Although it was just a 24hr course, this whole experience brought me a better understanding in what is math all about, how should it be taught (by understanding how children learn, good practices and the guiding principles - e.g. CPA approach) , the different ways of assessment and the correct terms to use in math.
It made me reflect the way we should carry out our math lesson. We should constantly get children to reason, connect ideas and think logically. Other than planning lessons, we should also take advantage of learning opportunities that happen naturally and turn them into teachable moments. Using these meaningful moments will bring a powerful impact on their learning. To add on, we should also ask open-ended questions to encourage children to think and allow children to explore different ways in solving problems.
We have to always keep in mind that it is the process that matter and we have to let children learn through their own mistake by letting them correcting it themselves.
Providing formulas or steps-to-follow will never do any good to children. They will be 'trained' to 'follow' closely and if they forget the formulas or steps, THAT IS THE END.
"If we do not have struggles and challenges inour work, we will never grow strong and capable. If life has no difficulties, we will become weak and helpless."
Lim Siong Guan, Head, civil service
Well,everything ends. But I will continue to seek for new knowledge in teaching math!
Thank you (Dr Yeap) for being such an inspiration; You brought me to look at Math from a new perspective! :) Math is never dull again!
Assessment is to aid the teacher in identifying the areas that the child needs to improve on and most importantly, use it to help the child improve!
There are many different form of assessment and they can be formal or informal. On top of that, assessment can also be in variation. Instead of getting children to work out the word problem, teachers can get children to come up with word problem. Assessment can also be a form of oral test or interview. I totally agree that teachers have to identify and be clear of what they are going to assess so that they can choose the right instrument.
"An instrument that does not measure what it supposed to measure is an invalid assessment."
Dr Yeap Ban Har
An invalid example that was shared in the class would be:
[Drawing of hr/min hand to tell time]
When we want to assess whether the child is able to tell time, simply just ask the child to tell it verbally / read the clock!! Why bother to ask them to draw the clock and the hr/ min hand. Children who are able to tell the time might not be able to draw the face of a clock. Thus, it is an invalid assessment.
Next, I totally agree with the point - when we are teaching time, get children to relate it to everyday event! I had experienced this before with my class of K2 and they soon began to develop the habit of looking at the clock before lesson, after lesson, tea break etc. Incidental learning is the most beautiful form of learning :)
Never under estimate the capacity of a small container.
(PS: This activity can be another form of assessment!)
Grouping meaning (e.g. in 12, how many groups of 4 are there?)
Sharing meaning (e.g. 12 is equally shared among 3)
The condition for division in fraction is, the unit must be the same with that grouping.
...Fractions seems to be easier after this lesson... :D
George Pick's Theorem
First, we were asked to draw as many different sizes square on the dots diagram. I was only able to come up with 6 different squares. When our classmate shared their no. 7 square, I began to see from another perspective!
After which, we had to calculate the area of those squares. It is interesting that we can find out the answers by dividing the square up, moving and joining them back so we can see a unit easily.
Following, we had to come up with a shape (any kind) that uses only 4 dots. The class came up with many different ones (polygon); some were big, some were small. We proceeded to calculate the area of those polygons - which is not easy at all!
... and...someone save the day!!
*Thumps up* to my classmate who figure out the formula!
Area = (p + i) -3
Writing it out allowed me to see the pattern clearly :) The formula makes calculating of those polygons so much easier :D
Change problems (unknown can be the final, change or initial)
Part-part whole problems (e.g. there are 37 students in a class. 19 students are present. how many students are absent?)
Comparison problems (comparing at least 2 quantities. e.g. i have $37, you have $2 more. how much do you have?)
Children do not learn well through repetition. Exposing children to a variation of word problems encourage children to use the same concepts to work with different problems. This will help teachers to find out how well the children understand.
The condition for naming is to first form equal parts.
The idea of 1 fourth:
We were all given a piece of square paper to fold it into four equal parts.
It was clearly demonstrated to us that no matter how we fold the square paper, as long as we get four equal parts, we can name it!
However, being equal does mean it have to be identical! - idea of variation.
And lastly, from this activity we experienced the process of CPA!
(So that children will focus on comparing more/less and not the properties of the items.)
2. Placing items in a line/ cluster?
(placing items in a line is at an easier level compare to placing items in a cluster.)
3. Use different representation (such as graph chart) to show more / less.
Besides, I also learn that we have to take note of :
-The seating arrangement during activities
-Giving quality instructions
-Asking questions to stimulate thinking
-The design of task to provide differentiated instructions to cater to different needs
-Use of manipulative/ materials
-Sequence of lesson
Case study 3:
Ms Peggy's lesson
Three things i would take away from her lesson:
1. The way to ask questions to stimulate children's thinking.
2. To take note of the different ability of the children and come up with differentiated instructions (using the same activity) to engage all the children.
3. Using of open ended materials.
I love the way Ms Peggy asked questions and using all opportunities as "teachable moment". In addition, I can see that the children were really engaged and learning math through a fun way. I will definitely take note of all these good practices! :)
Fun with 5 unifix cubes - Learning the idea of conservation of number.
This is a great hands-on activity to get children to be creativity and at the same time learn the idea of conservation of number!
This activity focuses mainly on counting (1,2). To cater to children with the higher ability, using the same activity, we can challenge them by finding the bad number.
From this, i learnt that activities should always have different levels to challenge children's thinking. It is important as teachers to be able to observe the children in the class and give differentiated instructions to cater to different needs.
Another 'magical' activity which integrates addition, finding patterns and communicating math ideas!
How Children learn Math
Children learn through the CPA approach (Jerome Bruner)
1. Concrete Experiences
Children will not learn anything by memorizing.
"Using memory to learn is using the HUMAN WEAKNESS to learn."
(That's why we invented paper to jot things down!)