Thanks to Matt Greenwolfe from North Carolina for having me think about using the bowling ball/broom lab in this way.
Traditionally modelers have used the bowling ball lab as a introduction to the Balanced Force Model, however in reality this lab has so much more to offer than just balanced forces. In reality it has EVERYTHING an intro mechanics physics course needs. Granted we won’t be able to dive into and develop all of the models of physics at play here, but the students will have a sense of them anyways.
I gave my students the following set of “Official Broom Ball Rules” as published by the United States Broom Ball Association (USBBA). Broom Ball. Before we started any competition I gave all the students about 20 minutes to practice their techniques. Once I felt they knew what they were doing we divided into teams of two. Each team took a timed run through the course. I found a student to be the official timer, and I was the keeper of any penalty time that needed to be assessed. I felt the students had a great time playing the game and competing for the pride of being the fastest broom ball team. Here are the final results:
After the competition each team discussed questions about the motion of the ball, how to produce that motion, challenges and recommended strategies to succeed. As a large group these same questions were discussed. During the course of the discussion I served as recorder of ideas. I tried to write down as much as possible and attempted to organize all the ideas into 7 big physical models. Constant Velocity, Acceleration, Balanced Forces, Unbalanced Forces, Circular Motion, Energy, Momentum.
At this point it’s unnecessary that the student understand any of these models fully, but I can see the benefit from having the words at least “out there.” Sometimes I feel modeling tries to “hide” the terms from students like it’s a big secret, when in reality they already know these terms and its now our job to break them from what they think they know about each one and model the correct way to apply the models in different physical situations. I was excited to start the year this way, and hopefully it sets the tone for a great year.
At the end of modeling and practicing density I provided my chemistry classes with the following Lab Challenge (this idea took shape for me after seeing a Flinn email about how to make measurement interesting). I’m not sure this makes it interesting, but at least there is some motivation behind the measuring, not just doing it for nothing.
1) Pick any 10 items from the front tables and rank them in order of most dense to least dense.
2) Identify the chemical makeup (specific substance type) of the 10 items you measure.
Students spent the first class period making measurements on the different items. Some chose to use water displacement for volume, others used rulers for the regular shaped items. One of my big goals of this activity was to see how well students would remember all of the measurement rules and techniques we’ve already practices. (On their first mass vs. volume lab many failed to estimate a digit in their measurements) I also wanted students to show me they can organize a data table that contained ALL of their measurements (i.e. initial and final volumes) not just the actual volume they calculated. This is my Lab Goal #1 LAB.1 – I can recognize the precision of a measuring instrument, and record data in an appropriate, organized manner.
The second Lab Goal I assessed the students on was LAB.2 – I can design and/or follow an experimental procedure that tests a hypothesis, investigates a phenomenon, or solves a problem.
After the first class period most groups had their measurements made and densities calculated. Good start.
On day 2 I had the students finish their measurements and then begin searching online for densities of the various items. I did not provide any lists or other resources for them, just told them to start searching. As tech savvy as the students are when it comes to searching for real, relevant information they have a long way to go. Some were fine, but others were just lost. Part of my reason for this part of the challenge was to allow them to struggle a little bit in finding this information.
Finally on the 3rd day I gave the class the task to sort all of the items from the front table from largest to smallest density. Since each group only measured about half of the objects this took some class collaboration and problem solving as to how to handle this. This task proved to be an interesting study in class dynamics. Of my 3 classes each went about this in a different way. One class had each small group put a post-it note on each item and then were able to sort them that way. Another class had each small group put their sorted list of objects on the front whiteboard. That class proceed to find the overall largest, and if there were multiple measurements of the same item took the average. The final class had one representative from each group work together and started with the largest (kind of like class 2, but without writing everything on the front board).
As you can imagine there were definite challenges the group had. But as I talked about with each class was that this was a good simulation of what “real world science” looks like. Multiple small groups set out to solve the same problem. Those small groups then need to come together and collaborate and agree on something. They need to rely on each other and their data, and at the same time solve discrepancies that arrive between the sets of data.
