How should Mathematics be experienced by the learner?
I agree with the author when he said that we tend to feel proud of our accomplishments when solving tough problems. Therefore, persistence, effort and concentration are important in learning Mathematics. It sure felt good that you were able to find the answer after a long struggle trying to understand the question. The learner should generate strategies for solving problems, applying those approaches, seeing if they lead to solutions and checking to see whether your answers make sense. It's always inspiring to see children find solutions to the problem themselves and often I used this observation as part of my assessment on that child. Learners should be given opportunities to interact with each other and with the teacher. Classrooms should be conducive for learners to provide structures and support to make sense of Mathematics in addition to what they already know. Learners should be given opportunities to build connections between what they know and what they are learning. More time should be given for learners to explore Mathematics. Learners should not be judged when they make mistakes instead, treat it as opportunities for learning. Flexibility and assistance should be given to learners who are new to the concepts. Learner's ideas should be valued and included in classroom discussion of the Mathematics. Growing up, I hardly felt that I experienced Mathematics the way I should have. It's either a right or wrong answers although there are times where I was lucky to earn 1 or 2 marks in problem sums that weigh 6 marks.
Coincidentally, I chanced upon this blog about a Teacher who posted his experience of learning and teaching Mathematics.
What does it mean to understand Mathematics?
Using bear counters for the lesson on sizes (small, medium and big)
Using straws to thread for lesson on length (short and long)
Using toy cars to learn counting
Students have different understandings of concepts. When children are given more ways to think about and test an emerging idea , they have a better chance forming and integrating it into a rich web of concepts and develop relational understanding. Figure 2.11 on page 24 showed five different representations of mathematical ideas. There are pictures, written symbols, oral language, real- world situations and manipulative models. For the age group that I'm working with, oral language plays an important part in the Math curriculum. When teaching numbers, they are exposed to different counting songs and rhymes where they picked up language of numbers. I could also relate to understanding Mathematics through real life situations. For example, as an extension activity to learning shapes in the classroom, children went outdoors to look for circular, squarish, triangular and rectangular objects. Manipulatives are evident in any classroom in my school. For example, there are bear counters for children to use when learning colors, sizes and numbers. Different age groups use it differently. There are also other learning materials for children to use placed at the Math corner. For example, ice- cream sticks or toothpicks where children explored with for counting and making shapes.
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