Posts Tagged ‘Estimation’
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.
If you are new to teaching Physics, you are probably going to expect the students to know how to manipulate numbers and variables. I’ve found that to be a big mistake. Yes, some of my students are very good with math, but I’ve learned not to assume this. As a result, my first two weeks of class are spent working on the skills they are going to use the entire year. Those skills are:
- Scientific Notation
- Estimation
- Significant Digits
- Unit Conversions/Dimensional Analysis
- Solving for variables
- Use of their TI-83 calculators
This is a big post. I have included all of the introductory worksheets, homeworks, and quizzes from the past school year. A lot of example problems I just make up on the fly, but I have attached quite a few word documents. Feel free to use them and adapt them as needed.
Scientific Notation
Last year I reviewed estimation first. That was fine until we started dealing with very small numbers, then the students were lost. This year, scientific notation comes first. I have a three part handout that I go over in class. I make up additional problems as we go, then I hand out the worksheet. They start it in class and are expected to complete it for homework.
scientific-notation-notes-part-0
scientific-notation-notes-part-1
scientific-notation-notes-part-2
Estimation
The point of estimation is for them to be able to get order-of-magnitude answers quickly. At first, they are completely amazed that I can get within 5% or 10% of the answer faster than they can do it on their calculator. Some of them get good at this, most don’t bother even though they see that I will estimate quickly and accurately throughout the entire year. My goal is for them to realize when their answer on the calculator can be wrong and their brain can be right. It does happen and it feels good when one of them comes over to the dark side with me.
Significant Digits
The first document is the handout they get with the guidelines. I think it is rather clear, but I think I want to change the example problem near the end with the sin( ) function. They don’t know sin( ) yet and it distracts them from the operation. I expect them to use these guidelines all year long.
Unit Conversion/Dimensional Analysis
Wow are they bad at this. Most of them almost randomly multiply or divide by the conversion to get an answer but never seem to know if it’s right or what the units should be. This is a real problem. The textbooks like to throw different units into the problems. It’s actually easy to miss, especially when the kids are struggling to learn a new concept. I’ve also found that very few of them are comfortable with the metric system. I feel like I beat this section to death, but still many cannot convert correctly.
Solving for Variables
I don’t have a worksheet made up for this section. What I have done in the past is gone to an Algebra 1 textbook and copied the problems from there. I gave up on this section last year, they just didn’t have the math skills to do this for every problem, and I had to choose my battles. If they plugged numbers into equations, most of them were able to solve for the unknown.
TI-83 Calculator
Here is the problem; the students are unaware of the key labeled EE that does the scientific notation. They also constantly miss the exponent that is shown as 1.2E33. Instead, they enter the number as 1.2 X 10 y^x 33. This works fine if all they are doing is multiplication. However, if they are dividing by the exponent, the 10 y^x 33 becomes part of the numerator. This totally screws up their answers and they have no idea why. There are two solutions: 1) They can use the EE function and only enter exponents in that form, or 2) they can use their longer form and put each term in parenthesis. Obviously, I prefer the first solution and I push them to use it.
I also have them solve simple sine and cosine problems on their calculator. Not all of them use the TI-83, I don’t require it, I only require a scientific calculator. It’s up to them to know how to use it, that is why I spend time in the beginning going over the functions we will use in the course.
The Finish
I give them the following quiz after all of this is completed.
If you have additional material, please share it. Trudi, I hope this helps.
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