Timed Writing Reflection

This is an interesting activity that I hadn’t expected to encounter in the math class. This activity would be able to provide students with different perspectives of approaching mathematics. It doesn’t always have to be the numbers! I would possibly use this activity as a warm up in the beginning of the class, in order to get students get started. It would also be nice to use this as a conclusion activity when there is some time left at the end of the class. It would help students review the materials that they learned and also provide the teacher some feedbacks.

Some of the weaknesses of the activity may be that writing in a specific amount of time could be a difficult task for the ESL students or students whose English is weak. In addition, it could also be difficult for those who need a longer time to process their thoughts when they are writing. They may have a difficult time with writing in such a short time limit. Also, some students may not find the relationship between this exercise and learning mathematics and lose interests in the activity.

Dividing by Zero

Dividing by zero is impossible as I was told when I was young.

The same thing I tell the students when they ask

As hard as it may be to explain why,

They need to know the reason behind it

Explain the non-reversibility

Or even better,

Argue by the limit

So that they can understand

Microteaching reflection

Our group taught variables and equations from the grade 8 curriculum. I realized how short 15 minutes can be as we were trying to be responsive to all of the students’ comments and questions. Overall, I thought that our group’s microteaching had both strengths and weaknesses that I can learn from.

Things that went well:
We were told that we had a good opening question, which grabbed the students’ attentions. We had a good intro to variables and solving equations, using the problem solving approach. Our peers thought that we taught at the appropriate level of the class and provided good examples to work with. We used the board space efficiently and had good visuals. Some of the peers also commented that we reacted well to the changes (ie. Students’ questions and comments). Also, many people liked the idea of the last exercise but we didn’t have enough time to work on it.

Areas that need work:
The major mistake we made was leaving out one of the tables during our discussion. I was occupied by the other two tables and I didn’t make any eye contact with the people on the other side. Another major problem was the time management. I spent too much time on going over the example on the board and we were running short on time. This left too little time for one of my group members to do her part, which was leading the class activity. We also need to work on coming up with better context for the word problems and make connection to other areas of life.

Lesson Plan-Microteaching

MAED 314 Assignment #2

Microteaching Lesson PlanGroup: 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: A rectangle with an unknown side length

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

Citizenship Education in the Context of School Mathematics

In the paper, “Citizenship Education in the Context of School Mathematics,” Simmit write about the critical role mathematics education plays in the development of democratic citizens. For many people, it is not easy to make the connection between the mathematics education and the citizenship education, because they do not realize that our society fundamentally operates on mathematical ideas. As Simmit says in his paper, nearly everything we encounter in the world is linked with some numbers. Then, why do many people not able to see mathematics as the fundamental basis of our everyday lives? Simmit blames this partly on the teachers and the current mathematics education system, in which students are led to view mathematics as a set of facts that they need to get right answers to. In order to overcome these challenges, Simmit suggests three ways of teaching, which are posing problems, the demand for explanation, and mathematical conversations.

In order to educate the students to become active and democratic citizens, they would need to build on their problem solving skills that they can apply in their lives. Thus, rather than teaching the students with facts and concepts only, I would try to help them have a relational understanding of mathematics. Using the “What-If-Not” strategies that I read from the book, “Art of Problem Posing”, I will help the students to look at the mathematical concepts from different perspectives and get them used to posing problems of their own. Also, I will engage the students in my classroom through various methods so that they can participate in the class discussion actively. Through the interactions between the students and the teacher, as well as the interactions within the students, they will be able to learn how to communicate their ideas effectively with each other. Through these ways, I hope to encourage my students to learn useful skills that they can use in their lives and become active and well-informed citizens.

Art of Problem Posing- Reflection 2

This section of the book dealt with the problem posing technique, using the “What-if Not” question. Asking “What-If-Not” questions are technique that can help us to look at the concepts and theorems in different perspectives and give us chance to obtain the broader sense of the phenomenon. By cycling through the five levels of the “What-If-Not” strategy, one can get in to the habit of posing creative problems and strive to learn more than just the given theorem. However, “What-If-not” technique may not always be beneficial. For some people, asking too many ambiguous questions may make them extremely confusing. It is important that the person understands the given theorem to certain extend, before posing so many different questions. Also, following each of the steps may be difficult and time-consuming. Even if we pose problems after “What-If-Not-ing”, it could be difficult to analyze the problem well enough to come to a useful conclusion. Thus, it may take some practice of using this strategy, in order to use it in the most effective way.

