Thursday, February 28, 2013

Coffee Taste Test Using Same Filter (Blind Sampling & Data Collection)

A question occurred to me today. As normal, I need my afternoon coffee. However, feeling excessively lazy, instead of making a new pot of coffee, I decided to simply fill the coffee pot back up and use the same filter from earlier this morning. As you can imagine, it wasn't exactly indulgent. Yet, I began to wonder if the coffee I was drinking was actually weaker, or was it my anticipation of it being weaker that made it so. Project!

Have your students conduct a blind taste test with other faculty members being their dummies. I would even let your students call them least for the day. The taste test will involve each faculty to sample 3 small cups of coffee and record their data without knowing which cup of coffee is which.

Cup 1: First pot of coffee.
Cup 2: Same filter, same coffee, 2nd pot of water
Cup 3: Same filter, same coffee, 3rd pot of water

The survey should be something simple, but measurable. For example, have them rank each cup of coffee on a scale of 1-10 with 10 being the highest.

Things to account for
  1. When ranking, will the dummy be comparing the tastes of one cup to the other cups only, or will they be comparing them to previous cups of coffee. For example, if the dummy loves a White Chocolate Mocha from Starbucks as their number 10, they may rank all three of your cups a 1's or 2's. Thus, to account for this, you may want to raise the ranking system from 1-10 to something like 1-100.
  2. Will the cups be served black or with sweater and cream? If the latter, you shuld make sure that each cup receives nearly the same amount.

After Results:
Have each student calculate some descriptive statistics (mean, median, mode, standard deviation, etc) and draw some conclusions. Does using the same filter and same coffee really make the coffee noticeably weaker? Or is it in our imagination?

Finally, the most important part of the activity is the after-activity discussion. Why might the tests be inaccurate? Was are sample size appropriate? What could we have done better? How might a double-blind test affect the results? Why might companies use blind taste tests when comparing their product to their competitors

Have fun...send me some pics if you decide to do the project!   

Tuesday, February 19, 2013

Representation & Modeling: Getting Your Students To Draw A Math Picture

A simple picture can go along way in helping your students solve an application problem. This is as true in pre-algebra as it is in calculus, however, representing the problem with a picture or diagram is often an overlooked step by students. The goal of the blog post is to help students see the value.

Drawing a diagram or other type of visual representation is often a good starting point for solving all kinds of word problems. It is an intermediate step between language-as-text and the symbolic language of mathematics. By representing units of measurement and other objects visually, students can begin to think about the problem mathematically. Pictures and diagrams are also good ways of describing solutions to problems; therefore they are an important part of mathematical communication. From Teacher Vision


Take one full class and introduce nothing but word problem with the emphasis on using pictures to capture the problem. Next, quiz students on this vary concept. Read aloud to them a word problem and have them represent it in a picture while at the same time labeling everything they know. Use some variation the following rubric when grading their work.

Quality of Representation 1 2 3 4 5

Proper Labeling of Parts 1 2 3 4 5

Unneeded Detail             1 2 3 4 5

Lets Call Upon Another Example From The Teacher Vision Article

Question: A frog is at the bottom of a 10-meter well. Each day he climbs up 3 meters. Each night he slides down 1 meter. On what day will he reach the top of the well and escape--From Teacher Vision
Here is a possible representation of this problem.