EDCP-342A: UNIT PLAN ASSIGNMENT

Link for UNIT PLAN RATIONALE
https://docs.google.com/document/d/1OLaXFjqMYFRQd8vgp4PjxuFGsYH0oRPjcjgjRxakxUA/edit?hl=en&authkey=CPX3_NYE

Link for EDCP-342A: UNIT PLAN CHART
https://docs.google.com/document/d/1MqZU6L0mkPLPEWxofobMt2-GD_bkElNVd4pPenGJ31I/edit?hl=en&authkey=CNz7l4UM#

Link for THREE LESSON PLANS
https://docs.google.com/document/d/1QMCS39_Hvtxf7Ojk4Mi51RQUxFAllpYAxJb92qlAV50/edit?hl=en&authkey=CPrWloMB

Link for UNIT PROJECT
https://docs.google.com/document/d/1l1y2ReLU37TZg6K3CJw3r4xUfAsdZQzfN-TPHoyGmVI/edit?hl=en&authkey=CKHA95II

Word problem: Problems with Problem

 Mathematics 10:


 Problem Statement: 
 Sandra lives in Salmon Arm, BC. She wants blue orchard mason bees to live in her backyard. She purchases a bee nesting box and intends to place it in one of her flower beds. The front of the box measures 15cm by 15cm on the inside. The outer diameter of each nesting tube is 8mm.

a. estimate the number of tubes that can fit inside the box.
b.  Draw and label a diagram showing the dimensions of the nesting box.
c.  Calculate the maximum number of tubes that can fit inside the box. then, describe one way to check your work.

Analysis: 
Firstly, this problem sounds very impractical, as generally grade 10 students don't engage in purchasing of the nesting boxes, and if Sandra was engaged in buying the stuff, then she could have asked the store owner the capacity of  this nesting box and did not need to engage in calculations. The imagery is not memorable, but kind of weird, and not helpful in interpreting the problem. I don't think a grade 10 student can interpret it. I mean students can't do it without help. Actually, the picture  provided for the problem in the book is distracting us from the real idea of the question, which only shows 2 tubes, creating problems in understanding of the problem. This can be a good question if asked by the teacher from a problem solving approach but with changed imagery, as it explores the idea of surface areas.

Math Project Assignment.

 Group Members: Maria, Hong Dang, Raman.

Project Description:  Students will research the life of a famous mathematician, and will post the highlights of his life and work in a life-size mock-up 2D or 3D model, to mark the ghostly presence of the mathematicians.

Project Objective:  To incorporate a human and historical element in math classes

Intended Grade Level: 11

NCTM Standard/Principles Addressed:  Connection:  Math is an integrated field of study.  Students must see the mathematical connections in the rich interplay among mathematical topics, in contexts that relate math to other subjects, and in their own interests & experiences Learning:  Students must actively build on new knowledge from experience & previous knowledge

Project Development Stages:

Stage 1:  Going through the project from a student’s perspective

1.                  Selected Emmy Noether, from list of Asian and women mathematicians

2.                  Extensively researched in the internet, visiting at least 20 sites.

3.                  Prepared an executive summary of life and work.

4.                  Analyzed contributions to Math and Physics. 

5.                  Constructed 2D life-size mock-up.

6.                  Posted highlights of life and work on mock-up figure.

7.                  Placed the mock-up in a corner of the classroom.

Stage 2:  Looking at the project with teacher eyes

Having gone through the full project, the weaknesses, strengths, and points for improvement are:

