I was really nervous about this course because I have never felt confident with my math abilities or lack of them. Also, I am not working as a teacher, therefore I never practice doing math except with my son who is probably better than I am at math. He is currently in Primary 4. However, I acknowledge that math is CRUCIAL and always have encouraged my own children to be confident in math and told them that they can do it. It is all about attitude; I believe you can do anything with support. Dr. Yeap made the lessons very interesting and I experienced how to DO math and that there are a variety of ways to arrive at an answer. In addition, I learnt that it is important to justify and check the results. Does it make sense?
Lesson One:
Name problem: We counted letters in a certain way (in Dr. Yeap’s name) and then tried to figure out which letter is the 99th.
B A N H A R
1, 2, 3, 4, 5, 6
11, 10, 9, 8, 7
12,13,14,15,16 and so forth…and then we arrived to 99 which was letter N.
It was interesting to observe the pattern that was created and it made me realize that yes, math is a science. As stated by Van De Walle, Karp and Bay-Williams (2010) mathematics is a science of concepts and processes that have a pattern of regularity and logical order. There is actually a logical way to figure this out and there is a variety of methods that we looked into. We looked at three methods:
1. Look at the pattern (9 in which place?)
2. Multiples of 10 or multiples of another number?
3. Division method (minus first row 6, then divide by 5). However, with this method how do we know which way to go left or right???
Another interesting way could be to look at the difference vertically. What pattern do we see now?
Also, we discussed how numbers are used differently.
Cardinal numbers:
We are counting the number of things. For example, number of cookies, people, etc. It is the quantity of something that we are trying to establish. We also use cardinal numbers when comparing.
Ordinal numbers:
This is when numbers are used to indicate position in space respective time such as 1st, 2nd, 3rd etc. For example, the 22nd of August is an ordinal number.
As teachers Dr. Yeap highlighted it is important to pay attention to the way we ask math questions. At times teachers make mistakes in designing ordinal number tasks.
For example:
Who is third in the race? (Ordinal number with respect to time). Please note that the teacher cannot ask this question when only showing the picture because we do not really know who will win.
However, when showing the picture the teacher can ask: Who is third from the finish line? (Ordinal number with respect to space).
As teachers it is important (especially when assessing students) to know the difference of “rote counting” this is when the child just recites the numbers instead of “rational counting” when the child actually has an understanding of counting and saying a number for each item.
Nominal Numbers:
The number is just the label. For example, bus number 14.
Measurement Numbers:
This is the number used to measure. For example, I am 1.57 meters tall. It is important to use non-standard units before primary school and get the children to compare a variety of items.
Continuous numbers are are limitless and used for measurement– For example, 1cm, 1.5 cm, 1.72 cm etc.
Discrete numbers are used for counting – 1, 2, 3, etc.
Lesson Two:
Sound of numbers: Is it possible to actually hear how many items are in the can? Dr. Yeap showed us the first can and inside he placed two buttons. Then shook it to allow us hear what two buttons inside a can sounds like. Next he had buttons in a bottle. The bottle had definitely more buttons inside judging from the - noise it made when shaking the bottle but how many buttons are inside…is it possible to guess?…well not that easy.
This lesson was about what we can count and cannot count. It depends on the unit…teachers need to ensure that the items to count are perceived as the same type (or set). For example, buttons do not have to be the same color but at least the same type of buttons. You clearly cannot add 2km + 1kg because there are not the same units.
Lesson Three:
5+6+7: We were discussing various ways children may count. It is crucial that children develop the basic number facts and operations. As teachers we have to look at a variety of different strategies children may use and the complexity of the operations. I learnt the value of introducing the ten frames. It helps the child to think in fives and tens. Also, teachers should do ongoing assessments to find out how the child is counting in order to understand which level he/she is at the moment and what other strategies can be introduced to facilitate counting. For example, count on, count back, make and count groups and how numbers relate to each other. Has the child reach commutative property of addition? This means that the child understand that 5+7=7+5. The child has addition facts.
This is an example of a ten frame:
The prerequisite to meaningful counting are:
1. The ability to classify and sort.
2. The ability to rote count in sequence.
3. One to one correspondence.
4. The last number that is uttered represents the number in the group (the cardinal number).
Once again, it is important to do ongoing assessments to see if the child appreciates the conservation of numbers (that numbers do not change by moving the items around). Does the child make a ten strategy (beyond addition of ten)? Or does the child not see the value to grouping the numbers and is just counting them? Counting them is the most primitive way of counting It is important to look at what the child does and does not have an understanding of.
Lesson Four:
Spelling Card Trick:
Here we were to arrange nine playing cards face down.
Tap the first card and say “o”, the next say “n”, the next say “e” (spelling “one”)and the fourth card you turn over and it is the Ace! (or one card)
1 |
O N E
Next spell t…w…o…starting with the 5th card. Then you will show the playing card number two and so on.
1 | 2 |
T W O
You have nine cards from Ace to 9 that you have arranged in this particular order face down.
6 | 5 | 4 | 1 | 9 | 3 | 8 | 2 | 7 |
Dr. Yeap asked us to arrange the cards using a variety of methods.
1. Acting it out. However, you had to rely on your memory. Do not use memory to learn because we forget easily. I agree!!!
2. Lining the cards up on the table.
3. Writing the cards on a piece of paper.
This is how it should be arranged from top to bottom:
Lesson Five:
Number Tiles Puzzles:
In this lesson we had to arrange five numbers so that they add to the same total, both vertically and horizontally. For example 1, 2, 3, 4, 5.
3
5 1 2
3
5 1 2
4
With this arrangement the total number is 8.
With 3 in the middle the total number is 9.
With 5 in the middle the total number is 10.
We also tried using number 2, 3, 4, 5, 6.
1 in the middle the total number is 8.
3 in the middle the total number is 9.
5 in the middle the total number is 10.
2 in the middle the total number is 11.
4 in the middle the total number is 12.
6 in the middle the total number is 13.
Observe the pattern! We also recognize that two even numbers can never equal an odd number. Two odd numbers always equal an even number.
We discussed how to observe a vertical pattern versus a horizontal pattern.
Numbers Total
1, 2, 3, 4, 5 8 Look at the pattern 1+2+5=8, then 2+ 3+4 = 9
9
10
_____________________
2, 3, 4, 5, 6 11 Look at the pattern 2+3+6=11, then 3+4+5=12
12
13
_____________________
3, 4, 5, 6, 7 14
15
16
_____________________
How about?
72, 73, 74, 75, 76
IMPORTANT! A pattern is a sequence that has a term (elements that make up a pattern) and a rule and both have to be stated in order for the student to solve the pattern. It could be a repeating pattern or a growing pattern. The teacher must state the terms and rules for the students in order for them to solve the pattern.
Thank you Dr. Yeap! I wish I had this hands-on math experience when I was younger… it would have made a world of difference to me. Exhausting but fun!!!!!!
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