Mathematics runs many of the complicated and seemingly simplistic operations running in our lives. Thus, children are exposed to mathematics as they go about their daily lives exploring and discovering things around them. And since mathematics has become increasingly important in this technological age, it is even more important for our children to learn math in school, as well as at home. The National Council of Teachers of Mathematics (NCTM) has identified the appreciation and enjoyment of mathematics as one of the national goals for mathematics education. This goal, together with the task of nurturing children's confidence in their ability to apply their mathematical knowledge to solve real-life problems, is a challenge facing by every parent today.
There are 5 process standards set by The National Council of Teachers of Mathematics (NCTM). They refer to the mathematical processes through which children should acquire and use mathematical knowledge
The 5 process standards are:
· Problem Solving
· Reasoning and Proof
The problem solving standard - children are naturally curious learners. They question, investigate, and explore solutions to problems Children may use different ways to arrive at an answer. You can encourage your child to be a good problem solver by involving him or her in family decision making using math.
The reasoning and proof standard - able to think logically, to notice the similarities and differences about things, making connections between cause and effect and making choices based on those differences. You can encourage your child to explain his or her answers to math problems for examples like where they got the answer, how they get the answer, why do they think that their answer is correct. As you listen, you will get to your child sharing his or her reasoning.
The communication standard - use words, numbers, or mathematical symbols to explain situations. You can help your child learn to communicate mathematically by asking your child to explain a math problem or answer. Ask your child to draw a picture of how he or she arrived at an answer to a problem.
The connections standard – Mathematics help us to understand the workings of the world around us. Therefore, children can use mathematics to make connections in the cause and effect relationship among the processes in the world. For example, queuing up according to height or separating into groups of threes.
The representation standard – Teachers use mathematical tools like graphs, pie charts or bar charts to explain figures and their relationship with the items they represent. Manipulative is a useful visual representation, thus a concrete objects that are commonly used in teaching mathematics. They include attribute blocks, geometric shapes of different colors and sizes that may be used in classification or patterning tasks, plastic counting cubes for solving simple addition and subtraction equations. Children might use manipulative materials to mold their creativity, transform that model to a drawing on paper to express their thinking. Your may focus on representing numbers with items, pictures or even family members. For example, learning the basics of counting can use pictures of balls to help children recognize that the number represents the items depicted. Teaching through representation or pictures will allow children to make connections between the real world and the math skills that are crucial for academic success.
There are two learning theories which go with how children carry out mathematics. In the constructivism theory, Piaget emphasized self-initiated discovery. Children can construct new concept upon prior knowledge and the new information expands an existing network. Like manipulating the Lego toys where the children can add on the Lego blocks to build a fantastic model. Children can even use old concepts as basic foundations on which they can use to build their ideas and thought processes.
In the sociocultural theory, Vygotsky placed more emphasis on social contributions to the process of development; Children interact with their peers is an effective way of developing skills and strategies. Teachers use cooperative learning movements where less knowledgeable children develop with help from more competent peers - within the zone of proximal development. It demonstrates children learning from their peers, or from their seniors through coaching, asking questions and even playing.