I think that the “What-If-Not” strategy can be very useful for the next week’s microteaching in helping students develop a problem solving technique. For my microteaching, I will first introduce my topic to the class and give brief explanations of the theorems. Then, I will have the class to look at the concepts from different perspectives and come up with some interesting questions. Following the steps of the “WIN” strategy, we will carefully analyze the problem to lead the class to understand the theorems better. (Our group didn’t pick a topic yet, so it’s hard to answer this question in detail..)

"The Art of Problem Posing" -Reflection

In the book, “The Art of Problem Posing”, Brown and Walter stress the importance of posing the problems. In many articles that we have read for this class, we were told how important it is to use the quality problems to create effective learning environments for the students. As a result, I have been thinking only about how to select good problem sets and how to use those problems successfully. Thus, this new emphasis on creating the question came to me as a new area of mathematics. By following the authors’ examples, I realized that the questions that we usually ask our students are limited to the instrumental understanding. By giving the students the chance to freely come up with their own ideas, we help them to extend the idea of mathematics into their real life. Students can start to think from different perspectives and approach the topic in various ways, gaining a deeper understanding of the concept. One thing that I thought was very interesting was the question that can provoke the historical background of the mathematical concepts. I have never thought that the historical portion is important in Mathematics. However, by asking “what might have encouraged people to come up with some concepts?”, students seek to have a relational understanding of the concept. I think that the idea of posing abstract and challenging questions can be a very helpful tool in teaching mathematics and I hope to gain better insights into it through this book.

Letters from the future students

Dear friend

I have just finished my grade 12 and I am going to start studying in the university next year. My favourite class during my high school years was the Calculus class. I particularly liked this class because I had a great teacher who has been teaching the course for 10 years. Her name is Ms. Kim and she is just an expert in mathematics. She was a very energetic and compassionate teacher who always tried to make the class more interesting for the students. I had always thought that the math is a boring subject. But, after taking her course, I realized how I fun mathematics can be! She was always open for questions and helped us after classes if we didn't understand some concepts. I really recommend that you take her class!

Dear Ms. Kim

I'm sending this e-mail because I want to let you know that I have not enjoyed my time in your class. In all my previous math classes, the teachers presented imporartant concepts and gave me some time to apply what we learned by working on the problems. Howevaer, what you taught us was all problem solving skill, which I don't think is useful at all. I need to learn the rules and concepts so that I can do well on my exams. Working on the problem solving questions just confused me and I didn't learn anything from your class.

Writing these two letters gave me a chance to think about what kind of teacher I want to be. I want to become an enthusiastic teacher who cares about each and every student in my classes. I want to create a fun and engaging learning environment for all. At the same time, I am afraid that there will be students who do not like my teaching style and do not gain much knowledge from my lessons. I hope that I can keep all of these in my mind even after 10 years of teaching. I will always try to remind myself of my goals as a teacher and become conscious of my concerns.

DVD reflection

In the video, Dave Hewitt illustrates a very creative way of teaching mathematics. Oftentimes, mathematics teachers tend to tell the students the new topic in the beginning of the class and present the materials. However, Dave Hewitt attempts to approach mathematics in different ways. He first starts out his class by helping students to visualize the new topic. For example, he uses a stick to point sequence of spots around the wall to visualize the number sequence. By counting back and forth, he allows the students to build up the pattern and helps them understand the relationships between subtraction and addition. He started out with the simple counting and then built up to the more complex system. What I really liked about his lesson was that he had the full attention from his students through the whole class. By not giving away the topic too easily and allowing them to work toward the topic, he made the lesson interesting and made the students eager to find out what he would do next. Also, the second part of the video showed how he approached algebra as if he was playing a guessing game with the students. This is much more interesting than just having the students work on a bunch of problems on paper. Again, he grabbed the students’ attention right from the beginning and kept them engaged in developing their problem skills.