Task	Strengths/Points for Improvements	Weaknesses/Points for Improvement
A.       Research on biography of mathematician in the internet	Easy access to internet with comprehensive database on mathematician To improve: 1.Use related links to provide an even wider net    of information for a more holistic understanding and appreciation of mathematician 2. Use related links see to how mathematician’s work impacted on other mathematicians, and the development of specific branches of math	1. Too much easy information available      may   lure students to read only a few     sources 2. Authenticity & integrity of information may not be verifiable   3. Over-reliance on the internet to the exclusion of other    excellent media sources like books, scholarly articles To improve:  1.Document at least 10 sources 2.Check the reliability of source 3.Include other media sources like books, scholarly articles
B.  Organizing research findings, and select highlights	1. Need to read entire biography to distill the      most important points of mathematician To improve:  1. Find unifying themes in the mathematician’s life and use these to  thread the summary	1.  Copy and paste portions from different sources,    Superficial editing of words, & pass as own summary To improve:  1.  Write key names, places and phrases in index cards Arrange cards in chronological order.
C. Mock-up model of mathematician with life’s highlights strategically       displayed in body	1 Resurrected ghost hovering in class, palpable, permanent, real member of class 2  Teacher can refer to mock-up during relevant points a math class discussion 3  Student are reminded of key details of mathematician every time they enter the math classroom	1. In time, the novelty will wear off and nobody will pay attention to the      mock-up, unless the teacher explicitly       refers to it. To improve: 1 Relate as many intellectuals and events to  Mathematician to continually “reinvent”  image.
C.       D.  Oral presentation of             mathematician’s life	1 Mathematician come alive for the class 2   Focus on high points of biography To improve: 1  Dramatize crucial or unusual highlights in    biography	1  Reading from notes, little audience contact 2         Too much lecture-type talk, little audience participation To improve: 1. Note cards used for presentation

Stage 3:  Devising a New Project

From a static and outdated mock-up to a vibrant and evolving one, reflecting the dynamic, interconnected nature of math and mathematicians through time.

Purpose:

1.      Bring the human and historical element in math classrooms

2.      To spark / create interest in pursuing higher mathematics

3.      To appreciate that math is a dynamic, evolving subject build upon the ideas of mathematicians through the centuries

Time frame: One grading period (one week for the mock-up, and highlights every two weeks).

New project

1.  Research on biography to include links and other media sources.

2.  Find unifying themes and select highlights of life and works­­­

3.  Oral presentation to include mini-play/skit of significant events

4.  Periodically add new information to existing posted highlights.

5.  Write a journal entry on the positive impact of the project on student.

The revised project will basically go through the same steps as in Stage 2 but incorporating the suggested improvements.

Posted highlights on the Model:

 

Accolades	Gender/Race	Educational institution
In a letter to the New York Times, Albert Einstein wrote:  “…Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.”	Jewish woman scholar in Nazi  Germany; Went to finishing school instead of college preparatory school	University of Gottingen,  founded by King George II of Great Britain, world-renown  center of math research, associated with 45 Nobel laureates
“Greatest woman mathematician in recorded history,” “mathematical originality absolute beyond  comparison,” “changed the face of algebra”	Academic Senate: coeducation would overthrow all academic order.  One of 2 women out of 1000 students, forced to audit class for 2 years.	Nazi – remotion of all Jewish scholars, positions revoked
Moon crater, asteroid named after her Association of Women in Mathematics Noether’s Lecture	Women: 16% of undergraduate and 11% of doctorate degrees in engineering; less than 22% of doctorate degrees in math and physical sciences. Women < than 1/3 of all full- and part-time faculty in US colleges/univ 1992, and only 18% of all full professors.	Academic Ranking of World Universities: Harvard (1), U.Cambridge(5), U .Toronto (27), UBC(36), U.Gottingen(93),

 

Professional Qualification	International Congress of Mathematicians	Teacher
After PhD,  lectured  14 yrs w/o pay nor official position	Visiting Prof: U.Moscow, U.Frankfurt	Nurturing, scholarly family
Faculty member: What will our soldiers think when they return to the university & find that they are required to learn at the feet of a woman?  Hilbert: I do not see that the sex of a candidate is an argument against her admission as a privadozent, After all, we are a university, not a bath house.” US/Can: PhD >tenure review>Tenured  Prof Europe: PhD>habilitation>Tenured Prof	1932 Plenary address – 1st woman 35 years after 1st congress in 1897 Karen Uhlenbech – 1990, 58 years after Noether’s address - 1990	Noether’s Boys: No lesson plan, spontaneous discussion in cutting-edge problems in math.  Lecture notes of students basis for several important textbooks;
2004:  major political debate to abolish habilitation: Jr Prof>Tenured Prof2004: : 2006: Hab restricted to top PhD grads	2010 ICM in India 26 ICMs-19 Europe, 2/2 US/Can, 3 Asia

Outstanding contributions in Math and Physics.

