Second Microteching (with Feda and Namrat)

Feedback from students:

The majority of comments on our microteching were very positive, most students thought that our lesson was well structured and paced and they didn't have difficulty following through the steps. They found the lesson engaging and liked the participatory activity. One student mentioned that our cardboard rectangles were more useful during problem solving than a diagram on the white board. A few students commented that the intoduction of the lesson was not grade appropriate, it was too simple for grade nines. One student commented that we have to pay attention to the whole group when explaining a concept and make sure that students at the back can hear it too. One student didn't find our example to real life applications
very relevant.

My conclusion of the lesson:

I think our lesson was well planned and structured, and most of the feedback we got was very positive. The hardest part for me was the lesson plan, and to think of an activity that is both engaging and age appropriate. Now that I had my first teaching experience in high school, I can disagree with the students who thought that the lesson was too easy for grade nines. I found the feedback very valuable since it gave me the opportunity to think of the areas of my teching that need to be improved. I liked both the instruction part and working with a small group. Comments regarding connections with real life applications made me think of other ways of enagaging students in learning activities. If they see a reason behind the concept, students will be more motivated to learn it.

Thinking Mathematically (Chapters 2 and 3)

For most of us, whose brains are mathematically wired, it seems obvious and natural to break down any problem solving question to the three phases: Entry, Attack, and Review. Most students, on the other hand, are rushing to figure out the solution right away, without even getting to the end of the question. And this is a problem because not reading the problem careful enough, they lose important information about it. By rereading the problem, and asking the question: “What do I KNOW?”, the students will be able to gather important information and find better approaches to solve it.
I think this first phase is crucial and more important than the other two, because without fully understanding the problem students won’t be able to get to the solution therefore it is worth spending extra time with it.
The second phase, the Attack, (What do I WANT?) has its importance too: you cannot solve a problem if you don't know what do you want to get out of the problem and soon might find yourself in a totally different direction.
The Reflection phase, ( What can I INTRODUCE?) is an opportunity for students to come up with different ways of solving a problem and maybe adding to it in complexity.

Poem About Zero

Most say that I am a Zero, a Nothing,
But think about it my friend,
The less you have of me the poorer you are
The more the richer.

I’m not proud of the fact
That bankers use and misuse me,
And, the debt they created
Is measured by a long sequence of me.

It is them, bankers, who
Divide and conquer,
Not mathematicians who say
That dividing by zero is infinity.

Timed Writing

Divide
there are language barriers that divide new immigrants from the native population
divide and conquer
share, divide equally,
share thoughts
mathematics, basic numeracy skill, i can' think of anythink else right now
bankers don't divide equally with the rest of us, dividing with zero doesn't make sense, the earth is divided into northern and souther hemispheres, division is the opposite of multiplication, negative divided by negative is positive, negative divided by positive is negative and vice versa,

Zero

Nothing, emptiness, NIL, hollow, number, word, group of letters, infinity, black hole, space, you cannot divide with zero; some have zero, some have all; for some zero is not a number; in mathematics it has its rightful space, zero money is no money, Mathematicians think that dividing with zero gives you infinity, other people say that dividing with zero is not allowed, disallowed value,zero is the middle of the number line, zero degree celsius is freezing cold, zero divided by any number is zero, there is no negative or positive zero- zero is signless,

Response to the "Citizenship Education in the Context of School Mathematics" article

I totally agree with Elaine Simmt, that mathematics education is crucial in the development of informed, active and critical citizens in today's society.
The study of mathematics cannot be resumed to the simple aquisition of knowledge, but it must focus on developing a way of thinking trough a permanent training of the mind. Thus, learning mathematics results in developing capacities that are necessary and useful in the every day practical life.

Learning mathematics results in logical thinking and reasoning, it creates the capacity of the individual to analyze and make well-thought decisions. Mathematics is an exercise of the mind, it is a preparation for all challenges of life, profession and career. Therefore, mathematical knowledge is essential and crucial in order for an individual to be active and critical participant in our society.

It is very important that us, future teachers, make our students love mathematics just as much they love their toys, bikes, computers or video games. By teaching them how to decipher the secrets of mathematics they can reach limits which, otherwise would seem unattainable. Our role is to convince our students that by learning mathematics they can have a better understanding of the world and they have the power to shape their future. They have the choice of becoming critical thinkers and decide for themselves rather than becoming frustrated, obedient and thoughtless consumers.