MAED 314A Unit Plan: Grade 9 - Chapter 9 Inequalities

My Lesson Plan

Assignment #3: Math Project

Grade 8 Math Project: The Number Devil
(1) Reader’s Theatre, Poster, Puzzle
We have chosen to do a reader’s theatre on Chapter 6 (pg. 112 – 116). As for the assigned presentation, we have a rough sketch of a poster focused on the chapter reading along with how to challenge the puzzle given at the end of chapter 6.

(2) Looking from the Teacher’s Perspectives
From the Number Devil, we saw that the project had various potential benefits. By incorporating the use of the reader’s theatre, the students have the opportunity to express their creativity. By acting out the mathematics, students may “own” the concept and ideas more, leading to a much more meaningful learning experience. The project also has its benefits as it is an exciting and new idea and furthermore, the Number Devil makes a great introduction to topics that may never be covered in class much. The book itself also provides a different perspective on mathematics and may help the students see that math is not purely number crunching. The reader’s theatre and poster project is a decentralized project that encourages independent thinking and encourages teamwork in the math environment- which is not often seen. The project could also reach out to other students aside from the classroom as well. The students in the math class could put on the play for the rest of the student body. By doing so, it would promote mathematical learning to an even larger audience.

On the other hand, there are a few restrictions on the Number Devil project as well. If not introduced well or if the students are not interested in the project, they could end up merely reading the book word for word without thinking too much for the mathematics. Furthermore, the purpose the author was to introduce concepts, so in return, the material is not covered in depth. If students do not get involved in the material, it could easily change from a meaningful learning activity to one that is geared towards fixed-mindedness. This is because there is not much higher learning and bloom’s taxonomy involved in the story. Another disadvantage to this project is that most of the material in the Number Devil does not cover the IRP. The project may also be very time consuming as well.

To modify this project, our group members have considered extending the reader’s theatre. Perhaps the each group can read a chapter and using the concepts found in that chapter, they could create their own script. By doing so, they could change the context of the story, however, the ideas introduced in the Number Devil would be present. This would promote the students skills in analyzing and synthesizing. Looking at Chapter 6 in particular, students can extend the project by answering higher level Bloom’s taxonomy questions such as “Would the numbers still be considered Bonacci numbers if we start at something instead of 1?”


(3) Our Designed Math Project
Grade level:
Grade 9 enriched

Purpose:
To further expand/extend students’ mathematical experience and adding their creativity into it. Through the activity, they will also be teaching their classmates about what kind of math they’re incorporating in the game.

Description:
Create a math board game that incorporates grade 9 math into the game. They must include rules and strategies for the game. Write up of what math concept they’re using and how it applies to the game.

Length of time in/out of class:
2 weeks in groups of 3 or 4 (with 2-3 classes dedicated to working on them and asking teacher questions)

What students are required to produce:
One board game for 2 actual days of fun (game days)!

Marking Criteria:
1) Peer assessment PMI (for extra mark):
-If it’s fun
-If they learn/practice any mathematical concepts during the game

2) Teacher Rubric

Problem Solving Using 2 Column Approach

How many Black Fridays the 13 are there in a year?
Maximum number of Black Fridays in a year is 3!!!

Short Practicum Reflection

Killarney Secondary School is my practicum school. It is said to be the biggest school in Vancouver with approximately 2000 students of various backgrounds. The school has very supportive administrative and staffs. It is a great school for me to develop professionally. I definitely have a great two short weeks experience and I am looking forward to go back there for my long practicum. During my two weeks there, I have been observing different classes. Every class has its own unique culture and every teacher has his/her own style.
Some of my most memorable experiences:
- I have been in a tutorial/help class for junior students who need extra support with school work. In one class, I have tried to help this girl with her Math homework (adding/subtracting positive and negative numbers). But the girl wouldn’t have me teaching her. Instead, she was being difficult and kept saying her teacher taught it a better way and what she’s doing was right (which wasn’t). The teacher responsible there then talked to her and asked her to work on other subjects since she didn’t like any of our methods.
- I have been in this Social Studies 11 class. The teacher has an interactive activity for the class on the topic of capitalism. She put big poster papers each with a question relating to the topic around in the classroom on the desks. Students sitting in the group then had 3 minutes to answer each question and kept rotating to the next question. The teacher then would walk around and even join the small group discussion. At the end of the class, the teacher then posed an open question for everyone to answer in a 5 minutes quick write. I think I can use this format as an unit test review for my class.

