Micro-teaching reactions

Micro-teaching reactions

:D

e-learning for Matrices - TLS

The e-learning for Matrices can be found in Blackboard under discussion board. We can continue to discuss the learning and teaching of Matrices here.

Math Modelling Survey - TLS

Can you all please take some time to fill out the following survey? Thanks so much.

https://spreadsheets.google.com/viewform?formkey=dDQybXFVRXM1a0oxb2MzOHdSZGNZOWc6MQ

The Monty Hall Problem on Youtube

Monty Hall Problem

Hey guys,

Here's there link to what I was talking about.

http://mathforum.org/dr/math/faq/faq.monty.hall.html

Scroll down to this,

"If you're still not convinced that 2/3 is the correct probability, here are two more ways to think about the problem.

1. It seems to make sense that you have a 1/3 chance of picking the correct door. This means, however, that since the probabilities must add up to one - and the car has to be somewhere - you also have a 2/3 chance of not picking the correct door. In other words, you are more likely not to win the car than to win it. Imagine that Monty opens a door and shows that there's only a goat behind it. Consider that the car is more likely to be behind a door other than the one you choose. Monty has just shown that one of those two doors - which together have the greater probability of concealing the car - actually conceals a goat. This means that you should definitely switch doors, because the remaining door now has a 2/3 chance of concealing the car. Why? Well, your first choice still has a 1/3 probability of being the correct door, so the additional 2/3 probability must be somewhere else. Since you know that one of the two doors that previously shared the 2/3 probability does not hide the car, you should switch to the other door, which still has a 2/3 chance of concealing the car.
   
2. What if there were 1,000 doors? You would have a 1/1,000 chance of picking the correct door. If Monty opens 998 doors, all of them with goats behind them, the door that you chose first will still have a 1/1,000 chance of being the one that conceals the car, but the other remaining door will have a 999/1,000 probability of being the door that is concealing the car. Here switching sounds like a pretty good idea."

Also, check out the next post for visual aids.

Merianna

Math Modelling Experience

I just want to share my math modelling experience that I had with contract school. Schools usually don't use the term 'modelling' but 'performance task'. Typically, schools integrate real world contexts into performance tasks. I rememeber doing one performance task with the secondary one students on floor tiling. Given a fixed floor area and 2 different types of tiles of different prices, the students were told to tile the floor based on a few criteria: optimum cost, least tiles wasted and least cutting of tiles involved. This kind of task really set the students thinking and at the end of the day, there is no fixed solution. But however, before the students even start to attempt the task, they will ask questions like 'is this counted in the examination?' and blah blah blah. I feel that in order to really engage the students' thinking in math modelling, the tone must first be set right; if not, you will have students giving superficial solutions, which you know they have not given much thought to it.

Another issue that arises is the evalution process, aka, rubrics. Does the rubric really provide the best solution? How do we assess the students? If the students fail in the performance task, does it mean that their ability is low? How do we train the students in mathematical modelling? These questions really pose some challenges in setting a performance task.

Well, I just feel that it may even take ages to come up with a good performance task with rubric that allows the teacher to assess the students' learning accordingly.

Group F