Advice with Significant Figures
Posted by: Scott on: January 18, 2012
Teachers – how are you handling significant figures? I’m a bit at odds with my textbook and I’m wondering what the rest of the world is doing. I’ve discussed my issues with our chemistry teacher, he tends to agree with me, but it’s just the two of us. Let me explain.
I teach from Holt Physics. The book treats sig figs mostly okay. When they provide numbers for problems, they are always precise. Usually the numbers are in scientific notation, so you know where you stand with your given information. The book does state that 1500 could be 2 or 3 or 4 significant figures because we don’t know about the two trailing zeroes. I tell the students to err towards caution in those cases and treat that number as though there are 4 sig figs. The book correctly states that the answers are rounded to the least significant number of figures. You all know what I mean.
Here is where we part ways. I teach my students to carry an extra place while doing calculations. For example, if I’m dividing 35 by 62, my working answer is 0.565. If this is my answer to the problem, I would round this to 0.57. If I’m using this number in another calculation, I would use all three digits. The textbook rounds this here along the way even when it is used later. I’ve even seen problems where they have rounded more than once in the same problem. (There is no way I can remember the actual problem right now.) The results are often an error of about 10% difference between my answer key and my calculations.
While we are at this, I have a question I’m stuck on. Suppose you read a meter stick and you get a reading of 8.65 cm. That is three significant figures. Now you move a little ways up the ruler and read 22.40 cm. The accuracy of the ruler hasn’t changed, but I’m now working with 4 significant figure versus 3 before. I wouldn’t round the second number, it is as accurate as the device, but the first number isn’t 8.600. How do you account for this when you are dealing with the significant figures of a problem?
New LEGO Robot Challenges
Posted by: Scott on: January 6, 2012
- In: Engineering | Projects | Robots
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In the last couple of weeks we’ve done some new LEGO Robot Challenges and I’m really pleased at how they turned out.
First was my LEGO version of the Hungry Hippo game. The students were tasked with creating a robot that drives around gathering balls and marbles. The robot that collects the most points worth of marbles and balls in 60 seconds wins the challenge. The balls are the colored balls that are included in the robot kits. The large balls are worth 5 points each, the marbles are worth 2 points. Students had to come up with a strategy and then build to that strategy. The best design drove around with a scoop on the front that shoveled the captured balls into a bin on top. Many designs had rotating claws in front to direct the balls into a pen.
About a week into the challenge, students were tasked with doing a design review with another group. They had to critique the other groups’ project and suggest ways to improve the design, then have the same done for their project. All of the groups felt they got something out of the design review process.
The arena was our own Octagon I created out of 1×4′s. Each side of the octagon was 24″ and the sides were held together with masking tape. It was sturdy enough that the robots could bump into the walls and trigger a touch sensor. The plan was to have the robots go head to head in the arena, but they all locked up so badly that each robot did individual one minute runs.
The latest challenge was a rope climb. I first showed the kids a couple short videos on the space elevator and we had a short discussion on the cost benefits of such a system. They were given a short week (4 days) to design a robot that could climb up a rope. I hadn’t tried this before so I didn’t know what to expect. I had a few robots climbing the rope within 30 minutes, so I had to up the ante. Basically, they got a C if the robot climbed the rope. If the climber carried a 0.5 kg weight up the rope, the group got a B. If the robot managed to carry a full kilogram weight up the length of the rope, the students earned the A. Only one group managed the A using an innovative design of tires and belts.
I’m going to challenge them to go back to the drawing board on this one and see who can carry the most weight up the rope. After that, we are going to do Robot Wars in the Octagon. The goal is to disable your opponent or remove them from the ring. It should be fun.
TED Talks
Posted by: Scott on: December 19, 2011
If you are not familiar with TED Talks, you need to come out of your cave. I have a problem with these videos. I can’t stop watching them. Life got busy and I guess I forgot about filling my brain with a little bit of inspiration. I was recently reminded of the TED Talks by Kaitlyn. She sent me a link to her blog with 15 physics talks. You can find her blog post here: http://www.onlineuniversities.com/15-fascinating-ted-talks-for-physics-students/.
When you are there, make sure you take a look at this talk by Dean Kamen. I’m showing it to my engineering and robotics students tomorrow. My hope is they see the importance of what they are doing.