Time Writing Exercise Reflection

At the beginning of the timed writing, I have struggled in putting what I know into words. This makes me wonder why am I being so restrictive on giving the correct/precise mathematical meaning. I shouldn't be scared in writing what I know. Math should allow for mistakes so that everyone can actually enjoy it and have fun with it.

This is a good activity for students to not be afraid of what they know about mathematics and to put it down into words (Personally when I have put my thoughts into words, I was able to understand the topic more). It allows students to be expressive which would provide a more dynamic classroom making the topic more fun to learn. Students themselves might also have a better mathematical understanding as they have the opportunity learning the concepts and be creative with them. This would be a good warm/wrap up activity where students can review and make connection of the concepts taught.

However, there are definitely some limits with this activity. Students of different learning needs might not be able to participate in this activity (ESL background, learning disability, etc). Also, students might not be able to see that big picture of how this exercise is related to their mathematical learning.

"Division by Zero"

Timed Free Writing

We have this in class writing exercise where we are timed to write anything that we can think of on 'division' and 'zero'. Here's the poem that I have written from this exercise.

Zero is a special number.
I know that it will be cold if it's at zero degree.
I know that my phone bill will be up if I have zero minutes left in my cellphone plan.
I know that my bank account will be sad at the end of each month as I need to pay my bills so that I have a zero balance.
I know that there is zero gravity in space but I wish I can experience what is that like.

Zero doesn't seem to be such a bad number.
But I want to know who has invented zero?
Do you have the problem about diving a zero?
If you have a zero, how do you divide nothing?
Don't you agree with me then that it is bad have zero.

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).

.....................................................................................

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!

Sir Ken Robinson UBC Terry Talk

We have had the opportunity to go on a class field trip to Sir Ken Robinson's talk hosted by UBC Terry Project. I really enjoy the talk and Sir Ken Robinson is superb. There are laughter throughout the whole talk. In one short hour, Sir Ken Robinson has talked about several ideas and shares a few stories which bring some light to the subject about education. After reading the article, "Battleground School", I have learned that the education system of today is formed in the industrialized period. Sir Ken Robinson states that we are in a time of revolution and we need to update our ideas. Sir Ken Robinson makes us question what education is and the education system we have today does not encourage creativity. The system makes people lose their creativity as a college degree is defined to success in life. In that sense I do agree with Sir Ken Robinson. We limit students' potential and we are not providing that ideal environment for them to grow (from the Death Valley story). If everyone can combine his/her talent and passion, everyone can be an expert of a field. Think deeply how this can affect the community of the world as a whole! Sir Ken Robinson has concluded by saying that we need to 'transform' not 'reform' our education system. He says to make that transformation, education should be personalized. Everyone has the power of imagination and education should provide that ideal condition for the imagination to flourish.

Dave Hewitt's Pedagogy Reflection

Dave Hewitt in the film has clearly stated about how he wants to change the traditional lecture format in teaching Mathematics. His lesson plan is indeed very interesting. Personally, I have been taught the traditional way of note-taking and lectures. I like the traditional structure in my Math classes. Hence, it really opens my eyes in regards of having creativity with Mathematics. I am impressed with how Mr. Hewitt introduces the concept of integers and algebra using non-traditional approach. He is able to teach his from very simple basics to complex; adding layers and complexity within a lesson. I also find that students or I should say everyone is good in finding the pattern. Once they find the pattern, the concept is easy to grasp. It shows that you don't necessary have to give out note and teach/lecture about the "rule". The concept might still be hard for some people to grasp. But in learning as a group as a whole and encourage them to self-problem solve seems more effective. Furthermore, I also appreciate that Mr. Hewitt uses some of the traditional teaching method, ie. he has his students work on a sheet of problems right after the lesson. This shows that it's possible to teach both in the traditional and constructivist methods. In addition, he is able to keep his students engage and participate throughout his lesson which also allows him to manage the class quite effectively. Mr. Hewitt's lesson has lots of good quality of a good lesson which is good to model perhaps in my practicum. His lesson is indeed eye-opening.