Eventually the final product looked like this:
I would have liked to have their predictions as to what each substance was made out of on the board here as well, but we had a tough enough time just getting things lined up. Maybe we’ll discuss that the next day, but maybe I won’t worry about it. I talked with most individual groups as they were using the internet and searching densities anyways, so we might not need that large group time to discuss that.
Overall I really liked this challenge activity as a way to conclude Unit 1. This activity contained everything from experimental design, measurement, mass, volume, and density. If there is one thing I would change for next year it would be that on Day 2 I would have the class begin the process of organizing all of the materials right away since the groups have the densities. I would then have the students do the searching as homework or at the same time as the objects are being organized. I think that might be a more efficient use of time and would save us a class hour. But then again maybe not. Can you really rush good science?
How to handle labs and lab assessment always seems to be an issue with teachers who use standards based grading (SBG). Wednesday (9/11/2013) night during the Global Physics Department meeting about SBG this was a topic of conversation. Like with most issues that arise with SBG there is as many different answers as there are teachers that utilizes the grading practice. In this post I intend to share with you my practices and ideas. As with most things I do in my classroom, these ideas and practices are always subject to change.
Importance of Labs
As a modeler, labs are EVERYTHING. This is where knowledge and understanding of the subject is gained by the students. Units usually begin with a model building lab and everything else goes from there. I need my students not only to perform controlled lab experiments, but understand exactly what the data obtained is telling them. I’ve come to realize that after about the 2nd or 3rd lab students “get that” and they are motivated to participate and complete labs correctly, including whiteboard discussions and model building.
For all of my years, except the first, but who counts the first year teaching anyways? I try to block those memories of awful teaching out of my head. Anyway, for all of my years prior to SBG I utilized a Lab Notebook in my chemistry and physics classes. Students would be provided a “Lab Notebook Criteria” in the beginning of the year, and I expected all labs to be set up and written in a uniform format. This included; heading, problem, equipment, procedure, data, analysis of data, and conclusion sections.
I like this setup for my labs. It keeps students organized, and forces them to take some responsibility for their own lab write-ups. However, giving points for the notebooks was always an issue. Because I never wanted to collect 50 or so notebooks after every lab; I didn’t. I would wait until the end of the quarter and collect all the notebooks then. From there I would flip through each notebook looking at all of the labs we completed from that quarter. I would “grade” each lab on completeness by using a checklist type rubric. Basically the only way students lost points is if they didn’t do something, like forgot a heading, or didn’t attache the graph, or didn’t answer the conclusion questions. (I didn’t even read answers, just checked to see that something was written down.) This process usually made for a couple of hours sitting at school on a Saturday or Sunday to “grade” each notebook.
This process troubled me for several reasons. By the time I scored a lab we might be 5-6 weeks past talking about it in class. Getting points for the notebook was just a “game.” If you wrote something for each section you got your points. This never really showed me what a student learned in the lab (granted I assessed for that in different ways throughout the quarter.) It didn’t hold them accountable, or give them the constant feedback they need. Plus those couple of weekends a year really sucked when I was at school just flipping notebook pages.
SBG Labs 1.0
Last school year (2012-13) was when I started SBG, but only in physics classes, so the following only pertains to that class. Chemistry followed the procedure above. When I was planning for SBG I relied heavily on Frank Noschese and Kelly O’Shea. By reading their blogs and stealing files I saw they had a nice set of lab goals, so decided to create a set of 5 Lab Goals myself. They were this:
LAB.1(C) – I can design a reliable experiment that tests the hypothesis, investigates the phenomenon, or solves the problem
LAB.2(C) – I can record and represent data in a meaningful way.
LAB.3(I) – I can analyze data appropriately, by representing data graphically, and by using the graph to make predictions.
LAB.4(I) – I can identify a pattern in the data, and represent the pattern mathematically. I can give physical meaning to the slope and y-intercept of a graph.
