Questions for teachers when planning Math lessons

1)  What I want the children to learn?

-Do not focus on the teaching, rather focus on the learning; children's learning outcome from the lesson.

2) How do I know they have learn?

-By observing how the children is able to understand and communicate teachings orally with peers

-By written practices

3) What if they cannot?

- Revisit the process by using concrete and familiar materials.

-Follow the 4 teaching strategies:

Teaching by modelling

Teaching by scaffolding

Teaching by providing opportunities

Teaching by explaining

4) What if they already can?

-Give enrichment to further challenge their ability on the particular topic.

How do avoid from making careless mistakes?

Tonight was the second last class with Dr. Yeap.
And tonight's topic was 'renaming algebra'.
Basically algebra means patterning in simplified terms.
We do not introduce 'algebra' in its term but we teach children to make patterns


I also asked Dr Yeap a question:
How do we prevent from making careless mistakes.
I remember failing my math tests during to careless mistakes!

Dr Yeap explained that making careless mistakes links to our meta cognition.
There are several reasons why one would tend to make careless mistakes when...
1) We cannot control our own mathematical thinking as we could not make connections with the concepts
2) We are given too much guidance and not given the opportunity to work out the problems on our own.
3)We do not have flexibility in using various strategies to solve a problem. Too structured.

I found this information which tells you the different types of meta cognitive skills.

FRACTIONS! FRACTIONS! FRACTIONS!

Today is indeed an interesting and mind-challenging day!

Honestly, I hate FRACTIONS! 

And unfortunately, today's problem is on fraction:

31/2 - 3/4

As what I could remember back in my secondary school days, the method I learned was to change the proper fraction into improper fraction and then multiply the fraction so both denominator are the same.

Thus it would be easier to subtract both fractions.

However the method Dr. Yeap taught was to visualize the fraction in  our mind, and illustrate the model rather than think about the structured method to solve the problem.

Hence I feel that it is easier in doing the Mathematical problem by visualizing rather than remembering the correct method of equation to use.

I also learned that as teachers we should use the correct noun or language in Mathematics.

Such us:

1) Avoid using the word 'LESSER' instead use 'less than' or 'fewer than.'

2) A fraction (3/4) is describe as 3fourths, 3quater or 3 is to 4.

If we are introducing fractions to the children, begin with concrete experiences such as using a familiar item such as a pizza. Ensure the denominator is the same rather than using different numbers for the numerator. Followed by pictorial experiences.

Cooking activities introduce children to the language of fractions and help them link fractions to their everyday experiences. As they take part in these activities, children become familiar with fraction terms such as whole, part, half, third, quarters. 

For example - Cut the muffin in half, fill the cup half full, let's use part of the whole orange, put peanut butter on one half of the bread and jam on the other half of the bread, cut the sandwich in quarters

;)

The 8 + 6 story

For today's lecture,

we did a problem titled ' 8+6 story' where each group has to come up with  problem story which consist of the equation.

So here is my group's problem story:

John has 8 marbles.

Johnny has 6 marbles.

How many marbles they have altogether?

After each group have presented, Dr. Yeap mentioned that he could see different types of problem story.

1) part - whole problem story

Example:

Ben has 8 pens.

Tim has 6 pens.

How many pens they have altogether?

It has no concept of time of what they have now.

2) before - after problem story

Example:

Lila has 8 pencils.

Shanti gives her 6 more pencils.

How many pencils does Lila have now?

There is a change in lapse of time.

3) comparison problem

Example:

I have $8.

You have $6 more than me.

How much do you have?

Therefore I have learned that there are different types of problem story. It requires the student to be able to understand the problem and visualize in order to solve it.  And I found this table that illustrates the different types of word problems.

