After reading NCTM's six Principles for School Mathematics, I obtained a better understanding of the features required to produce a high-quality educational environment for mathematics students. NCTM emphasizes that the Principles are not mutually exclusive, i.e. they address overlapping themes. I believe the Principles are also collectively exhaustive, i.e. they try to encompass all of the features necessary in the math classroom.
I agree that all students are capable of learning mathematics. However I believe some students are more advanced than others. Like sports, some athletes are good at baseball while others are good at hockey. In the academic setting, there are going to be students ahead of the learning curve and behind the learning curve, and these students will vary from math to English. Teachers should be able to accommodate for this aspect of diversity (among others) while keeping expectations high.
Mathematics is a subject that well exhibits the Curriculum Principle. Math itself is cumulative, so I find it easy to make connections between content areas within the subject. As the NCTM says,
the strands are highly interconnected (2000, p. 15). The more easily students can see and realize this, the more connections they will make. The NCTM recommendations for curriculum will help narrow in on the tasks I will need to accomplish while constructing lesson plans.
I never realized the impact teachers make on their students until I heard it. One school year might not seem like a long time, but in the minds of the students it can make all the difference. Looking back on my own experiences in high school and reading about the effects of a single teacher on an entire class enforces this view. Realizing that one can change the lives of children forever may be a scary thought but it can also be a good one if teaching is done effectively. I think an effective teacher has a good balance of content knowledge (knowledge about what the students know and what they need to learn) and pedagogical knowledge (knowledge about how to teach). Teachers also need to continually seek improvement on their own part. As a teacher I plan to continue my exposure to research on mathematics and education so that my teaching practices will be continually improving. This is furthermore in the best interest of the students because as generations change, pedagogical methods (along with content) will change.
I believe the best way to learn is to be in one's Zone of Proximal Development. Students need to be challenged and supported. When a task is challenging enough to overcome boredom, but not too challenging as to promote anxiety, the student is in the ZPD and will learn with understanding. Students need to be able to build on previous knowledge, elaborate on new concepts, and organize concepts in a way that helps them remember them the easiest.
New opinions about assessment open up doors that I had not realized existed in the past. Assessment is foremost used as a tool to detect what students learned and how well they learned it, but it is also used as feedback for the students. Students should easily distinguish their place in the curriculum so they know exactly what their strengths and weaknesses are. Assessment should be used as an intermediary to help students learn, not as the end to a unit where students will never have to use that information again. On the other side, assessment can be used to aid teachers. For example, teachers will know which students are excelling or falling behind in certain areas, and will be able to make decisions for future instruction.
The aid of technology helps level the playing field. This goes back to the Equity Principle. Technology helps students focus on the bigger problems at hand, such as those involving decision-making and problem solving. The increase in technology yields changes in curriculum and changes in views on which concepts are essential in the classroom. Technology shifts the students’ attention from thoughtless algorithms to more complex thinking.
There are a few Principles that stand out when regarding mathematics: the Curriculum and Technology Principles. I favorite these two Principles because I believe they are crucial in the mathematics classroom. As I’ve stated above, math is one of the subjects that is a continuous field with overlapping grey areas rather than a collection of discrete facts or figures. There are more connections that can be made in math than any other subject in secondary school (in my opinion), so building on these connections is essential for students to learn effectively. Technology is the other Principle that sticks out to me. It is true that technology can be used in other courses, but I believe it can be most appreciated in a math course. Not only does technology act as a tool that enhances the learning of math, it is also determines the behavior of students and teachers with regards to content. The more (and better) technology is available, the more students will be able to make decisions, think critically, and focus on meaning.
- The National Council of Teachers of Mathematics. (). Principles and standards for school mathematics. Reston, VA: NCTM.