MAED 314A: Battleground Schools Summary & Reflection

Battles over Mathematics education in North America has been fought over and over again ever since 1900. These conflicts are based on the dichotomies of conservative and progressive views. Gerofsky has summarized that the debate in Mathematics teaching and learning is related to the broader arguments on the nature and location of knowledge, the democratization of education, and views of authority and obedience.
Complicating these conflicts is that Math education is generally not well-received by the public. Gerofsky has stated that the math-phobic attitudes from the different interest groups of parents, administrators, policymakers, and teachers have contributed to a conservative Mathematics education in North American public school systems. However, there have been three major movements in the twentieth-century: the Progressivist, the New Math, and the Math Wars based on NCTM Standards reforms that are influential to the Mathematics education today. During the Progressive reform movement from 1910-1940, traditional teaching is criticized to be ‘meaningless memorized procedures’. In addition, with the change in societal structures, the reform for a meaningful mathematics curriculum is inevitable. One of the representative figures of this era would be John Dewey who believes in allowing students to do math would help them in actually gaining knowledge. Dewey’s work has definitely refocused the emphasis in the curriculum for more independent and problem-solving skills. Moving onward to 1960, the New Math movement has been brought about by the scientific competition with the Soviet Union. With the pressure of competing, the curriculum has drastic changes in the goal of better preparing American children to excel in scientific fields. The change however is controversial and has ended by 1970. Lastly, there is the Math Wars movement that has begun in 1990s and continued to present. By mid-1980s, National Council of Teachers of Mathematics (NCTM) has set its own standards and there are changes made to follow the standards. Nonetheless, due to the different interest groups and their views on mathematics curriculum and teaching methods the ‘Math War’ does not seem to end anytime soon.
After reading this article, I definitely have a better understanding over the history of Mathematics education and movements. I do not know about these conflicts before and how they have contributed to the curriculum we have today in the school systems. The subject of education is a heated debate for all the different interest groups. Everyone has his or her own opinions on what teaching and learning should be. Incorporating political and religious agendas, it is wisely said that it is indeed a never-ending battle. These conflicts are essential to the movements we have had over the past century. But Mathematics education is still relatively quite conservative. It seems impossible to reach a consensus to make everyone happy. Nonetheless, we should continue to make changes for the better.

MAED 314A Assignment 1 Reflection

Personally, I really like this assignment as I get to hear about other people’s experience with Math. The responses are some as what I would expect but I also found some other opinions to be interesting. In short, it was great to have the whole class report back their findings and to learn from this experience.
As expected, that common theme we have found is that students find that Math ‘boring’. Many of the students don’t seem to be interested in pursuing any fields related to Math. A lot of them feel that Math is just like a tool useful to have for other opportunity in life. I find that to be something we all need to work on as to show our students you can do many great things with Math. You are taking Math not because the school curriculum requires you to do so. Another interesting point is how some students prefer the old-fashioned note and lecture format. Despite that students find Math to be boring they still like how teachers feed them the required curriculum through the traditional method. This raises the question of performance and understanding. What can we do to balance that is definitely not going to be easy. But gladly, some students did say that they like to have brain challenges and puzzles to have ‘fun’ in Math classes. In addition, another common theme is that students like their teachers who can use some humor in the class and who really care about them. Personally, I prefer to have funny teachers as well. I know I will need to work on my humor.
Before I have decided to enroll in the Education program, I have had done my research talking with my former teachers. But it’s definitely a whole different mind-set once I have become a teacher candidate in the program. I am grateful of other teachers’ advice for us. It’s important to be patient and to care sincerely about our students. Student can tell if you care about them or not and thus, you wouldn’t need to worry about not being respected. I also learn that it’s okay to make mistakes and not to stress out if a lesson plan goes wrong. It is not hard to teach the curriculum. But the difficult part is to teach a class of students with different levels of interest, understanding, and learning needs. In short, I find this assignment provides a great insight into becoming a teacher. There is still the challenge in teaching but I feel less intimated by it as it really comes down to how deeply we care for our students.

