How do I view Mathematics?
In one of the tasks given, there was a statement that said, "Doing a math problem is like finding your way through a maze. There are lots of possible pathways to go down". I feel that a Maze is really suitable to describe my view regarding Math because in a maze, even though there are many ways in order to get to the destination, but most of the time I got lost in it. Mathematics for me is a slow process that I always need time to understand them. Besides, growing up as a mild Asperger person, a maze-like feelings towards math is not a surprise since some Aspergers have problems in mathematics (Griswold, Barnhill, Myles, Hagiwara, & Simpson, 2002 )
What is my assumptions about early childhood mathematics?
My assumptions on early childhood mathematics is that children would learn them when they enter kindergarten at the age of 5 as they would have a formal learning on numbers and some addition. However, after the first workshop, I realize that children grow up with mathematics as they explore the things around them. Likewise, i was once a child who may not know what is 1-10 but in truth, I had already experienced mathematics while I looked at the different flowers at my backyard, played with my mothers’ shoes, when we baked some cookies or looked at the heights of the coconut trees around my house. That was mathematics!! Thus, I should not say that i’m not good in mathematics as I am used to the concepts of mathematics since I was a small child.
Now, I am a student and I also work part timely as a babysitter where I would take care of kids from different age groups. Therefore, studying this subject has made me more conscious about the kids that I have babysitted. Some beginning processes started to make sense for me and I also reflect on my own development in mathematics when I grew up.
The beginning processes in mathematics are:
1. Identifying and describing attributes
2. Matching
3. Sorting
4. Comparing
5. Ordering
6. Patterning
2. Matching
3. Sorting
4. Comparing
5. Ordering
6. Patterning
These processes are the vital before moving on to higher mathematical concepts. Children use their 5 senses in these processes which are, taste, see, smell, hear and taste (Irons, 1999). Besides, it is also essential to highlight Vygotsky theory of zone of proximal development which is the gap between what children can do by themselves and with assistance from adults (Smith, 2009,p. 10). Thus, they need the adults and their peers in order to understand the beginning process through negotiation with friends and scaffold by adult (Smith, 2009,p. 10).
1. Identifying and describing attributes
Children learn how to be more perceptive in this process as they talk about similarities and differences of two objects. Language is central in identifying and describing in details of the objects because they have to make reasoning of the similarities or distinction made. For example, when they look at the two boxes in the picture above, they would say that they are the same because both are gift boxes or have the same shape. They would also make reason of why these two boxes are different from each other based on their colour, decoration and even the texture of the box for instance the pink box is smooth and the yellow box has uneven surface.
Matching on the other hand allows children to choose and describe two objects that have similarities with each other (Irons, 1999). Likewise they would choose on the attributes that they think the two objects share for example; when given the miniature dinosaurs above, let the children match them together and then ask them to talk about their choice. They may talk about how the dinosaurs in one group are the same because both of them have long tails or have sharp claws. Further, they can move to matching activities which involve symbols or illustrations such as matching pictures of dinosaurs with the outlines of dinosaurs (Irons, 1999).
3. Sorting
When given large number of objects, children can do sorting where they would match them according to more than one attributes and group them together (Irons, 1999). Adult can use the wooden 3 dimensional objects and let children sort them; additionally, questions for scaffoldings purpose can be asked such as, 'how do want you arrange the objects?' 'Can you explain the features of each group that you have sorted?'. Besides, children can also try sorting real things for example, the fruits in the picture above.
Children also can do sorting using this board game where 2 dimensional pictures are used; this game particularly is highly challenging for children and suitable for group activities since they can interact with peers in making decisions to complete the board.
4. Comparing
In comparing, children learn how to observe the differences in various characteristics such as size, weight, temperature or loudness (Smith, 2009,p. 57). They can compare weight by lifting up two objects and decide which one is heavier. For instance, they can be given two luggages and adult can ask them questions such as 'which one is bigger than the other?' or 'which one do you think is heavier than the other', then, allow them to measure the size using measuring tape and decide the weight by lifting each luggage. Comparing process promotes children to practice using comparing words such for example, ‘smaller’ or ‘bigger’ than the other objects; nevertheless,adult need to model their usage to children in order to enhance children understanding in this process.
5. Ordering
Children learn to organise three or more objects or pictures in decreasing or increasing manner (Irons, 1999). For example, adult can give a set of Russian dolls and ask them to arrange them according to height; children can be scaffolded via comparing questions such as 'which one do you think is the tallest?' and 'which one do you think should be the first when you arrange the dolls ?'. Other than that, they can also practice ordering using ‘realia’ namely, everyday objects such as books in different sizes.
7. Patterning
Children make easily identified and expected repetition of objects or pictures (Irons, 1999). For example, children can make a pattern using the jigsaw mat above by ordering a repetition of the colour yellow, red and blue. In addition, they can make a pattern using colourful shapes or beads.
Learning experience during math class
Patterning- I always thought that pattern can only be done using objects but the first workshop had made me realize that it can also be done in the form of sounds as long as it is done in a pattern either ascending or descending. watch the video below to understand more on making a sound pattern~^^
These bells were used for making the sound pattern, in classroom, teachers can ask children to make their own sound pattern by shaking it once, twice and then three times repeatedly. It is a fun activity especially for children who learn best through musical instruments (Armstrong, 2009)
Learning experience during babysitting a soon to be 4 years old kid~
This is Talah, i’ve babysitted her since last year. So, as mentioned before, taking this subject had made me aware of her mathematical development as well as her language development. One significant event which made me realize that she is doing the beginning process is when we were playing Lego together as she sorted the Lego according to the colours when she put them back in the container. It was so amazing to see her putting the yellows and then blues before the greens into the container. Besides, when I asked her which Lego tower is taller between the two towers that we have built earlier, she pointed out at the correct tower. Therefore, this had made reflect that I must have gone through the same process when growing up. In future, I would be more observant towards the kids that I babysit in order to help them develop their mathematical skills and at the same time reflect on my teaching abilities.
Armstrong, T. (2009). Multiple intelligences in the classroom. USA: ASCD
Griswold, D. E., Barnhill, G. P., Myles, B. S., Hagiwara, T., & Simpson, R. L. (2002). Asperger syndrome and academic achievement. Focus on Autism and Other Developmental Disabilities. 17(2), 94-102.
Irons, R. (1999). Numeracy in early childhood. Educating Young Children: Learning and Teaching in Early Childhood, 5(3), 26-32.
Smith, S. S. (2009). Early childhood mathematics. USA: Pearson education
Grist, M. J. Story craft [image]. Retrieved August 23, 2011 from
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