Three Epochs of Noether's scholarly work. First Epoch (1908-1919) ·         dealt primarily with differential and algebraic invariants. ·         produced her seminal work for physics , the two Noether’s theorems. Second Epoch (1920-1926) ·         crafted new theories of mathematical definitions of Ideals in Rings. ·         Renowned for developing ascending chain conditions, ·         Commutative rings ,ideals, and modules, ·         Elimination theory ·         Invariant theory of finite groups  ·         contributions to topology.  Third Epoch (1927-1935) ·         Hyper-complex Numbers, and Representation Theory of Groups ·         Non-commutative algebra, linear transformations and commutative number field

Assessment Rubric: 

1.     Posted highlights -  5

2.     Oral presentation - 5

3.     Iconic figure  - 3

4.     Individual participation - 3

5.     Journal entry - 4

          Total:  20

My Reflections: Creativity, Flexibility, Adaptivity, and Strategy Use in Mathematics

    The article has discussed very crucial aspects of strategy use in mathematics teaching and learning - creativity, flexibility, and adaptivity. When I was going through the Ferit,s example, I was thinking that it happens with most of us while using  strategies,and wandering why this is so. Although the previous knowledge is crucial for the understanding of the new concepts, but it acquires so much space in our mind and don't let anything new to grab some space there.  Most of us try to follow one direction and find it very hard to look  for some other ways, that is, finding  it hard to adapt to the new conditions, and getting the better ways.

      I strongly admit that the conceptual understanding is the base for the adaptivity, which is not given the due preference in the traditional teaching methods that are based on instrumental understanding,instead of relational understanding. The strategies are therefore developed once the problems are understood properly. I want to share my personal experience. I taught my 5 years old son (who already knew counting 1-100) to add 4and 1, 5and 1 on his fingers, but when I gave him the third question to add 9and1, he answered me without counting on fingers and reflected that I was just asking for one number ahead. This is what Threlfall viewed about use of strategies in arithmetic that strategies are developed, not selected and applied.

      The analysis of the six contributions on the strategy use discussed in the article,is very insightful, and I feel that in order to make our students use the strategies, flexibly, creatively and adaptively, we are needed to change our instructional strategies in teaching mathematics. We must reconsider the role of teacher and the curriculum developers, so as to achieve the objectives of mathematics teaching and learning.

Practicum Memories

Practicum is the most exciting part of an education course as it sets the stage for the students to preform their roles as teachers.This experience is especially memorable for me as it is my first teaching experience in a new system of education. On the first day, I  was so nervous, and just adding to this nervousness, when I reached the school I got to know that the school had no information  regarding  my arrival. I was so confused, but soon they figured out everything, and I was able to meet one of my sponsor teachers. Even my F.A. gave a surprise visit  to observe my first lesson  at very short notice,  which was in grade 12 Calculus, although I started with nervousness, but was able end up positively.

        I want to share a touching experience during my short practicum.On my 3rd day of practicum, I was in my grade 10 class for principles Mathematics, to do a review on sine and cosine ratios.There was a blind male student in the class, who just love to do Mathematics. After the class he approached me, and said that he liked today's lesson, and got the idea properly.Even his two teacher aids appreciated the lesson, and were happy that they are able to get the idea of using trig. ratios, and convey the lesson properly to him. The student expressed his views regarding the deep relationship between Mathematics and music. His views regarding his passion for the music, and love for Mathematics inspired me a lot to think more passionately about the students of his kind.