LAB.5(A) – By using the results of an experiment I can propose an appropriate model for the situation.
These five goals seem to be the essence of what students should be able to do by participating in lab activities. The problem I ran into was how and when to assess these goals. The idea of SBG is that I want to see students accomplish these goals by the end of the semester or year. These goals would be constantly reassessed throughout the year, and only what you have shown at the end counts.. What I decided to do then was not use lab notebooks, but try to find ways to include items on quizzes that would address these goals. (Except I found the first two to be difficult to assess that way.) Instead of lab notebooks I included lab forms in my unit handouts along with practice sets and other activities. This caused the problem of never being able to conveniently collect the labs, because I wanted to students to have their packet for practice throughout the units. Overall, this system worked out alright, but some students figured out there weren’t really being held accountable to actually write anything down during labs. I saw this as an issue.
SBG Labs 2.0
The following describes a work in progress. I’m working with a lot of theory here, hoping some changes will address some issues.
Overall I liked the idea of having general lab goals so I’m keeping that. I did make a couple of adjustments though. This summer I consulted with Terry Schwaller, an awesome modeler from Shiocton, WI, to help develop Modeling Chemistry Goals. His ideas merged with mine and I settled on the following six lab goals:
LAB.1(C) – I can recognize the precision of a measuring instrument, and record data in an appropriate, organized manner.
LAB.2(C) – I can design and/or follow an experimental procedure that tests a hypothesis, investigates a phenomenon, or solves a problem.
LAB.3(I) – I can analyze data appropriately, representing data graphically when necessary, and use it to make predictions.
LAB.4(I) – I can relate the results to the purpose of the experiment, and include appropriate analysis (slope, y-intercept, % error, % yield, etc.) when necessary to show if the purpose was met.
LAB.5(A) – By using the results of an experiment I can propose an appropriate model for the situation.
LAB.6(A) – I can connect experimental outcomes to the content of the course.
I’m using these goals with both my chemistry and physics classes, so I needed to keep them a little flexible in their interpretations.
I also realized this week that I missed a couple of important goals for chemistry so I added them:
LAB.S(C) – I can follow accepted laboratory safety procedures.
LAB.E(C) – I can recognize and properly name commonly used laboratory equipment.
The main reason for this addition is that I like to have a “Safety Quiz” on file that shows me, and administrators, that the students know basic safety procedures and equipment.
What I’m going to try to do this year is not do labs in a lab notebook OR in the unit packets. My thought is that I will provide students with lab handouts for each lab. Some labs will have written procedures from me (chemistry) and some will be more “design you own” where students need to write about their procedures (physics). The general lab handout form is here: General Lab Handout.
As of right now my thoughts are that I will be able to easily collect these when I feel it is appropriate without worrying about hauling a ton of notebooks around, and at the same time not “stealing” other valuable stuff from students in packets. I’m also going to only assess a few things at a time. Maybe for the first 2 or 3 labs I’m only going to assess students on goals 1 and 2. By lab 3 or 4 I might look at graphs (goal 3). By the end of the semester I will be able to assess on all the items contained in the lab. I could also use this form as a guide for students to turn in a more formal lab report. Something I’ve never done before. I also will also still be able to add assessment items on weekly quizzes or unit assessments. Especially items that assess goals 5 and 6.
Like I said, this is all very fresh in my mind and hasn’t been classroom tested yet. If you have any thoughts or ideas I would love to hear them. Comment below or tweet @MrBWysocki
It’s amazing what some students have heard and believe on “school faith.”
As the first activity in my Physics 2 class we do the Pinhole Camera with a light bulb and view the image on a screen. The first day I showed the class how to create a simple pinhole camera out of a box and some aluminum foil (if you want to see what mine look like let me know.) This year I rewrote the lab to be totally inquiry based. They made a number of general observations and wrote 7-10 “I wonder…” statements or questions, they then experimented and tested their “I wonder…” statements and made observations. This rewrite to an inquiry lab was great. All of the groups wondered about and tested the same things I had on my previous version of the lab (move the screen, move the bulb, make a bigger hole, make multiple holes, use two bulbs, etc). So that part of this process was excellent.
