MAED 314 Assignment #2 - Reflection

The 15 minutes microteaching is a very simplified version of an actual lesson. My group and I have tried to teach the lesson of solving for the unknowns of grade eight mathematics. One area that I think we did well is that we have a clear pictorial illustration of sample word problems and we have tried to lead the class by working together using a clear detailed step-by-step approach to get the solution. However, I do admit that we did not have a variety of participatory activities or relating this to subject areas other than Mathematics(we did want to implicitly allow them realize how useful is it to be able to solve unknowns in our daily life).

Some comments that we have received from our peers:
-classroom management issues: we might need to play the stern teacher's role when students don't pay attention
-more clear instruction with our last activity: many liked the last activity, but felt that they didn't have clear enough instruction as in making their "own" word problem
-suggested shared and equal amount of group work: many commented that Prem did not get to speak much (due to our limited time)
-need to consider the whole class: the group of people sitting by the door felt left out as we seem to be focusing on the groups who are actively responding to our lesson; we should work on getting everyone to participate in class
-need to consider the various types of students with different mathematics understanding: our lesson might be "boring" for those gifted students or not enough background information and support for students with exceptionality

MAED 314 Assignment #2 - Microteaching Lesson Plan

Group: Elaine, Alice, Prem

Topic:
Math 8 Variables & Equations
model and solve problems using linear equations of the form

Bridge:
Simple Word Problem:
Say on Sunday you went shopping, you bought 5 video games and in total you have spent $100. How much is it per game?

Take a minute to think........how did you come up with your answer?

Pre-Test:
The area of the rectangle is 35. What is the length of the unknown side?

Teaching Objective:
-To effectively teach the concept of solving linear equations
-To develop student's problem-solving/thinking ability
-To relate the Mathematics of the lesson to real-life applications
-To allow students working in groups and to encourage group learning
-To help students take responsibility of their learning by asking them to design a word problem using the concept learned

Learning Objective:
-Students will be able to solve for the unknowns of the linear equations by the end of the lesson
-Students will be able to design a real-life problem using the concepts they have learned
-Students will have the opportunity to present their learning and also to learn from each other

Participatory:
We will teach the PLO's on solving.
5 word problems to teach the equations.

Eqn 1: ax=b (introduced in Bridge)

Eqn 2: x/a=b, a is not zero
Agnes has a bag of candies. She distributed the candies equally to her five friends. It turned out that each of her friends received 3 candies. How many candies were in Agnes' bag in the beginning?

Eqn 3: ax+b=c
Find three consecutive integers whose sum is 258.

Eqn 4: x/a+b=c
Peter's teacher gave him a container full of 140 bricks.
One-sixth of the bricks were red and there were 20 blue bricks. How many red bricks were there?

Eqn 5: a(x+b)=c

Ask how they got their answers and do people have different methods of solving the problem.

Post-Test:
Make your own word problem (group) and present it with solutions to everyone.

Summary:
-We will adjust the amount of teaching accordingly under the time constrain
(we might not be able to teach all 5 main types of solving for linear equations)
-We want our students to understand the importance of the lesson and how applicable it is to our daily life
-We want to encourage students to have different methods of solving a problem
-We want our students to participate in their own learning

Reflection on Mathematics' Role in Citizenship Education

Elaine Simmit has presented the importance of Mathematics education in developing informed and active citizens of the world. Personally, I have taken the 'relationship between mathematics and society' for granted. Thinking about it, I realize that our society is indeed obsessed in quantifying everything with numbers from weather forecast, sports statistics, and even as simple as buying and selling goods. Mathematics is definitely the foundation of our society today. Hence, as mathematics educators, we have a great responsibility in not just teaching the mathematics but also educating for active participation in the world.
To achieve the goal of citizenship education, Simmit suggests us to look into our practices. According to Simmit, the following 3 strategies would potentially conflict with our goal:

1. Mathematics is a "set of facts, skills and processes".
2. Mathematics are facts and fact.
3. Mathematics is either right or wrong.

I agree with Simmit that such teaching would prohibit our students in becoming individuals with critical thinking ability. If Mathematics is taught with focus in computation and getting the right answer, students lose the ability to question and to think. Thus the question, "why do we have to learn this" should be encouraged in our classrooms. Simmit has also suggested the following 3 strategies that would promote our goal of citizenship education:

1. Variable-entry prompts and investigations: problem posing.
2. The Demand for Explanation
3. Mathematical Conversations

I can see how important it is to incorporate these 3 strategies into my teaching. In encouraging our students to problem posing, not only do they strengthen their mathematics understanding, they also gain the ability to negotiate and evaluate the solutions. This is applicable to daily activity that we often have to deal with when difficult situation arises. In addition, it should be emphasized with our students that math is not just about giving the right answer. They should realize that they need to be able to demand and to give explanation. Only by doing so, can they become independent and responsible individual in the society who can think critically. Lastly, I hope to have an open environment where everyone feels comfortable in expressing their opinions. I believe that open communication and interaction can further everyone's learning experience.

