math unit plan

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B1lSVtqwYLy0YTIwZjFiNjktNDk0MC00MWNiLTgyNTctNjZhZDUzY2M3MDM1&hl=en

Math Project: the 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

Views on "Creativity, flexiblity, adaptivity and strategy use in mathematics" bt Selter

In Selter’s article, Ferit’s story is really interesting. Even though he was not good at mathematics, he has creativity to solve the problems. A person, who has creativity to solve the problems, can be good in mathematics. This story reminds me of some teachers who always force their method for solving problems. This is very wrong strategy.
We, as teachers, should encourage students to be creative rather than forcing our methods on them. Creativity is accompanied by flexibility, adaptivity and strategy. As a teacher, we should guide the students to solve the problems at their own. The students should be taught how they can switch between different methods. This is not easy for a teacher to develop this kind of strategy in the students. In our daily routine, we can easily forget to develop these techniques in the students. However, we can find some time to give them some problems which force them to develop these characteristics.
The other interesting thing is that research on this topic is just started. Math is always considered as a tool to develop thinking. I think that thinking includes creative thinking. The other terms like adaiptivity are new to me. But this research caught my interest. This research does not give any data. I like to observe in my class rooms how many students work with method and how it affects their learning and mathematical thinking.

Word Problem

Problem: On a warm sunny day, Clark went to the car races to watch an automobile race. As the cars sped around the track and Clark tried to watch them, he got dizzy. So, he decided to keep his eyes on one particular car- the bright green one.  Clark then decided to count how many cars were in the race. He noticed that the total number of the cars was equal to one-third of the cars in front of the green car plus three quarters of the cars behind the green car plus the green car. How many cars were in the race?

Is it practical?

I cannot see any practical use of this problem. First of all, if he is feeling dizzy by watching speeding cars then how can he feel comfortable by counting cars? The other thing is that a person, who is going to a race, usually knows how many contestants are there.

Is it imagery memorable?

Imagery can be memorable.

Can it be solved with the given info?

Yes, it can be solved easily with the given information.

Can it be interpreted in more than one way?

No, there is no other way to interpret it in any other way. However, it may be confusing for students. There is too much information in the problem which is not relevant to the question.

Would the kids be able to interpret it as intended?

As said above, this problem is too wordy. It may be confusing for them to interpret.

Is there anything strange about it?

Yes, if Clark is feeling dizzy by looking at cars, then why he is counting them.

How would you change it?

I would prefer to give them fractions only to add rather than giving them an illogical word problem.

If I have to change it, I will make it simple.

In a car race, the total number of the cars was equal to one-third of the cars in front of a green car plus three quarters of the cars behind the green car plus the green car. How many cars were in the race?

Square take-away

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. (Pg-194)

                   

                                                       

Stories from my practicum

During two weeks of my practicum, I have mixed feelings. Some times I felt that it is getting too hard. My first lesson went good. The students were responding very well. During my activity part I got little messed up. Also, I asked them to take notes during the lesson so that they can stay on task but I realized that this is not a good idea to ask them to write too much. So, I figured out that it is better to give them notes rather than asking them to write too much.  I was not happy with my lesson at all. It seems to be worst lesson of my life. I changed my strategy for the next lesson and find out that it works well. Also, I got a feedback from a teacher  on my last day of the practicum which was very constructive and lifted me up again.
Also, I observed a class in which a teacher was using very different techniques like daily life examples, fun activities, humor etc. After watching that I realized that using variety in your lesson can keep the students interested throughout the period. This encouraged me to use more variety in class to keep students on task and well behaved in the class.

Reflection on Micro Teaching

Micro teaching is good experience before going to the practicum. Peer assessment is very useful. Most of them mentioned that lesson was well paced and clear. I got a personal comment that I was teaching with patience and with expressions. One of them said that use of cardboard was good instead of using board for diagrams. However, use of symbols for introduction was considered very simple for grade 9. Also, there was suggestion to use real life examples to introduce the concept. I really liked this suggestion. To create students' interest in math, we should bring real life examples.

