Feedback & Reflections on Team Microlesson

Overall, the lesson was okay but certainly had room for improvement.

• Most people felt that the use of the large prism shapes was a good idea especially when unfolding the shapes to flatten them.  However, some felt introducing all shapes at once was a little confusing and also 1 person felt they were distracting because I was fiddling with it.
• Most people like the hands on exercise but felt that the instruction of the exercise could have been much clearer.  We had decided not to use specific numbers, but almost all responses said we should have included the actual numbers.
• Most people felt that there was not enough connection to the real world.  Our real world examples were not convincing enough.
• Lastly, there were mixed views on how engaging the presentation actually was.  This seemed to be pretty split amongst the respondents.

My self reflection on the lesson was that I was disappointed and felt I could have done better.  We should have really had a more real world example up front.  The model would have been a good way to explain the surface area, but I did think it ended up being a distraction.  Also, the lack of concrete measurements for the hands on exercise was a mistake. In summary, it was a good learning experience.  We worked well as a team.

Team Lesson Plan

Surface Area of Prisms Hong Jiang, Edward Liao, Donna Braaten
Section	What	Time	Materials
Bridge	Show prisms.  Define what a prism is. Pose problem of how much paint, chocolate or gold it would take to cover.  What dimension do we need?  Intro to Surface Area and why you might need it.	2	- 3 large unfoldable shapes - prisms (rectangular, circular, triangular)
Leaning Objectives	- Each student will learn: -- how to calculate the surface area of a prism (rectangular, circular and triangular), building on past knowledge of area -- practical applications of measuring surface area -- to breakdown any shape to simplest known areas to be measured	1
Teaching Objectives	- Get all students involved. - Complete exercise with closing remarks	0
Pretest	- Review measurements of area including units	1
Participatory learning / Lecture	After opening (hook and learning objectives) - Open up each shape to break down shape to set of simple shapes for each - Split into groups to build a structure --- put wooden manipulative on the tables --- ask each group to build a village/structure (<= 10 shapes) --- have them calculate the service area - formula, then we provide dimensions	8	- wooden manipulatives - dimensions of the shapes
Post-test	Review their group work and hear their explanations	2
Summary and Wrap up	Review the key concepts: - break down the shape - add the areas	1

Chapters 2 and 3 from Thinking Mathematically by John Mason

In the first two chapters ("Phases of Work" and "Responses to being Stuck") of Thinking Mathematically, a model for approaching problems is presented.  The model has three main parts: Entry, Attack and Review.   The most important parts of the model are the Entry and the Review with the least importance on the Attack phase.

I find the phased approach very interesting, as the natural tendency is to jump into a problem and spend most of the time on the Attack phase.  The book really emphasizes that people/students should not rush into a problem.  The author also provides rubric words (or simple key words) to keep in mind during that phase.  I would use this in my teaching by spending more upfront time on really framing and understanding the problem.  We have done this within our 342 class and I have found it very useful.  Spending more time on the entry is critical to help students really get their head around a problem.  This includes identifying what they know and what they want.  This then leads to them introducing a possible solution at which time they are ready to attack.

In addition to spending more time and discussion on the entry, students should also relish in the “getting suck part”.  For until a student is really stuck and has given the problem lots of thought, s/he cannot truly appreciate the solution once found.  I like the idea of one must get stuck before they can learn.  I plan to emphasize this in the classroom.  The only difficult I see is that within a classroom of 30 students, each may go through these phases at different times.  I will need to pay extra attention to ensure that each phase is given the appropriate amount of time as needed by each student.  A difficult task!

Dare to Divide by Zero

·      Dare to Divide by Zero

We were curious about the outcome, but were discouraged to go there
We continued …

We approached from the right, which led to a never-ending launch
We continued …


We approached from the left, but embarked upon an endless descent
We continued …

The closer we got, the further away we became
We continued …

“Impossible”, they said.
We continued …

“There is no meaning”, they said,
We continued ...

“It is not allowed”, they said,
We continued …

“There is no answer”, they said,
We continued …

For how will there ever be an answer, if we do not continue to search for one?
We continue!

Timed Writing - 3 minutes per word (raw)

Divide
Divide is the action word for division.  Mathematically, divide means to split things into parts.  Parts can be any number.  We can divide into 2, 3, 4.  Like cutting a pie of 8 slices, we have divided the pie into 8ths.  When dividing only in half, this can also imply a separation even to the point of opposition.  Like two sides to an argument.  Our opinions are divided.  Nations or polictical views are often divided.  As dividion can be more than just separating into 2, people can also be divided into 3 camps or opinions.  The most opposite parts of division are 2 where the views of one group are diorectly against the other.  Typically, I thi k mathemtaically when it is a higher number, but more perwsonally when it is only dovided into 2 or 3. Divided into anything over 4 seems more about equality than separatation.  To divded into 2, often implies opposition.  Divison can have a very negative connotation, but can also have a very fair, positive connocation.

Zero
Zero often has a negative connotation.  I immeidately go to the movie Holes (great movie by the way) where one of the main characters were nicknamed Zero - which meant amounting to nothing.  there are also many gestures that show Zero which is often equated to Loser, again, you will never amount to anything.  Even the negative connotation of Ground Zero, mean start building from the very bottom.  Zero is the pure mathemtical sense does not really carry a negative connotation.  It is more of a neutral one.  It is not positive or negative, but neutral.  Much like a neutron in physics.  Neutral, in that case, can be seems as indifferent, but not in a negative or positive way.  I cannot think of an application of Zero which is actually positive.  It is typically only negative implocation or neutral.  You could think of balance but it is rare.

Response to the Simmt Article

"Citizenship Education in the Context of School Mathematics" by Elaine Simmt (University of Alberta)


I found this article very inspiring.  Not only did it explain the significance of math but it also gave practical examples of how to make it happen.


"Mathematics as part of the human experience".  What a wonderful concept.  The author explains the very basics of needing math to understand our current world, but also goes further to say that it can shape the world.  I had not considered the shaping before.  Though I have not seen it yet, previews for the Facebook movie suggest that there was an "equation" which served as the basis for the whole creation of the Facebook social network.  The significance of math in our society is huge.  We do live in a very math-oriented world, always looking for ways to model reality to better understand it and predict the future.


In my career as a Computer Scientist, I worked for a company that created Business Intelligence software, mainly software to help model the business.  There was a strong desire to quantify everything such that it could be measured and compared/improved over time.  We had graphs for many things in an attempt to measure quality and efficiency, a life long learning process.


What I particularly enjoyed about this article, is that the author left us with 3 key suggestions to help us realize this potential.

1. Use variable entry problems - great to understand what is really going on and be able to apply it elsewhere.
2. Demand for explanation - one must focus on discovering the truth and not just finding a right answer.
3. Conversation - this goes beyond monologue and dialogue but represents an active, exchange of ideas that generates many connections.

In short, this is by far the best article I have read since entering this program.