Archive for the ‘Ask Dr. Cotter’ Category

Carson Jody’s Birthdate


This post is a personal post with a delightful math twist. I am Kathleen Cotter Lawler, Joan Cotter’s daughter.

Today, December 1, 2011, my daughter Megan gave birth to a beautiful healthy baby boy. Carson Jody was born at 12:44 this afternoon. This amazing event turned me into a grandma, my mom, Joan, into a great grandma, and her mother, Florence, (who is 97 years and 1 day old) into a great great grandma.

I was honored and blessed to be present at Carson’s birth. Yes, I cried. There just aren’t words for what I experienced today and I will never forget this day. Ever.

So, rather than gush on and on and on (which I’ll probably be doing for the next 50 years), let’s look at the math aspect of today.

Clue: I’ve already told you.


Check out Carson’s birthday.

December 1, 2011.

Also written as 12-1-11. Now take out the dashes.

12111        Not bad!

Now write the date as the Europeans do: date – month – year.

1 December 2011    or

1-12-11        or


Pretty cool, right?

OK. Maybe not totally fascinating, but I liked it and I love love LOVE my new grandson. Life is incredible.


P.S. We had a colt born a while back on May 6, 2007. That’d be 05-06-07. We named him Trigonometry and called him Trig for short. Carson’s lucky he didn’t get named Symmetry.

Spiral or Mastery?


Is RightStart™ Mathematics Spiral or Mastery Approach?

RightStart™ Mathematics is a unique program that has aspects of both spiral and mastery approach. Both approaches have some validity as well as some drawbacks. First we need to define our terms.

Spiral learning is based on behaviorism, which says we are programmable machines and we need endless repetitions to master something. Spiral curriculums cover the same material year after year in ever widening circles, with the anticipation that increased exposures will eventually lead to mastery of the basics. The number of topics covered is broad, but they never go deep. It is more of an exposure philosophy.

Mastery approach curriculum builds sequentially. This philosophy states that there is no need to move to the next step until the preceding one is mastered. Therefore, lessons may take many days or even weeks if necessary for students to master the facts. Fewer topics are covered. Pre-testing and post-testing are done to assure mastery.

The human brain works by attaching new information to something already known. The more ways information is attached in the brain, the better it is learned. Children need more than one exposure and one way to learn a topic, but repeated exposures to the same material are not enough for mastery.

RightStart™ Mathematics introduces a large number of topics, but they are built sequentially for greater understanding. Students need to be challenged by many topics in order to see the interconnectedness in mathematics. For example, one of the goals of mathematics instruction is that students be fluid in their basic facts. So, students learn strategies for mastering the facts. They master them by playing games, which gives them a reason for learning the facts.

We need to teach students to be problem solvers. Thomas E. Clark, author of VideoText Algebra, defines the goal of arithmetic as finding an answer, and the goal of mathematics as solving a problem. In RightStart™, students learn techniques for thinking mathematically. Lessons systematically introduce principles of mathematics that lead students to self-discovery.