Daniel+Brown's+Blog

7/26/2010 Day One

Very slow day. Spending a lot of time talking about underpinnings that don't exist and how to help students by not letting them use words or ideas unless they deeply explain them. Pendulum lab was very slow but the way Nick worked with the small groups and steered them was good, but the best part is definitely the group discussion where Nick spent some time outside of the group and some inside and the discussions of what a big group would look like in a class of 25.

There is a lot we take for granted as teachers that we know and our kids have only a shadow of knowledge. This opening unit is hard to imagine doing because it is so slow to develop the underpinnings. I could imagine

7/27/2010 Day Two

Opening discussion. Question asked about how do you get these discussions working in classes of apathy. Two prongs, comfort discussing things and building knowledge. As they get comfortable and more knowledgeable they will be more willing and wanting to discuss. I find candy at first for everyone who shares, then candy for all who share on topic in a constructive way on the first and second day encourage a lot of conversation. Some comments on not telling students they are wrong. It has a negative psychological effect that is not needed. Find another way to judge each idea on strengths and weaknesses and helping them to see what is right in what is said. Important group considerations are heterogeneous in terms of ability and race and never having groups with one young woman with two or three young men. Students from ninth grade through seniors struggle equally on ratios. What are we looking for to know that they 'get' ratios? When they use the language of $5 for ONE item. If we hold these questions for two or three days we will see much more and we will have less questions of how to see this working in a classroom. And it is OK if they tell us in their own words even if those words are not fully articulate or developed yet. The balance between challenging their language and being a cause of frustration. Motivating involvement using candy, free grades or any other thing that motivates them. But perhaps we should not use grades in order to put all our focus on learning process and not grades. They begin to care as they see you care. One of the great goals is that the students begin to question each other. If the teacher is doing all the questioning all year then we are not getting there. As they question each other they learn to ask good questions and they learn the form of the Socratic type questions we teachers ask. The circle is like a peer reviewed journal where science develops and progresses. Should kids have a hypothesis? No, because a hypothesis is an educated guess. Most of the time they cannot make a hypothesis because they do not have a basis for doing so. Instead let the data speak for itself and build the knowledge.

====Constant velocity lab: Focus observations on the car not on the teacher action or questions about the observations. Which observations contribute to the model? the observations about motion matter. Questions what does moving and 'one direction' and 'constant speed' mean? Challenge some observations and ask how we will choose to see if the speed is constant or not. Let students develop a procedure. Emphasize that students don't measure speed, they measure distance and time and calculate speed. What kind of time are we measuring? What time when the car is at a point or how long it takes car to reach a certain spot. How do you measure elapsed time for an event? This is not intuitive for a student. Now the car is started long before it gets to the meter stick so t(0) is not the beginning. But starting it before the stick gets rid of letting the car get up to its constant speed. How do we know when it is at the middle of the meter stick? Do we need to say time, date, year, era, age of the earth? How specific should we get? We need to have clock time defined as time passed since a specific reference point. We can start our clock at the beginning of the experiment mark? Let's ask "What time the car reaches 50 cm and 70 cm mark? What time has elapsed when the car has moved from 50 cm mark to the 70 cm mark?" **//We then make the distinction between clock reading (time on the clock) and elapsed time.//**====

How long is the car at the point of 50 cm? Zero seconds. If we can get the kids to that it is huge. How do define distance. We help the students to see that position and distance are not the same and are analogous to clock time and elapsed time. Distance involves a difference in two positions. Set the car at point 1 and move it to point 2, how far did it move? d(2) - d(1). Now move it back to 1, how far did it move? same answer. how far did it move total? Twice that distance of d(2) - d(1). How far is it from where it started? How much did it's placement move? Zero. We call that displacement. So should we call them west and east or positive and negative? Positive and negative is a nice tool because it allows us to do math with these. We now have 5 vocabulary word;, clock time, elapsed time, position, distance, displacement. We will use this to record data.

Should we measure distance in a seconds or position at each second? Position is better because it tells us where we are going and where we are. Distance also involves calculation to subtract and find distance.

The ultimate goal of the model is to develop a model to describe the motion of the little toy car in terms of position and clock time.

Left laptop far away during the white board discussion of this lab. Highlights are that we all went around first and talked about how our first and second trial were different due to instructor directions like changing the initial position, direction of a car, measuring at constant intervals of distance or of time. Then we looked for similarities in all boards. Next we talked aobut the meaning of the slope and after 20 min. decided it meant something we would call velocity. Then we talked about the y-intercepts of the equations. Lastly we got down a general equation of x = vt + vi

Now we looked at the graph and looked a motion map or diagram. We looked at its key features which are the displacement between the dots and constant time interval. We can also add an arrow on our motion map representing the velocity of the object.

Wednesday 7/28/2010

Started with 30 min. discussing a quote on the board, "Nothing works for everyone. What matters is having as much in your 'bag of tricks' as possible."

Spent one hour on a lab practicum for constant velocity. We raced two cars in a head on collision from fixed positions a few meters apart. Our job was to predict the exact time and position they would meet using at least two representations from our model and our only major constraint was that we could not turn on both cars at once. So we, as a class, made multiple calculations of constant speed for each car across 5 meters, graphed the data and found trend lines. We generated a equations of motion for each car and solved for system of equations. Our second representation was the graphing where we traced the intersection of the lines and got the same position and time as the equation representation. 50-75% of the grade comes from the work and presentation as a scribe of these representations to the teacher. The rest of the grade is an individual grade for our lab report. We cold have found the area of a velocity vs time graph and found the area of the combined curves would be their initial distance apart. We also could have used a motion map, however we would have gotten less precision even if we drew the lines very carefully.