MAED 314A Assignment 1: Open Conversation

5 Burning Questions for High School Math Teacher & Students - Group Summary
We have chosen to pose similar questions for the 3 math students and 1 math teacher that we interviewed (even though we have asked more than 5 questions).
The Math teacher we interviewed has been teaching for over 10 years and now mainly teaches the senior math courses, generally Grades 11 and 12. He is well known among students and faculty and is quite popular within the school environment; many of his former students still keep in touch with him and visit with him surprisingly regularly.
Our student interviewees happened to run in the grades and we were able to have one A student in Gr. 12 (graded at approximately 90 – 95% across all her high school math courses), one B student in Gr.12 (regularly scores approximately 75 – 80% on tests) and a C student in Gr. 10 (who wasn’t terribly concerned with her math scores). It seems presumptuous and slightly disheartening to be classifying our students by their scores, but we thought that it might help to add a sense of significance to their attitudes towards math. All 3 students are in the Principles of Mathematics stream and have no interests to seriously pursue Math after high school.
The interview with our C-student was shorter compared to the others and was therefore fairly stilted. She informed us that she was only studying math because it was required and would probably have stopped if it had been optional except that her parents are making her. She also indicated that she didn’t like math because ‘[she wasn’t] good at it’ and that she had a peer tutor to get her through the course. However, there are times where she does enjoy math classes and those are the ‘rare’ times when she feels like she understands a concept. The classes she does enjoy are Music and Science because she ‘gets it’.
Our B-student is a former D-student whose marks were forcibly pulled up after she decided to do math by distance with a private tutor. She indicated that she had been having trouble understanding concepts brought up in class and was too afraid of looking stupid to acknowledge her confusions in class; having a tutor allows her to ask questions immediately and one-on-one which greatly increases her confidence and ultimately her skills. She said that she was constantly unsure of herself and felt lost in the big classroom where many of her peers understood the concepts and it just made her ‘feel dumb’. She anticipates taking math in a higher level institution only if the program she chose required a math prerequisite. She seems to support the idea of some group work within mathematics to add to the lectures to allow her some time to listen to her peers’ ideas, commenting that ‘math just seems so lonely’.
The Grade 12 student who had been pulling an A-grade had a slightly different take on her math class than I had expected. Her attitude towards math was not a question of like or dislike but of competition. This was a class that she felt she could compete in and makes an effort to do so. She likes having other people consider her to be good at it and so she works hard for her grade. She is taking Math because she feels that it is an essential skill for people to have and that it provides her with the option of taking sciences in post-secondary. What surprised me was her attitude towards rectifying confusion during math lectures. She said that she was too intimidated to ask questions during class and would often just relegate her attention to copying down the notes so she could review on her own or ask her teacher after class. According to her, math class would be more accessible if teachers would take small breaks during class to diverge attention elsewhere for a short while. This would allow her time to digest the information and refresh her mind so she could return to the lectures with a renewed concentration. Her ideal math teacher would be kind, understanding and fun.
The interview we had with the teacher was equally informative, if not more so. He likes to teach from a relational standpoint and stresses that a student who aces tests is not the same as the student who really understands the material. It was important for us that he did not think that it was a challenge to get through the curriculum in the proposed timeline. In fact, he thought that there was a lot of time and the challenges of teaching were at a far more personal level. He warned us to ensure we are friendly towards our students but not be their friends because teachers are still in a position of authority and must have their students respect them as such. He also advised us to take our practicum seriously and treat it like a ‘real job’, not just as a ‘practice run’.
Our group really enjoyed this project and found that the varied and sometimes surprising answers to our questions helped us to be more aware of how everyone else views math. It is easy, as students who had relatively successful high school math class experiences, to forget the challenges that others may have. We expect that this will help us in our practicum and future teaching posts to be aware of the difficulties some of our students face and to encourage them and adjust our teaching accordingly.