Group Microteaching Lesson: Peers' Feedback and Reflections

 Peers' Feedback

"Never learned before, happy to learn finally,how algebra tiles work," was one of the various responses we got from our peers as feedback for the use of algebra tiles in our micro-teaching lesson, and it was just satisfying for our group to know to have achieved one of the teaching objectives. Almost all of them appreciated the use of manipulative, the algebra tiles, with which we were able to engage all of them actively in the process of teaching and learning. One of the observers pointed out the idea that connecting factorization visually to the area of rectangle can  prove to be a different kind of learning experience for a student.The observers also liked the idea of using the website resource, the virtual manipulative, to make the lesson more interesting.
         Although the lesson was a good one, but it lacked the proper time management, pointed by almost all of them. The introduction, no doubt, was very appropriate, but, was too fast, and I strongly agreed upon their view that it can be hard for a grade 10 student to follow. The pace of the lesson was fast, and students were not be able to get time to think before they could answer any question.

Self Reflection

     
I also found my group's lesson to be an excellent one, but, no doubt, it lacked the time factor. This was the reason that we had to be fast,and the observers couldn't follow the instructions at the beginning of the lesson. A teacher has to be very particular regarding the time factor. Indeed it was  a different kind of experience to teach with manipulative, to make it possible for the students to make sense of the mathematical situations. I also found it very useful to connect factoring with the area of a rectangle, and making it possible for the students to enjoy this connection as a new learning experience. At the end of the lesson we arranged for expressing their views regarding their self evaluation, that is, what they learn today, to be responded together with the question sheet provided to them,and this was indeed, very useful as a teacher as you got to have some insight of your teaching at the end of the lesson.Truly, micro-teaching was a fruitful experience for me as a teacher candidate.

Microteaching Lesson Plan: EDCP 342A

EDCP 342A:  Lesson Plan
Topic:  Factoring Quadratic Trinomials Using Algebra Tiles                                          
Group:  Howard, Maria, Raman                  

Intended Students:    Grade 10  Fundamentals and Pre-calculus

	WHAT	HOW LONG	MATERIALS
BRIDGE	Give everyone a small  sheet of paper.   In 5 seconds, write as many factors of 60.	1 minute
LEARNING OBJECTIVES	Using the algebra tiles, students will be able to: 1. Factor quadratic trinomials, including perfect square trinomials 2. Relate the dimensions of a rectangular area with finding the factors of a trinomial 3. Experience three modes of factoring trinomials:  algebraic method, concrete algebra tiles, and virtual  manipulatives
TEACHING OBJECTIVES	1. Maximum engagement of all students 2. Individual hands-on-learning using math manipulatives  (algebra tiles) 3. Demonstration of using virtual manipulatives in factoring trinomials
PRETEST	Each student will be given a worksheet sheet      1. Factor the trinomial: x^2 + 5x + 6.  Write answer in worksheet. Ask for answer.  Show of hands who got the correct answer.  Ask a student to briefly explain his/her answer.	2 minutes
PARTICIPATORY LEARNING	1. State the learning objectives.  Tie-up bridge and pre-test to objectives. 2. What are the factors of 6? (3 and 2)  How can we illustrate this geometrically? (Draw a 3 by 2 rectangle, divided into 6 squares).  How are factors related to dimensions (of length and width), and product related to area?  (Finding the factors of a number is the same as finding the dimensions of a rectangle whose area is the number).  Will this geometric representation work for finding factors of a trinomial? 3. Distribute/introduce the algebra tiles, as a geometric method of finding factors of trinomials.  Each student will be given a complete set of tiles, with a transparent tile board.  Walk the students through the 3 different tile sizes representing x^2 (green), x (white) and 1 (red).  Explain that x is a variable that can represent any positive number. 4. Assemble 2-green x^2, 5-white x tiles and 2-red 1-tiles.  If all the 9 pieces represent the area of a rectangle, what algebraic expression represents this area?    (2x^2 + 5x + 2)  How can we get the dimensions of this rectangle?  * In your worksheet, complete equation #2:  2x^2 + 5x + 2 = (2x + 1)(x + 2) 5. Empty your tile board.  For our second rectangle, assemble 1- green x^2, 6-white x and 9-red 1-tiles into a rectangle.  What expression represents the area of this rectangle?  (x^2 + 6x + 9).  What are the factors?  (x + 3) and (x + 3).  What do you notice with our rectangle?  (It is a square).  Introduce the perfect square trinomial (PST).  * In your worksheet, complete equation #3:  x^2 + 6x + 9 = (x + 3)(x + 3) = (x + 3)^2 6. Virtual Manipulatives:    Reiterate that finding the linear factors of a quadratic trinomial is very much related to finding the dimensions of a rectangle that contain the trinomial.  The internet is full of virtual manipulatives that offer fun, creative, and interactive ways of factoring trinomial, which may appeal to today’s technology-savvy students.  Factor x^2 + 7x + 12.  (x + 4)(x+3).	9 minutes	* Algebra tiles * Virtual manipulatives
POST-TEST	Using your algebra tiles, find values of k, where x^2 + kx + 6 factors into 2 binomials. (k = 5, 7).  Write answer in #5 of your worksheet.		* Algebra tiles
SUMMARY & WRAP-UP	Ask students what they have learned today, which should touch the following points: 1. That to the concept of factoring is very much related to finding the dimensions of a rectangle of a given area. 2. That a quadratic trinomial factors only if one can arrange it into a rectangle. 3. That we know that a trinomial is a perfect square if the tiles neatly arranges into a square, with 2 equal dimensions. 4. Ask students to complete # 6 & 7 of their worksheet.  Collect worksheets.	3 minutes

