I’ve learnt many things during this module but the 3 things that have the most significant impact are:
1) The goal for teaching Mathematics, and that is to develop the mind, gives purpose to what we are doing as Early Childhood Educators. Having established that Mathematics is a tool used to develop the metacognition of the child, becomes clear for me as a teacher because it affects how I teach.
2)The objective od teaching Mathematics is to develop problem solving skills with a keen sense of patterning, visualization and number. Therefore whatever we do cannot be done at random, because we want to make a point. The consciousness of how we deliver content is so critical so as to ensure that we capture every opportunity for the learning of the child.
3) Jerome Brunner’s Concrete, Pictorial and Abstract theory is a constant nag for me now, as I enter the classroom. I believe strongly too that children move from concrete to pictorial and from pictorial to abstract way of learning.
We cannot control the learning stage of children because they learn and move on to different levels at different times. Therefore differentiated learning is important to ensure that at any stage, the child is challenged in her/his learning.
1) Is it possible for children who do not have a strong process foundation in doing Mathematics, pick it up later in secondary school?
2) Can children with dyscalculia learn Mathematics? They may have issues with numbers, but how about learning patterns and visualisation? and training their mind to problem solve?
What attracts young children to learn are the fun things around them that they can explore and play with. One of these interesting thing is the calculator. It is especially so when children have “discovered” numbers. Knowing how to read and play around with the numbers make them feel important because they see the adults doing it. My niece who is about 4 years of age was with me one day. I had been doing some work and she was at the table with me. I saw her using her tiny fingers pressing down at the key pad of the calculator. She was trying to press on the numbers that she saw on a piece of paper. She had managed to get them all correct. She was able to recognise the numbers and correspond with each number that she saw on the paper to that of the calclator. I thought it was a good way to revise recognition of numbers. She had begun developing some fluency at pressing on the key pads of the calculator allowing her to develop her proprioceptive muscles.
Children today also have the advantage of playing games on the computer allowing them to have both visual and sound effects in their learning. In many Mathematic games on the computer, are both interactive and engaging, therefore keeping the children “occupied in learning” for long periods of time. Although I am not a fan of children engaging themselves with computers, I also realise the benefits it provides for the children to learn. Technology in Mathematics for children’s learning need adult supervision, especially for young children. This is so that new challenges can be provided to develop metacognition, allowing children to grow and construct new knowledge.
One thing that keeps repeating itself everyday at each of the lessons given, was going back to the goal of mathematics, and that is: 1. looking for patterns 2. visualisation – the ability to see things that are difficult to see 3. number sense.
I think that it is important to have this at the forefront of all the lessons that we plan for our children, so that we will be able to look at how we are helpiing them learn mathematics.
It was reassuring to hear that exposing children to looking at the analog clock everyday and talk about the time of the day are concrete ways in learning how to tell time. I have seen teachers who have spent mathematic lessons (2 or 3), teaching time and the blank look on the faces of the children. I wonder to myself “the children can’t see the time”. It makes no sense.
The goal of mathematics applies to all aspects of our lives. We look for patterns in our everyday situations and relationships, we visualise challenges and we probably, not use number sense, but common sense in handling our everyday affairs. I think it is a good philosophy of life to have especially in the Early Childhood environment whioch we work, because it is also good role modelling for the children.
I agree that counting plays a key role in constructing base-ten ideas about quantity and connecting these concepts to symbols and oral name for numbers. As I was reading p.194, I was overwhelmed by the complexities of counting. I then thought of the children in my K2 class who have visual spatial and co-ordination issues and those with learning differences (dyslexia, SLI-Specific Language Impairment). These are the children who struggle with base-ten phrase, the symbolic scheme use for writing numbers (ones on the right, ten to the leftof ones, and so on), or even grouping, because of orientation, spatial and reversal issues. I think it is important to know our children and be sensitive to how they learn. They are unable to “make sense” because they have barriers in their learning. However, I strongly believe J. Bruner’s learning theory, to start with concrete before pictorial, and pictorial before abstract is an excellent approach to allow children to “make sense” od counting and construct for themselves the relationship of counting by ones and grouping-by-ten concept.
To be able to solve the problems today during class and then feel a great sense of achievement was definitely inspiring for me. I think that it is important that we have different perspectives to an answer, rightly or wrongly, because it allows us to explore. The lessons today did just that for me, it allowed me to explore. I did not feel so threatened and therefore felt that I could move forward. It was definitely good for my self esteem and confidence in learning.
Last week, a group of K2 children were asked to pack away the big blocks back in the shelves after play, by their teacher. I walked pass and saw the children trying to push the blocks in, even where there was hardly any space left. I was about to intervene but stopped short when I saw one of the boys pulling out the longer blocks. I thought to myself “What on earth was this boy doing?” Then I saw his friends moving away from him, not wanting to have anything to do with the blocks. He continued to clear the 2 lower shelves and started to put the longer blocks in first. He stacked them one on top of the other and put in a few of the square blocks at the small spcae at the corner. There were still a few odd-shaped pieces left and he managed to make space by adjusting the upper shelves, arranging the rectangular blocks, stacking 3 upwards, making space for the odd-shaped ones, by also stacking them.For me, this boy was “doing Mathematics”. He saw rgat there was no way to put all the blocks in by shoving them in. So, he decided to arrange them according to size and length. I think he tried to apply a bit of the concept of measurement, and was exploring ways to solve this problem of the different sizes and shapes of the blocks, and how to get them into the shelf.
I am so impressed and excited by the 5 process standards on p.4 of the texbook. For me, they make sense. However, I am now challenged by this boy, how do I teach in a way that will reflect these process standards?
Got to learn more about it.