ASSIGNMENT #4

UNIT PLAN RATIONALE

https://docs1.google.com/document/d/1c3oVCm5yRKxtacKMr5j3KgcohyiCqAh5r11KfFbbu8Q/edit?hl=en#

UNIT PLAN OVERVIEW

https://docs0.google.com/document/d/1_w68PMeBzHFhz5aT1V2MQkgpSvxupt9aAq-NquTzCWM/edit?hl=en#

LESSON PLANS
https://docs.google.com/document/d/1mKx3TydrV4-wzG3orea__w6kylNbua1fifaxWGMd_SE/edit?hl=en#

UNIT PROJECT
https://docs2.google.com/document/d/1FVDm53tEQSNUWJlJJtn_lwiduMLO3LN1uo74Qp0VPBA/edit?hl=en#

MATH PROJECT - NUMBER DEVIL

Team Members: Namrat, Paramjeet, Erica

ANALYSIS

We chose Susan’s project for “The Number Devil”, which is a very interesting novel to read. Erica already read the novel, so she gave us the idea about the novel. Also, she told us which chapters are more interesting. We read those chapters and decided to work on the chapter which deals with “unreasonable numbers” (irrational numbers).

While doing the project, we find it very interesting, especially the part which deals with the play. We find that this project can arouse students’ interest very easily and has something to offer for all kinds of learners. Some students may like to read, and they have a novel to read. Some students are more artistic, and they have posters to make. Some may like drama and acting, they can write script and act. So, this project covers a variety of interests.

Some of the potential benefits are as listed below:

• Students get to explore numbers in a fun way.
• Reader’s theatre encourages students to be creative.
• The use of words such as rutabaga (square root) and hopping (taking exponents), is interesting (though as teachers we will need to address this and introduce the correct terms).
• Group poster can be appealing for visual learners and can be used for class decoration.
• It will change class routine.

This project has enough for everyone in the class. However, there are some points need to be considered. One of the important factors is the level of concepts. There are some topics in the novel which grade 8 students may not understand. Also, it is hard to provide the books for whole class. The project requires a set of books for whole class or lots of photocopying. To overcome this problem, we can give students photocopies of the chapters which are suitable for grade 8.

While doing the project, we had a difficulty in finding the puzzle, so we are not sure how difficult it would be for grade 8 students. The puzzle we thought of is asking students how to convert a repeating decimal (such as  0.264264264...) to a faction, but that is because we have the math knowledge. Also, this project is time consuming. It can take two classes for all groups to present.

In addition, some students may be shy and do not like acting. Although it is good to encourage them to try out everything, they may not be comfortable in front of the class. A student may feel embarrassed, if he/she is not a good actor. To overcome this problem, we thought that we can ask students to tape video of their play and present it in the class.

During the presentations, students may not pay attention. There should be some kind of strategy to keep them on task. For example, we can ask students for peer evaluation.

PROJECT: The Number Devil (Grade 10)

Purpose: To encourage students to explore mathematical ideas in a creative way

Descriptions: Students will be working in groups of four. Each group will read one chapter of the book as a sample. Then each group will pick one topic from their Math 10 course and write a script on it. They will do theatre presentation for about 5-6 minutes or can play their recorded video. Secondly, they will make a group poster showing their mathematical idea. The poster has to be informative and attractive. Finally, they will leave the class with a question or a puzzle related to their topic to think over. Students will be evaluating their peers during the presentation portion.

Length of Time: The project will span 3 classes (around 100 minutes). In the first class, the students will be given 25 minutes to read a chapter from The Number Devil and discuss which topic they are interested in presenting with their group members. In the second class, the students will be given 25 minutes to work on the project (discussion, group poster, scripts, etc). In the third class, students will be given around 50 minutes, with the assumption that there will be 7 groups. Students are expected to spend about 2 hours outside of class.

