Wednesday, 31 August 2011

Day 6 - 31st August 2011

Day 6 - 31st August 2011(last lesson of the module)

Lesson 22 - Assessment

We learned about assessment today.

Most of us have the tendencies to say Problem Sums. I learned it is better to say it as word problem.

We ask children to make up a word problem so that we can see that learners have a 
procedural and conceptual and convention understanding. We must teach conventional knowledge explicitly.

I can assess a child to see if he can calculate. Does he understand calculation? If yes, Does he
also has conceptual understanding.

We need to assess the child on the strategy he uses. Sometimes we can use the paper pencil
method and sometimes it is better to use the interview or oral test method. Some may not be able to draw but know the answer and another child maybe able to draw then the instrument is not valid because the child has the same ability but different score.

Hot park     

Using Arrays to Explore Numbers

Arrays are useful models for multiplication. An array is formed by arranging a set of objects into rows and columns. Each column must contain the same number of objects as the other columns, and each row must have the same number as the other rows.

The following array, consisting of four columns and three rows, could be used to
represent the number sentence 3 x 4 = 12.

Three rows, four columns

Many ways of counting the pots of plant. (Example given by Dr. Yeap)

The Basic way of counting - Children can count 1, 2, and 3 and so on

Advance way of counting - 7 X 5 =


 35 (Multiply the number of rows)

Skip counting 5, 10, 15 …

Skip counting 7, 14, 21 …

Repeated addition 7+7+7+…

Counting in 10’s

If the child is counting in two, teachers need to see," Do they face difficulty". Do they get blocked or do they have strategies to go ahead and count. This is a way of assessment.

Rate situation is a situation where not all problems can be multiply. Rate is not constant.

We learned about International Standard of Measurement and the Imperial measurement

Another mistake teacher commonly make is when talking about weight – "How much does 
this weigh?", instead we should say, “How heavy is this?”. When using non standard measurement we must always say, "This rod is about .....paper pins long.

Time has 2 concepts – Time as a point and Time as duration

It is advisable to use an analogy clock.

Teach children time relating to event.  Look at the time relating to time everyday events

We learned that when we test children on time getting them to draw the hour and minute hand
is the wrong assessment to use we should instead use the interview method.

Lesson (23)-Height of the MRT Stairs.

The height of each stairs looked the same but when we measured we found that 4 stairs in each
block of stairs were not the same and they measured 13.5cm as compared to the rest 14.5cm. The calculation  is below:-
Total number of stairs 62
Height of 4 stairs - 4 X13.5


Height of 58 stairs were 14.5 cm                                              
4X13.5 cm =54cm
58X14.5cm = 841cm 

54cm + 841cm=895cm

Volume and Capacity –

The term of volume refers to the capacity of a container but it is also used for the size of solid object and the space occupied.

Capacity is used to refer to the amount that a container will hold.

In these six lesson I have gain so much  knowledge of teaching the children.  I too have learned the common mistakes made by most teachers.  Dr. Yeap, you have covered a lot of materials and included many worked examples.I have learned that Math is about problem solving.  I also learned that the teacher is crucial to a student's success.  The teacher  must know several ways to explain certain concepts.  In school I never had a teacher that I could understand their teaching method.  There are several things I never thought about which I learned in your class.
Thank you for the wonderful 6 days.

Friday, 26 August 2011

Day 5 - 26th August 2011

Day 5 26th August 2011

Lesson 18 – Fraction – Word problem

We started today’s lesson with solving a word problem given by one of our classmate.
Hassam has ½ litre of orange juice. He needs 5/7 litre of orange juice. I have to change the denominator to be a common denominator and that is 14. So it is 10/14 – 7/14

___________1/2__________________      ===He needs this much=

10/14 – 7/14 answers 3/14

Today, I learned two new words again that are application level task and assessment task.
Bloom’s Taxonomy.  For Primary 5 this problem sum is of a comprehension level

Bloom’s Taxonomy:

1. Knowledge level

2. Comprehension level

3. Application level 

.Lesson 20

George pick theory says that the area of a figure is related to the dots. Pick theorem says that the area of the figure is by counting the dots inside and add to the perimeter.
Some more new words learned today and that is reflect, rotate, translate, sheer and pull, this are some of the words we can use  when we want to change the position of the shape. These are the 5 transformation for changing shape.

Number of dots
4 dots at the side and 1 dot in the centre = 2 squares

4+0 = 1 square                                                      

4+2 = 3 squares
Look at the picture below.

Lesson 21 - Graph

Form a graph with the numbers of peg collected.
Graphs and charts are great because they communicate information visually.

There are many ways to do a graph. This is a bar graph


of Students

of pegs collected






Graph using concrete objects.