Problem Type
Join	(Result Unknown) Connie had 5 marbles.  Juan gave her 8 more marbles.  How many marbles does Connie have altogether?	(Change Unknown) Connie has 5 marbles.  How many more marbles does she need to have 13 marbles altogether?		(Start Unknown) Connie had some marbles.  Juan gave her 5 more marbles.  Now she has 13 marbles.  How many marbles did Connie have to start with?
Separate	(Result Unknown) Connie had 13 marbles.  She gave 5 to Juan.  How many marbles does Connie have left?	(Change Unknown) Connie had 13 marbles.  She gave some to Juan.  Now she has 5 marbles left.  How may marbles did  Connie give to Juan?		(Start Unknown) Connie had some marbles.  She gave 5 to Juan.  Now she has 8 marbles left.  How many marbles did Connie have to start with?
Part-Part-Whole	(Whole Unknown) Connie has 5 red marbles and 8 blue marbles.  How many marbles does she have?		(Part Unknown) Connie has 13 marbles.  Five are red and the rest are blue.  How many blue marbles does Connie have?
Compare	(Difference Unknown) Connie has 13 marbles.  Juan has 5 marbles.  How many more marbles does Connie have than Juan?	(Compare Quantity Unknown) Juan has 5 marbles.  Connie has 8 more than Juan.  How many marbles does Connie have?		(Reference Unknown) Connie has 13 marbles.  She has 5 more marbles than Juan.  How many marbles does Juan have?

Dr Yeap also shared some significant information on what are the basic knowledge a K2 child should posses before going to P1.

1) Language - to read, to communicate with peers

2) Concrete Experiences - plenty of concrete experiences leads to visualization and imagination.

3)Number Sense 

4) Patterns

5) Social skills

:)

Meeting Dr. Yeap in person:)

First day of class went well.

Dr Yeap began class by showing us a video from Sesame Street ' As I was going to St. Ives'

At first I didn't understand his attention of showing us the video, but after he explained, I learned something about Mathematics.

It not just about using the different equations to solve the problem, but rather how we see the question.

Whether we understood the problem and how we analyse it, is more important.

Dr. Yeap also discussed about the roles of teacher in teaching Mathematics.

1) Teaching by modelling
(For example using appropriate 'math' language)

2) Teaching by scaffolding
(With intentions to remove in the later part )

3) Teaching by providing opportunities
( Allowing the child to work on the problem, rather than teaching the strategies)

4) Teaching by explaining

(For example: how a problem can be solved using several methods. A  high level process of understanding)

I also learned the the difference between acceleration and enrichment.

Accerelation means by going to the next stage of a particular topic such as counting

By giving the children acceleration, means the teacher introduces another element.

For example, counting with sorting.

Enrichment means staying on the same topic or content but of a higher challenge or diffciculty.

For example counting in 2s followed by counting in 3s

Dr. Yeap organizes his lecture very well and what I look forward most is the 30 minutes break he gave.

I feel more 'alive' and receptive after the break rather than having 2 interval of 15minutes.

:)

Exploring What It Means to Know and Do Mathematics

In this chapter, I learned that doing mathematics helps children to analyse the pattern, create strategies to problem solve and to understand the relationships between the process and concepts.

According to Piaget, children construct knowledge to generate new ideas which happens in two ways - assimilation and accommodation in a equilibrium. Therefore in mathematics, children uses their prior knowledge to understand the problem and try to 'insert' new knowledge to see if the problem could be solved.

Children uses such representations to translate their knowledge on mathematics. In the early years, I understand that if teachers provide various opportunities to allow children to understand such representations, they are able to translate a concept from one representation to another, thus enables them to  problem solve and understand the computations. One example is providing manipulative or counters for children as they are visual learners and it helps them to understand and grasp the concept, such as addition or subtraction, better. 

Teaching Mathematics in the 21st Century

Back during my preschool days, I could recall learning maths through route counting and representational counting. But times have change and the content of learning for mathematics in the early years have deepened. To become an effective teacher of mathematics, one must comprehend the concepts and skills of mathematics and know how the children learn  mathematics. 

The NCTM has come up with principles and standards to act as a tool to guide and support teachers in teaching pre-K-12 mathematics. Each principle plays an interrelated role of emphasizing the importance of  teaching mathematics to young children. Out of the six principles, I feel that the Equity Principle is the most important as teachers should be given opportunities and support to learn mathematics. When I was younger, I hated maths so much because I often make careless mistakes while doing my sums. And no matter how my teacher explains it, I could never get the concepts right. 

After reading chapter 1, I have learned the basic concepts that my preschool children should acquire and the positive characteristics a teacher should have when teacher mathematics. I feel that I could adapt such dispositions and apply it into my daily teachings.