Deliverable:

• video or role play
• group poster
• puzzle to share with the class

Rubric for the New Project (50 marks):

	Not Yet Meeting Expectations	Meets Expectations	Exceeds Expectations	Grade
Content	Does not illustrate the mathematical concept or illustrates it incorrectly	Illustrates the mathematical concept with clarity	Displays deep understanding of the mathematical concept	/15
Presentation (role play in class or video)	1. Lack clarity 2. Over 7 minutes or shorter than 4 minutes	1. Generally clear 2. On-Time	1. Exceptionally Clear 2. On-Time	/15
Group Poster	1. Few details about the mathematical idea 2. Little effort spent on design of the poster 3. Text not eligible 4. Does not include references	1. Informative 2. Original 3. Attractive 4. References included	1. Exceptionally informative 2. Exceptionally Attractive 3. Original 4. References included	/15
Peer Evaluation				/5

RESPONSE TO SELTER'S ARTICLE ON CREATIVITY, FLEXIBILITY, ADAPTIVITY, AND STRATEGY USE IN MATHEMATICS

     After reading this article, I felt that I had already read this article. The ideas in this article were not new. This article talks about importance of creativity, adaptivity, flexibility and strategy use in mathematics. "Thinking Mathematically", by John mason gives us the same ideas but in terms of Phases, namely - The Entry Phase, The Attack Phase, and The Review Phase. The entry phase is comparable to creativity, attack phase is comparable to flexibility and adaptivity, the third phase is comparable to strategy use in mathematics.
     To solve math problems accurately and efficiently, students need to develop flexibility—they need to learn multiple strategies, and how to choose among them in tackling a particular problem. But what is the best way to help students acquire this knowledge and skill? If we want our students to achieve these skills, we should not tell them which method is to be chosen to deal with the problem. Otherwise it will act as resistor in the student’s minds and they will not be able to invent strategies. But at the same time, this does not mean that we should leave the students on their own. We should act as a guide who instead of telling the answers, asks questions in way that students should think what they are doing and why. This will help all students especially those who are struggling in mathematics. This is a big leap from just solving the problems, without understanding the logic behind it. Making students creative is not a single day process. It will take time, but once they adapt it, they will be able to use appropriate strategies that are creatively developed  for flexibly selected.   

TWO COLUMN PROBLEM SOLVING

SQUARE TAKE - AWAY ( P. 194)

Take a rectangular piece of paper and remove from it the largest possible square. Repeat the process with the left over rectangle. What different things can happen. Can you predict when they will happen?

SOLUTION:-

WORD PROBLEM ANALYSIS

WORD PROBLEM - grade8 :
  Silver's Cleaners decided to raise the price of dry cleaning a sports coat from $4.00 to $5.00. The same percentage increase was applied to dry cleaning a jacket. The old cost of dry cleaning a jacket was $10.00. What is the new cost of dry cleaning a jacket?


Is it practical?
I think it is practical.

Let x = percent increase

Can it be solved with the given info?
Yes.

 4.00 * x = 5.00
 x = 5.00/4.00 * 100% = 125%
10.00 * 125% = $12.50 is the new cost of cleaning a jacket

Can it be interpreted in more than one way?

No. The language used is simple and realistic.

Would the kids be able to interpret it as intended?

Kids may not be able to interpret it as intended.Students with out thinking anymore can come up with answer as $11. This solutions is abvious for them to come up with because they can misinterpret the word "same" as same price increase instead of paying attention on same percemt increase. If the price increase is from $4 to $5 then  for $10 it will be $11.

Is there anything strange about it?
I didnot found any thing strange about the problem.

How would you change it?
I will rephrase ther problem so that can understand it. 

Silver's Cleaners decided to raise the price of dry cleaning a sports coat from $4.00 to $5.00. The old cost of dry cleaning a jacket was $10.00. What is the new cost of dry cleaning a jacket, if the price increase in terms of percentage remains same.

PRACTICUM STORIES

 Before I Joined this program, was told by so many people that there are lot more behaviour issues with students here in comparison to east part of the world. When I was observing the classes, I found it true for about 40%. Students were really nice when the lesson was being delivered by their respective teachers. So, I thought it would not be hard for me to do the teaching.

I had a very bad experience the very first day I delivered my lessons. Every thing went wrong from the very begining. The font of the transparencies was not big enough that students could read. One by one every student started questioning and I lost the class control. I found it difficult to work on overhead and looking back to see if my writing is visible to students. I got nervous as was being observed by my faculty advisor as well. I was very upset that day. I did not give up. I worked on my lesson plan. Practiced to write on overhead and constantly looking back to see if my writing is visible to students.