Lesson 22 – Word problem

Problem solving fraction

Cloud Callout: 6+6+6+6=24
24÷4=63/7 of the apples in the box are red apples the rest are green apples. There are 24 green apples.
How many apples are there altogether?
4 units = 24 apples

1 unit= 6 apples                                                                                







24   +       18

20       4         10      8   

= 20+10 +4+8=42


Thursday, 25 August 2011

Day 4 - 25th August 2011

Day 4 25th August 2011

(Lesson  14) -Think of two numbers

Tell one number
Example 1+2= 3
12-3=9 . 
To get the answer we must multiply by 9

8     72

3      27

9      81

4      36

6      54

7     63 and so on

(Lesson 15 )-Subtraction

37                      -              19                                    37

Cloud Callout: 20Cloud Callout: 17                                                                               - 19 
_-19                                                                          18

20-19 = 1 + 17 = 18                                      

Many ways of doing it
Then we came up with a word problem that can be solved using 37-19.

Tommy had 37 marbles.  He gave Peter 19 marbles. How many marbles has he left?

This is a common subtraction situation.

There is an initial amount. Then there is a change and the final is unknown (result)

We learned that marbles are discrete quantity and $37 is continuous quantity.
Then there was another variation taught in the class that is the part part whole situation which
is describe below:

There are 37 children in a class. 19 are boys. How many girls are there?

I learned we must provide children with different variations So they are more exposed to the
different way of doing the sum.
Zoltan Dienes.Said. 

Lesson 16-FRACTION
We were all given a square piece of paper and told to divide it into four equal parts.

The square piece of paper represents 1.
When this one is folded into equal part and as long as they are equal we can give
it a name. 
The name for one part out of the four parts is one fourth and four fourth make up 1. 

A piece of paper when folded into two. One equal part is called a half.

When folded into three equal parts, one part is called one third.

When folded into five equal parts one part is called one fifth.

2 fifth + 1 fifth is 3 fifth

Any child who knows that 2 cookies + 1 cookie will know how to do this because it is a noun.

5   are not advisable as the child will not make connections.  You don’t count 2/5 and ½
together. In order to add 2/5 +1/2. We need to change the denominator of 5 to that of 10. And the denominator 2 to that of 10. Once there is an equal denominator the addition becomes easier.

Fraction as a part of a set – (Which will be learned in primary 4)

Fraction of a quantity

½ is only larger than ¼ when we talk about quantity.

A rectangle can have equal parts. I never thought so until I saw how in class today. Reason because I know that it has two long sides and two short sides unlike a square that has four sides all equal.
How wrong I was.  Glad this was pointed out in class today.

Division has a sharing meaning and a grouping meaning
12 cakes divided by 3 children will give the answer that each child will get 4 (Sharing)

There were 12 cakes.  Each child is given 4 cakes how many children will get the cake (Grouping)
We tried division with fraction and many ways of doing and getting the right answer.

¾ divided ¼, when division change to
multiply we have to invert the fraction so it is   

3/4 X  4/1 =3(Ans) or we divided
3/4 divided 1/4 =3

Wednesday, 24 August 2011

Day 3 - 24th August 2011

Day 3 24th August 2011
Case study 1

Few things we should do when teaching young children.
How do we create a collaborative supportive and challenging learning environment?

Some things that I notice were that the children were not able to see the dice - seating arrangement must be changed. Teacher raised and answered her own questions. She needed to use the same materials but she used two different types of materials that was she used dice and apples.  
I learned in the first lesson that we should use the same materials when teaching  children so as not to confuse them.

Second Lesson
Things that went well?
Seating arrangement. The children could see the dice.
Children had materials that they could manipulate.
Children were engaged.Teacher used identical materials.

What did not work in this lesson?

Lesson delivery could have been better.

Teachers Attitude could be improve maybe
show more enthusiasm.

Communication with the children could have been more.

She could have ask the children ," How many possible answer is there if I have 5 cubes".

Case study 2
Research theme:  How can we help pupils to explore different options, articulate their 
thinking and apply what they have learnt in new situations?

In this lesson the focus was on constructing different structures/models with 5 cubes.

1) What I realized was that the sitting arrangement was suitable in a sense that the teacher could see all and could focus on those who needed attention.

2) The children were engaged and they participated well and all the children were involved in the task.

3)  There was only one type of material and this was a much opened ended material.  It could be used in many ways.

4)  Flow was good.  It started off with the teacher telling rules and she started with simple and then complex that is the teacher got the children to work with 3 manipulative and then, 4, and then 5.

5) There was communication between teacher to pupil and pupil to pupil.

6) The teacher was warm and friendly with clear set of instruction as to what the children are supposed to do.