Standards-Based Grading Moves to Physics
Posted by: Scott on: November 17, 2011
Lame graphic, I know. Sorry.
As I mentioned in my 3-part update, my students absolutely love SBG in Calculus and have requested I move the system into my Physics classes as well. However, after studying the problem at length, I have to take the tact that Frank took. SBG as it is implemented in my Calculus isn’t a clean fit in Physics.
I’ve had to make some modifications, and I’m pretty sure I’m there will be modifications in the future. Instead of solving two problems perfectly to achieve mastery, Physics students will have three, but they will be tiered. Here’s how it’s going to work:
- Most concepts will have three levels of problems: C-level, B-level, and A-level.
- Students must get a C-level problem perfect to take a B-level quiz. The B-level problem must be perfect to take the A-level quiz.
- If they get the C-level correct, they earned a 75% in that concept. A correct B-level gives them 85%, and a correct A-level problem boosts the concept score to 100%.
- C-level problems are basic. Everyone should be able to solve them. B-level problems are a little more advanced, but everyone should be able to get these correct with practice. A-level problems are challenging and most of the class will not get these unless they really put in the work.
- The 4 point grading system in still in effect, there is no partial credit. This makes grading much quicker. A 2 on a C-level is worth 60%, a 3 is worth 70%. On the other levels, they only improve the score if they are perfect.
Quiz day will not have a standard group quiz. I have lots of 1/2 page concept quizzes. A student gets the quiz level for each concept based on what they have mastered. Yes, this is a hell of a lot more work, but my classes are small.
Here is how I divided up the concept “Upwardly Launched Projectiles:”
- A C-level problem is a projectile launched and landing on the same level. They are given an initial velocity and an angle. They have to find the time in flight, max height, and range.
- A B-level problem involves different elevations for the launch or landing, or a building or mountain to hit or go over.
- An A-level problem requires more math, like simultaneous equations or the quadratic to solve for initial velocity.
Points for the concepts are going to vary based on the depth of the concept. Projectiles will be worth 50 points while Relative Motion is only worth 30 points. Some of the topics will only have two levels, a B-level and an A-level, simply because there isn’t enough difficulty to warrant three levels. But those levels, like relative motion, will also not be worth as many points in the system. I’m still keeping grades for Homework (5 pts), Labs (25 pts), and the occasional WebAssign (around 15 pts).
We had our first quiz today and it went well. A few of the better students got 4′s on the C-level problems. I was able to grade about 15 full quizzes in under 15 minutes because of the 4-point system. I was also able to be a real stickler on the significant figures because the kids have time to correct their mistakes and get it all right.
I’m incredibly optimistic about the change. The students are a bit nervous, but they’ve heard so many good things from my calc kids that they know this is going to work to their advantage. I know they will be doing a lot more work and keep at the lessons longer than they would under a normal grading system. I’ll keep everyone apprised.
SBG Success – Part 3 (Concepts & Quizzes)
Posted by: Scott on: October 31, 2011
I think you can try to plan to implement Standards-Based Grading, but the first time through you really need to be flexible and open to change. I didn’t start the quarter with SBG in place because I was coaching soccer and there was no time after school. Not a good place to start, if anyone is thinking of doing the same thing. However, once soccer ended, we were in full SBG mode. Being that it was new for all of us, it took everyone a while to get into the swing of coming in for help and taking quizzes.
Right after soccer ended, kids started coming after school for concept quizzes. I started throwing problems on paper, trying to get a pile of quizzes together, it was a mad-house at first. Some days I would have 5 students all wanting different quizzes. Each concept quiz consisted of two questions. At least I kept a list of the problems I gave out. It was chaos, I had to improve my methods.
I had been keeping the after-school quizzes in a pile. One night I finally sat down at my computer and created two or three quizzes for each concept area. I put a 31-day divider into a binder and put the quizzes in each section by concept number. At work, I made several copies of each quiz and put them in the section behind the original. Now when a student needs a quiz, I open the binder and pull out a quiz. The front of the binder contains the weekly quizzes that cover from three to six concepts. These are given sequentially every Friday. Any of this material will be available to any teacher that requests it. Feel free to borrow and improve, or just borrow – whatever works for you.
