The Rule of Four
Mathematics should be expressed in the following four ways:
1. Algebraically
2. Numerically
3. Graphically
4. Verbally
In order to understand mathematics holistically, it is important that students connect each concept with the rule of four.
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The beauty of this way of understanding mathematics is that it is so versatile; students can work with information presented in any one way and manipulate that information to find or interpret the information in other ways.
All students can learn
Three goals for the students:
1. Work accurately with basic operations:
2. Be able to apply basic operations to more complex problems.
3. Incorporate technology with the goal of higher level mathematics.
First and foremost my job is to ready my students for the next level of mathematics. Often, the level of mathematics dictates teaching methods.
When working with college-prep 9th graders in algebra, I focus heavily on a deep understanding of basic operations. The focus is essentially rote learning initially, and then we move to more involved problems. I teach and re-teach the basic skills that students will need to be successful when they reach algebra 2 and tackle the complexity therein.
When working with students in pre-calculus or calculus, I teach basic ideas fairly quickly and then move to complex applications of knowledge with the use of technology. I expose my students to the most rigorous IB or AP problems I can find or produce and sometimes much of class is spent discussing ideas rather than crunching numbers.
When working with college-prep 9th graders in algebra, I focus heavily on a deep understanding of basic operations. The focus is essentially rote learning initially, and then we move to more involved problems. I teach and re-teach the basic skills that students will need to be successful when they reach algebra 2 and tackle the complexity therein.
When working with students in pre-calculus or calculus, I teach basic ideas fairly quickly and then move to complex applications of knowledge with the use of technology. I expose my students to the most rigorous IB or AP problems I can find or produce and sometimes much of class is spent discussing ideas rather than crunching numbers.
"In order to understand Math, you must do Math."
Having too much
fun with the graphing calculator!
"Understanding of math is more than
following examples. It is the conceptual 'why' and 'how' and being
able to apply that."
"The
Rule of Three: Every topic should be presented geometrically, numerically and
algebraically."