I, also, realised that our lesson took less time than we thought. We should have something else for extra time i.e. emergency lesson plan. Overall, it was a good experience. I learned alot for my short practicum.

Micro Teaching Lesson Plan

What	How long	Materials used
Bridge	Review the definitions of rectangles, squares and circles. Take several responses to get an idea of what the students know.	2 min
Learning Objective	Students will calculate the area of a rectangle, a square and a circle. Students will solve problems involving the areas of rectangles, squares or circles.
Teaching Objective	Students will be able to solve problems individually and cooperatively. Students will be able to clearly and logically communicate a solution to a problem and the process used to solve it.
Pre-test	Ask the students about the formula of areas of rectangles, squares and circles.	2 min
Participatory learning	Ask the Students to solve a problem that involves the calculations of the area of a rectangle and a circle combined. Ask students to describe in words the steps that they will need to take to obtain the answer. Students will work in small groups to find the areas by using the formulas for the area of a rectangle and of a circle.	5 min	Rectangle shaped cardboards with a cut-out circle in the middle.
Post-test	Ask students to solve a similar problem involving many circles marked on a rectangle. Compare results with other groups.	5 min	Another cardboard with many circles marked on a rectangle

Summary

Give overview

1 min

Response to Simmt article on math education and citizenship education

I like that Elaine Simmt introduced mathematics as a tool to understand and shape our society. I have never thought of math as shaper of society. I agree with Simmt when he says that math should not be taught as fact rather purpose of teaching mathematics should be to create mathematical thinkers. Students should be educated to understand how math is used in formation of society rather than teaching them just computational skills. They should be involved in mathematical conversations in the classroom through which they learn how to pose problems and learn to explain solutions. So, purpose to teach math should be to develop good citizens.

Response to "Thinking Mathematically"

It tells us how we can train our students to think mathematically. I like the way author break the problem in three parts: entry, attack and review. It is really important how you ENTER the problem. I will follow this rule to teach my student how to understand the problem by looking at what we know, what is wanted and what can be introduced to make it simpler (eg. Chart, diagram). The second point which I liked is that visualizing the problem is root to solve the problem. I find it important in two ways: 1) visualizing helps to clear the problem and 2) students can feel that math is not abstract. By training students to visualize the problems, we can convince them that all math problems are related to the real things in the world in some way. He mentioned that being stuck is important part of the problem solving, which is very important to encourage the students. Most of the times, when students could not solve the problem in first time, they get discouraged. Emphasizing this point in class is very important that being stuck at least once is really important and it is natural for real understanding of the problem.
Overall, these two lessons contain many tips to teach mathematics and to encourage students.

EMPTINESS CAN’T BE DIVIDED……

Division is the basic human instinct;
We have been divided by caste, religion, color etc;
But division with zero leads to nowhere;
For god sake,
Something is there to remind us that division is not always possible;
But zero is what, nothing…;
Nothing in itself means emptiness;

Oh yeah,
Emptiness cannot be divided at all;
Just like 0/1=0 and 0/999=0;
But division, in itself, leads to emptiness;
Emptiness in attitude of being a human;
So why divide;
Just because Dictator’s policy of “divide and rule”;
But if division leads to emptiness,
Then what is the use to rule on an emptied world?

Dividing positive and negative numbers in two parts;
Zero tells the division of “good” and “bad”;
Oh, for GOD’s grace,
Positive numbers are on the “Right” side;
In a way;
Zero tells that good (positive) is always right;

What a great concept it is, Zero;
Presented as a small circle;
Put it between “L” & “ve”;
It will give you the way to live;

random writing

divide:

divide and rule dictator's policy.money should be divided equally among people. divide the clothes. divide food. divide the land. what else we can do with divide. whole world is already divided. even students are divide in a same class. people are divided on basis of caste, religion, views.

zero

there is no world without zero i guess. zero is base of everything. we judge persons by saying zero or hero. zero is kind of circle it never ends. we keep revolving around same issues throughout our life. zero zero zero. where it comes from and become the base of everything. if you look at moon it looks like zero.