Suggested student worksheet format:
Name:  __________________                                                                                    Topic:  Factoring Quadratic Trinomials
1.    Factor:    x^2  +  5x  +  6
2.    2x^2 + 5x + 2 = (                )(                  )
3.    x^2 + 6x + 9   = (                 )(                  )  =  (                )
4.    x^2 + 7x +  2  = (                  )(                  )
5.    x^2 + kx + 6   = (                   )(                    ) or (                   )(                   )
6.    One thing I learned today is _____________________________________.
7.    Algebra tiles do/do not help in understanding factoring trinomials because_______________________________________________________.

My Response: Formula for Thinking Mathematically

I find these two chapters, "Phases of Work" and "Responses to being Stuck"  to be very-very interesting, and informative, as they have provided the detailed analysis of various stages of dealing with a problem. The three phases of work involved in solving a problem, are really crucial for developing of thinking mathematically, and a teacher must have the knowledge of these stages, as well as enough skill to apply the same during his or her teaching process, in order to achieve the required learning outcome. Although, I also feel that these stages occur naturally while we encounter a problem, but by highlighting them beforehand we can train our students to enjoy the process of discovering beyond the solutions. Consequently, their thinking will be more mathematical.
      I, especially, liked the analysis of the "Attack" phase in 2nd chapter, where the remarkable use of the words "stuck" and "aha" has provided a more practical illustration of a mind's activities while going through this significant stage of exploration. I just want to share my own practical experience of developing mathematical thinking. When I used to teach solving Mathematical problems in India, I always asked my students to write down all the steps involved in solving a problem, together with making down where they got stuck, and how they got the way to come out. These readings have really provided me with concrete information, and I can now use it more effectively to train myself and my students in actually thinking Mathematically.

Division's Boast

Division boasts,
"I am a politician
             ruling over the numbers,
             to break them into pieces,
              using them against one another
Just see  how capable I am 
              to use even the empty headed,
              against the biggest powers,
              And scatter them into,
              in an infinite number of pieces.
You must have come to know who is that empty headed,
               And that one is the Zero."

Divide and Zero (in my views)

Divide

Divide is one of the four mathematical operations. It is used to make divisions. We need this to apply in our daily activities. For example, dividing the things among different people. Sometimes politicians use this in order to create different groups, for example, in the history of India, the Britisher Colonialists used the policy of 'divide and rule' just to scramble the whole unified empire of India in small city-states, and it worked.

Zero

Although placed on the neutral position, zero has a significant part to play.Dividing any number by zero will lead to infinity. It has very significant uses in ordinary language, as one who is out of every thing is regarded as zero. It is the empty set too.we must multiply our stresses with zero just to remove them from our life.

