We looked at differentiated instruction today. We looked at the variations of lessons and how it differed: through content, process or product.
Through the differentiated instruction, we can plan for struggling students and advanced students. Using this form of instruction gives me a better idea in planning lessons. It gives me a guide, a structure to think about when planning a lesson; how to better cater to the needs of the children.
Overall, I think this module has helped me look at math from a different perspective. It has also changed how I think children should learn math: the way I was taught. Now, I believe that it is more important to equip children with the understanding of the content more than drilling children to get the answer to the content. When children have the understanding and knowledge to apply it, then they can solve any problem that they are given.
Below is a video that stresses the importance of visualization in children learning math. I think it further emphasises on what was discussed throughout all the lessons on how children learn.
Monday, August 19, 2013
Session 5 - Angles
We did a word problem from last year's paper.
Doing this problem gave me a good chance of putting what I have learnt many years ago into good use. After attending so many sessions of Dr Yeap's, I started questioning myself and reminding myself that every sentence in the question is a piece of information that will help me in solving the question. I was able to solve the question halfway and gave up because I thought it was a dead end. Awhile later, my classmates gave the answer and their solution was the same as mine! They managed to solve it till the end and reminded me that some of the angles were the same because of the properties of the shapes. I was still proud of myself because if I was given this question before attending all these classes, I would give up after reading the question. At least I made some improvements and managed to solve it... halfway.
Always, when we finish discussing a question that was done by primary school students, I would think, is our math that bad?
Doing this problem gave me a good chance of putting what I have learnt many years ago into good use. After attending so many sessions of Dr Yeap's, I started questioning myself and reminding myself that every sentence in the question is a piece of information that will help me in solving the question. I was able to solve the question halfway and gave up because I thought it was a dead end. Awhile later, my classmates gave the answer and their solution was the same as mine! They managed to solve it till the end and reminded me that some of the angles were the same because of the properties of the shapes. I was still proud of myself because if I was given this question before attending all these classes, I would give up after reading the question. At least I made some improvements and managed to solve it... halfway.
Always, when we finish discussing a question that was done by primary school students, I would think, is our math that bad?
Session 4 - Geoboard
We did a lesson on geoboard today. I personally enjoyed this lesson. We were asked to form a shape with one dot in it and guess the area of the shape.
This was my shape in purple:
I counted and there are four squares in my shape.
Many different shapes were shared in class and the class managed to spot the pattern where we could count the dots outside the shape, divide it by 2 and know how many squares are in shape. It then led us to Pick's theorem where Area = i + b/2 - 1
I find it quite fascinating that there is a theorem to finding area on a geoboard. I always thought that geoboards are used for children to make a bunch of shapes using rubber bands. I never knew that an activity like finding area can be taught using geoboard let alone that there is a theory for it. This made me think twice about Math. Math can be interesting too.
This was my shape in purple:
Using the square in the corner, how many squares can I count in my shape?
Many different shapes were shared in class and the class managed to spot the pattern where we could count the dots outside the shape, divide it by 2 and know how many squares are in shape. It then led us to Pick's theorem where Area = i + b/2 - 1
I find it quite fascinating that there is a theorem to finding area on a geoboard. I always thought that geoboards are used for children to make a bunch of shapes using rubber bands. I never knew that an activity like finding area can be taught using geoboard let alone that there is a theory for it. This made me think twice about Math. Math can be interesting too.
Session 3 - Dice
Dr Yeap showed us two die today. He put them together and was able to guess the sum of the numbers that was covered. We discussed ways to how we could manage to do that too. Honestly, I find it difficult to imagine where the number should be to guess the unknown numbers. Up till now, I still do not understand fully how it is done.
However, I did learn something new: subitize, which means I could look at the dice and tell how many dots are there without counting. Turns out that what I always thought as using symbols to represent the value of numbers actually has another word and another meaning to it. There is more than meets the eye. It is not just a bunch of pictures or dots that are there to show children the value of numbers.
This video below gives an example of an activity to do with children on subitizing. I think it is a good activity but I would prefer to use one coloured dot stickers instead of different coloured dot stickers as suggested by the person who made the video. I think one coloured is easier and does not overwhelm children. If different coloured dot stickers are used, then children will be counting instead of subitizing, which defeats the purpose.
So, what do you think? One coloured or different coloured dot stickers?
However, I did learn something new: subitize, which means I could look at the dice and tell how many dots are there without counting. Turns out that what I always thought as using symbols to represent the value of numbers actually has another word and another meaning to it. There is more than meets the eye. It is not just a bunch of pictures or dots that are there to show children the value of numbers.
This video below gives an example of an activity to do with children on subitizing. I think it is a good activity but I would prefer to use one coloured dot stickers instead of different coloured dot stickers as suggested by the person who made the video. I think one coloured is easier and does not overwhelm children. If different coloured dot stickers are used, then children will be counting instead of subitizing, which defeats the purpose.
So, what do you think? One coloured or different coloured dot stickers?
