From Steve
Mastery – Why
The question keeps coming up – how do you define mastery? Equally important to our consideration is Why aim for mastery? Math is sequential in that it builds upon previously-studied material. But when I teach a student, I only want them to be focusing on one new idea at a time.
For example, if I am presenting the symbolism of long division to a student, I am assuming he knows place-value, subtraction, and multiplication. Since he has mastered these topics, he only has to learn how we write out a division problem. But if he doesn’t understand place-value, and is weak in his multiplication facts, then he will be working through three ideas at one time! This can be overwhelming and discouraging to a pupil.
I want him to experience success. I want math to be doable. I want to break down complex problems into bite-sized pieces so he can concentrate on learning one concept at a time, and not be juggling two or more ideas in his head simultaneously.
Mastery – What
So then the question is, How do you measure mastery? My definition of mastery is when a student has moved from learning to knowing. As you work alongside your student, this will become easier to discern.
Some programs use speed drills and timed tests as an attempt to measure mastery. I do want a student to be able to tell me multiplication facts without skip-counting, and addition facts without making vacuum cleaner noises. If I ask, “What is 6 times 7?” then I want to hear “42″ without any hesitation.
I also want them to understand what they have committed to memory. I want the student to know that multiplication is fast adding of the same number, and that you can represent a multiplication problem by building a rectangle. If a student can “show” me a multiplication problem and explain in his own words or teach back to me what he has learned, then he probably understands this important topic. A teacher who is working regularly with their student will know when the student has moved from learning toknowing.
I hope this helps clarify and explain the importance of mastery as you teach math.
Steve Demme
