Mental Models Part 2

The title of the previous post really does not relate with the post itself. It pertains to this post but I split them up due to laziness and time. {I've been too lazy lately, I need to stop that.}

Anyway. Part II.
Dr. Mazur discussed the importance of mental models. He makes the claim that mental models override our visual memory and affect what we see. He had a nice example. Imagine a balanced scale with a weight in the middle. The weight is then moved to one end of the scale but the scale does not move, it remains parallel with the table it sits on, instead a dial on each end of the scale changes to reflect the weight shift of the object. Viewers who watch might perceive the lack of change in balance of the scale to mean the object is weightless when in fact the object has a weight, it is just reflected in a different manner (And in fact some of Dr. Mazur's students said that since moving the object to one end of the scale did not make the scale move downward but rather it remained balanced meant the object has no weight, or the scale is broken.) In this situation the observation reinforces the misconception.

We have to somehow provide opportunities to revise our mental models. This is especially true for young students going through school. If a misconception is already established as a mental model for a student it is harder than just trying to teach the student something new. You have to first break down that mental model and restructure it with a correct mental model. And if their misconception is a common misconception, it may continue to be reinforced and thus strengthened. We have to somehow provide opportunities to revise our mental models.

Mazur gave three points on how to revise our mental models.
-Predict outcome before observation
-Record observation
-Reconcile prediction with observation

Mazur also had a couple nice movies which demonstrated how we can be distracted by what see. In one such movie, six people had two basketballs. Three people were in white shirts and three people were in black shirts. Mazur told us to watch this 60 second long video and count how many times a person in a white shirt passed the basketball to another person in a white shirt. {While this was going on, the people were moving around, throwing the ball to one another or bouncing the ball to one another. And keep in mind there were two balls being passed back and forth.}

When we finished watching the movie clip he asked us to raise our hands if we saw the gorilla. About half the audience raised their hands and the other half looked completely puzzled. Mazur asked how many did not see the gorilla and the other half of the audience raised their hands. The movie clip was then played again. Sure enough about 20 seconds into the clip a person in a gorilla suit walked out and stood in the middle of the six people throwing the basektballs to each other. The gorilla even waved at the camera and did a little dance. He then exited the opposite side after being visible for about 25 seconds. A man in a gorilla suit waving at the camera is surely a hard thing to miss and yet half of the people in the audience missed it! They were focused on counting.

The other movie you can check out here. If you want to watch it, first stare at the green dot in the center before reading on and make a note of what you see.

Half the audience was asked to stare at the green dot in the center (I was in this group) while the other half of the audence could look around where ever they wanted. Mazur asked my group what we noticed when the movie was finished. We said the green dot was blinking and the yellow dots would also disappear. Mazur asked the other half if the yellow dots disappeared; they said no. We watched the movie again switching roles and sure enough the yellow dots did not disappear even though my eyes saw them disappear. It's funny sometimes how the mind works. Mazur has other presentations and publications on his website for those who are interested. He also talked about color and luminance with respect to visual pathways and studies he has done involving focus of attention which was also very interesting. I really really enjoyed his presentation.

He concluded with the following three points to ponder:
1. My reality is not your reality
2. What you see depends on what you believe
3. We store models, not facts

Mental Models Part 1

Last Friday, I attended a talk given by Dr. Eric Mazur, a professor in the physics department at Harvard University. The title was "How the mind tricks us: visualizations and visual illusions".

Abstract: Neurobiology and cognitive psychology have made great progress in understanding how the mind processes information – in particular visual information. The knowledge we can gain from these fields has important implications for the presentation of visual information and student learning.

It was a marvelous presentation and I enjoyed it very much. At the beginning of the talk the audience received a gadget (to borrow) and at various times during the talk we were asked to vote. I.e. on a scale of 1 to 5, rate your agreement on the following statement: "Information can be transferred more quickly and more effectively visually than verbally." 5 being agree and 1 being disagree. And while the gadget took in all the information from the audience quickly and created a nice visual bar graph of our responses, I can't help but wonder if all the effort of handing out the gadgets to each audience member, getting the gadgets on and setup for this specific talk (three or four button pushes), and showing us how to enter in responses was worth it in the end. (Nevermind the people that came in late and distracted their neighbors from the talk trying to get their gadget to the correct state.) Couldn't we have raised our hands and the same goal would have been accomplished? What exactly did we gain by using the gadget? We could have raised our hands and given responses that way. People have been voting that way for years.