School Mathematics for Citizenship Education

I just enjoyed the article as it has provided an opportunity to view Mathematics as an art as well as science of  society. By highlighting the relationship between school Mathematics and modern society, Elaine Simmt has put forward the need for the strong foundations of Math education in schools, which is crucial for developing the, active, well informed and responsible citizens.  I strongly feel that it is the power of Mathematics that this modern society has been able to acquire its modernity with the strong applications of Mathematics, in its pure as well as applied form. The numbers in the form of quantitative data are used, as a part of statistics, in almost all walks of life. Thus, Math education is the need of the hour in order to make our citizens play their part actively in this highly mathematized society, as well informed and understanding individuals. It is, therefore, required that we must change our way of dealing with the subject, that is the curriculum must be set and instructed in a way that it leads to develop thinking ability in the individuals. Indeed, merely following the rules and getting the right answers aren't going to develop citizenship. I especially like Simmt's views about revising the curriculum ,together with reviewing the ways it is instructed in our classrooms.

       Although the instructional strategies provided by Simmt  are all appropriate for the desired outcome, I find the demand for the explanation to be very significant, as it will help in better understanding of the concept, and also, make the individuals feel confident and learned who will then be able to prove their view point as educated citizens in the society.

Fictional Letters

Following are the imaginary letters that I have imagined to be written by two of my students, one of them liked me a lot, the other who didn't. Take some time to look into my imaginative world, and share my imaginary thoughts.

Student #1

Dear Mrs. R.

I am Grace, one of your students of grade 12, in 2010 batch of ABC Secondary School. Last Sunday, I saw you in the XYZ store, and all my memories of Mathematics journey became fresh. I still remember the very first day in your class when after the introduction, you took a promise of hard work from our (student's) side,and motivated us to do our best in the subject. I used to be an average student with a view of "not so good at Math" before I got you as my Math teacher, but you taught me in a way that I was able to come out of my complexes. With your motivating spirits, extra help and care, I started developing confidence in Math as well as in other subjects too, as you developed my ability to think to get a solution for a problem. You will be happy to know that I have done my Masters in Mathematics, and also did my Bachelor of Education with teachable subject as Mathematics. Presently, I am working as a Mathematics teacher in MM Secondary School. I will always remember you as my role model.

yours student

Grace

Student # 2

Hi Mrs. R.

I am Sam, one of your students of Mathematics from grade 11 in ABC Secondary School. Last weak I happened to come across you, but couldn't manage to talk to you. However, my mind just started remembering those days when I was one of the intelligent students,and if you remember, I always had problems with your teaching style. I used to be very fast at calculations, and getting the solutions, but you always insisted on understanding of the concepts. I also, used to become bored by the different activities that you undertook for the understanding of the slow learners. Now it is been almost 10 years, and I am presently running a small business of my own. I am satisfied in my life.

Your student

Sam

My Reflections to the Fictional Letters

Writing fictional letters is an amazing idea to have a look into our future, and imagining our lives after 10 years is just exciting. Thinking about the brighter, and the darker side of your future in advance,is a kind of valuable experience, that can motivate us to plan ahead our strategies to hope for the better results. I just enjoyed the idea of having a glimpse into my future professional relations.

Summary: Battleground Schools: Mathematics Education

The article has discussed the base of the standards of Mathematics education in North America since the beginning of the 20th century til present, which is actually, based on the two  view points: the progressive views, and the conservative views.There has been a kind of war between these two opinions to decide the standards, and implement the same. The progressives view understanding, eliciting, inquiry and sense making vital for Mathematics teaching and learning process, while the conservatives consider  fluency, authoritative, presentations and deductive explanations to be more important.The conservative views are influenced by a set of assumptions that are based on several attitudinal factors, that are responsible for creating fears in the minds of parents and educators that has resulted in a Math phobic society comprising of fearful parents and educators, untrained teachers, and bewildered students.