I prepared new lesson for both math and science and delivered them with more confidence and with a much improved class room management. I gained my confidence back.

I did learned that as a new teacher, one should practice their lessons prior delivering in the class. Students need perfection. Lesson plans should have to be made in a way that students should be kept on task to avoid any behaviour issues.

REFLECTION ON GROUP MICRO TEACHING

PEER REFLECTION: Most of the peers found the hook very interesting. According to them we successfully related the Counting Principle to every day life. Some were not clear about the learning objective. Few of the students found second example (ice cream) little difficult to understand. Many of the peers do suggested that time was not properly managed. They need more time to understand the ice example. Two of the peers suggested that question given for home assignment wasmuch more difficult that examples disscussed in class.

SELF REFLECTION: After doing our micro teaching, I realized that learning objectives should be in small chunks. We should have discussed only counting principle and not the permutation and combination. It would have been better if would have selected one cone with one topping, instead of one cone with two toppings. It was a big leap from first example.The example given for home work was actually planned to be explained in class, but as we run out of time so asked them to do as home work. But, I will consider time as one of the most important factor while preparing any lesson plans in future.

At the end, I found microteaching a meaningful activity as I came to know about the areas that need improvement.

Lesson Plan On Teaching The Fundamental Counting Principle

	Content to be Covered	Time spent	Materials	Modifications
Bridges	Asking whether teacher candidates have ever felt what they learn in math class they don't actually use in real life	30 seconds	Paper-made outfits and ice cream cones and toppings
Learning Objective	To be able to use the  Counting Principle in everyday life
Teaching Objective	To teach grade 12 students the essence of the Counting Principle
Pretest	Ask students whether they know the Counting Principle	30 seconds
Participatory Learning	Get the students in one group and work together to solve the outfit and ice-cream problems	9 minutes
Post-test	Write out problems relative to Counting Principle on board and get students to solve	3 minutes
Summary & Wrap-up	Then restate the key components of the Counting Principle	2 minute

Group Members: Paramjeet, Zhi Song and Mandeep

RESPONSE TO CH 2 & 3 OF THINKING MATHEMATICALLY

I not only enjoyed reading these two chapters but found them very rich in terms of motivation and information. Reading of these articles made me to redo my approaches towards mathematical problems. The idea of moving from simple to complex or abstract to concrete is really helpful in having a better understanding of the problems. The concept of breaking the problems in small chunks would definitely help students to solve the problems. This will give more space to students to work on the problems rather than just memorizing the problem. I do not remember of doing reflection or thinking of extensions where the result can be applied very often in my career so far, may be twice in ten times. Nobody is perfect to solve the problems in one go. It is important for us being teachers to build a positive attitude in students if they get stuck in problems. All the examples are important as each is full of different ideas. I found Leap Frogs example very useful while explaining the probability.

Undoubtedly, with this approach students will have meaningful learning.

DIVIDE ZERO

zero is a magic number
It can added,subtracted or multiplied,
with a number,
but it cannot divide a number.

zero is amazing,
we can divide every number,
and get a lower value,
but its the zero that cannot be divided.
and its always as a whole.

Although zero means nothing,
but it exists at the center,
almost everywhere.

RAW MATERIAL

DIVIDE
LESS HALF PARTITION DIVIDE AND RULE DIVIDE IN GROUPS SPLIT DISTRIBUTE GIVE TAKEN PARTIALLY MINE ACHIEVE LESS POLITICS USE RANDOMLY TO SUCCEED

ZERO
IMPORTANT BASE
ANYTHING CAN BE ADDED GIVES SAME
MULTIPLIED WITH ANY NUMBER GIVES ZERO
NOTHING LEFT
WHOLE
MULTIPLY OR DIVIDE GIVES ZERO
EARTH IS ZERO
FACE IS ZERO
EVERY WHERE
NO ONE
ALONE

