EDU 330 Elementary Mathematics

Elementary & Middle School Mathematics

Reflection

Chapter 1 Teaching Mathematics in the Era of the NCTM Standards

In this chapter there is a lot of focus on the NCTM Standards, which may not be the standard used in Singapore. However, I read on to see what is there in for me as a teacher.

Under the heading Principles and Standards for School Mathematics, six principles are mentioned. Each principle emphasises the way Math should be taught. However, I find the Assessment Principle as an interesting and purposeful one. Assessments should be carried out to display students understanding and how and where they need assistance. It should not be to judge if the student is able to give the correct answer. The assessment should be for the process used by the student and the teacher and to evaluate if it works for both. In learning Math there is no one correct way. What works for a student may not work for another and the same for teachers. How I teach may differ from another teacher. I believe that being result oriented is not going to work for students in the long run of learning Math. It is a skill that needs practice and building on.

The Five Process Standards clearly states the way Maths is to be seen as a means to develop thinking and problem solving skills and not to be taken as a subject to study for getting a grade. It is entwined in everyday living. Though five, it is not seen as separate skill or concept but as a process to be utilised for teaching. Looking at different ways to solve a problem is enhancing thinking skill. In my class, I always ask children to think of different ways to display number values using their fingers and different arrangements of cubes. Children enjoy doing this on their own during free choice play.

The Reasoning and Proof standard is very interesting. It gives the chance for children to explain their process and be able to correct their own mistakes if any. It also gives opportunities for teachers to comprehend the way the thinking process is taking place in children.

Chapter 2 Exploring What it Means to Know and Do Mathematics

The first part of this chapter involved the reader to be engaged in working out some sums. It was fascinating to view the various ways in which it could be solved. No correct answers were given but the process in which the problems could be solved made my thinking process work in various ways too. The author said, “In the real world of problem solving outside the classroom, there are no teachers with answers and no answer books. Doing mathematics includes using justification as a means of determining id an answer is correct.” How do I apply this in the classroom where children are to be taught to pass exams which wants the correct answers? I am glad that I am working with the preschoolers who learn through play. I can and have applied this with them to show that there is no one correct way but many.

The Constructivist theory and the Sociocultural theory may seem like two different aspects stating two different process of learning. However, in the learning process both have to be applied to enhance the learning journey. Connecting prior learning to new ones need the assistance of others most of the time. What exactly is prior knowledge was once also new knowledge. Thus, though two by name these two theories have to be connected to enhance growth. I do not think that any one of these theory can work by itself. As a teacher I have to know the prior knowledge of my students to provide them with challenges to bring them to the next level. I have to be the scaffold for my children to act on their prior knowledge to connect to new knowledge.

In teaching mathematics, it is important to accept that “concepts and connections develop over time”. What the child do not comprehend today may be seen to be applied by the child after some time. Engaging in related tasks and constant practice make students see connections. In mathematics practice is something that has to be constant. To engage children various means of practice is necessary. This will make children see the connections and be able to relate.

These two chapters in this book has shown various aspects of teaching and learning mathematics not only for the students but also for the teachers.