The three reform movements emerged during different time intervals in North America who battled against the preexisting system of Math education, and opened new gates for hope. The first was the progressive reform movement, which dated back to early 20th century, and opposed to the system of meaningless memorizing of the rules and algorithms. This movement was influenced by the changing patterns of the society as a result of rapid urbanization and industrialization. It urged for inquiry approach, active participation of the students that needed teacher as a facilitator who has to carefully structure the learning situations, in order to make their children think independently and democratically. The second movement was the "New Math" around 1960, emerged out of the post war situations as a result of increase in competition in science and technology at international levels, and aimed at producing future scientists.Their reformers advocated for unified logical, and highly abstract algebraic structure, but it soon came to an end because of the problems in implementing the curriculum as it needed fully qualified Math teachers, and also, the parents found it hard to help their kids in their homework.     

A new shift in setting the standards of Math education took place around late 1970s, and further NCTM developed its own standards and principles around 1980. They emphasized developing of the  problem solving skills, ability to represent mathematical relationships in different ways, use of technology,and ability to communicate mathematically. It urged for developing curricular material, professional development workshops for the teachers, new modes of assessments, involvement of the parents, and the use of the new technology. However it was not so easy to implement these curricular reforms as it had to bear the criticism from various organizations advocating traditionalists and new Math reform supporters, in many parts of North America.Thus mathematics education has been a puppet in the hands of concerned authorities on  various political grounds.

My Response

The article has been successful in presenting the history and the present of the Math education in North America. At first I was shocked to know about the political motives behind the educational policies, and the reasons why these motives were given more preferences, rather than actual reforms. I, personally, would like to go with NCTM reformed standards, which aim at developing the ability to think in the  students, so that they don't consider Mathematics as a hard, cool and dry subject, and use it as a way of life to become more capable citizens.

First Micro-Teaching : Feedback and Reflection

Micro-teaching lessons have set a small stage just to asses our performance as new teachers, and getting a feedback from our peers. Lesson planning and demonstration are the two main components of micro-teaching. According to my peers' views my lesson was well-planned, and and there was proper time management. Every one was involved in the lesson. However, my demonstration part needed some improvement. One of my peers said that she could not see properly while I was presenting the stress relieving tip, and I should have asked them to practice on their legs before they do it on someone Else's back. Being a teacher candidate, I found it very much useful and beneficial to know my weakness. All enjoyed the lesson, and found it very useful in their daily life.

I find micro-teaching to be an amazing activity, truly informative, creative and entertaining in such a short duration of time,as there is so much fun in learning small lessons. Micro-teaching provides an opportunity to explore the hidden talent of a person. We are able to show our abilities, and also get a chance to share our learning experiences with others. In a multi-cultural country like Canada, we got a chance to know some particular cultural activities of different cultures. I learned how to create the "best out of the waste." Learning how to  make use of chopstick wrappers was really informative. I also learned how to design a bobby pin with beads. The 10 - minute stress releaving exercises can do wonder. Another important outcome of micro-teaching is the opportunity for more interaction within in the classroom.

Lesson Plan - Releaving Stress in 10 minutes.

Bridge (1 minute)
All of us bear some kind of stress now a days, and look for some stress releaving techniques which take short time. I am going to teach one of the Chinese stress releaving exercises, that takes a few minutes, and can be done any time, any where. You will also enjoy and be amazed how effective are they. No materials required.

Learning Objective
Students will be able to perform this tip of stress releaving technique without spending a penny, and also enjoy while performing the same.

Teaching Objectives
Teacher will be able to teach using participatory activities, the tip of Chinese stress releaving exercise.

Pretest (2 minutes)
Teacher will ask some questions:
1. How many of you are going through stress these days?
2. Can you suggest some ways to releave it?


I have a way for you, which is easy to learn, at home/school, without spending any money.

Participatory Activities  (3 minutes)
We need two person for this activity. One who will be performing the stress releaving tip on the other. Learning steps:
1. Put your hands together in prayer position.
2. Open your figures wide, so that they do not touch each other.
3. With the hand in this position, bang the same on back of the stressed person, just 5 inches below the neck
    i.e. on and around the shoulder blades. While doing so, make sure the particular sound made by the   
    banging of the fingers. 
4. This should be done for 15 times in one set.