Session 2 - Whole Numbers
This session was all on whole numbers. It also talked about adding, dividing and multiplying.
We were asked to tear a piece of paper into 9 smaller pieces and number them 1 to 9. Then we had to do multiplication with the numbers with no numbers repeated.
At first, I just mixed and matched the numbers and could not find a solution. Then, I stopped and tried to reason with myself a way to do this. I first tried to find the 2nd digit where there would not be repeated numbers.
For example, if the 2nd digit of the first number is 7, then the number that it multiplies with is 2, the 2nd digit in the answer is 4. This way, no number was repeated.
To find the first digit, I could use 1. The solution would be 17 x 2 = 34. None of the numbers were repeated.
Doing this activity made me think. Although it is trial and error to get the answer, but thinking is involved when finding a number to try out.
The video below shows different ways of solving multiplication problems which I found to be very useful as it visualises the reason behind doing multiplication the traditional way that I was taught.
We were asked to tear a piece of paper into 9 smaller pieces and number them 1 to 9. Then we had to do multiplication with the numbers with no numbers repeated.
At first, I just mixed and matched the numbers and could not find a solution. Then, I stopped and tried to reason with myself a way to do this. I first tried to find the 2nd digit where there would not be repeated numbers.
For example, if the 2nd digit of the first number is 7, then the number that it multiplies with is 2, the 2nd digit in the answer is 4. This way, no number was repeated.
To find the first digit, I could use 1. The solution would be 17 x 2 = 34. None of the numbers were repeated.
Doing this activity made me think. Although it is trial and error to get the answer, but thinking is involved when finding a number to try out.
The video below shows different ways of solving multiplication problems which I found to be very useful as it visualises the reason behind doing multiplication the traditional way that I was taught.
Session 1 - Tangrams
The first lesson we had for this course was on Tangrams. We were given 7 pieces of tangrams. The problem was to make rectangles with the tangrams.
It was fun to mix and match the tangrams to make rectangles. It made me think and I used trial and error to find ways. I remember feeling excited when I found several ways but gradually got a little irritated when I could not find a way to use all 7 pieces to make a rectangle. This reminded me that it takes patience to do an activity like this. It also makes me think about what children would feel should they be posed with a problem like this.
Nonetheless, we still managed to solve the problem. There are actually many ways to solve the problem. The pictures below are just some examples among the many.
Making a rectangle with 3 pieces of tangrams:
4 pieces of tangrams:
7 pieces of tangrams:
It was fun to mix and match the tangrams to make rectangles. It made me think and I used trial and error to find ways. I remember feeling excited when I found several ways but gradually got a little irritated when I could not find a way to use all 7 pieces to make a rectangle. This reminded me that it takes patience to do an activity like this. It also makes me think about what children would feel should they be posed with a problem like this.
Nonetheless, we still managed to solve the problem. There are actually many ways to solve the problem. The pictures below are just some examples among the many.
Making a rectangle with 3 pieces of tangrams:
5 pieces of tangrams:
6 pieces of tangrams:
7 pieces of tangrams:
Sunday, August 11, 2013
Note to Parents #1
Dear Parents,
Learning math today is different from the past.
In the past and in my own growing years, learning math was sitting on the floor or at my desk, listening to the teacher go on and on about concepts that I hardly understand. Today, learning math is about being interactive and actual application of the concepts taught.
Looking at the readings, there are six principles, five content standards and five process standards in what children learn in math today.
As for the teacher who teaches math, she needs to equipped with seven standards and be able to create six components in a mathematics classroom.
Out of the seven standards, persistence is what I feel is greatly needed in every early childhood educator when teaching math to children. Personally, I do feel the frustration sometimes when trying to deliver a concept to a child. However, as what is suggested, persistence is the "very skill that your students must have to conduct mathematical investigations (Van de Walle, Karp & Bay-Williams, 2013, p. 10). It is essential that we display such quality to children when dealing with the subject of math.
Next, we talk about conducting math lessons in the classroom. It is important that we do math as it is in the real world and not as a form of accomplishing a stack of worksheets. Children should be allowed to participate in math actively when they experience the process of reaching a solution and not just drilled to know the answer to a question.
One interesting fact is the use of tools and manipulatives. I must admit that I teach children the use of such tools by asking them to mimick my actions when dealing with a certain form of questions, for example, addition. However, by doing so, I am not teaching children math at all. I am only teaching them to follow my actions; drilling them to know the answer to a question. I am not allowing children to participate actively in the process. I can show them how I solve a problem with the help of the tools or manipulatives. If I explained well, children will be able to use the tools to solve their own math problems based on their understanding and not by the steps that I make them follow.
Overall, I did learn something by reading the first two chapters of the book, "Elementary and Middle School Mathematics: Teaching Developmentally (8th Ed.)". Parents, if you are interested, you might want to read the book as well as we embark on this learning journey of teaching children math together.
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References:
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally. (8th ed.). Pearson: New Jersey.
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