We all understand the great responsibility that teachers have. Simmit however, has further the concept by presenting that mathematics education is essential to citizenship education. As a mathematics teacher candidate, I would strive for teaching my students of various abilities and interest in mathematics to become active participants of today's world. I would keep in mind not to just teach in terms of curriculum but also to teach in terms of being active citizens and empowering them to make positive changes in the world. It is definitely not an easy task but nothing is impossible if we set our minds to.

Reflection from "The Art of Problem Posing"

Pg.33-65

I agree with the idea that we often 'take the given for granted'. With a given problem, we usually focus on the given information. It is important that we can use whatever information we can get from the problem to help us to solve the problem. But as the author has demonstrated, by doing that we often limit ourselves in problem solving.

I understand that if we could teach our students to think independently, they would be able to have a better understanding of the taught concepts. In the context of Mathematics teaching, many students would prefer the traditional lecturing style due to academic performance pressure. Are we teaching our students the learning as memorizing and getting good grades?

I do like the author's approach of 3 levels of problem posing: attributes listing, asking "What if not attribtes", and problem asking. I can see that I incorporate even one or two levels in my lesson.

It is a good idea to first ask students to brainstorm all they know about a topic. This can help in making connections of ideas learned. Then we can ask the "What if not attributes" questions. This would definitely encourage/trigger for different thinking about a concept/problem. I also think this can help in extending the concepts.

However, not all lesson plans can be taught using the WIN approach. If for example the lesson is to teach algebraic manipulation, WIN strategies wouldn't be effective. In addition, students can be overwhelmed by the cylcing of new questions making them more confused with the extra problems. We also have to keep in mind that there's the time and curriculum constrains and it can be easily off topics with the WIN method.

10 Comments/Questions from "The Art of Problem Posing"

Reading response from the book "The Art of Problem Posing"

change the traditional method of teachers giving problems for students to solve(instead have a shift in the control of posing problems)
-What can we do to effectively encourage students to ask themselves "helpful" questions in order to solve problems? Sometimes I have troubles asking myself the "right questions" to solve a hard problem.

-What would this be like in an actual class of 30 students with all different skills and interest levels in Mathematics (including the time and curriculum constraints)? It might be interesting for students who like Math but it definitely would frustrate students with lower level of understandings

-Using x^2+y^2=z^2, the author demonstrates how we limit ourselves in learning by only interested in just finding the answer. I agree we definitely need to ask ourselves the significance behind the problem.

-The questions generated from the given x^2+y^2=z^2 are impressive. I can see that some questions are helpful in further extending the concepts and while some others provide space to play around with the concept. I also like the possible response of "it is the only thing I remember about geometry". I feel this questioning process can be an honest dialogue with yourself which in return can help organizing all the thoughts that have arise.

-But what can we do to stay on topic and to achieve the purpose of these questioning is to learn the concept desired?

-I think it's useful to have a list of guiding questions to ask students. This helps students to develop independent problem-solving ability. It is also a good assessment tool to use in checking student's understanding.

-In addition, all the related questions that we can ask about a given problem can help us make connections between concepts.

-From personal experience, it is essential to know how to rephrase a question or ask in another way. A lot of times I find that students need to be asked in another way to fully understand the question.

QuickWrite October 2, 2009

Scenario:
Fast forward the time 10 years ahead. Put yourself in your future students' position and write in any format to the teacher you have become in 10 years.

Student who Loves me:
Hi, Ms. Weng! You are still teaching? Are the kids behaving in your class? I still remember the first day when I sat in your class and how you were telling us about to respect nerds who rule the world. Even though you have said that you are not a nerd, I said to myself, "Gee! My Math teacher is a nerd." But I don't know if you know this, I end up loving Math so much that I have become the "nerd" as well. Nerds ROCK!!

Student who Hates me:
Ms. Weng, I never think that Math is fun. I understand that you want to help us in learning new concepts by using different teaching techniques. But I feel like a lab rat being tested/experimented. Math is just not my thing and I am terrible at it.


I hope to have good relationship with my students and also to make Math fun for them.
I fear that by being open to other methods of teaching might in turn make Math even more frustrating for students who have other interests/passions.

Nerdy Cheesy Love Lines

There are these "Weekly Engineering Love Lines" inside the UBC Engineers' Handbook which I find to be really Nerdy and Cute(&cheesy).
I think some of the lines are good to use in a class.

-If I am sin^2(theta) you must be cos^2(theta) because together we are 1.
-Our love is like dividing by zero, you cannot define it.
-My love for you is a monotonically increasing unbounded function.
-You're so gneiss, I'll never take you for granite.
-I less than three you! (I <3 Y)
-You're hotter than a Bunsen burner set to full power!
-"You want to see me solve a quadratic?"
-I'm overheating because you're stuck in my head like an infinite loop.
-You're so hot you denature my proteins.
-Are you the square root of 2? I feel irrational when I'm around you.
-Forget Hydrogen you're my Number 1 element.
-You must be an asymptote, because I just find myself getting closer and closer to
you.
-If they made you in Java, you'd be the object of my desire.
-You are the ln(e).

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John Mali "What Teahcers Make"

Mike in my EDUC 311/316 class has done a wonderful job reading John Mali's poem today.
It's a must see video!