The first concept would be
The Six Principles:
The Equity Principle
For all learners to have equal opportunity and support when learning mathematics without any bias, most importantly, to have great expectations for all.
The Curriculum Principle
The curriculum to be 'coherent' in a sense that learners see mathematics as an integrated whole and not a variety of different pieces/activities.
The Teaching Principle
1)For teachers to possess depth of knowledge of mathematics
2)For teachers to possess a keen awareness on how individuals pick up mathematics
3)For teachers to possess the ability to select appropriate tasks/strategies that would complement learners ability.
The Learning Principle
To allow learners to learn mathematics with comprehension and also allow learning to take place while building on learners' prior knowledge - to make meaning on their own, thus, developing the ability to problem-solve.
The Assessment Principle
The goal of assessment to be done for learners that would result in meaningful information that would be of advantage to both teachers and students. Thus, assessment should be done through an array of techniques.
The Technology Principle
To embrace technology as a teaching/learning tool that would enhance the process of learning mathematics through the exploration or these tools.
Opinion:
Principles play a deeply rooted role in almost everything. These six principles summed up the base of what there must be before any school's mathematics program comes in. Two principles I especially feel for is the teaching principle and the technology principle.
First of all, I feel that the three points stated in the teaching principle are of equal importance. It is difficult to teach without knowledge; Teaching without understanding learners' ability and way of learning is of tantamount challenge. Last but not least, to teach without possessing the ability to select appropriate tasks/strategies to aid the learning process would ultimately backfire on both teachers and learners. The problem I face would be when faced with struggling learners, I would often run out of strategies in approaching a problem in aiding their learning process. This would fall under the 2nd point whereby teachers have to possess a keen sense of awareness in order to select an appropriate task/strategy to go about with the learner.
For the aspect of the technology principle, it is important for both teachers and learners to recognize and embrace technology as part of our teaching and learning tool in education. It enhances the learning process with exploration of these tools and also extends the boundaries of problems that can be approached. Personally, I am especially keen in integrating technology in all subjects (:
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The second concept would be
Becoming a Teacher of Mathematics:
Knowledge of Mathematics
It is critical that educators in mathematics possess profound understanding of the subject in order to impart these knowledge to learners because mathematics is unlike any other subject - what learners learn would come most probably come solely from their teachers and not in any other way like language or science. Hence, the emphasis of knowledge importance for educators in mathematics.
Persistence
To possess the ability not to be frustrated/give up easily. This is one of the key factors to overcome barriers during problem solving and teaching. When a teacher is able to model this characteristic, it raises the probability that his/her students would be able to do so too.
Positive Attitude
It is of importance for educators of mathematics to have a positive attitude towards the subject. This can be achieved through expanding knowledge of the subject and actively approach new strategies in solving problems so as to enjoy the mathematical activities.
Readiness for Change
Summed up as "Let the familiar become unfamiliar, and the unfamiliar become familiar." To be able to embrace the difference in individuals whether it is the concept or strategies used in problem solving.
Reflective Disposition
To constantly improve oneself by looking for opportunities to learn new things or being open to different practices etc.
Opinion:
I picked this as the other important concept because I feel that the factors mentioned here are keys to becoming a good teacher in mathematics. It shows that beside the basic knowledge required to teach this subject, other personal characteristics such as persistence and positive attitude play crucial roles in imparting knowledge to learners too.
Many a time, educators fail to see the importance of personal disposition and stance in their take on the subject they are teaching. Certainly, having the knowledge is of utmost importance in teaching but we must not oversee other factors like possessing a positive attitude and a readiness for change etc. These factors are the ones that would enhance our teaching and students' learning processes.
Reference:
Van De Walle, J., Karp, K. & Bay-Williams, J. (2010). Elementary & middle school mathematics. Teaching developmentally (7th ed.). Boston, MA: Allyn and Bacon
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