Day 1: Creating A Mathematical Clmate in the Classroom

Mathematics has always been my Achilles' heel:-((
No matter what I did to grasp what was going on in class from Primary school through Junior college, I had not been successful. I learned to live with the red mark in my report cards: FAIL!

Why was I failing Maths when I was acing other subjects? Last evening, I discovered the reason for my failing grades: My Maths teachers had not taught me well!! They didn't know how to teach Maths, the correct way, that is.

PROBLEM 1:  Which letter in the name is 99?

 

more than just a bunch of numerals

Count off each letter of the name forward and then backwards and continue...

1) How can you deduce from the pattern in the numerals where the 99th numeral will be?
2) What methods will you use? How many methods will you use

 

 

 Can you see some patterns formed by these numerals so far? I did.

 

Method 1

Simply count from 1 to 99 and you will get the answer although this is tedious and there are faster ways to arrive at the answer.

 

Method 2

Looking for multiples of 10.

Knowing where the multiples of ten are, I will be able to locate 100. I then count backward and discover that letter N is the 99.

 

Method 3

Under the letter B,  we can see the following pattern 11, 21, 31, etc.

We then locate 91 and count forward to 99 or locate 101 and count backwards to 99.

 

Method 4

Look for numbers with the digit 9 in the ones place and you will get 99 in no time.

 

Method 5

Look @ multiples of 3 or 5 etc.

 

 

Just when I thought there was only one way to arrive at the answer, was I surprised that there were at least 5 methods to solve this problem!

 

 

PROBLEM 2: Card Trick

How do the 10 numerals arrange themselves? Example o-n-e-1-t-w-o-2-t-h-r-e-e-3 etc...

Take out your deck of cards and start problem solving!

 

 

Can't figure it out? Give up?

 

After several attempts, I worked this out:

  

 

PROBLEM 3: Tangram

 

Can you use 3 pieces to create a rectangle?  5 pieces?

Can you create congruent rectangles (using different pieces to form the same)?

Can you use all 7 pieces to form a rectangle?

 

Must Read: The classic "Grandfather Tang: A tale told with tangrams" by Ann Tompert

 

 





What do we need to solve the Math problems?

1. time to explore to get to the solutions

2. use different methods

3. discuss with someone (2 heads ARE better than one)

4. use concrete materials

5. see patterns

 

Theories

 

A. Dienes Stages:

 

1st: "Play" --- incidental or informal...explore, explore, explore!

 

2nd: Structured Learning --- unfolding information

 

3rd: Practice --- avoid practice too early or it will lead to practising the wrong things or what

                         they are unsure

 

B. Vygotsky -- social learning (working with people)

                       Zone of Proximal development (ZPD)

 

C. Jerome Brunner's CPA Approach

 

C oncrete

P ictorial

A bstract

 

 

What Children Learn In Mathematics

 

1. Looking for problems

2. Visualization

3. handling abstract ideas

4. persistence

5. belief that there is more than one way to solve problems 

 

 

Suggested links:

 

 

http://www.gregtangmath.com/Books/Books?bookID=mathterpieces

 

 

 

   

   

 

 

 

 

 

 

                                                      

 







 

 

 

 

 

 

 

 

 



Notes to Parents

Many of you have shown keen interest in facilitating your pre-schoolers' grasp of mathematical concepts in a fun and meaningful way. I am so pleased to inform you that I will be sharing diverse ways of making the acquisition of mathematical concepts and skills relevant and hopefully, stress-free. The activities, methods, theories, videos, photographs etc. that I will sharing are based on my course lectures, research and the textbook "Elementary and Middle School Mathematics: Teaching Developmentally" by John A. Van de Walle, Karen S. Karp and Jennifer M. Bay-Williams.   Do contribute your comments and suggestions so that we can make this a useful platform for learning and doing Maths.

Teaching Mathematics in the 21st Century

 

"All students should have the opportunity and support necessary to learn significant mathematics with depth and understanding" (National Council of Teachers of Mathematics, 2000, p. 50)

 

Why do we need to teach math?

 

We teach Maths because young children need to learn how 1) to generate strategies to solve problems, 2) to apply the strategies & see if the strategies lead to solutions 3) to check if the answers make any sense. .

 

Secondly, we also need to teach children that there are many ways to solve a problem and understanding how other people solve a problem can develop their own understanding.

 

 

 

According to Schifter and Fosnot (1993, p. 9), "No matter how lucidly and patiently teachers explain to their students, they cannot understand for their students."

 

This portion of the reading has helped me re-align why and how I should teach Kindergarteners maths daily, making inquiring activities practical and relevant. I also need to provide sufficient time and a lot of opportunities so that my students can generate various strategies to solve mathematical problems.

 

 Why do children need to understand math?

Children need to understand math  so that they know what to do and why they are doing it.

It’s amazing how technology can be used to teach math in the 21st century.

 

 

However, we must remember that when we teach math to children, we as teachers and parents need to remember that children need to develop mathematical understanding.

This can be achieved in various ways:

 1.    Creating an environment that offers all children equal opportunity to learn

2.    Focusing on a balance of conceptual understanding and procedure fluency

3.    Ensuring active children engagement in the NCTM process standards

4.    Using technology to enhance understanding

5.    Incorporate multiple assessment aligned with instructional goals and mathematical practices

6.    Helping children recognize the power of sound reasoning and mathematical integrity (NCTM, 2007a)

5 Content Standards

1. Number and Operations
2. Algebra
3. Geometry
4. Measurement
5. Data Analysis and Probability

Of the 5 Content Standards, Number and Operations is the most heavily emphasized strand from pre-K to Grade 5 and continues to be important in the middle grades with lesser emphasis in Grades 9-12.

It is vital that people have skills that are lasting and will survive the ever-changing landscape of available jobs. These are what Thomas Friedman calls "untouchables"--the individuals who outlast all the ups and downs of the economy (2007).

 

It is now my opportunity to align my current practice with that suggested by the authors so that I may raise your children up as math lovers!