Reflections on Microteaching

It was a fun and good experience to work in a team to microteach.  Each member had new ideas and a different perspective to contribute.    We learnt from each other as well.   For example, Min used magnetic fridge magnet strips to tape onto cardboard to make pieces that would stick on the whiteboard.   What a cool idea!   Erica had puzzle pieces cut out for showing that the squares forming the 3 sides of the triangle have a relationship.

Regarding our lesson,  general feedback told us that the activities were fun and generally enjoyed (except by the team that was slowest at finishing the puzzle --oops, sorry!).  We learnt that it is difficult to predict how long an activity will take, especially if that activity involves the students.    Our puzzle game went by much faster than anticipated.      It would be have been good to provide an overview of where this lesson fits into the unit plan,  so students can see a big picture.    For example,  we can mention that in the next class, we will continue this lesson to look at ancient and modern day applications of the pythagoreas theorem (our lesson only focussed on introducing the theorem).  

It is also difficult to judge the students "prior" knowledge when you jump into a lesson like this.   Life as a substitute teacher?   This challenge affects how much time we spend explaining things, and how deep we go into it etc.

Was it useful experience?  Yes!
I will use these activities again if I have a chance to teach this topic, and know how to refine the lesson to make it more effective.   I can't wait to try it out again, in real life!

Microteaching Lesson Plan - Pythagorean Theorem

Group Members: Carly Orr, Min Jeong Kim, Erica Huang

Bridge/Pretest	Review of different types of triangle and right triangles * Using a geoboard, review definition of a triangle:  3 points, 3 lines * Ask if someone can define a “right triangle”.   * Ask one volunteer to come up, blindfold, and move one peg to create a “right triangle”. * Review:  right triangle 90 deg. angle. Today we will focus on the right triangle, and learn an important property about it.	3min	Boundary Board Game (geoboard)
Learning Objective(s)	PLO from Math 8 IRP: develop and apply the Pythagorean theorem to solve problems model and explain the Pythagorean theorem concretely, pictorially, or using technology explain, using examples, that the Pythagorean theorem applies only to right triangles determine whether or not a given triangle is a right triangle by applying the Pythagorean theorem determine the measure of the third side of a right triangle, given the measures of the other two sides, to solve a given problem solve a given problem that involves Pythagorean triples Note: We will only have time to address 1, 4, 5 but will mention that this only works for right triangles.
Teaching Objective(s)	To get everyone involved in group activities
Participation	* put the class into 3 teams * each groups gets 6 pieces (1 green, 5 blue) of construction paper and an instruction sheet * Race 1: put 5 pieces of blue paper to form one square (the side of the square is the same as the long side of the green right triangle) * Race 2: use the same 5 pieces to form two squares (the sides of the squares are the same as the two legs of the green right triangle) * what does it mean? (areas of 2 smaller squares add up to the big square) * compare the triangles each team has – they are different in size	6 min	puzzle pieces, instructions
Post-test/Summary	* Explanation of the Pythagorean theorem: First summarize what students learned in the previous activity, then start using examples with real numbers (eg. triangle with sides 3, 4, 5), and finally shows the formula and introduce the theorem. * Introduction of Pythagorean triples: students work on the worksheet individually, where they use the Pythagorean theorem to find out length of the missing side of a right triangle given two sides.	6 min	visual displays of squares and a triangle  as well as list of perfect squares for 1-20 worksheet for Pythagorean triples

Thinking Mathematically

Why do so many students have difficulties with word problems?

These two chapters interestingly and adequately enlightens me about why students often get frustrated when first attempting to tackle a problem, especially the word problem.    Often it is because we have not spent enough time to actually understand the problem.     This sounds funny, but it's true!   The entry step can be broken down into writing down:   "What I know",  "What I want to find",  and "What can I introduce".    Writing, and perhaps diagramming, the answers to these questions,   will help understand the problem,  and guide towards how we can now attack the problem.     When students are STUCK, we can guide them back to ask these entry questions,  breaking down the problem,  and eliminating some of the the fear and frustrations.   Spending sufficient time in the entry stage, gives students the confidence to continue, and reach the "got it!" moment.   This habit of dwelling and returning to re-examine the problem again helps to shape and guide our thinking.    We want students to not waste time going down unnecessary paths, and consequently feeling discouraged.

As teachers,  we should emphasize to students the importance of thoroughly understanding the problem first.   Once this groundwork is done,  solving word problems will not be as ominous a task.

Poem: Division By Zero

I am the forbidden fruit in the garden of math

perfectly shaped without start or end

simple, elegant, curious

                                                                    infinitely tempting

But no one dares to eat me as I don't really exist

in fact I'm actually not on the graph

irreversible, inconsistent, untraceable

                                                                    eternally troubling

I am "division by zero" and life is not easy for me

even the smartest of computers think I'm crazy

undefined,  ERROR,  out of bounds

                                                                    forever elusive

Continue your discussions of philosophy and math

but please oh please don't lose sleep over me

one day you may understand 

                                                                    I await patiently

Timed Writing

Divide.  share, split, separate,  break into separate parts,  this word can be used in sharing food with your children or siblings, like dividing a piece of cake, or dividing a room,  In math, we use divide to manipulate numbers, a process to separate a number into equal portions. there is a divisor, and a dividend, and in some cases, a remainder.    there is short division, and long division, which is more complicated and involved.   long division is hard to do and remember for those of us who have been using calculators and computers for so long.   division can also refer to difference in opinions in a family,  or a company, or a group, where the people are not agreeing and there are different groups separated on a topic.  there is no in between, you are divided,  there is no unity, you are separated in where you stand on the topic.  happens in politics,  or controversial issues.   usually a negative thing in business.

Zero.   this is a mathematical representation of a quantity of nothing.   it is in the centre of the number line, and is the middle point between negative and positive numbers.   Zero is nothing,  and is written like a big "O" when you first learn how to write it.    Zero is the name of some laundry detergent for washing clothes in cold water, I think.   Zero is the number we start counting from, sometimes, especially when doing a countdown.    I think zero is a beautiful number.    In computer science, zero sometimes is written with a line diagonally across it so as to not confuse it with the letter O.   Sometimes in our phone numbers,  or credit card or other numbers, people will call zero an O, but most will understand it is number not the letter.

Simmt Article Thoughts

This article was down-to-earth and interesting.

Math is integral to so many aspects of our lives as citizens.     Some goals for math education include:  gaining personal satisfaction in knowing math;  participating in a cultural heritage of mathematics;   applying mathematical thinking and problem solving in the workplace in all professions;   and mathematics for the scientific and technical fields.    Acquiring quantitative literacy is part of everyone's day to day living in our world.

There are strategies for teaching that can potentially inhibit citizenship education.  If it is taught as a rigid emphasis on right or wrong, or a set of facts, skill, or process, then the student may not be able to transfer their knowledge to other realms of applications with similar parameters.    On the other hand, there are strategies that can help promote the usage of math beyond the classroom and traditional scope of the subject.    For example,  using  varying ways of posing  a question, involving students in explaining and seeking diverse solutions,  and in constant engaging of in mathematical conversations.