The next day after a brief discussion about some of the observations we saw I instructed each group to create a model on a WB for the situation. I reminded them that the model should be simple, but yet be able to explain ALL of the observations they made. Here are two of the models I got:
Student justification: “Light travels in waves”
“I was told light is a particle that travels in waves.” Thus the dots in wave form here. I find it interesting that the waves keep getting bigger. The student had no particular explanation for that, just that they were waves.
I keep trying to ask “what about this lab shows that light travels in waves?”
“I don’t know, but it does.” was a common response.
It took myself and another student group about 20 minutes to finally convince the bottom group in particular that we don’t need to model the light as waves. And even now I’m not sure if they bought it or just wanted to be done with the conversation so they gave up.
“Why can’t we use straight lines.” another group said. Their board did show a linear model for the light, and they had the arguments to back it up.
“We have no evidence to back up the claim that they are waves.” I said. “Straight lines explain the behavior and it’s a lot simpler to use then draw crazy wave forms.”
I went on to say that “we haven’t “disproven” the idea of light as waves, but we surely haven’t proven it. Science comes with the burden of proof.”
So as I analyze this class discussion a couple of questions come to mind:
1) Do other modeler fight this battle of using a model that we have evidence for vs. what they have been told. (I find it A LOT in chemistry too, especially with the atomic model)
2) Was this a lesson for my students about science at its finest? Did I end the discussion too quickly because I wanted to “keep moving?”
3) Should I let them use their mental model until it totally breaks down and/or becomes too difficult to use?
If you have any answers or thoughts about these questions, please comment below.
As my paradigm lab for Acids and Bases in Chemistry 2 we do a very simple classifying lab. My lab handout is here: Classifying Lab
Basically what this entails is that I give the students 7 substances. HCl, H2SO4, HNO3, NaOH, KOH, Ba(OH)2, and H2O. They know the formulas and proper names, but NOT acid names (i.e. Nitric Acid). I have each group do some qualitative tests in well plates using various indicators and other chemicals. They take observation data in the table provided.
After all test are complete the students are to group the 7 substances into as many or few categories as they need. They just need to justify their groupings. After a little staring at the data most lab groups are able to see the pattern that emerges. They almost always create 3 groups. One contains HCl, H2SO4, HNO3, One has NaOH, KOH, Ba(OH) and H2O is by itself.
During our whiteboard discussion each group explains their reasons for putting certain things together. Sometimes they talk about only one indicator but most groups see the patterns emerge across all the tests. After we have an agreed upon grouping system I then pose the question, “Now look at your groups what do each of the substances have in common within a group?” Obviously you always get a variety of answers but the initial responses usually revolve around how one group has begins with Hydrogen and the other ends with Hydrogen. I remind them about what is significant about the order compounds are written in, and also what is significant about the Conductivity test we did. They realize we are dealing with ionic compounds, and the first ion is positive, while the second is negative. They also see the Hydrogen “on the end” always comes with an Oxygen, and we have hydroxide. Someone usually also realizes that water is really just HOH, thus a combination of both of these groups.
My class this year is quite bright and it didn’t take them long to verbalize these patterns. Within only a couple of seconds of this “light bulb” going off one young lady exclaimed. “Can we make this a Vin diagram!?” “Why not?” I said, “that would be a great way to model this!”
How perfect! Never a mention of the words Acid or Base, and we have Arrhenius’s Model! Concept before name!
Naturally the next day I challenged them by testing NH3.
To which a young man exclaimed. “Here we go again, we create a Model one day, and the next day we prove it wrong!”
I said, “Don’t shoot the messenger, that’s the way the world works.”
He then added, “in English they call it an exception to the rule, but in Science we create a new rule! That is why science rocks!”
Holy cow, have I done my job here? At least it made me feel good that I’m getting through to a few kids!