10 AM Parks now showed us a new demonstration of a cart rolling down a hill of 10 degrees or so. We observe and talk about it. Some say the cart is changing speed. Others say they cannot see that by watching the car. We all got equipment and went and measured position and time as it rolls down the track and graphed it. Our graphs were all curved. We whiteboarded our data and graphs and had a circle session. Our goal is to have a model of the motion of the cart on the track but we don't know how to handle this curved graph. Main points brought out were comparison and contrasting our graphs of the cart to our graphs in last model. We spent a lot of time talking about how the line segments are valid measurements of the average velocity during that interval from what we saw in worksheet 3 in the constant velocity model.

Now we break up again with the same data and our whiteboards and try to graph the changing average velocities during each time interval. Parks left as an open question what time we would plot on the horizontal axis since the average velocity is over a range of time. We may want to address this in small groups as we go around the room and help groups to choose the midpoint time. As we came back to the circle after lunch we saw a lot of similarity in the graphs and all groups found a linear trend. Now in my Pre-AP classes I would also help the students to see how to linearize the position graph by plotting position vs time^2. We go through and revisit what the slopes of average velocity vs time mean and how we found them. Why are the slopes different? If the slope means the speed is changing, what will we call that new slope? Acceleration. So we define a = (change in v)/(change in t). If we also did position vs time^2 carefully then we also see that the slope of the latter graph is half of the first and lends itself to the equation x = 1/2at^2 + + xi and the middle is deliberately left blank for now. Also look at a constant velocity model of a v vs t graph and remember how the area under a curve was displacement. What does it mean for a v vs t graph with acceleration? This let's the students use the equations from the model in the paragraph above and check and see that it works with numbers!

I am not sure if this is confusing for kids to use the equation with a blank in it. I think I would instead use the area arguments with letters and not numbers to develop the 'distance' equation without the second term. Change in position = 1/2(base)(height) which for a vel vs time graph is dis = 1/2(t)(at) and we have the same equation. Now we can also handle a graph of vel vs time that does not go through 0,0 and we have a triangle on top of a rectangle and the area of the rectangle is vt so we have our full equation of x = 1/2at^2 +vt + xi and it was not too bad for the kids. We could also do a quad fit to the dis vs time graph and see the coefficients match half the acceleration we found.

This is a very slow but thorough development of ideas. What will I leave our later in the year to make time for this? I don't know. I like the emphasis of Arons that these subtleties of motion were 'teased' out over hundreds of years and our students will not master them quickly. This is something worth doing, but I wonder what it will cost me later. Less time on dynamics? Momentum? Energy and its conservation is too critical to cut short but something has to trim a lot from my teaching model because this takes time. We started talking about these concerns and then pushed it back until another time when we understand modeling better and can see how to pace it various ways.

2 PM Spent 90 min. looking at car on ramps prediction, data, motion maps etc. Only would spend one class period on it though likely.

3:30 Working on Unit 3 worksheet 2 #1-6. We are not using the distance equation for this assignment, just graphs and vf = at + vi equation.

Ah ha moment of the closing of the day was to break the large triangle under the velocity vs time graph into lots of little triangles each of base of one second and hieght of 6.25 m/s. The last second has only one triangle, the next to last second has 3 triangles, the one previously has 5 triangles and so we see the displacement is quadratic and incremental of one unit in the first second, 3 units during the second second, and 5 units during the third second, etc. A very nice graphical method for understanding a constant acc, linearly changing velocity and quadratically changing displacement.

Off to read for tomorrow.

Day Four 7/29/2010

Started with a ranking task that challenged all of us with its coordinate system changing.

Now we will make a concept map for the acceleration unit and I am curious how we do this with a class. Parks asks for the name of our model and puts it on the board. Parks asks for the first representation of constant acceleration and we draw a x vs t graph with a curve. We discuss the other three curves that could also be there. Parks asks for corresponding v vs t graphs that go with them as our second representation. Now we add the equations for distance in to the first graph and a=(delta v)/(delta t) with v = at + vi to the second graph Then he asks if we did any more graphs and we add in an a vs t graph and the equation a = ai (constant) Now we did a motion map of an object starting at v =0 with velocity and acceleration vectors as well as a motion map for an object slowing to a stop with vectors. We also circled back and had a discussion at some length concerning what is instantaneous velocity. We also will have to add in Galileo's equation, but Parks holds off on that until we need it. I like that. I usually throw all the equations at them at once as a set of tools to help, but the tools mean more if you work a problem that is hard without them and easy with them.

Parks said something that really got me thinking yesterday. He said he did 3 weeks of modeling in 2001 or so and then 3 more weeks of modeling for E&M in 2003 or so. He said he did the second set of three weeks because he still had a lot of questions as to what modeling really was. That surprised me because after three days in the workshop I felt I had a handle of the style of how things are done so far. If after three weeks of modeling at ASU and a couple of years of using it he still had fundamental questions, it makes me see that perhaps I have missed much or most of what we have done. I need to be in student mode more here.

Unit 3 Worksheet 4 did #3 and 8 and we all white boarded one of them and presented. A lot of poignant thoughts came out of it. I liked one of the last points given.

Most students want to take an equation they really don't understand, put #s into it and get an answer they really don't understand. This approach takes a graph of concrete motion we used in a lab and begins to connect concepts to the graph. Then second we connect the equation to the graph so that the equations have a conceptual meaning from the very beginning. We obviously work MANY fewer math problems this way but they have multiple representations of each problem and likely understand them very well. I like the way the math not only comes from data, like any lab, but the math comes from lab data represented in multiple ways so that the graphs and motion maps are as valid a tool as the equations, not an afterthought that adds a little icing to the cake of the math. Here we often use a graph as the end of the conversation, for me as a teacher they have always been a tool to get an equation. Now I am seeing a lot of value in this.