Response to Elaine Simmt's article

Simmt’s article discusses about the value or importance of mathematics in different fields. It is very important for our society to know about the practical applications of mathematics. Many people are using the mathematics in their daily life, but are unaware that they are using mathematics. I liked Simmt’s emphasis on “ school mathematics is much more than simply teaching them to think quantitavely or statistically. Students should be educated in a way that begins to understand and critique the formatting power of mathematics. Simmt, also gave some useful strategies to promote active and critical participation in society. I found it very useful to use conversation as mode of dialogue, during teaching mathematics. As, it will give space to accommodate different ideas of the other people. This kind of interaction will have the potential for the community to discuss and solve any kind of problems that arise in the community. I would definitely use the conversation during teaching.

GREATEST HOPES AND FEARS

I enjoyed at the same time learned that we are the ones responsible for students future.We should give our best for the bright future of students. I hope that i will become their role model and leave them with sweet memories. AS i did my studies overseas, so I am totally new to BC education system. I am worried about if i would be able to adjust with this new system.

BATTLE GROUND SCHOOLS: MATHEMATICS EDUCATION

This article describes about the ongoing battle between the conservatists and progressivists about mathematics education in North America since 1900. Conservatists think it should be taught as absorbing and applying the ideas whereas progressivists think that mathematics should be taught through inquiry so that it should make sense or they can relate with real world. Many battles took place between the conservatists and progressivists in order to improve the mathematics education. These can be grouped as-1) Progressivist Reform (1910- 1940), 2) the New Math Reform (1960) and 3) Math Wars on NCTM standards. John Dewey one of the progressivist, emphasized on mathematics learning through activity and inquiry. According to him, students should have active participation in order to have better understanding of the concepts. His ideas were accepted by the progressive teachers and got implemented in some classes, whereas the rest of the classes still followed the traditional lecture – homework method. The “new math” movement is the result that came into existence, after America realized that they are lagging behind USSR in technology. They promptly involved university mathematicians to improve mathematics education curriculum. By this time, there was a democratic view that each student has a potential to learn math and become a future scientist. In the late 1980’s, NCTM came into existence. NCTM developed its own standards to improve the mathematics curriculum. Initially, both government and teachers accepted these standards. But later on the debate started again. NCTM standards emphasized on relational learning, problem solving skills and on the use of new technology for better understanding. But still there are many mathematics researchers who are speaking on the conservatists side.
REFLECTION: This article informed me about the difference of opinions towards mathematics education. It reflects the idea of relational understanding verses instrumental understanding. What I believe is that a new concept should always be developed by inquiry, exploring and relating it with real world. Once the student understands the concept then traditional method can be used gain fluency in solving the problems.

5 BURNING QUESTIONS

BURNING QUESTION FOR TEACHERS:-

1) How do you assess your students?
2) What kind of new ideas you use in your class?
3) what are you views on incorporating relational understanding to clear the basic concepts with that of instrumental understanding based on memorization?
4) How do you make your teaching interesting for students who do not like mathematics?
5) What do you do to draw attention or engage your class when students do not seem to be interested?

BURNING QUESTIONS FOR STUDENTS:-

1) Do you find mathematics interesting or are you scared of mathematics? Why?
2) Are you interested in knowing how formulas are derived which you are using to solve formula?
3) Do you like your math teachers or not? Why?
4) Do you think maths is useful for you in your daily life? Why ?
5) What change you will like do in math?

MEMORIES

Dear Ms.X,

I was one of your students in grade 12. I never payed attention in your class. I found your class so boring. Just the routine problem solving each and every day without any purpose. During my whole year i just could not figure out the use of calculus / algebra. If i would have been able to relate it with a purpose then i might have been a different person than what am i now.

MEMORIES

Dear Ms.X,

When I was showing my old pictures to my nephew, i found one of my grade 11 picture and remembered you as my one of the most favorite teacher in the school. I did liked your way of teaching math by relating it with the real world. I still remember the concepts. Because of your efforts to clear the concepts i dare to do masters in mathematics. You would be surprised to know that I have chosen teaching as my career and will certainly use your ideas to teach the students. so that they will like the mathematics like me.
Thank you very much for all your efforts.