To me measurement is one of those topics that doesn’t seem like is should be a challenge. BUT every year and every teacher I talk to finds that measurement is a HUGE PROBLEM with students. I’ll let you form your own theories as to why this is the case. This post is to describe the process I use to “reteach” students how to measure correctly, with the emphasis being on using a system of 10 divisions.
I personally treat this activity as a lab, but it can be done any number of ways. Here is the handout I use: How Many Nerds Lab. The lab begins with me giving each student a ruler that looks like this:
They are asked, what do you notice about this ruler? Things such as “no markings,” “a 0 and a 10,” “10 inches,” and many other things come up. First thing I tell them is that this is NOT 10 inches or any other unit of measurement they have ever used. So I have given the units a name: NERDS! I tell them that since I’m kind of nerdy I wanted a unit of my own.
In reality the credit for this name and the rulers goes to Mr. Ryan Peterson of Brillion High School. Any unit name you see fit can work.
From there I ask: “What is this ruler good for.” The usual response is “not much.” I usually have to hold something up and say “really, you can’t tell me anything about the length of this object?” Someone usually realizes they can tell the object it either shorter or longer than 10 nerds. “Ok, so what should I do to report the length of the object?” “Guess” seems to be a popular response, but I quickly say guessing is random, like how many Jelly Beans are in a Jar. Someone will finally say “Estimate.”
“Ok, now go and measure 8 things around the room. Try to get at least 2 or 3 things that are longer than 10 nerds.”
I give them about 5 minutes to make their 8 measurements. Then I hand out this ruler:
After a very brief discussion revolving around the fact that this ruler has the whole numbers marked, and that in science WE DO NOT USE FRACTIONS, I send students to remeasure the same 8 objects.
They are off to remeasure the same 8 objects they have already measured.
Before I explain my discussion, here is how these rulers were created. Again credit for the original Excel file goes to Ryan Peterson.
Nerds Rulers. This Excel file contains 3 tabs, each containing 6 rulers on each tab. Print from each tab. I then copied enough sheets to make a class set of ruler on colored paper. Finally I sent the pages through the laminater and cut out each ruler. The set I made 5 years ago is still going strong. The only real issue I’ve had is kids fold the blue ruler in half.
Back to the lab.
Once all measurements are made the students see a pattern of increased precision with each ruler (they don’t call it precision, but that’s what it is). We quickly discuss things such as which ruler is best for measuring different objects, what makes a measurement “correct,” and how to handle measurements that we right on a marking. The next thing is to have small groups discuss and whiteboard a rule or rules for using a ruler.
I give groups about 10 minutes to discuss some things and come up with what they think we should consider as “rules.” Most groups come up with things like:
- Start at zero
- Measure the same object
- Measure twice
I tell them that those are good and true and all, but how do make sure we are using a ruler correctly? I sometimes have to give them the hint about what they did with the 3 different color rulers. Most of the time that helps them realize that they ESTIMATED something in the answer. Ultimately, after all groups have shared their rules I want the class to agree that we should:
- ESTIMATE ON PLACE MORE THAN WHAT THE RULER TELLS YOU FOR SURE
This usually makes sense to the class, and they agree this the #1 rule. PERFECT!
I extend the discussion with what that estimated number means. I show them how the number they estimated is really reporting a range of numbers. So for example a measurement of 3 is likes saying somewhere between 2 and 4. A measurement of 3.6 is the range of 3.5 to 3.7. Reporting 3.65 is something like 3.64 to 3.66 (this range might be a bit larger depending on the ruler). Something I don’t stress at this point.
The next step is to introduce our more typical units of measurement: METERS! Students know it is coming but they grumble and complain, and raise a fit over why we can’t just do it the “easy” way (inches, feet, etc.) I then proceed to ask them something like; “so what increment comes after 7/32?” Someone says 8/32. “Ok, but I’m not going to find a wrench marked that.” 4/16, 2/8. oh 1/4. “Congrats that just took you 1 minute to figure out.” “What wrench comes after 7 mm?” 8mm. “1 second, nice job, now which way is easier?” I will then of course have the discussion about english vs. metric.
