Discussion of the Dave Hewitt videos

When watching the video in class, I was surprised and confused about his teaching style. To me, teaching a math lesson should be in visual forms: writing on the board or using tablet or projector and of course the contents of the lesson must be explained from teachers. At that time, I was wondering how students could learn integers by hearing the sound of his stick tapping on the walls in the class room ?

It has been 2 months since I watched that video in class. I already forgot most of the details of his lesson but there is one thing that I can not forget: the image of Dave tapping his stick on the wall when he taught his students integers and the number line. 

Thinking deeply about his lesson, I begin to realize the purpose of his technique. The set of integers includes whole negative and positive numbers, adding the number zero. The concept of negative numbers is abstract in students mind since they can not visualize those numbers. Students have the habit of trying to avoid negative numbers as much as they can during calculations. In other way, I could say students ‘treat’ negative numbers differently with positive numbers. Even us as teachers, when doing calculations, sometimes we do exactly the same: we prefer to work on positive numbers more than negative values to avoid as much as possible arithmetic mistakes. Eventually, this habit may lead students to misconception about negative numbers.

In Dave’s lesson, one sound illustrated an integer on the number line, students would treat negative integers and positive integers equally because there was no difference between two kinds of integers in any way except the sound tapping on the wall. Even more, since students didn’t see the numeric symbols of integers, they had to use their imagination to visualize those numbers in their mind. This practice would improve the abstract thinking of students which according to my opinion, very useful for students in learning math at high levels (especially useful when students learn Calculus in 1^st year college).

Dave’s teaching style using sound is a complete new idea of teaching. Now I realize that there are many different way of teaching. As teachers, we should be more creative to discover different teaching techniques, even it may look strange at first (like Dave’s !) in order to improve our teaching performance.

Response to Mason "Thinking Mathematically" reading Chapter 2 & 3

‘Problem solving’ has been a big PROBLEM of students from elementary levels to high school levels when learning mathematics at school. When I tutor my students, I always hear those these sentences from the students ‘I hate problem solving’ or ‘I can do all kind of math except problem solving !’ In order to help students over come the difficulty of solving a math problem. I have been trying to come up my own technique based on my own experience. The technique I came up with basically can be summarized in one sentence “Working Backward”. Starting from ‘What do I want to have?’, trying to find the ‘bridge’ that connects back to ‘What information is given’. The process of building the bridge from the starting point to the end point is based on knowledge of students to come up with the connection. The diagram below illustrate the technique I try to teach students how to solve a math problem

Actually, my technique of solving a math problem is not always working for my students. I am trying to find other way of teaching which could be clearer, easier for students to attach a math problem.

The two chapters 2 & 3 in ‘Thinking Mathematically” explain clearly how to solve a mathematical problem with stages: Entry Stage with 3 entries: Entry 1 (What do I know?), Entry 2 (What do I want?) and Entry 3: (What can I introduce?). Attach Stage and Review Stage. I’ve realized that what I was missing when I try to define my technique is the Review Stage and what should be done when being stuck. I’ve seen that the process of solving a math problem is broke down in details and the author introduce many examples to explain his technique. These examples are very useful and easy to understand since the concepts of finding the way to solve a problem is emphasized, not the levels of difficulty in those examples. I really appreciate Mason's work since I have learned the technique of how to approach and attack a math problem. I will apply that in my teaching 

Teaching problem solving in mathematics is a challenge task as I have been experienced. It is not easy for both sides: teacher and students in terms of teaching and learning. Being able to attack and solve a math problem is a very important skill that students should know how to do. In my own opinion, that ability plays the most important role in the process of learning mathematics at all kind of levels

Response to Elain Simmt Article "Citizenship Education in the context of School Mathematics"

Sometimes, I ask myself a question ‘How many decisions do I made in one day?”. That question came out during the time I was studying Computer Science. Our brain is like a super computer, in order to made a decision, our brain goes through a number of process: gathering information, analysis those information, evaluating and finally made a decision which we think that is the best solution among other possible choices.  For example, when we wake up in a morning, we decide which clothes we will wear in that day; which route we will take to go work or school; what time we will show up in class or at work; who we will talk; what food we will eat for lunch ..and so on ..so on ...In one day, during our daily activities, we do made hundreds or even thousand of decisions a day

