## Saturday, March 19, 2011

### Where Have I Been?

## Tuesday, October 5, 2010

### Part One: Mathematics in Education

- Is it mathematically important, both for further study in mathematics and for use in applications in and outside of school?
- Does it “fit” with what is known about learning mathematics?
- Does it connect logically with the mathematics in earlier and later grade levels?

**Why haven't we made the shift from rote learning and drills to thinking and making connections in the math classroom?**

## Friday, October 1, 2010

### Thinking And Mathematics

*What kind of thinking is required of mathematics students?*## Wednesday, July 7, 2010

### The Bases are Loaded

Base Ten | Base Two | Base Five | Base Eight |

1 | 1 | 1 | 1 |

2 | 10 | 2 | |

3 | 11 | 3 | |

4 | 100 | 4 | |

5 | 101 | 10 | |

6 | 110 | 11 | |

7 | 111 | 12 | |

8 | 1000 | 13 | |

9 | 1001 | 14 | |

10 | 1010 | 20 | |

11 | 1011 | 21 | |

12 | 1100 | 22 | |

13 | 1101 | 23 | |

14 | 1110 | 24 | |

15 | 1111 | 30 | |

16 | 10000 | 31 | |

17 | 10001 | 32 | |

18 | 10010 | 33 | |

19 | 10011 | 34 | |

20 | 10100 | 40 | |

## Saturday, June 12, 2010

### Types of Prime Numbers

- Twin Primes - a set of two consecutive odd primes, which differ by 2. Examples: 3 and 5, 5 and 7, 11 and 13.
- Symmetric Primes, also called Euler Primes - a pair of prime numbers that are the same distance from a given number on the number line. Examples: Given 6, 5 and 7 are symmetric primes. Given 16, 3 and 29 are symmetric primes.
- Emirp - a prime number that remains prime when its digits are reversed. (Emirp, of course, if prime spelled backward!) Examples: 13 (31), 347 (743).
- Relatively Prime Numbers - numbers whose greatest common factor is prime. These numbers are not necessarily prime. This definition is referring to the relationship between numbers rather than the numbers themselves. Examples: 4 and 9, 10 and 27, 8 and 9.

- Can you find all of the symmetric primes for 24? (hint: there are more than 3 pairs - and no, I am not telling how many there are. That would spoil the fun!)
- How many emirps exist between 1 and 200? (The number when it is listed its initial way - so 13 and 31 would each count as unique emirps.)

## Wednesday, June 2, 2010

### Do As I Say, Not As I Do.

**Are we past this, or is it still alive and well?**

**A Mathematical Way to Think About This**

- Assume the opposite of the statement is true. For example, in Geometry, if you were supposed to prove 2 lines are not parallel, you would assume that they are parallel.
- List all of the information that supports your assumption. Using the same example, there would be some conclusions that could be drawn because of the parallel lines.
- Keep going until you find an indisputable contradiction. Once the contradiction is found, the proof is finished. In the case of the lines, a point of intersection would be concrete proof that the lines are not parallel.

***I have to put a disclaimer here for all of my mathematician friends. This is truly done in a sense of fun rather than mathematical correctness, so please view this in that frame of mind!*

*Note: I am working hard not to be sarcastic here. If it sounds that way, I apologize and would welcome help in rewording anything.*

- I was raised this way and I turned out fine.
- People aren't really bothered by the inconsistent messages given them by their parents, teachers, employers, etc.
- People with power and money have earned the right to do what they want, and to tell other people what to do. They have the power, so what they think must be correct.
- Young people understand that the instructions are for their own good and that being an adult has its privileges.

*I was raised this way, and I turned out fine.*

*People aren't really bothered by the inconsistent messages given them by their parents, teachers, employers, etc.*

*People with power and money have earned the right to do what they want, and to tell other people what to do. They have the power, so what they think must be correct.*

*Young people understand that the instructions are for their own good and that being an adult has its privileges.*

**"**

**Do as I Say, Not as I Do" or Raising Kids with Moral Intelligence.**If you would like to read the entire article, click the link.

In his book,

The Moral Lives of Children, Dr. Robert Coles defines our conscience as our "moral intelligence." More simply, he defines moral intelligence as how we behave—"moral behavior tested by life, lived out in the course of our everyday existence."PBS

NewsHour'sDavid Gergen interviewed Coles several years ago and asked him how to encourage morality in our students, our children, and ourselves. Coles told Gergen that adults can only teach values by living them. "I'm trying to insist upon for myself as a parent and a teacher and for all of us, that any lesson offered a child in an abstract manner that isn't backed up by deed is not going to work very well," Coles said. "We live out what we presumably want taught to our children. And our children are taking constant notice, and they're measuring us not by what we say but what we do."

**So, is the proof done?**

Mathematically, maybe not, but I think I gave it a good try. I have tried to work some things out and maybe some people have something to chew on tonight. I think the good news is that "do as I say, not as I do" doesn't seem as prevalent as in my youth. I felt compelled to write anyway. Just because something is happening less doesn't mean that it has stopped completely or even enough.

Don't get me wrong, I don't think that adults have to stop doing things like having a cocktail at happy hour because their kids can't, but we can do so in a responsible manner. The societal norms that make it okay to have a drink at happy hour, but not in the classroom are well established and I think it gets the job done for most people. It's the other things that I think should be questioned. *If your students are required to wear uniforms, should you wear flip-flops? Should school principals turn a blind eye when they see misbehavior in a classroom that a teacher is struggling with, and then reprimand the teacher later? Should the boss be allowed to drink or smoke on company time, a la "Mad Men"? Should a parent curse a blue streak and then punish their child for saying "damn"?*

Anyone reading this who thinks "do as I say, not as I do" is fair - I challenge you to ask the people around you, particularly those who look up to you, and give a true ear to what they say. It would be a good thing to do.