The truth is raising your hand or pressing a button on this gadget accomplished the same goal. The data from the gadget was simply used as a counter, x number of people voted 5 and y number of people voted 2. And yet I felt as though I had some responsibility during the talk. I had this gadget. I had to follow directions and press keys to get to a particular point and even before we turned the thing on, I knew somehow I would be contributing something to the discussion. But even if Dr. Mazur had asked the question to the audience and we had raised our hands, I would still be contributing something. But, would I recognize it in the same way as I had when given the gadget? I don't believe so. Why did the novelty of having this gadget prevail over its purpose?

Free Stuff!

Who doesn't love free stuff? Certainly not this chica. Today when Sharon came into work she handed me a plastic bag and said, "Here's some free stuff from Health Services."

"What? That's awesome!" I exclaim.

I opened my bag of goodies to find: green apple flavored gum, some feminine supplies, and a sample of shower moisturizer and lotion.

Audacity

Audacity is a neat little free audio program. I first started using it to try to analyze student verbal responses via intonation and tone in a mathematics classroom. (It ended up not working out so well.) I later learned I could also use it to take mp3's and make ring tones. I had some fun with that. I pulled it up again today once I learned I could choose a sound file in my email client to alert me to new messages. How fun! I now hear a brief audio clip of "Mailman, Bring Me No More Blues" by The Beatles whenever I get a new message.

Let's see how long until I get sick of this.

My personal guess: 3 days.

ICTCM Conference

I suppose I should post about the conference.
Thursday night I headed up to Boston for the 19th annual International Conference on Technology in Collegiate Mathematics (ICTCM).

SH and I were supposed to led a workshop with the SimCalc software on Friday but SH ended up having a prior commitment and so James and I led the workshop instead. For my first session as a lead and first time speaking with James, I think it went fairly well. It could have, of course, been better. There was not a large turnout and I was disappointed about that but considering it was a 5-6:45pm workshop on the first day of the conference when the keynote speaker spoke at 8:30am, it was surely a long day for people.

I need to be more animated and personable with the audience. I was semi-nervous, and SH is so animated and colorful when giving presentations. Perhaps I just need more practice. Or perhaps I need to develop a character I can transition into when giving presentations, like an actor would. Luckily there were no people I knew at our session. (Possibly because I convinced the few people I knew at the conference to not attend or possibly because they were not interested.)

We spent too much time talking about the software. It is hard to develop that balance between talking about the software and throwing participants into the software. The small group definitely came more alive when we started going through the activities and discussing the work as a teacher in a class would.

We survived our session and I was then able to (semi) relax with some food, wine, and friends. It was not a late night, and after grabbing dinner and a drink I headed to bed; I was assisting with another session at 8am in the morning. That session went really well despite my non-enthusiasm for the software used in the presentation. I was able to check out some other sessions and the exhibit hall before becoming exhausted and deciding to head home. It still baffles me how tired I can get from nervousness.

Commercial leading to a tangent of thought

Have you seen this commercial?




I think it is more clever than any of the Superbowl commercials this year; all of which were really a let down. This divide and chose method is a wonderful idea for a parent. I will have to remember this in case I ever have children. And once again, it all goes back to mathematics.

"The problem can be extended to three or more people, but the method for finding an optimum solution becomes complicated. One method continues the division to successively smaller "equal" portions. The first person divides the resource into what they believe are equal halves. The second then chooses a half, leaving the remainder for the first person. Each of these two people then divide their respective portions into thirds. The third person picks two of the resulting portions: one from the first person and one from the second person. If there are four people, each of the first three people divides their portions into fourths, and the process continues."

Cutting something, like a piece of cake, in roughly equal pieces is easy enough but cutting something into thirds is more difficult. I, for one, do not have a good eye for this at all. I think I have a fairly good sense of numbers, but cutting something into thirds is tricky. For instance it is common to divide a letter into thirds to put into an envelope. I am terrible at this. If I am lucky my letter will fit into the envelope but usually I have to make a second attempt. (Although in today's world who writes letters anymore?) Perhaps those people that are quite good at this have had lots of practice and can "eyeball" it better than I.

Professional photographers, for instance, generally must have a good eye for breaking things up into thirds if they follow the rule of thirds which suggests it is more aesthetically pleasing to break a photograph into nine equal parts and aligning a picture with the intersection points of the vertical and horizontal lines formed by making the nine equal pieces. For example the horizon would line up with the lower third of the picture and the focus would not be centered, but in either the left third of the picture or the right third. I believe artists use this idea for portraits. I remember my grandmother trying to teach me about facial proportions when drawing. She always told me to draw eyes about two-third's above the chin. I always stuck them clear blue on the forehead and too close together.