Sometimes, we have to made ‘big’ decisions, such as which career we should chose, what job we should apply and even who we will marry !..etc.. It does matter a decision is ‘small’ or ‘big’, our brain still goes through the same processes: gathering information, analysis, evaluate and made the best choice (which we think that the choice we made is the ‘right’ choice)

A student when doing a multiple choice test, he/she read the questions, gathering given information, analysis and evaluating (based on knowledge which he/she learn in class) and finally chose the best answer among other possible answers

Is that amazing? We actually do math everyday. Our daily activities or even our lives are an infinite sequence of mathematical processes and logical selections. Just like we do hundreds or even thousand of multiple choice questions per day and I just can not came up to a number of how many selections do we made in our life time.

I absolutely agree with the author that mathematic education plays a critical educational role in many aspects of student education: society, work, career, social conducts ..etc...Teaching mathematics we don’t only teach our students how to choose  ‘wrong’ or ‘right’ answer in term of numbers, we also teach our students how to choose a ‘wrong’ or ‘right’ answer in many aspects of life. The process of learning mathematics will improve students the skill of processing given information or experience, analysis, evaluate and made the best solution.

Mathematic education can improve the courage of confronting and conquering real life difficulties, exploring and pursuing new ideas, because life has a lot of problems which are needed to be solved. Young generations of this century are not afraid of exploring new ideas and as we’ve seen, many of them succeeded: the creators of Face Book, Google, Youtube....are our examples. 

Mathematics Education doesn’t only give the benefits of knowledge to our students, but also give our students the key elements of success in life. All the skill of analysis, evaluating, making the decision that our students need, could be obtained and improved during the process of learning mathematics

Unit Plan - Linear Functions - Rational and Connections

1. Rational and connections (Why is this topic included in the curriculum? Why is it important that students learn it? What learning do you hope they will take with them from this? What is intrinsically interesting, useful, beautiful about this topic?

The applications of linear function occur in everyday activities, in our normal life Sometimes, we even don’t notice that we use linear function in our activities everyday. For example, a student buy 1 a box of pencil which the price $2.00, then that students could easily notice that if buying 5 boxes, the payment will be $10.00 (that student use linear function y = ax) to calculate the payment. Another example of the use of linear function in our everyday lives is to calculate the cost of printing wedding cards. Cost of printing wedding cards include the initial fixed cost (set up machines, design the layout ..etc..) and the number of printed cards multiply with the cost of printing each card. The total cost is equal to the sum of the initial cost plus the cost of printing n wedding cards. Let say the initial cost is b, the cost of printing one wedding card is a then the payment of printing x cards is ax + b  (y = ax + b)

Linear function has the form of y = ax + b. This is the polynomial function of degree of 1, a is called the slope of the function and b is the y – intercept (the intersection of the graph of the function and the y-axis). Linear function is an important topic in math curriculum. We can use linear function to teach students the concept of functions and relations, domain and range, x-y table of values. In addition, students who takes Physics 11 should have knowledge about linear function in kinetic topic, one of kinetic equation has the form of linear function

Vf = Vi + at 

2) The break down of the big topic into lessons and projects: the break down of this big topic is based on the new curriculum of Math 10. In this new curriculum, the concept of relations is introduced, using diagrams, graphs and tables of values. Then the concept of function is introduced, based on linear functions. The following topics will focus on the properties of linear functions: domain, range, slope, x-intercept and y-intercept and applications of linear functions.