At first I kept their quizzes so they couldn’t share them with friends. Once I got organized, I realized these were a valuable tool. I created a folder for each concept and stored the quizzes in the folders. This let me keep track of who took what quiz and what problems were giving the class trouble.
I soon realized I had to slow things down a bit. Students would show and take another quiz after school, but not do any better on it. I changed my method completely. Now I make them explain the concept to me. If they sound like they understand the concept, I’ll give them the quiz. If they don’t, I insist on tutoring them on the concept before I’ll give them the quiz. This has significantly increased their success rate.
Concepts
The first SBG concept was Symmetry, the second was Domain & Range. I still have several students that have not mastered those one or both of the concepts. If I hadn’t switched grading systems, those students would have done poorly on the quiz or test and moved on. They might have worried about the concept for the midterm or final exam. Some of my kids have been working to learn Symmetry and Domain & Range for six weeks now, and they won’t give up. Yes, I’m sold on SBG!
When I started this, I was really concerned about dividing the course into concepts. I was hoping to find a concept list online, but I didn’t. The key is to look at the big picture – not everything needs to be its own separate concept. For example, the Power Rule is part of the Product and Quotient Rule. You can’t do a product or quotient derivative problem without knowing the Power Rule, so it is tested sufficiently. The book is organized well, we use Larson’s AP Edition of Calculus of a Single Variable. So far, my concept list is:
- Symmetry
- Domain & Range
- Graphical Limits
- Algebraic Limits
- Continuity
- Infinite Limits
- Limit Process
- Product & Quotient Rule
- Chain Rule
- Implicit Differentiation
I closed out the list for the first quarter at number 7. As I write this, we are about to start the Chain Rule and we have almost two weeks left in the first quarter. We are adding roughly one new concept per week, most quizzes have six concepts. I probably won’t update this post as the year goes on, but if you email me, I’ll share whatever you need to get this working for you.
I’m extremely happy with the results. The kids are happy and they are learning calculus, not just trying to get through the course. I think I’ve made the course a little tougher knowing they can come back and take the time to learn all of it. I asked them today what they liked and disliked about the new grading system. I asked them for changes, anything at all. They unanimously said the loved the new system and didn’t want to change anything.
Personally, I’m struggling with not grading on a normal curve. My class average is too high, but they have learned the material, really, deeply, honestly, learned it.
SBG Success – Part 2 (Grading System)
Posted by: Scott on: October 30, 2011
With weekly quizzes and so many additional concept quizzes, I was worried about the time it would take to grade everything. I’ve been pleasantly surprised at how quickly I can get through a set of quizzes, it’s quick because I don’t worry about partial credit.
Each problem gets one of four grades:
- 4 – The problem is done correctly, no errors
- 3 – The student understands the underlying concept but made at least one or more mistakes
- 2 – The student is starting to understand the concept, but clearly isn’t there yet
- 1 – No real understanding
- 0 – No attempt at a solution
Grading in the grade book is simple. Students get the highest score achieved times ten. If they do worse on a quiz, nothing happens to their grade. When they get the first 4 on a concept, they get 40/50 in the grade book. Get a second 4 and the 40 becomes a 50 and they are done with that concept. The kids love to write “MASTERED” on a completed concept.
I’ve set up a spreadsheet (Gradebook – names are removed) in Excel to handle the grades. Each student gets their own block. When I enter a quiz grade, I change the header grade and change the color to orange to remind me to change their grade in the school system. Blue means the concept is complete. Red numbers means the grade came from an after school quiz and not a weekly quiz.
The students use a Concept Checklist to keep track of where they are on each concept. Every week or so I cut up my spreadsheet and hand out the pieces to make sure their scores agree with mine. I plan to start a new spreadsheet each quarter since I can’t change the previous quarter’s grades. So far, this is handling my grading requirements.
Next post – Setting up concepts and creating quizzes
SBG Success – Part 1 (Point Distribution)
Posted by: Scott on: October 28, 2011
(This is a follow up to a previous post on Standards-Based Grading. I’m so pleased with the success, I started writing and created a monster post. I’ve gone back and broken it into bite-sized chunks to scare off fewer readers.)
The first quarter is almost done and I’m incredibly pleased with my conversion to Standards-Based Grading (SBG). I’m glad I started with Calculus, the kids have been an understanding group and open to trying something new.