Five 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?

reflection on micro teaching

I really enjoyed micro-teaching. I was quit comfortable because I was presenting within the group. My group mate gave me all nice comments. however, I realized that I should work on making more strong bridges. Also, I felt that my finished early than anticipated. So, I need to work on time management and should prepare emergency lesson plan.

Summary and reflection on “Battle Ground Schools: Mathematics Education”

This article highlights the issue of “progressive” and “conservative” approach toward mathematics. This battle is going on since late 19th century. While conservative approach emphasis on fluency in mathematics by authoritative way, progressive approach believe in understanding mathematics from own experiences and stimulation by teachers.
Mathematics was always viewed as “hard, cold, distant and inhumane” by most of the people. Condition becomes worse when it is taught by teachers who are not skilled in mathematics. Administrators think that instruction can be given by anybody from the textbook. Clearly, they just believe that math is memorization of facts and ther is no understanding involved the subject.
To improve the quality of mathematics, three movements occurred so far i.e. progressivist reform (1910-1950), the new math (1960) and the math war over the NCTM (1990-present). Accelerating industrialization was main reason for progressive reform and it emphasizes on meaningful mathematics rather than mere memorization for productive roles in a democratic and industrial society. John Dewey, main activist of this reform, encouraged “the process of experimentation and inquiry”. However, his recommendations were not fully followed. Then the New Math comes into play after the post war period when America wants to go ahead of USSR and want all students to be scientists, which was influenced by mathematicians in France and it spread across the world. This math was again “highly conservative”. In late 1980’s, math was brought back to basic curriculum. NCTP set the standards for mathematics which were “initially well-received by both government and teachers”. However, in mid-1990’s, anti-progressive views started coming up again.
The battle between conservatives and progressivist is still going on. Political and educational leader should think about the students rather than being rigid to their own believes. There should be balance of everything in the curriculum and present and future needs of students should be taken in care equally.

reflection from a student

letter from a student who does not like his/her teacher


hello Ms......,

I realized that if I have done math properly then I could succeed in university. You always tried your best, but it was your teaching style which makes hard to understand. You keep doing things by yourself in class and never involved us. You should had some activities in your class which could keep students awake.

I just want to suggest you that try to involve your students in your class as much as possible in future.

with regards,
.....


Letter from a student who like his/her teacher

hello Ms...

I am your old student ..... I hope you are doing well. Today I have joined as math teacher. I want to tell you that is all because of you. I got inspired from your way of teaching.The way you try make us understand all concept from the very basic make me study mathematics in my university. I always liked the way you approached us with warmth and care. You allow all students to come to you for any kind of extra help after class. You always tried to find the reason if somebody was not doing well in class. I remember when you just stared teaching us, I was not able to do my homework because of being sick. I was so afraid that you asked me to see you after class, but I was surprised when you welcomed in your office with love asked me reason of not doing it and then gave me extra time finish it. since that day, I never hesitated to ask you anything. Your love and warmth for students always encouraged to learn more from you.
I wish I will be a teacher like you.
Thanks for being my teacher.

With regards,
.....


Thoughts

From above letters I have realized that a good teacher should communicate with students as much as possible and should include activities for students for effective learning.
My biggest fear is when you have to finish whole curriculum in such a limited time, how is it possible to create different kind of activities for every lesson.

Teaching and Learning Mathematics

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.

LESSON PLAN FOR MICRO- TEACHING

	What	How long	Materials used
Bridge	Have you ever used paper to make something?	1 min
Learning Objective	To learn how to use used tissue papers
Teaching Objective	Every one participate and enjoy
Pre-test	Has anyone used tissue papers before to make flowers?	1 min
Participatory learning	Ask everybody to follow the steps	5 min	Tissue papers and twist ties
Post-test	Can they make flower by themselves now?	2 min
Summary	Give overview	1 min