that I need to put a larger emphasis on language and verbal descriptions than I ever have before, most especially in improving my OWN language and verbal descriptions.

Today's discussions and the reading from the text have confirmed that clear communication is vital to understanding physics. To someone on the outside looking in on our discussions, it may appear that we've wasted a vast amount of time arguing about seemingly trivial words (What do you mean by //origin//? What do you mean by //away from? "//What do you mean by //faster//?) This could not be farther from the truth. I think that our discussions of language and word use are the most important things we've done so far. Someone (probably my mother) once told me that sloppy speaking/writing reflects sloppy thinking, and by forcing our students, and ourselves, to communicate ideas clearly and accuratley, we are actually forcing them to //think// clearly and accurately.

I've always known that vocabulary is one of the barriers to my students' success. Students are familiar with many of the words used, but their casual meanings are extremely ambiguous and interchangeable and students have trouble distinguishing between the concepts that //we tell them// the words represent. I think I see now that my attempts to tackle this problem may have been ineffective partly due to __my__ vocabulary and word usage. I know that they constantly use words like speed, acceleration, force, and power interchangeably. In response, I have always said "in science, that word has a very specific meaning - similar to the way you use it, but different. In science, that word means //this,"// Or, at the end of a discussion in which I've attempted to use a rudimentary version of modeling methods, I would try to condense all their ideas by telling them "what we've talking about is //XYZ,// and //XYZ// is //ABC."// I think now that statements like this, simplifications (or oversimplifications) of the subtle concepts I'm trying to convey, can do more harm than good.The book discusses the fact that, for example, velocity and acceleration are not things that ARE, but things we CREATED to more easily describe and predict motion; the author points out that this means that there is a fundamental difference between saying "velocity is..." and "velocity is defined as..." This seemingly trivial distinction is not trivial at all. It's the difference between "because I said so, memorize it and solve these problems" and actual critical reasoning done by the students. We //should// be wasting time arguing about trivial words because the trivial words //matter.// We discussed today that the word "time," used casually, represents two distinct ideas, and "distance" represents three. Later in the chapter, the book mentions that even using the words "at" and "for" interchangeably when discussing time can reinforce incorrect student assumptions about which of the two meanings of "time" we're talking about. If we only use one word for two different but essential ideas, it's no wonder students quickly abandon reasoning and resort to rote memorization.

__**Day one - 6/26**__ My notes from today: [|Summary - 6/26]

I think having a specific procedure for helping students develop their own understanding should be MUCH more effective than the half-hearted attempts I’ve made in the past at using this method informally. I am still worried about my own (and others’) low expectations of our students. Many of us seem to believe that these methods will be difficult to carry out with our regular crop of apathetic teenagers who only show up to school to see their friends or avoid truancy tickets. Upon reflection, it seems to me that my students are apathetic because I haven’t given them anything so far to be interested in. I’m beginning to see that, even more than just a more effective way to teach Physics, modeling instruction may be just the key I needed to turn on their interest. (Also, I need to think more and talk less – less half-articulated ideas spewing out the second they hit my brain, more well though out and helpful comments where appropriate!)

Reading Notes/Summaries from today: [|Reading - 6/26]

As I read trhough the paper about the FCI quiz we took today, I found myself continuously returning to the same questions. Where did we pick up these false beliefs in the first place? For example, the trajectory of falling objects: if we ever observed them, they would match the Newtonian concepts, so why do we think they look otherwise in the first place? I’ve always thought merely showing them what actually happens, as in a demo, would be enough to change their false beliefs, but after 4 yrs of teaching, it just isn’t so. WHY is that not enough? As pointed out in the text, I don't remember ever having many of these of misconceptions, much less how I replaced them with "Newtonian thinking," which leaves me less prepared than I have always hoped at helping students make the same leap.

At the begining of Chapter 1 from the textbook, I felt I was on familiar and sympathetic territory; I have seen and grappled with these deficiencies in my students on a regular basis. When I reached the discussions on scaling (1.12), I was horrified to realize that the deficient student the author was describing was me. I am fairly comfortable with ratios, and the different relationships they describe, but in more complex situations, I also “want initial numerical values…to substitute into the formulas without having to think through the ratios…” I have a lot of work to do.