I began by setting up the scoring, each concept was worth 10 points. The only other grade they have is a weekly WebAssign grade. Those are usually worth between 15 and 25 points. I found the WebAssign was too heavily weighted and the concepts didn’t have enough impact, so I did some analysis last week and seven weeks into the first quarter I changed the concepts to 50 points. I printed grade reports and noticed that the point change lowered everybody’s score. I expected an outcry, but it didn’t happen.
I explained that with three weeks to go in the first quarter, any new concepts will get entered into the second quarter. Since I will not have the option of going back and changing their first quarter grade later in the year, I needed to give them enough time to master the early material. What I explained to them is that their grade report showed the lowest possible grade for the quarter. They all have three weeks to bring their grades up to an ‘A’ and they all can do just that.
Suddenly it clicked and the kids are coming in during their study hall and after school. The rule is they can take a single concept quiz each day; plus we have a quiz every Friday in class. At first they were dreading the quizzes, now that they understand that a quiz can only improve their grade, they love the quizzes (well, maybe not love – I do make them rather challenging).
The students are motivated to learn the material, they finally feel like they have control over their grades. I know this is creating a positive learning environment. All of my calculus students that have me for physics asked me to switch the grading system in physics.
Next post – The Grading System
LEGO NXT Mindstorm Frustrations
Posted by: Scott on: October 5, 2011
My two robotics classes have been working on an obstacle course. I made it challenging, but it seems to be too challenging – not because the kids aren’t trying but because the robots do something a little different every time. I’m confused. I called LEGO Education support and they told me the motors are accurate to one degree per rotation.
I’m seeing errors much more than ten times that number. I can’t seem to find a way to solve the problem. We are using yellow RESET block, light green MOVE blocks, and orange rotational WAIT blocks. We have a spot carefully marked on the floor for the start and way points. Starting at the same spot may have the robot as much as an inch off within about 10 rotations. The total motor error should be about 0.17 inches. I can’t determine if it’s a problem in NXT-G or the motors.
I’ve searched the NXT books, blogs, web sites, and books, and I can’t find any references to the inaccuracy issues. Has anyone else seen these problems? How do I fix this?
Two Free Apps I Can’t Live Without
Posted by: Scott on: September 18, 2011
The first free app, and on the top of my list is DropBox. DropBox is a website and an application. You have a folder on your desktop on every device you own; your PC, Mac, iPhone/iTouch, and android phone. Anything you place in your DropBox folder on one device is synced to all the other devices. Phones can see the files but don’t sync or download it unless you open it. You can also create shared folders. I have one set up with my daughter in college. If she wants some photos or a video, I just drop it in the box, it instantly appears in our shared folder. She can leave it in the DropBox folder or move it to her machine and save our DropBox space.
Because of DropBox, I no longer have my lesson plans on a USB that I have to carry around. The files reside in my DropBox folder, and more importantly, there is only one version of it and it is always the most updated copy.
There isn’t much of a downside to the app. People don’t have to be members or download the app to be able to use your shared folder. You start with 2.0 GB of space and earn 250 MB each time someone you invite installs the app on their computer, up to a total of 8GB. People can access the folder without downloading the app, but if they don’t download the app, you don’t get the bump in storage. You can also increase storage up to 50GB for $100 a year. I’d probably consider subscribing if it was about half that, I just don’t need 50 GB right now.
If you want an account, do me a small favor and let me send you an invite. Click on my Contact Me link. Doing so will get you an extra 250MB, and do the same for me. Then you can share it with your friends and coworkers if you love it. I love it.
The second app on my list for today is called Evernote. Evernote took some figuring out for me, but once I saw the light, I’m a convert.
Here’s how you use Evernote – you upload photos, pdf’s, and random stuff. You write lists, send web pages, and scan business cards. All that crap that you need but you don’t know what to do with it, it goes in there. Here’s the golden nugget of Evernote – anything in there becomes searchable. So that business card, just take a picture and upload. Now you can search for that person or company or title. Instead of keeping the instruction manual for all those electronics gizmos, upload the manual. If you ever actually need it, you can search the manual through Evernote.
