Chapter 2 Reflection

Mathematics and language is inter-related. Nowadays, mathematics is a test of language, understanding of words. Besides knowing adding, a child needs to know that, the sums, altogether, in total and etc means the same. Because of this, math is no longer straight forward. You have to understand the language, the logic, the patterns and the sequence in Mathematical concept. 


Theories
In the textbook, it discuss the two theories which can be used to explain how we learn mathematics.

First, it's the constructive approach of Piaget, we learn math through constantly building on our prior knowledge and creating new knowledge out of it using the tools and materials which we know. It's like building blocks, we build our foundation before building the top but at times, the blocks may fall and we build it up again based on what works and does not works on our previous experiences.

Second, it's the sociocultural theory of Vygotsky. In sociocultural theory, mental processes exist between and among people in a social learning setting. Secondly, the learning depends whether it is within the learner's zone of proximal development, a range where the learner is able on ones own and learning from the support of others. Next, it's semiotic mediation which refers to the use of language and culture which is interrelated which includes the use of mathematical symbols and it is through learners' interaction in class through activities which develops the meaning of these symbols.


Implications for Teaching Mathematics
However, it is good to be informed of the theories but it is not a teaching strategy. Theories give us an idea how children learn and process their knowledge and how we teacher can support their learning process:


Providing opportunities for children to talk about mathematics in their normal routine and classroom activities. One of the good example is to do counting while waiting for children to clean up or to line up for the next activities. Different numbers can be use to count down or even shapes. Another good opportunity is to get the children to keep learning materials by sorting them according to their characteristics. Children will have opportunity to reinforce what they have learn in a different context. This is a funny activity which children of different age group can do. Teachers can also find opportunities during their outdoor play too.


Building in opportunities for reflective thought through planned activities which engages children in interesting problems in which they use and build on their prior knowledge. Learning corner activities and construction play are good opportunities for children to engage in independent reflective thinking. After all, play is the most natural setting for all children.


Encourage multiple approaches through different variations of activities from hands-on to visual cards to paper-pencil activities. These will encourage children to transfer and relate their knowledge and skills across different activities. Children will be able to learn how to relate what they have learnt and apply in different context. In our school, besides learning mathematical concepts through hands-on activities and activity sheets, we also engages the 21st century technology in using computer software in engaging children in math. Math concepts are presented in interactive games which children can play as a group or as an individual. This is use to reinforce the concepts whiche the children had learnt during class time.


Engaging students in productive struggle which allows children to work with different level of activities and to challenge them to the higher level when possible and giving them appropriate time frame to work on it. This will give time for children to try to on it on their own, rather than depending on their teachers for solution.


Treating errors as opportunities of learning and exploring different ways of solving the errors. Confidence and positive learning needs to be cultivated to young children to persevere in their learning and treating mistakes as learning point. Teacher needs to reinforce by affirming and encouraging the child to try other ways instead of jumping in to give the right answer to the children. Facilitation is important, which is the role of the teacher. 

Scaffold new content and remove when the children are able to be independent in working on the mathematical concept. Teachers are encouraged to do observation of children in order to assess the readiness of a child in the mathematical concept. This will allows the teacher to know the zone of promoxity for the children as to move them to new learning concepts when they are ready.

Honor diversity learning in young children has they all have different prior knowledge and background in their learning. Teacher should be sensitive and provide opportunities for young children to learn in different stages. For myself, I uses exercise books for differentiated learning. Example, different math sums and problems will be given to the weaker and stronger children and the average children will work on the common sums given. The sums will be written into their exercise book to challenge the children at the right learning level. The use of computer software programs also provides opportunity for children to learn math at their own level. The program which we use has different learning levels for different concepts.


Mathematics Proficiency

Mathematical Proficiency requires teachers to put in alot of effort as mathematical concepts and connections are developed over a period. Activities are selected to help children to progress developmentally.

Learning math in an instrumental manner will help children to be effective learner of learning new concepts and methods in solving mathematical problems. Children are constantly engaging in building on their existing knowledge. Through this children can make more connections based on what they are learning and what they had learnt as we constantly challenge them to think further.

Children will also have less to remember as they learn in an instrumental manner. Children will be able to connect and "big ideas" (Brooks & Brooks, 1993) which are interrelated concepts.

In order for children to connect to more concepts, children needs to retrieve inoformation and connect to their ideas. As children connect, it increased retention and recalling of information for young children.

As children work and connecting with more concepts, it enhances problem-solving abilities. When children is familiar with the concepts adn the relationships between a situation and a context, and they will be able to identify and solve the problem.

When children are familiar with the concepts as they work with over a period of time, children will be more confidence in their learning. Children can also improve their attitudes and beliefs as they make sense of what they are leanring. It also develops a positive self-concept and confidence in the child's ability in learning mathematical concepts.


Math is like connecting different dots together to make sense of what they are learning and they are going to learn. It is how teachers facilitate children's learning in connecting the dots.