Notes for ALL & A recap

Thank you Dr Yeap Ban Har!
It has indeed been a fruitful and interesting journey on the concepts of Mathematics.
I have learn so much within the 6 days and I wished you were my Mathematics teacher because probably I would love and do better in Mathematics.
Nevertheless, I hope to be able to plan better Mathematics Lesson and help children in Mathematics.

When Planning a Lesson:

•  What do i want the children to learn? ( Learning goal)
•  How do I know? (Assessment)
•  What if they cant? ( Revisit the process, using concrete)
•  What if the already can? ( Enrichment)

4 Teaching Strategies

1. Modelling (Show)
2. Scaffolding (don't show) (get the child to do and as a Teacher, we will help the child)
3. Children do it themself
4. If children cannot, go back to scaffolding.

5 Big Ideas

1. Visualisation
2. Pattern
3. Number Sense (the human ability to make decision)
4. Communication
5. Metacognition

Day 6 Algebra

Mathematics is not magic but rather there is a pattern to it and if we can see it, we would not find mathematics difficult.
 
Try this out.
 
Take 2 numbers and form the biggest number possible from the two digits and subtract the smallest number possible.
The Answer is (the two 2 digits of the asnwer equals to 9)
 
Before I reveal the number trick,
 
Here are a few examples....

Example 1

2 Numbers = 9 & 2

Biggest number possible - Smallest number possible

                               92               -                 29                       = 63 (6+3 = 9)

 

2 number = 9 & 2

9 - 2 = 7

The answer is a multiple of 9 and the answer is the difference between the 2 numbers choosen, multiply by 9.

Hence, 7 x 9 = 63.

 

Example 2

 4 & 5

54 - 45 = 9

 

Example 3

1 & 5

21 - 15 = 36 (3+6 =9)

 

Amazing? Well, let's find out the Number Trick

 

Why is works?     x   y

10 x + y             10 y + x

(10 x + y)           (10 y + x)

9 x - 9 y

9 (x - y)

 

Day 5 Perceptual Variability

Teachers use variables to teach children 'How many"
 
Hence,
- The choice of material is important
- The shape, the size, the colour matters
 
*Avoid giving different types of variables such as (long sticks & short sticks)
*Use different variable colours, because it is not the colour we intend to teach children.
 
Day 1     All identical colour
Day 2     Change colours
(The aim is to look at the numbers and not the variable)
 
 

Perceptual Variability

 

Start with things that are real and can be bundled up  

Comes in 10 Closest to reality, easiest to perceive ( natural)

 

Comes naturally as a bundles (not in 10)

 

Hard to perceive



 

As Teachers, it is important in knowing this spectrum.

Day 4

Let's solve this together...

How many 3/8s are there in 1/2?

Day 3 Fractions

Fractions

Fraction must be equal.

As teachers we make the mistake of teaching children the concept of fraction using apples. 
We overlook that 1/2 of the apple is not equal. What do I mean? 
One half of the apple could be bigger or smaller than another half and hence, it is not equal. 
Although the item used (apple) is concrete but it is not Concrete Pictorial Approach. (CPA)

When the parts are equal, we can name them. 

3/4 can be said as 3 out of 4 or 3 fourths or 3 quarters.
It should never be said as 3 upon 4. 

3/4 
3 - number; while 4 is the name (noun)

1/5 + 2/5 is the same as saying 1/cat + 2/cat

However, if the denominator is different, then we cannot add them up together because they are considered to be of different noun. 

1/2       + 1/4            (it has different denominator - different names) 
1/apple + 1/orange

2/4       + 1/4 = 3/4 

Another example of fraction: 

3/4         x 2 = 6/4 
3 apples x 2 = 6 apples


Whole number and Fraction

7/5 = 1 + 2/5 = 1 2/5 

1 and 2 fifths
"And" separates whole number with the fraction.  

Day 2 Whole Numbers

10 Frame

Dividing a paper into 10 boxes and using kidney beans.

8 + 2 = 10

2 more to 8 is 10


We can use 6 beans, and thus it will be... 

6 + 4 = 10 

4 more than 6 is 10. 



Children will learn alot about the numbers without explicit teaching. 

I agree that we should start from concrete and then, move to abstract and this activity will definitely engaged children. 

If we intend to teach children 8 + 6, we can use 10 frame. 
8 on one of the 10 frame and 6 on the other 10 frame. 

Then, to get the answer. 
1. Count it all. 
2. Making 10. (10) + (4) 
3. Counting on from 8... adding another 6 more. 
4. 5+5+4
5. Counting in twos, counting all. 
6. Counting backwards from 20, because with 2 (10 frames) it adds up to 20. Therefore, it has to be less than 20 (6 less)
7. Double of it. (7+7) 

As you can see, a simple addition but there are various methods to derive at the answer. 

Day 1

Today was the first day of the Module, Elementary Mathematics. I was indeed looking forward to class, hoping to learn mathematical concepts that I could use and teach children. 

I have learnt that there was more than 1 way to solve a problem and in teaching, we begin with teaching children by modeling first, followed by scaffolding children's learning either through prompting or questioning. Next, we provide and finally the last stage of teaching is explaining to children. 

Mathematics is not only about numbers but also the language we use. 
I learn terms which I would love to share with all. 

Ordinal numbers = position (Time & Space) 
Time = I am 3rd in the race. 
Space = I am sitting at the 4th row. 

Cardinal = To tell the amount, quantity (Counting)

Nominal = Names (eg. bus no, block no)

Measurement = Units (eg. 3 litres)

Chapter 2 Exploring what it means to know and do mathematics

'Children learn mathematics when they are engaged in productive struggle.' I agree with this statement because children will learn that it is a part of the process of doing mathematics and they will embrace the struggle when they reach a solution. As a teacher, I feel that we should know our children ability to do mathematics well enough, because they should not be given a problem out of their reach and yet not be given a problem that is straight forward.

 

 

Both constructivist and sociocultural theories describe how students learn mathematics and emphasize on the learner building connections among existing and new ideas.

The more ideas used and the more connections made, the better one will understand.

I strongly agree that in the continuum of understanding, we would want children to fall into relational understanding of knowing what to do and why rather than the instrumental understanding of doing something without understanding.

Mathematics should be learned through 'doing'. As teachers, we should provide ample tools for children to learn mathematical concept and as mentioned by Piaget, he says that children learn best through hands-on experiences, when they play with concrete materials.

 

Chapter 1 Teaching Mathematics in the 21st Century

Mathematics is said to be the way we think, the study of patterns and relationship, the tool for solving problems as well as a set of interrelated concepts.

Math takes place in our everyday life and it is a matter of whether did we take notice or not. Integrating math into our everyday math activities include setting the table for mealtimes, whereby children are given a number of plates and as each plate is being put down, the child is claims, “One plate down, I am left with 3 plates.”

'Math should be learned in a fun way and not drill and kill.’ Learning should be learned in a fun manner so as to allow children to acquire more math skill rather than repetitive drill on rote counting and doing of worksheet because they are a low-level of cognitive activity. Hence, I feel that all teachers should try new ways to approach problems so as to engage children in activities.

 

 

I agree on the Five Process Standards, which students should acquire and use mathematical knowledge which are: Problem Solving, Reasoning and Proof, Communication, Connections and Representation.

 

Mathematics is an essential life skill. Therefore, a teacher need to model and nurture the passion and joy in children when solving a mathematical problem. In addition, parents should integrate math into their child’s everyday life with fun, so that children will have a liking towards math.