Just like DropBox, the app is on everything. You can install an add-on to Firefox (and probably other browsers) to directly upload to Evernote. Just highlight, right-click and at the bottom of the menu is “Add to Evernote.” The limit here is you can upload only 60MB per month (each month), which I’m finding is an enormous amount of stuff. I saw something at Home Depot that I wanted to remember, so I took a picture and sent it to Evernote and added notes later. I’m sure there are other ways of using it, like they have tags you can attach to everything and notebooks for organizing, but I’m using it as a warehouse for manuals, business cards, recipes, and other things that just don’t fit anywhere else.
You can go premium with them for just $5 a month and they have educational discounts as well. Most of the negative comments were about not being able to share the data. I don’t want to share this stuff, it’s my junk drawer and attic all in one.
Robotics is Now Robotics & Engineering
Posted by: Scott on: September 5, 2011
Last year, the course was actually called Robotics and Astronomy, or Robostronomy for short. The intent was half-year of each. The result was more like three weeks of astronomy and robotics all year-long. Don’t get me wrong, I love astronomy. It’s just, well, Robots took over the Earth. Between the great things we could do with the MindStorm, and then the SeaPerch competition, we were all robots, all the time. This year we are adding the First Tech Challenge. Yep, Robots have taken over the Earth, and it looks like they landed in my classroom.
The goal here is STEM, that’s what opened the door for the robot invasion in the first place. Clearly missing from our program these days is what we called in the old days, ‘drafting.’ Drafting isn’t done on a board with a T-square anymore, but you all know that. Today, 3D mechanical Computer Aided Design (CAD) is available for free from Google (Sketch-up), and from a number of companies who cater to the high-end. I actually know this industry well, I spent 25 years in the CAD/CAM/CAE industry (M for manufacturing, E for Engineering, meaning simulation).
So with some guidance from some friends at Drexel University, and a little research on my own, I decide to go with SolidWorks software. All of the vendors have aggressively priced programs for the educational market, I think we are paying just $1000 for a 10-seat license. What makes this software connect to the students is what we spit out of it. The school invested in a 3D printer, specifically uPrint Plus from Dimension.
If you have never seen one of these, think Star Trek Replicator. The replicator creates parts from ABS+ plastic directly from the output of the 3D CAD. How better to teach engineering principles than to give the students a design challenge, have them work through designs and then fabricate it in the printer. Here is a great video from a customer talking about how they use a 3D printer in their engineering design work.
My new printer is due here any day and I’m pumped up. Yep, geek boy has a new toy. Tea, Earl Grey, Hot!
Coffee Shop Physics
Posted by: Scott on: August 29, 2011
I would like to have coffee available for the students while they work, but my administration frowns on kids having food and drink in the classroom. But that is not where this story is going.
Last year, one of my students came into class second or third period and said how much he loves coming to my room. I thought it was odd because he wasn’t a particularly enthusiastic physics student. Then he said he loves the way my room smells.
Every morning I make a pot of coffee, often flavored with vanilla or hazelnut. I never thought about the impact something like a nice smell has on making a student feel relaxed. I’m still making coffee every morning, but this year I picked up a bunch of scented tea lights from IKEA. These things smell so good, my son and I bought a pack of every flavor they offered.
I have heard stories of real estate agents putting a drop of vanilla on a warm oven at an open house to make the home subconsciously remind the potential buyers of home-made freshly baked cookies. Maybe getting another one of their senses involved improves learning.
SBG – Jumping In, But Only Up to My Knees
Posted by: Scott on: August 17, 2011
I’ve been following a fellow science & math teacher, Frank Noschese, and his writings on his blog “Action-Reaction.” He has some great stuff that I am going to steal and use in my classroom. One post in particular has really had me thinking, “My SGB Journey” (http://fnoschese.wordpress.com/2010/06/29/my-sbg-journey/). He is talking about Standards Based Grading. I knew nothing about this form of assessment, so I dug deeper.
I won’t lie, it took me several hours of reading to get the gist of it. Frank refers to a post by Dan Meyers. Follow that link and read through the comments. Others readers had many of the same questions I had; reading the questions and Dan’s responses pulled it all together for me.
I haven’t got it all worked out just yet, but I plan on implementing this in my honors Calculus class. My administration backs me on all of my adventures and didn’t bat an eye at it, “sure, go ahead.” After all, this one isn’t going to cost them thousands of dollars (I’ll fill you in later). I’m going to steal everything I can from Frank while I work out the methodology and the glitches in a small and forgiving class, then move it to my physics class the following year.
