Odds and Ends -- Week of 2-15-10

Catchup time...

• So where are the answers and followup discussion to the previous two problems I posted? They're coming. I plan to make a video of the investigation in the "143" problem. 
• I think it would be so useful to post videos of actual lessons that demonstrate how some teachers implement explorations in the classroom at all levels from K-12. I'm sure there are some of these already online but they seem to be few and far between and I'm really referring to "best practices" here to serve as models for others. We have NCTM Illuminations for example but I'm really looking for something else here.
• More important than investigations is to see models of daily lessons which incorporate the best of what we know about effective practice. Lessons which show HOW to blend procedural and conceptual understanding, help students develop skills mastery while engaging in rich problem-solving. Easy to do? Of course not, but if we want the US to be academically competitive, we had better move quickly in this direction and use international models to guide us.
• How are you, the mathematics teacher, dealing with all of the confusing and overwhelming issues in math education today? OR have you learned to ignore all the "noise", close your door and simply go about the business of teaching? If you're able to, that is! Unfortunately some of the decisions which are being made independently of your input will have significant impact on how well you will be able to do your job today and in the future...  Issues like
  
• "Algebra for All?" So where has that experiment gone?
• States joining consortia to develop a common standards and assessments in math
• How many consortia should there be? Will most eventually merge into one or two?
• Will common math standards ultimately lead to more consistency in content  -- i.e., that which is actually taught in the classroom?
• Are math ed departments in colleges and universities adapting rapidly enough to prepare preservice teachers for the paradigm shifts which are occurring? 
• Will "methods" courses in ed schools increase focus on actual content, e.g.,
  
  "You will all prepare a lesson on the effect of changing the parameter "b" in a quadratic function. Your lesson should utilize multiple representations and include a carefully planned series of Socratic questions which develop meaning and conceptual understanding for the algorithms. Specify what actions you took to balance procedural learning with conceptual understanding. Also, be prepared to answer the essential question: "WHAT ACTIONS DID YOU TAKE AND HOW DID YOU ASSESS THAT LEARNING TOOK PLACE?"
  
• How can we all use emerging technologies to enhance our teaching repertoire. Regardless of whether you "tweet", "Buzz" or Facebook, or all of the above, how can networking and sharing make us more effective teachers? This is sort of obvious, but how many of us are using these on a daily basis in our planning and in our classrooms? 25% 50% More?
• What are the most effective online learning tools for mathematics, particularly middle and secondary math? Many excellent bloggers have researched and compiled excellent lists of resources, but specifically, what are the best online video sites (interactive or not)? This is crucial for me and it's something to which I want to dedicate myself.
• I choose not to get into NCLB or Charter Schools debates at this time...
• So where is my new website I've alluded to? It's taking forever to set up, but I want to do it right. More to follow...

Ok, so we have to have a little problem for your students to think about. This is part of a well-known genre of "puzzles" which frequently travel across the web and are always intriguing for students and adults alike. You've probably seen it...
For this blog, the essential question is, how we can make this a teachable moment in our math classes?

MIND GAME

2% or 98%

This is strange...can you figure it out?

Are you the 2% or 98% of the population?

Follow the instructions! NO PEEKING AHEAD!

* Do the following exercise, guaranteed to raise an eyebrow.

* There's no trick or surprise.

* Just follow these instructions, and answer the questions one at a time

and as quickly as you can!

* Again, as quickly as you can but don't advance until you've done each

of them ..... really.

* Now, scroll down (but not too fast, you might miss something).

Think of a number from 1 to 10

Multiply that number by 9.

If the number is a 2-digit number, add the digits together.

Now subtract 5.

Determine which letter in the alphabet corresponds to the number you

ended up with

(example: 1=a, 2=B,  3=c,etc.)

Think of a country that starts with that letter.

Remember the last letter of the name of that country

Think of the name of an animal that starts with that letter.

Remember the last letter in the name of that  animal.

Think of the name of a fruit that starts with that letter.

Are you thinking of a Kangaroo in   Denmark  eating an Orange  ?

I told you this was FREAKY!! If not, you're among the 2% of the

population whose minds are different enough to think of something else.

98% of people will answer with kangaroos in  Denmark  when given this

exercise.

COMMENTARY

Is there some basic number theory here? 

What would you want your middle schoolers to do with this after they play it a few times?

"All Truth passes through Three Stages: First, it is Ridiculed...
Second, it is Violently Opposed...
Third, it is Accepted as being Self-Evident."
- Arthur Schopenhauer (1778-1860)


You've got to be taught
To hate and fear,
You've got to be taught
From year to year,
It's got to be drummed
In your dear little ear
You've got to be carefully taught.
--from South Pacific