3) The pedagogy of the unit: I will use examples of everyday life activities to introduce the relations, and then move to the concept of functions (such as the relation between teacher-students: one to many relation, husband – wife : one to one relation). The students will be encouraged to find other examples of linear functions in everyday activities. Graphing is focused and always being parallel relating to real situations. By doing so, I hope students will understand how we can apply mathematics in real life, which engage students more in studying and understanding the sense of logic and imagination of linear function. I will mention the mathematical foundation of physics by introduce kinetic equations so students who are interested in taking Physics 11 will know what they should prepare to study in order to well in Physics 11 next year

4) Assessment and Evaluation: I will assignment homework for each lesson. In addition, I will prepare my own handout for students to practice on graphing linear functions. Problem solving using linear function will be emphasized to help students understand the connections between mathematics and real life situations. Quizzes will be given in class as many as I can. There is an unit test at the end of the unit. In addition, a project will be given. Below are the percentage weights of assessment of this unit

Quizzes:  25% 

Homework Assignments: 25%

Project:   20%

Unit test: 30%

Total: 100%

5) Project Plan: I will give students a project relating to linear functions or relations. The class will be divided into group of three. The requirement of the project is

a) Finding applications of linear functions in any different subjects besides mathematics: such as Physics, Chemistry, Medical or real life situations.

OR

b) Finding real life situations which can be illustrated by relations

OR

c) Any interesting research topics which can be found from libraries, internet, newspapers.. etc..

Unit Plan - Linear Functions

Unit Plan (Please click on the link to open the document)




 

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Lesson Plan #1: Representing Relation

Hung Dang Le

Lesson Plan

Foundation of Mathematics and Pre‐Calculus 10

Section 5.1: Representing Relations

Rationale

• Develop the understanding the relationship among data, graphs
• Develop the algebraic technique to find mathematical pattern between two sets of data
• Graphing Relations

Prescribed Learning Outcomes

It is expected that students will:

• Know how to represent a Relation Given as a Table
• Know how to represent a Relation Given as Bar Graph
• Identifying a Relation from a Diagram
• Understand the concept of set, elements
• Know to use circle and arrow to represent relations

Strategies and Activity

Hook (5 min)

• Using example of a mapping student names in the class and the scores of a test to introduce the concept of a relation
• Show a bar graph of temperatures vs. months or days from weather network website

Teacher Activity (20 min):

• Demonstrate the concept of set, elements
• Demonstrate the concept of using arrow and circle in diagram
• Demonstrate how to represent a Relation Given as a Table
• Demonstrate how to represent a Relation as Bar Graph
• Explain how to identify a Relation from a Diagram

Student Activity (35 min):   

• Ask students do exercises from provided handout and text book for assessment learning outcome
• Divide students in group of four to practice exercises
• Checking home work from previous lesson
• Divide students into group of four and work on exercises from given handout

Closure & Wrap-up (20min)

• Summary important points of the lesson
• Assign homework
• Short Quiz (10 min)

Materials

Text book

Work Book

Calculators

Handout

Projector

Preparation

Handout exercises

Lesson Plan #2: Properties of Functions

Hung Dang Le

Lesson Plan

Foundation of Mathematics and Pre‐Calculus 10

Section 5.2: Properties of Functions

Rationale

• Develop the concept of a function

Prescribed Learning Outcomes

It is expected that students will:

• Be able to identify a function using vertical line test
• Be able to describe Functions
• Use Function Notation to determine values

Strategies and Activity

Hook  (5 min)

• Extent the hook from last class, introduce some examples of many different relations in real life
• 1 to many relation: teacher – students
• Many to 1 relation: students to a class
• 1 to 1 relation: Husband – Wife

Teacher Activity (25 min):

• Demonstrate how to identify a function from diagrams or set of ordered pairs
• Demonstrate how to identify dependent and independent variables
• Demonstrate the use of function notation to determine values

Student Activity (40 min):   

• Ask students do exercises from provided handout and text book for assessment learning outcome
• Divide students in group of four to practice exercises
• Checking home work from previous lesson

Closure & Wrap-up (10min)

• Summary important points of the lesson
• Assign homework
• Exit Slip

Materials

Text book

Work Book

Calculators

Handout

Projector

Preparation

Handout exercises

Lesson Plan #3: Representing Relation

Hung Dang Le

Lesson Plan

Foundation of Mathematics and Pre‐Calculus 10

Section 5.3: Interpreting and Sketching Graphs

Rationale

• Construct understanding the connection between given situations and functions
• Construct graphing a function from given situation

Prescribed Learning Outcomes

It is expected that students will:

• Be able to calculate the slope of a line segment
• Understand the meaning of the slope of a horizontal line and a vertical line
• Be able to sketch a graph from a given situation
• Be able to describe a possible situation for a graph
• Interpret a given graph

Strategies and Activity

Hook (10 min)

• Story about the race of the turtle and the rabbit Ask students how to describe the graph of each one
•  

Teacher Activity (25 min):

• Demonstrate how to calculate the slope of a line segment
• Explain the meaning of the slope of a horizontal line and a vertical line
• Demonstrate how to sketch a graph from a given situation
• Demonstrate how to describe a possible situation for a graph
• Demonstrate how to interpret a given graph

Student Activity (35 min):   

• Ask students do exercises from provided handout and text book for assessment learning outcome
• Divide students in group of four to practice exercises
• Checking home work from previous lesson
• Playing game

Closure & Wrap-up (10min)

• Summary important points of the lesson
• Assign homework
• Exit slip

Materials

Text book

Work Book

Calculators

Handout

Projector

Preparation

Handout exercises

Reflection on Group Microteaching Assignment (Sketching a Quadratic Function)

After forming a group of three: Esther, Maria and myself, we discussed the topic about our micro teaching right way. We were eager to get started. The topic was quickly chosen through our emails exchanging. We chose sketching a quadratic function since it seemed to be more interesting and a little easier to teach, compare to my proposal: drawing a trigonometric equation since I watched a video in class about this lesson and I wanted to explore that. Anyway, since the topic was chosen, we discussed the content of the lesson which would be taught in class. We simplified the lesson, decided not to mention about the numbers of x-intercepts based on the value of the determinant of an quadratic equation. We wanted the lesson to be simple due to time constraint: 15 min only

To prepare for the teaching lessons: we borrowed calculators in from John, practiced how to draw quadratic functions and planed to use projector to show in class. We even prepared graph papers for our classmates to use during class activities. And especially we went through the presentation (Power Point slides) many times to make sure all the contents of the lesson was well organized

 It didn’t matter how much we tried to prepare our teaching lesson, there were a number of unexpected technical problems: one slide in PowerPoint presentation was missing, one miscalculation during the teaching, no time to show how to use calculator to draw a quadratic function in class, no time to do activities as we planned. However, we were still be able to react and went to plan B: using white board to continue our teaching lesson and we still had sometime to go around the class to show a number of our classmates drawing the function on calculators and our class loved the quadratic formula song which was played as a hook for our teaching lesson.

Our teaching lesson was not a good lesson as we thought, we had some negative feed backs from our classmates. However, it was quite a valuable experience for us. I thought when I actually was a teacher in class, there were times that we couldn’t follow lesson plans as we planned before coming class. There always were unexpected problems which would happen and we had to be able to change our plan quickly to scope with the situations.

I’ve learned that in order to give a good teaching lesson, I have to prepare everything carefully, be well organized regarding to materials and technology tools which I plan to use during the lesson. And if there are some unexpected problems happening, I should try to deliver the main topic of the lesson first, despite how eager I am to use different approach which I plan before the lesson.

Response to Selter's article on "Creativity, flexibility, adaptivity, and strategy use in mathematics"

In this article, the author focuses on three ways of teaching and learning mathematics:

• Creativity: is the ability to invent new or modify known strategies
• Flexibility: is the ability to switch between different strategies
• Adaptivity: is the ability to use appropriate strategies the individual has creatively developed or flexibly selected

The content of this article is quite important to us as educators. Especially the results of a number of conducted experiments on students in elementary are fascinating. Through the results of those experiments, we can learn a great deal about student learning mathematics. Which in term will help us to teach mathematics more effectively. Teaching creativity, flexibility and adaptivity in mathematics for young students is not just to prepare our students to the challenging of high level academic in university, but also to provide our students practical skills of problem solving in their future working environment.

To my opinion, Mathematics is the foundation of all sciences, not just because of the mathematical knowledge as prior requirements, but also the logical thinking which are obtained through the process of learning. Knowing how to apply creativity, flexibility and adaptivity in learning process students will have a deep understanding what they learn and be able to obtain high level academic achievement.  