Here is my understanding of the concept in a nutshell: The course is broken down into approximately 40 key concepts. Students are assessed on those concepts. Once they get two questions perfect on that concept, they no longer need to answer those questions on later quizzes because they have already mastered the concept. They can keep retaking quizzes on the concept until they get two of them perfect. In the mean time, class moves on. (We hit the wall a few times in calculus last year where we didn’t move off a section for over a week because about half of the students didn’t master the concept.) Students track their own successes and know what they need to practice and get tutoring on. They can get a 100% in the class, but my guess is you still end up with a normal distribution curve because many of them will feel that a 60% or an 80% on some of the concepts is acceptable. However, if they choose to work hard and improve their grade, they can keep relearning and quizzing on the material until they master it.
Frank and Dan both have their own grading system. I would read their posts and decide what makes sense for you. I’m just getting started on mine, but my guess is I’ll steal one of theirs and tinker later.
It’s going to be a bit more work the first time around and a lot more time tutoring and retesting after school, but my goal is for the students to master the material. I want them to take the Calculus AP exam and knock it out of the park. This seems like the right approach. I’ve ordered the three books Frank has recommended, you can find them very reasonably priced on half.com. I think I paid about $25 for all three including shipping.
I’d be really interested to know if any of you have used similar systems and how they have worked for you. My gut tells me this is the right way to go. I nervous at the increased workload (again).
Cool Award
Posted by: Scott on: August 16, 2011
I’d like to thank the academy, my family, my producer, my agent, Isaac Newton, Leonardo DaVinci, Richard Feynman, and all the people out there that voted for me.
Okay, I’m done being silly. I did really get this, although I only found out because I was on the site and saw I was one of the listed blogs.
So no, there was no cash award, no gold statue, not even an email telling me about it. And as the new school year approaches, the hit count is heading towards half a million. That just blows my mind.
Do click on the badge, there is a pile of great teacher blogs in the list.
Final Exams – I’m Working Harder Than Them … Again
Posted by: Scott on: June 8, 2011
- In: Assessment | Humor | Teaching Techniques
- 2 Comments
As I sit here grading my final exams, I realize I am putting in way more effort than my students. I am making a promise to myself and I intend to keep it.
My final exam next year will…
- begin with a multiple choice section on basic concepts & terminology
- have lots of basic problems with multiple choice answers
- have a very small written portion – I’m keeping the Road Runner cartoon, it’s my favorite part
- be graded in under two hours
One of the questions this year asked the students to discuss three principles used in their Rube Goldberg project and explain the application of the principle. I was looking for concepts like inertia, momentum, kinetic energy, and force. I just graded a paper where the principles listed were ball, dog, and ball.
If it’s multiple choice, I won’t have to learn that after a full year of physics, one of my students thinks “dog” is a physics concept. I just wish it was a joke and not the truth.
Creating a Unit of Measure to Teach Measurement
Posted by: Scott on: June 6, 2011
There has been a lot of talk on the NSTA Physics list server lately regarding a way to teach a measurement lab. I had one of my morning shower brainstorms. My thoughts went to the story of the MIT students measuring a bridge using a unit of measurement called the “Smoot,” named for Oliver Smoot.
I think many of us teaching a measurement lab have the same problem. The students don’t understand measuring or estimating. Given an object, they will always have the same answer, regardless of whether it is right or wrong. So I am hereby creating a lab using fictitious units. We will use a willing volunteer from each lab group and declare his or her height to be one “Smith” or “Jones” or whatever his or her name happens to be. We will then do some exercises to estimate fractional distances. I think I will give them string and make them use a meter stick to get a measurement of the “Smith.” They will need to figure out how to divide the string into tenths and hundredths and then estimate to the thousandths. I won’t tell them how to do it, they are going to need to figure it out on their own.
My hope is that they will come up with their own method and get a better understanding of estimation. The beauty of an inquiry lab is how little detail they get from me. Personally, I’m excited about this one. I think we are looking at a first or second day of school lab here.
Here is my first pass at the lab handout. Lab 00 – Measurement Lab
You can read about Oliver Smoot and hear an NPR interview here.
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