Upon completion of reading only the first chapter of the textbook, I could envisage the amount of information that I will be gettting by internalizing the contents of the book. I see the importance of being in the right mindset before I could ever attempt to teach mathematics to my student because, my attitude and perception towards math will affect my method and teaching strategies, which will then leave an impact on how my children will perceive math as a learning subject.
I have learnt that there are two important tools that can be acquired in order to be an effective teacher; my knowledge of mathematics and how students learn mathematics. I feel that more importantly is not for the children to derive at the correct answer, but to be involved in the process of thinking or to problem-solve in finding the answers.
I see the need to be aware of the six principles and standards for school mathematics which explains the underlying principles governing the teaching of mathematics. What I find truly enlightening is 'The teaching Principle' which states that 'what students learn about mathematics almost entirely depends on the experiences that teachers provide everyday in the classroom.' This means to say that the teacher needs to have a prior knowledge and a certain level of interests deemed necessary before he or she could impart learning to children.
Chapter One also explains the differences between 'Traditional Curricula' and 'Standards-Based Curricula.' It is mentioned that students for the latter perform much better on problem-solving measures and at least as well on traditional skills as compared to students in the former.
I really liked the quote written by Schifter and Fosnot at the beginning of Chapter Two which states, "No matter how lucidly and patiently teachers explain to their students, they cannot understand for their students." This is indeed so true and it does not only apply to the teaching of mathematics but in other areas of learning too. It is also important to note that mathematics is more than completing sets of exercises or following the processes the teacher explains. It is also means generating strategies for solving problems, applying those approaches and see if they lead to solutions and making connections to what is happening in the real world even within the confinement of the classroom situation.
I liked the fact that this chapter uses colourful picture representations and illustrations to demonstrate explanations on a problem situation. It makes it clearer for the readers to understand the intended message brought forth. I have gathered the importance of the teacher's role in setting the right kind of mood and environment for the students so as to make teaching and learning more effective.
Chapter two also touches on the two theories; Constructivist and Sociocultural. The former focuses on the cognitive schemas of assimilation and accomodation and also the process of reflective thought. Though learning is constructed within the self, the classroom culture contributes to learning while the learner contributes to the culture of the classroom. These two factors are influencing one another. Siciocultural theory touches on ZPD, also known as 'zone of proximal development.' Another major concept regarding this theory is semiotic mediation, which is a term used to describe how information moves from the social plane to the individual plane. It involves interaction not only through language but also through diagrams, pictures, and actions.
I see the importance of getting children engaged, involved and interacting actively among peers and their teacher in the process of solving mathematical problems. This involves active learning and thinking and teachers must be mindful not to feed students with too much info and explanation. It is also important to allow room for making errors and for them to learn from it.
I have learnt that mathematics proficiency encompasses two areas; conceptual and procedural. The former refers to knowledge about the relationships or foundational ideas of a topic and the latter refers to knowledge of the rules and procedures used in carrying out mathematical processes and also the symbolism used to represent mathematics. These two therefore, work hand in hand and the absence of conceptual understanding will lead to errors and a dislike of mathematics.
The two chapters above have proven to be comprehensive and have provided me with a clear understanding on the aspects and requirements of learning and teaching mathematics. I will revisit the mathematical problems posed in these chapters to test myself on my capability to solve them. What is most important for me is to come into the classroom with a proper mindset regarding mathematics and prove to the children that learning mathematics is so much fun!