I usually like to get on my soapbox a little bit and complain about how “the US is the greatest country in the world, and by gosh we aren’t going to change our ways for anybody.” I play that angle up a little bit, and we get to the point that metric is easier to work with, just not as common for us in America, but they hopefully see the point.
I now show the class a dowel that is marked as 1 meter long, but that is it. Kind of like the blue ruler from above. I then discuss and demonstrate how you can split a meter into 10 equal sections called decimeters, show them a ruler with only dm marks. Each decimeter into 10 centimeters, show a cm ruler, and finally centimeters into 10 millimeters, show a typical meter stick with mm markings.
My lab hand out is here: How Many Meters
Basically, I have a set of different metric rulers, and whatever the smallest markings are on the ruler is the “type” of ruler it is. So a standard metric ruler is a mm ruler even though the numbers are cm. This is just another complication in the process we have to deal with. I have each student measure the same stuff with the same type of ruler so that we can compare results.
This is all for practice, and the whiteboard discussion is pretty minimal. I usually focus on the different prefixes used in the SI system. Why it is called SI and why it is important we have a standard unit of measurement for scientists.
Uncertainty of Measurement Activity
The questions I usually get about all this emphasis on measuring is “Why is this important?” To me this activity nails it and relates why estimating measurements is so important as well as demonstrating exactly why significant figures work the way they do.
I distribute a index card and blue ruler to each student. (something smaller than 10 nerds is a must, otherwise the uncertainty becomes too great.) Each student measure the length and width of the card. They then calculate the area, and I instruct them to write down exactly what the calculator says.
They remeasure with the pink ruler and again calculate and record area exactly as is displayed. Finally they measure a third time with the gold ruler.
After all measurements and calculations are made I have each student list their calculated areas on the board. One column for each ruler. I forgot to take a picture of the entire set of class data, but it was something like this:
Notice how sweet this data is! The discussion revolves around where the uncertainty in each calculation shows up. For the Blue ruler it is in the tens place. The Pink ruler the ones place, and the Gold ruler is in the tenths place. Coincidence?! I don’t think so.
Because of our “rule for using a ruler” the significant figure in each measurement comes out to be where our uncertainty shows up in our calculations! Amazing!
Bottom line is the blue ruler gives us calculations that are uncertain plus or minus 10, thus we can only report an answer that is rounded in the tens place, which just so happens to coincide with 1 sig fig!
The pink ruler is uncertain plus or minus 1, thus rounded to the 1s place; 2 sig figs!
The gold ruler is uncertain plus or minus 0.1, thus rounded to the tenths place; 3 sig figs!
I think it is really cool how nicely the data comes out for students to “see” significant figures really work out. In all actuality I not huge on make significant figures a huge issue as the year goes on, but I tell students, you better never ask me: “Where do I round?” That is one of the biggest pet peeves I have and when the do I’m going to tell them to look at sig figs.
WOW! That is a lot of information in one post. Please use it for your benefit, and as always, if you have any questions or comments please leave them below.
Last week was our first week with students for the school year. For the first time (I think ever) I’m actually quite pleased with how my classes went. This post will outline my week in Physics I class.
Physics I is class that consists of Juniors and Seniors. All have taken Science 9 (mostly physical, but other as well) and 10th grade biology, some were in Chemistry last year but not all. Mathematically the range is from Algebra 2 to Trigonometry to Pre-Calculus.
This year I’m trying Unit packets (i.e. Kelly O’Shea), so on Day 1 I handed out my Unit 0 Packet. More on Unit 0 later. Using a packet will free students from individual Lab Notebooks and hopefully guide them to focus on lab content rather than organization. The strategy allowed me to by pass all the Lab Notebook setup stuff I’ve done in the past. So I was able to just get started.