MAED 314A: Using Research to Analyse, Inform, and Assess Changes in Instruction

The article grabs my attention in wanting to find out how research and theory based practices can be used to improve actual class instruction. As I read on, I realize that it is Robinson’s own ‘self-analysis’ of her teaching methods. Robinson is admirable in being proactive in becoming the teacher she visions for herself to be and in how she desires to improve herself to benefit her students. I also appreciate how she studies hers teaching methods by honest examination of herself as in videotaping herself in class. Despite that she finds out the ‘devastating reality’ that she is the type of ‘lecture-driven’ teacher, she now has the opportunity to improve her instructional practice. It definitely takes a lot of courage to self analyze and to find faults. But it is through the self-examination that enables Robinson to devise an action plan to improve her teaching methods. I will definitely keep it in mind the importance of self-assessment in my future teaching career after reading her personal experience. In addition, a study by Kazemi and Stipek find that in order to have active learning environment, it is essential to orient “students toward learning rather than toward performance”. Generally, one’s understanding level is assessed by performance in examination and the percentage grades. I think it is not easy to keep students in focusing on learning first as they ultimately want to achieve the actual performance.
Robin’s research changes her instructional method from lecture based to focus more on students learning and teaching on group activities. I wonder if all topics of Mathematics can be taught in such approach and if this type of participatory learning would work in younger grades. I wish that I can find out more about some of Robinson’s actual lesson plans that are effective in involving the students to be active in learning.

My Two Most Memorable Math Teachers

When I have been given with this timed-writing, I immediate recall which two most memorable Math teachers I am going to talk about. I will call them Ms. A and Mr. B respectively. When I start thinking of my experience in their classes, I realize they are somehow very similar yet different as well in their teaching methods. They are similar as both are very responsible of their work in teaching. They are organized in their lesson plans in teaching the required curriculum.
However, Ms. A is known to have a mono-tone in the classes. She has a perfect set of note that she would teach off from by giving out the note in the overhead. The note in class is perfect with a mixed level of difficulty of examples relating to a particular lesson. Some people do not like her standard teaching method and some people like her class because it is clear what they have to do to perform in getting the grade. On the other hand, Mr. B has a set of note of his own as well. But he does not present his note in the super neat format as Ms. A. In a typical Mr. B’s class, his note is break into sections of concepts that we are learning for the day. I appreciate how he can explain concepts in the simplest way that we can understand. After teaching the concept, he would make up questions that are not perfect textbook-like problems. For example, in learning derivative, he would teach the basics and he would combine the basics giving us a problem such as finding the derivative of 5(X+5)^2X (just say, I don’t remember exactly what the problem is). He challenges us to think by first giving us the basic tools we would need. Mr. B has a great sense of humour and has no problem of making fun of himself which makes the class fun to go to. In addition, he has no problem admitting that he has done something wrong or missed writing something on the board. In addition, Mr. B is very involved with the student body and the school.
Both Ms. A and Mr. B have influenced me greatly in what teaching can be like. Teachers have huge responsibility and are role models that students look upon. In becoming a teacher, I definitely need to recognize such important role. From what I have experienced personally, I know great teachers are not just about giving perfect notes and teaching the material. You also have to care for your students and be involved with the school community. I have been fortunate to have great teachers whom I look up to. To become a teacher myself, I will keep it in mind to work on getting respect from my students.

Self & Peer Assessment of My First Lesson Plan

My Wonderful Peers found that my lesson plan of how to throw a Frisbee disc has:
- a good bridge: Ultimate Trivia
- clear objective
- good hands-on activity and engaging, pairing up in practice the throws
- a good structure but a bit too jumpy and the conclusion or wrap part needs more connection
- lastly i spoke a little too fast at the end

Self-Assessment:
- I have enthusiasm for the topic
- I think the trivia was good as my peers did not know that much about some facts of Ultimate
- I might have focus a bit too much on explaining about how to play Ultimate - might be a bit off my
objective of how to throw a disc/peers was a bit distracted when I was explaining
I also need to work on not to speed through the lesson; I tend to be too simplified in my instructions
I should start by pretending my students know nothing about the subject matter
I definitely notice that I speak fast towards the end of my lesson and I need to work on ending the
lesson
- I was lucky that I get to see Amelia in presenting the same topic
- I notice that she was more at ease and did a superb job in explaining the basic throws
- One thing I really like about her participatory structure is that she taught everyone one throw and let
them have the opportunity to practice it right away then brought everyone back to learn the next
type of throw - that was what I needed, not to rush through the actual teaching part
- Other than that, I have had great peers who all seem happy to learn how to throw a disc
I also get the chance to learn something else, too

My First Lesson Plan - BOOPPPS!

