Sunday, 18 August 2013
Concrete, Pictorial and Abstract Approach, Scaffolding and Modelling.
I like the mathematics exercise using the 'Ten Frame' which I can use for instructional. On the other hand, the children get to explore and to conceptualize the number bond in more than only one way to experience whole number.
Another important lesson I learnt through this session is that 'never count the number with different nouns'. I used to think that counting is counting, so why the children in my school were not able to add the sum of boys and girls as the overall number of children in the class. I need to rephrase by asking the children to count as a class then sought the number of girls from the boys. I have to more mindful in the structure of language as not to cause ambiguity that mislead their understanding.
The five-frame or the ten-frame concrete apparatus for number bond enable children to visualise as they explore and experiment the whole number by counting one by one using manipulative. With concrete manipulative they are developing the computation and internalised the connection of number bond and number sense.
To develop children ability to learn with understanding, teacher support the process by scaffolding, modelling and allow them to explore and to achieve the baby step success. The use of language and the construction is equally important as not to cause confusion and ambiguity.
Thumb of the rule never to count number with different nouns such as to add four apples and two pears.
Session 6 on 17th August 2013
The key words of solving mathematics problems are patterning, generalisation, visualisation, reasoning, and inferring.
Monday, 12 August 2013
How children learn mathematics?
Interestingly children undertake every mathematics task is problem solving. It is the construction and connection of the existing ideas to the new ideas that link to the meaning of the potential relevant ideas when learning a new concept.
The existing ideas on their prior experience of knowledge with the combination of drill and practicing to reinforce in scaffolding new knowledge from prior knowledge further their conceptual understanding.
Children learn well when they are able to relate with concrete manipulative, pictorial visualise in their brain. Therefore it is concrete before pictorial and pictorial before abstract.
Thursday, 8 August 2013
(Van de Walle, J.A., Karp, K.S., and Bay-Williams,J.M. (2013), Elementary and middle school mathematics (8ted.). USA:Pearson.
Learning mathematics is fun! Children learn better as “doers” when they are involve with mind intriguing verbs such as compare, describe, explain, explore, investigate, predict, represent, solve, use and represent. These mind intriguing verbs definitely will spur them to think further; in addition with encouragement and development opportunities creating higher-level ideas in ‘making sense’ and ‘figuring out’ to a solution.
Doing mathematics required effort with the combined collaboration together with the families and the community in order to enhance mathematics learning development, (National Mathematics Advisory Panel, 2008).
In mathematics, the conceptual understanding is when the children apply their previous knowledge, testing ideas, making connections and comparisons. In the process the children take the struggle into their strike and sense their achievement when they are able to solve a solution, (Carter, 2008).