I began with a circle drawn on the board. My first question was, “How could you describe this shape, WITHOUT using the word circle.” Things such as ’round,’ ‘curved,’ ‘360 degrees,’ ‘all points equidistant from the center,’ were stated. Good enough.
Since I introduced this lab as and exercise in measuring I next ask the students what could we measure about the circle. The usual things were brought up: radius, diameter, circumference, area, and maybe something else. Next I said we needed to narrow our list down to the two easiest things to measure. We agreed upon circumference and diameter. I have a classroom set of 10 meter tape measures, so from there I let them go.
I made sure to emphasize that this lab was a MEASUREMENT lab, because a few students always try to get away with calculating circumference. One thing I did not mention was whether to measure in inches or centimeters. I got about a half and half return. I set students free to find circles around the school building, with the goal of measuring between 10 and 12. This takes about 30 minutes.
The next day the students returned to class with all of their measurements. From there it is time to graph. In the past I’ve gone directly to LoggerPro, but this year I decided it was important to at least draw a couple of graphs by hand. I gave them the following guidelines:
One your Graphs be sure to:
- Use Pencil
- Label your axes with symbols and units
- Give the graph a title (“[vertical axis variable] vs. [horizontal axis variable]”)
- If the data is linear, draw a Linear Fit line (don’t connect the dots)
- Find the slope of the line using points on the line (not data points)
- Write the equation of the line (EOL) using the variables from your axes (not “x” and “y”); make sure the slope and intercept have the correct units attached to the numbers.
- Put units on numbers, but never on variables
I did NOT tell them which axis which variable need to be on. I again got about a half and half return, which is good for the whtieboard discussion. I did have to do some “teacher talk” regarding the Linear Fit line and the EOL. Since these are things that we will be doing ALL THE TIME I feel it was important to spend a few extra minutes to introduce common terminology and expectations. Hopefully it makes my life easier in the future.
Once graphs are drawn by hand on paper each group transfers their graph to a whiteboard. It doesn’t need to be a perfect graph, but something that shows approximate locations of data points, and most importantly the Linear Fit line and the EOL.
The final piece to the puzzle is the whiteboard discussion. We take our time presenting and discussing things such as methods of measurement, variety of sizes measured, why they decided to put C and D on the axis they did, how they calculated slope, etc. We then compared all groups graphs to each other.
The first thing that was noticed by the students was that graphs that were C vs. D were different than D vs. C. GOOD! Then they realized that the graphs that were done the same all had slopes that were very close to each other.
Me: INTERESTING, why would that be?
Students: Because we all measured circles.
M: Oh, ok, so what does this slope mean then (looking at the C vs. D graph)?
S: Well they are all around 3.
M: Exactly 3?
S: No, just a bit more.
M: Who had pie? I like pie.
S: No the slope is pi.
M: Cool, what about this one? (D vs. C graph)
S: Inverse of pi
M: What does that mean?
S: 1 over pi
S: The variables are graphed on the opposite axes.
Ok, you get the idea, but more importantly SO DID MY STUDENTS!
Based on all of this discussion we are now able to write and mathematical model for circles. From the C vs. D graph we get C = πD. From the D vs. C graph we obtain D = (1/π)C. Someone usually notices that these models are one in the same. This is awesome, because most students realize they have seen these equations before in some form or another, but never had the experience of knowing where they come from. Thus I give them one of my favorite sayings: “Equations come from experiments NOT textbooks!”
The very last thing I added this year was a quality addition. I took time the next day to do a summary of how models were used in this lab. On the whiteboard I created a summary that looks like this:
The final thing I wanted to do was come up with a definition for the term Model. With a little guidance both of my classes agreed on the fact that a MODEL IS A REPRESENTATION. I can now refer to this simple definition anytime students wonder what the heck I’m talking about when I call and equation a model. It simply represents the situation in a mathematical form.
I absolutely love the way this lab introduces my students to just about everything we are going to do in physics this year. Defiantly worth the 3+ days to complete.
WOW! How can something as simple as measuring circles turn into this ridiculously long post?