Problem Solving Assignment From "Thinking Mathematically" book

Problem Solving Assignment From the book ‘Thinking Mathematically’

Group members: Meghan, Eddie, Hung Dang 

Problem “31” page # 179

Description: Two players alternately name a number from 1, 2, 3, 4 or 5. The first player to bring the combined total of all the numbers announced to 31 wins. What is the best number to announce if you go first?

Analysis:

31	30	29	28	27	26	25	24	23	22	21	20	19
W						L						L

18	17	16	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1
					L						L						L

Starting from the number 31, I notice that if I can force the other player announces his number when the total announced numbers at 25 then I can win the game. From 25, the maximum number he can reach is 30,  the smallest number he can reach is 26, within the range from 26 to 30, I can reach to the winning number 31 by announcing any number from 1 to 5

Using the same strategy, if I can force the other player announce his number with the total equal to 19, from 19 he can reach from 20 to 24 then I can announce my number to bring the total to 25

In general, if any player announces numbers when the total are 25, 19, 13, 7 will lose the game or in general 6n + 1 

Strategy

So the best strategy to play the game if I go first is starting with 1 because the other player can not bring the total up to 7, the maximum number he can reach is 6. And then my next move is to bring the total to 7

Modified Problem

We can modify to obtain another problem such that: "Two players play a game which has the rule as following: there are 27 balls, each player can pick up 1, 2 or 3 balls alternately. Who picks up the last ball will lose the game. How do you play to win the game?”

Comments: 

This problem is interesting and the key point to win the game is to find out numbers which are called 'losing numbers' in order to come up with the winning strategy. Those losing numbers will be written as a pattern. Those problem look complicated at first but if we understand one particular problem then we can easily solve another ones

Problem Solving - Unclear problem

From Math Power 10, Section 3.9, Factoring topic, page 130, question# 21

Question: 
Factor if possible 9x^2 - 15x - 4, the answer in the text book is not possible  

To my opinion, the question is unclear when students are asked to find the solution with integers only. Actually, we can factor this expression, as long as the determinant b^2 - 4ac > 0, the corresponding equation has 2 distinct real roots, let call them x1 and x2 then we can factor the expression as   a(x - x1)(x - x2).

In this case the determinant is (-15)^2 - 4(9)(-4) > 0, so the corresponding equation has two different real roots, they are irrational numbers, so we can factor this expression as 9(x - x1)(x - x2)

This section, to my opinion, gives students a misleading concept about factoring a quadratic expressions since the irrational roots of quadratic expressions are ignored in the process of factoring.

My Practicum Story

My Practicum Story

If someone asks me what is the most important day during my practicum then I would say that is the day that I do my teaching lesson. And until now ..I still don’t believe that I didn’t show up in the class room at the day I supposed to give my very first math lesson in my teaching career, of course if I still want to pursuit this career. This event was just like a wake up call to my conscience, being a teacher is just not standing in front of the class room and teach a lesson. Teaching is a lot more than that, the lesson I have learned is to prepare well in advance, be responsible to what you do and be a good model

And here is my full story …

John Oliver high school is my practicum school, because I have two teaching subject areas: Computer Science and Math so I have two SA’s (Sponsor Teacher) and my schedule during the practicum was set as following: the first two blocks I went to my IT sponsor teacher class, the last two block after lunch I went to my Math sponsor teacher class room. Unless I went to another class to observe another teacher, otherwise I sat the my sponsor class room and tried to help students as much as I could during activities in class. Things went well in almost two week practicum until the day I supposed to give a Math lesson in grade 10 class. That was the day that I was waiting for a long time because math is my favorite subject and I was eager to do the best I could during that class

Somehow, in my mind I thought that I would teach in the third block as usual because that was the time I supposed to spend with my math sponsor teacher…But in fact, my lesson was in the second block. Which meant I showed up in the class when the lesson was over, and of course, the sponsor teacher had to do the job which was mine and she didn’t prepare for that..

What happened next? A lot of explaining going on ..saying sorry …and I was really upset about myself   

Poem about zero

How your world look like when you have no zero?