The objective of this lesson plan is to experience the BOOPPPS planning procedure!
This is not a Math lesson plan. I have decided to have a lesson on throwing a Frisbee.

Bridge:
First, I am going to have an Ultimate Trivia!

1. What is the standard weight for a Frisbee disc?
2. What is the pro-level Vancouver men's team name?
3. What does VUL stand for?

I will briefly explain how an Ultimate game is played. Ultimate is easy to pick up. If you can catch a ball, you can definitely catch a disc. So you have gotten the throwing skills down, it's even better. But note to everyone, ultimate welcomes all different skill levels of players!

Teaching Objectives:
-To share my love of the sport
-To demonstrate clearly the how to hold a disc
-To engage all students in learning the the basic throws

Learning Objectives:
Hopefully by the end of my teaching, students will....
-gain some 'Ultimate' knowledge
-have interest in the sport
-be able to throw either the backhand and forehand throw

Pre-Test:
Have students show me their throws!

Participatory:
-Demonstrate how to throw a disc
-After demonstration, separate students into 2 groups and get them to throw a disc to each other

Post-Test:
Have students show me their throws after the practice throws!
If time permitted, we will do a CHEER!

Summary:
-I will ask for comment and feedback about this activity.
-I will also encourage the students to learn more about the sport.

MAED 314A: Relational Understanding and Instrumental Understanding Reflection

MAED 314A: Relational Understanding and Instrumental Understanding Reflection
During the class, we have had a brief discussion about the relational and instrumental understanding in Mathematics. We have talked about the pros and cons to the two ways in teaching Mathematics. When I have started reading the article, “Relational Understanding and Instrumental Understanding”, I notice that Skemp is a firm believer in relational understanding. Reflecting back to the days I have started learning Mathematics, instrumental understanding has definitely helped me in learning at first.
By the end when I have read the whole article, I appreciate Skemp’s effort in presenting these two types of understanding by giving really good analogy. It makes me think deeply why instrumental understanding has been so effective for me. I realize that relational understanding is also part of the reason. For me, the instrumental methods are effective in learning the basic foundation; the relational methods allow for strong problem-solving skills. Therefore, I believe both methods are essential in Mathematics education.
5 Favorite quotes/statements from the article
1) Page 2. “You may think you understand, but you don’t really.” Skemp has made me ponder the meaning of ‘understand’. Is it ‘understand’ if a student can do a set of similar problems correct; but not a set of slightly modified problems?

2) Page 8, Number 2 in Devil’s Advocate. The point about students who described themselves as “thickos”; they need good marks to build up confidence. This speaks to me because I have experienced this all through high school and in university. Instrumental methods are definitely effective for achieving the desired good performance on tests.

3) Page 13. “At present most teachers have to learn from their own mistakes”. This is one of the advices that I appreciate. As a new teacher, lesson plans do not usually go well as planned. But we can definitely learn from our mistakes and try to improve it. The idea to gather all the teaching experience/knowledge for use by new teachers is great but it will not be that applicable if the actual experience is missing.

4) Page 14. “A person with a set of fixed plans can find his way from a certain set of starting points to a certain set of goals”.” Skemp’s analogy of getting to places strongly presents the importance of relational understanding. Everyone needs to be able to think critically. If we were so inflexible to change, then the world would be problematic.

5) Page 15. “The more complete a pupil’s schema, the greater his feeling of confidence in his own ability to find new ways of ‘getting there’ without outside help.” What a teacher can teach is limited; the students need to work hard themselves to achieve their own success. As a teacher, we can only present them the tools they need.

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