7)  Questioning technique was good.  She rephrases the question.  But there was a part where she asked the same question again and again but the children didn’t understand. I felt here she could have prompted the children so that the children know what she is looking for.

8) Attitude of and disposition of teacher – She provided positive reinforcement.

Conservation of numbers – using 5 cubes,
Make as many patterns as you can.

Our group came up with 20 models of which one was a unique pattern.

Lesson study      
It is a professional development process/tool that teachers engage in systematically to 
examine their practices.This is how it works:-

In conclusion
Learning points from 2 case studies,

1)Designing a task

2)Giving clear instruction and demonstration

3)Effective use of materials and manipulative

4)Differentiation for different ability learners

5)Lesson study as a professional development too.

Homework for today is-Tan gram

Tuesday, 23 August 2011

Day 2 – 23rd August 2011

 Day 2 - 23rd August 2011

Subitize- look and know

Lesson 6 - Stick game
“Pick up Sticks” is a game for 2 players and they have to take turns to take away 1 or 2 sticks from the partner. The winner is the one with 1 or 2 sticks. In the process of playing, children learn: To count – how many sticks, to look for patterns – number sequence, to problem solve, to subitize –visualize the things and know how many.

Take I, take 2. This game is to decide the bad numbers.  The multiple of three
became the bad numbers but when asked to take 1, 2 or 3 sticks then the bad
number changed to multiple of 4.
Lesson 7- Spin a number

Spin the number, was an interesting game where we had to get the biggest even number.
The minute an even number was spun I would write it down at the end of the whole number this is to avoid the odd number appearing in the end.  Well I never got the highest number because I never took risk. But when asked, if we used game cards instead, would that have changed our way of thinking.  One question came up ,"Are you going to put the card back or is it kept away?”  Once Mr Yeap said it would be kept away.  We said our chances of getting the highest number increases as we know which numbers are taken away.

Game Dice
Skills needed for this game is whether they can add, whether they can see a pattern and whether they can communicate, whether they have number sense.
1 6 7 =14

3 5 6 = 14

2 5 7 =14

4 2 8 =14

5 4 5 = 14 
In the class lesson, the children were able to add.  The two ends and the middle add up to 14. Amazing.  I would have never come up with such logic.
Lesson 8 - Division

Yes, you were right I was taught exactly the way you did the sum on the board. 
The teacher would say, “You better listen to me and don’t question
because that’s the way it is, there is no two ways about it.”

         217     (Explanations)
     6        (2 ×  3 = 6)
     05       (6 -  6 = 0)(five is brought down)
      3       (1 ×  3 = 3)
      21      (5 -  3 = 2)(one is brought down)
      21      (7 ×  3 = 21)
       0      (21 - 21 = 0)

We can also divide like this.

Cloud Callout: 51  6             5 1                          divided by 3                                          217     
Cloud Callout: 600                                                        600        
Cloud Callout: 21Cloud Callout: 30                                                         30       

200          10                7 = 217                                                                                                               
We learned about the CPA Approach that is the lesson should be taught in with concrete first, than pictorial and then abstract. Jerome Bruner Theory.

Multiply using the columns and rows. Students can more readily develop an
understanding of multiplication concepts if they see visual representations of
the computation process.

If the child knows 10X3, to find 9x3 is not very difficult, The child takes 10 rows of three and
then subtract 1 row to get 9x3.
Today we also talk about Teach less learn more.
Thinking school and learning nation and about Malcolm Blackwell who said if you spent 10,000 hrs at anything you will be good at it.

Subtraction – 
Take two numbers and subtract a single digit number and the answer is 3
10-7 = 3

11-8= 3
This is called a growing pattern.  After brainstorming we came up with a pattern: - The answer 3, has three solutions, the answer 5, has five solutions, the answer 2, has two solutions and 
the answer 1, has one solution.

Lesson 9– Fraction
John spent ¼ of his money on a gift. He spends 1/3 of the remainder on a book. If he had $72 How much did he spent on a gift?  How much did he spend on a book? How much did he spend altogether?
I have learned today when teaching young children we must get them to look at the sum one step at a time.

4 units = 72
1unit = 72 divided by 4=18
Therefore John spent $18/- on gift and another $18/- on book. He spend $36 altogether and he had $36/- left. (Model below)

For high achiever we can challenge them by changing the fraction.  Enrichment programme is better than acceleration. Children learn procedure understanding.  Learn conceptual understanding that is relation.  
Learn convention in which some are universal and some are contradictory.
I learn a new word today – Metacognition which is a part of the brain.

To sum up: Broad goals are thinking and problem solving, Making, Reasoning , Communication – justify, make connections.
The 5 Big ideas
Patterning, Representation, Number sense\visualization, Metacognition,                                      Generalization, Communication