How math would be if there is no zero exist ? 

Zero is nothing but it is everything
How much do you know about zero?
 

Did human know zero when they just began to know counting concept?

Then add zero there are whole numbers

Without zero can we find positive or negative?

Don’t divide by zero when you come up with ratio

Multiply with zero then you have nothing left

Power to zero then you just have one

Take zero then power to zero do you know how much ?

That’s a limit problem when you learn Calculus one !

No log of zero, don’t divide by zero

No root to zero

No cotangent of zero or you call infinity

Nothing come out when multiply by zero

Group of zero is empty set

The neutral number when you add is zero

Don’t cancel out zero when multiplying in math

Otherwise one could equal two !!

Do you know since when time begins to float?

What I mean is when the clock began from zero

If universe now has zero dimension in it

Then where you are when you read this poem?

Microteaching: Sketching a Quadratic Function by Maria, Hungdang,and Esther

	WHAT	HOW LONG	MATERIALS
BRIDGE	*Review Quadratic Formula by introducing the fun song from the web: http://www.youtube.com/watch?v=CnJT1ojHT28&feature=related *Tell students being able to graph basic quadratic functions without using a graphing calculator is important (why?) and the Quadratic formula will be a useful method to remember in graphing a quadratic function	1 minute
LEARNING OBJECTIVES	*to learn how to graph a quadratic function of a standard form, , by hand
TEACHING OBJECTIVES	*to teach effective ways of graphing a quadratic function: 1.        using domain, range, vertex, x/y-intercepts 2.        using a shortcut (a, b, and c relations in)
PRETEST	*Test if the students can rewrite the general quadratic equation in standard form by using the method of completing the square	2 minutes
PARTICIPATORY LEARNING	*Observe changes in graphs by altering a, b, and c in : - discuss the role of a, b, and c  (use the following simulation to demonstrate the role of ‘a’ http://phet.colorado.edu/sims/equation-grapher/equation-grapher_en.html) *Do a specific example by sketching a quadratic function of standard form by finding:       1. vertex       2. maximum and minimum       3. x & y-intercepts  - analyze the domain and range *Compare the graph on paper with the one on the graphing calculator screen	1 minute 4 minutes	graphing calculators
POST-TEST	*Give students an example to work on their own and let them check their graphs with the graphing calculator *Each of us will go to a group of 5-6 students and help them if questions/difficulties arise	5 minutes	graphing paper, graphing calculators
SUMMARY & WRAP-UP	*If the students grasp the main idea, then we can introduce the shortcut method. (a, b, and c relations in )      1. x-coordinate of vertex = -b/2a      2. y-coordinate of vertex = c-b^2/(4a)          (or by plugging in the x-coordinate to the           given function)      3. y-intercept = (0, c)      4. x-intercept = (x, 0), where x can be found by            using the quadratic formula *For some quadratic functions with complicated numbers, we might not be able to draw by hand; however, it is important to understand the process and the basic shape of the graph.	1-2 minutes

Fast writing articles in class

Division is an operation that we learn. Divide could be the process of breaking a whole into smaller pieces. In term of human meaning, divide means  different opinions, different religions, different ideas. We can divide a task between more than one person, so we can complete the whole task together. Divide has negative meanings as well as positive

zero means nothing. add zero to integers set then we have the whole number set. zero has important meaning in mathematics. zero is neutral entity in addition. everything multiply with zero is zero. We can not simplify zero in algebra. zero is a reference value, is the middle value between negative values and positive values. without zero, the whole mathematics foundation could be collapsed. zero is very important thing in math but not in your banking account.

Battleground Schools: Mathematics Education

This article described the ‘battle war’ in Mathematics education in North America since 1900. That is the battle between two different approaches in teaching mathematics. Two different approaches could be characterized as ‘progressive’ and conservative’ or ‘traditionalist’. This battle around mathematics education  could be divided into three periods and movements:

(1) the Progressivist movement for mathematics through activity and inquiry (circa 1910 – 1940),  led primarily by John Dewey:  John Dewey proposed that students must engage in doing mathematics as part of a reflective inquiry if they were to increase their intelligence and gain knowledge. He advocated the development of high quality mental process and a scientific attitude toward learning mathematics. He focused on sense making activities of reflective practice rather trying to cover a large number of mathematics topics in curriculum design. Dewey’s ideas won a high degree of acceptance in progressive teacher’s colleges during this period.   

