Reflection on Micro Teaching

Our presentation went fairly well but we definitely needed to watch our timing more closely. We did not anticipate how long it could actually take to introduce our problem, however we could have done a slightly better job at being a bit clearer during this portion of the lesson. The use of some higher level mathematical language/terminology could have been avoided and would have helped us to be a bit faster as we wouldn't have needed to explain our language. Aside from this the rest of the presentation was much clearer and methodical.

Our opening question was a good question to help introduce variables without introducing the ever scary x and y, as well it was a fun relatable question which got people engaged and involved. In terms of how the actual presentation went we tried to use the smart board in order to give us more writing space, however this was not such a good idea because of its physical situation in the classroom, it is very hard to see from the opposite side of the room.

Because we were short on time and did not get to all of our activities there was a lack of variety in activities and not a lot of student participation, even though we did have other participatory and engaging activities planned. Judging from the feedback received, this was a decent lesson with the potential to be a really nice lesson had we managed our time more efficiently and been able to complete all of our planned activities.

Systems of Linear Equations Lesson Plan

Lesson Plan for System of Linear Equations (342)

	What	How	Who
Bridge	There are situations in our daily life where we want to know two (any number) unknown pieces of information at the same time, (I will give you an example) and as long as you can find two (any number) independent relationships between these two (any number) unknowns, you can set up a system of equations and find the exact value of these unknowns.	Explain this, using words, and perhaps giving more examples.	Niyaz
Learning Objectives	Students should be able to: 1.    Solve a system of linear equations with two variables using the method of substitution. 2.   Understand the different types of solutions that can arise	We’ll mention that we will cover this information and will make sure that they will be able to do this by the end of the lesson.
Teaching Objectives	To get students to develop the algorithm for themselves	We’ll give suggestions, but  expect them to come up with each step	Shannon
Pretest	Asking questions while showing how to go about solving the given example.		All of us.
Participatory learning	1.    Giving them different examples to practice their knowledge. 2.   When doing the first example together, get students to go up to the board to do each step	1.    Handing out the examples to all of them. 2.   When they give a suggestion, invite them up to the board to show us what they mean
Post-Test	1.    Asking them questions as they are solving their given problems. 2.   Get them to share their solutions with the class. 3.   Engage in a discussion about the different types of solutions		All of us. 2 & 3 will be Matt
Summary	Telling the students what they have learned today.		Shannon will summarize part way through. Matt again at the end (about the different types of solutions)

Thinking Mathematically: Ch 2-3

These two chapters provided a relatively interesting look at the thinking process going on behind solving problems, difficult or simple. It made me stop and think about the way in which I myself approach a problem and how I think about, the steps I take.

I liked the breakdown into the three different phases, however this may work well for me but it brings about the question of how will I model this approach and this thinking to my students? Or, how will I encourage them to realize that this three phase method can help them to further their learning and understanding of mathematics?

For myself, these questions do not have straight forward answers as I reflect on my thinking processes, especially when it comes to the final phase of reviewing. The way in which this final phase is described in these two chapters makes it seem like a lot of work, almost as much work as the actual problem, this can make it cumbersome, redundant, and tiresome. Thus, for myself, even though I think that it is important to review and go over and reflect, I believe that there can be too much emphasis put on review, making the work seem long and boring and then it becomes very unmotivating for students and they will quickly loose interest.

One other point that was touched on in these two chapters was that it is good, and OK, to get and be stuck on a problem. This greatly encourages deeper understanding and makes solving the problem more satisfying in the end. I also feel that it is important to acknowledge that we all get stuck at times and to make it known to our students as well.

Mathematical Poetry

Worked Up                                                                                                                                 Nothing                                                                                   
                                                                                              My calculatrice reads ERROR.
                                                                                                       Input: 8 ÷ 0 = ERROR
                                                                                              Input: 137 ÷ 0 = ERROR
                                                                                     Input: 49 436 ÷ 0 = ERROR
                                                                            Input: anything ÷ 0 = ERROR 
What is the meaning of this error?
Zero groups of eight are zero
But split eight into zero and ERROR!
How can eight be split into zero groups?

An algebraic absurdity
Spurious proofs
An operation of derangement
Infinite possibilities

Division by zero
∞ ?

Timed Writing: Divide and Zero

Divide, split, multiply, decide/decision, torn in two, make sets out of a number of objects of either equal or different sizes, group things together, fractions, I don't know, remainder, portions, rations.

Zero, nothing, poor, fail, cannot divide by, empty, out of gas so to speak, either literally or figuratively, null, zilch, void, break even with, get par, something that I would be extremely happy to do once in my life.

Response to Simmt Article

It may not always be so obvious, but mathematics is very relevant and apparent in many facets of today's society. I have never before thought of the connection between developing "informed, active and critical citizens" and mathematics education and how important it is to have an understanding of mathematics and the societal structures that are heavily based on math. As math teachers we should have in mind these ideas of developing responsible citizens by challenging our students to become critical thinkers. After reading this article and thinking about it, I realize that mathematics is not something that is separate and abstract, but it is something that is very involved. Math is based in logical reasoning's and it is this ability, to think logically, which is necessary for citizens to have and use to make well informed decisions in society. From this, it is important to note that the overall answer is not always the most important aspect of mathematics, but rather it is also the method, or process, which needs to be emphasized and looked at in order to expand our knowledge and to gain the ability solve problems which we are unfamiliar with. Being able to solve these unfamiliar problems, or to come up with something that is sensible can be a very rewarding experience. This feeling can be a useful tool to inspire students to do mathematics and to breakdown misconceptions around mathematics.

Battleground Schools: Mathematics Education

This article presents a brief and concise history of mathematics education from the early 1900's to the present and outlines, and speculates at, the issues, problems, opposing views and struggles that surround math as a subject. 

There are three distinct phases to note throughout the past century, the Progressive Reform (1910-40's), The New Math (1960's),  and the "Math Wars" NCTM Standards Reform (1990's to present), as well as two main stances, progressive and conservative. A progressive view of mathematics is one of a better understanding and less memorization of strict rules, theorems and algorithms for the sake of fluency, which is more of a conservative approach. I personally believe that fluency will come with a deeper understanding of mathematics and that the two are not separate.
 
The reasons for the three aforementioned phases of math education throughout the past century are political reasons, i.e. the push for The New Math curriculum during the 1960's was largely influenced by the Cold War era and the Space Race, but they are also due to a number of reasons around a sort of math phobia.

Many people hear the word "math" and cringe. Some reasons for this sort of a reaction given in the article, which I agree with, are because math is hard, only a select elite need to know it, there is no shame felt for not knowing, or "liking" math, and there seems to be a stigma attached to  those that like math, that they are socially awkward. Also, it is important to note that there is a flaw with our  school system, in that teachers are teaching subjects that they are not really qualified to teach, such as mathematics. By allowing teachers to teach math when they are not qualified to, it is very likely that they may impart a view on their students which adds to this fear of math and a very destructive cycle is formed.

I don't feel that teaching math from either a progressive or a conservative stance really matters, but there should be a mixture of the both and I would probably lean a little towards the progressive. However, whatever way the teacher wants to teach the given curriculum they should have a good knowledge of math and they should have the goal of making math interesting for their students to break down the math phobia which is so prevalent in North American society.