Post test (3 minutes)
Now I am going to call two my friends and one person will do this exercise on other person, so that I can check whether you are able to perform it easily. 

Summary and Conclusion (1 minute)
Everyone is now able to do this exercise that is easy to learn as you have seen, and  must remember the sound of the figures is important. Do not forget to perform this exercise 14-15 in one set.

Students and Teacher Interview Summary (By: Raman Dhiman, Zsofia Szigeti, Marija O’Neill).

We interviewed a teacher with more than twenty years of experience both in public and private schools. She is currently teaching grades nine and ten. Following are some of the highlights of our interview including interesting points from teacher’s answers and our responses.

When we asked the teacher how she manages students with different abilities and work habits she said that she does not like to give her advanced students work which is ahead of the curriculum. Instead, she keeps them busy by giving them work that is broad in the subject and by encouraging them to help others. As a parent, I would like to have this teacher teach my kids, although this may not be a wish shared by some other parents. There are parents and kids who focus on raised goals, raising them as far ahead of curriculum as possible. I like my kids and my students to enjoy more stable growth and not be working ahead for one period then be bored the next, and then possibly even loose the academic momentum, work habits, and the ability to look into the subject deeper.

We were impressed that she was fond of using technology such as Tablet pc, overhead projector, and the Internet. The tablet pc appears quite helpful to give live displays of the graphical presentation, while she is facing the class.

When we asked her what she finds most rewarding about being a teacher she responded by saying that creating a safe environment where students feel understood and that they matter was on top of her list. She added that she enjoys the fact that she can focus and direct their attention to certain things without controlling them. Students on the other hand, are active participants in the learning process because of teacher’s ability to keep them interested in learning.

Showing genuine interest in students and listening helps determine their needs, which allows a teacher to adjust the curriculum accordingly. Offering help after school is very important because there are students who are shy and do not dare to ask questions in class.  Being too shy to ask questions in class is not something I had ever previously given much thought about. Given that many students find math difficult she takes extra steps in motivating and even has quotations on her wall such as “It is the attitude not the aptitude that determines the altitude of you success” and “I-m-possible”.

Being a substitute teacher appears to be the most difficult position to be in because there was no relationship between the teacher and the students and she could not bring her own material to make her lesson more appealing. We may be in this position before we get a permanent job and it is good to know that.

Student's interview:

In addition, we interviewed a grade ten student whose strengths she stated are not in math. She shared her thoughts about her learning experiences as well as her emotions towards the subject of mathematics.

In the very beginning of our conversation with the student we gathered that she  was one of those typical kids with fear of math. She said that math was the hardest subject and feels very nervous about it. Even if she knew that she is using the right methods to solve problems she was never fully confident about the outcome. The anxiety would usually be over once she had a confirmation that her answer was correct. As a result, she needed more time to complete her work in class. 

When we asked what she liked about her teacher she said it was the fact that her teacher listens to her students and adjusts curriculum based on what she feels suits them. For example, the teacher allows them to take extra time to complete their exercises in class if necessary. One of the things she did not like about her teacher is that although she would give enough time to finish work in the classroom, she did not allow enough time to prepare for exams. Also, she would like her teacher to help her build confidence that she needs in order to tackle some of her mathematical challenges. She realizes the importance of math in her daily life. Some of the examples of math applications in her life were: addition and subtraction, percentages in the stores (for discounts), and interestingly she mentioned speed again. 

One of the greatest discoveries about her learning was when we asked if she would like to have a career related to math. She answered that she was fascinated with proofs and how and why mathematical theories work. She is one of those kids who takes time to think what the meaning behind a quadratic equation, for example, is and not just trying to solve it quickly. This is why she is slow and needs extra time. From this article, we learnt that we as future educators must be aware of HOW students learn and maybe investigate the reasons why some students take longer to perform math operations.