(2) The New Math reform movement of the 1960’s:  a new curriculum was designed to satisfied the demand of public (during the Cold War with Soviet Union). The new curriculum was written, focused on abstract topics such as: set theory, abstract algebra, linear algebra, calculus and removed the teaching geometry from the curriculum.  The new design had caused huge problems to teaching mathematics in class room since teachers had little or no familiarity with the new mathematics topic. By the early 1970’s, the New Math program came to an end. 

(3) The so-called “Math Wars”, based on NCTM Standards reforms, from the 1990’s to the present:    the National Council of Teachers of Mathematics (NCTM) developed its own standard program in the mid 1980’s and later the new California Mathematics Framework. Both programs emphasized the depth understanding in mathematics  In the mid 1990’s, conservative attitudes toward mathematics education were adopted by a number of religious group. The battles over mathematics curricula and teaching methods have begun and continued until now

Mathematics is the foundation of almost modern scientific researches.  In the process of learning mathematics, students will develop crucial skills which are necessary for further developments and researches. All of those are the results of depth understanding mathematics rather than influence math skills. To my observations, students who have achieved high mathematics academic in high school. still find mathematics in university entrance levels very difficult to study, especially about learning abstract concepts in mathematics. Public attitude toward learning and teaching mathematics is an very important factor which would decide the result of the mathematics battle..

A letter to former teachers

Letter to a favorite math teacher

Dear Mr. X

I guess you would be surprise when receiving this letter ! I am Hung Dang, your former student at Templeton High School, I graduated in 2000 and your were my Math teacher in grade 12. I was the guy who came to your office almost every day during your lunch time. I don’t know how many time you had to skip your lunch so you could give extra help before my provincial exam. I hope you still remember we often had our lunch together in McDonald restaurant, the one was just 2 blocks away from our school. I hope you remember me now. I really ..really hope so ..

How are you doing? I hope everything goes well for you. Let me talk a little about myself We should do some catching up now I guess. After my graduation, I went to Europe because I wanted to explore the world ! I had been traveling almost every place ..Europe, Australia, Asia, Africa. I did a lot of works just for supporting myself and find some money to keep me going. And guess what …I never forget you ! You were my best favorite ! and even now you still are my best teacher. Thanks for helping me so I could pass my last exam and thanks for all your lessons about life. You taught me not only about mathematics but also about life. I still remember what you used to tell me…Never give up hope, even when you are in the worst situation of your life. I did just exactly what you taught me

I just got back to Vancouver last week and Daren gave me your email address. So I hope we could get together again.  See you soon. 

Take care,

Your former student

Hung Dang

Letter to my worst math teacher


Dear Mr. Y

I wish that I didn't have to write you this letter. But when I think about all the high school students who are currently study with you then I feel that I have a responsibility to write this unpleasant letter and send it to you. 

During the school year in which you were my math 11 teacher, I was a very bad student and I knew that. I didn’t study at all I didn’t do my homework, I failed all my tests, I even skipped your class regularly. I knew that in your eyes, me and a number of my classmates, our IQ levels were not high enough to understand and learn math, and you treated as such as we were very stupid to understand what you taught in class.  But the true was that we had been trying very hard to study, just the method you used to teach very hard for us to understand. I seemed to me that you forgot we were students, we came to class to learn and we needed your help. We didn’t come to your class to do mathematics researches or develop new math theories with you. So please change the way you teach, not for us because it is too late, but for your students who are learning with you at this moment.    

I hope you understand why I write this letter and I hope you would spend some time to think about what I’ve said in this letter. I know that you have a vast knowledge in mathematics. Please find an effective way to transfer your knowledge to your students and please remember that they are students, not mathematicians. They are still in the process of learning

Thank you very much for your time

Your former student

Hung Dang