TEACHING AND LEARNING MATHEMATICS ( BY: NAMRAT, MARIA, PARAMJEET )

TEACHING AND LEARNING MATHEMATICS

It is well known that good teachers love the subject they are teaching. On the other hand, if you as the teacher feel negative towards mathematics, it may show up when you are teaching your students and can affect them similarly. Little children usually like numbers and math - yet many kids in schools develop 'math anxiety or phobia' or end up disliking math. A major factor in that is the way math is taught and the way the teachers feel about math.
We have been to a Senior Secondary School, and asked several questions to both math’s teachers and students. The results were not that surprising. After interviewing several students, we found that most of them do not like mathematics and find it boring. By analyzing different students, we realized that they want to be taught by instrumental way. However, they want to understand purpose of math they are studying. They could not relate the purpose of learning math other than measuring, estimating the bills. Even when they are asked that what they want to change in curriculum, their answer was that want math which can be used in daily life. Therefore, the students might get more motivated if she/he knows where all maths is needed. So many times kids question the needfulness of things they study. Emphasizing and pointing out the everyday applications of math may help them. Even when they are asked that what they want to change in curriculum, their answer was that want math which can be used in daily life.
Also, students prefer hands on learning rather than lecture method. They like teachers who involve activities in their lessons. One student said that she wants math more hands on which means that they want more activity oriented curriculum. Thus, by including different activities in class we can motivate students.
We had a chance to interview and observe secondary mathematics teacher in a class. Students were taking interest and paying attention to what they were taught. We talked about her teaching strategies. She told us that one very important factor in motivating students to study math is that you yourself, as the teacher, stay positive about math - if possible, enthusiastic! .
Secondly, we need to get the student involved! One of the reasons for math anxiety is the way math is often taught as "There is only ONE way to do this, and you need to do learn it and do it right." Math is presented as 'given from above'. Students can be much more motivated if they are asked open questions, involved in the development of concepts, given very open-ended exercises. Granted, this kind of teaching style may require a lot of planning from the teacher, probably a good understanding in math, and good materials.
Thirdly, the teacher should not put a wrong answer down. Instead, say, "Please can you explain how you came up with that?" In a classroom, a teacher can ask, "Did someone else get the same result as you? OK. Did somebody get a different result? OK, we have two (or three) different answers here. Let's figure them out." Wrong answers are valuable. You get insight into student's thinking and where he went wrong, and what needs a rethought. Students and kids need to be treated as humans and not feel put down or stupid for their answers.
Last but not least, take the emphasis off from tests. Tests are a part of school but they don't need to be the ultimate goal. She told us that, she returns the quizzes back to students and ask them to do the corrections. The goal is to learn math so the child can use it in her life.

IT’S THE ATTITUDE NOT THE APTITUDE THAT DECIDE THE ALTITUDE OF YOUR SUCCESS.

PEER REFLECTION

I thank all my peers for their valuable feedback. Everybody appreciated my lesson delivery. From the feedback I recognized that one of my strengths is being patient and polite. Also, good at time management and within the time frame have been able to attain the learning objectives.

SELF REFLECTION

I enjoyed while doing a micro teaching lesson. Also, learned new teaching techniques from the peers. In my lesson have engaged everyone to tie a tie. We should come prepared before presenting the lesson in class. I managed to complete the lesson in the given time frame as per my lesson plan. All the student teachers actively participated and learned with great enthusiasm.

LESSON PLAN

LESSON PLAN #1

TOPIC: How to tie a tie?

TIME: 10 MIN

	WHAT	HOW LONG	MATERIALS
BRIDGE	Have they seen their parents wear a tie? Students will be asked had they ever wore a tie while going to a party?	1min	6 TIES
LEARNING OBJECTIVES	Students will be able to tie a tie.
TEACHING OBJECTIVES	Students will learn to tie a tie.
PRE TEST	Do you know how to tie a tie? Have you ever tried to wear a tie?	1min
PARTICIPATORY LEARNING	Students will be asked to follow the procedure while explaining	3min
POST TEST	Students will be asked in pairs to tie a tie on each other.	4min
SUMMARY	Short recap will be done on the procedure.	1min