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