Wednesday, February 17, 2010

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?


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

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


    Jason Dyer said...

    I'm not ready to decide how Common Core is going to go until I see the current draft, which has supposedly been circulating privately and undergone a lot of changes.

    I know a lot of people are completely unaware that the Common Core initiative even exists, so the answer to your "are colleges going to be prepared?" question is likely "no".

    Drake said...

    But.... 9*n where 1 <= n <= 10, when you add the digits, will always be nine.. so you always get 4, therefore D, at the number to letter part...

    And I knew what was coming, but I couldn't get a country that started with D but wasn't Denmark... No way was I getting Djibouti, Dominican Republic might have happened, but didn't =/

    Dave Marain said...

    Isn't it strange that the challenge isn't the math here, but rather coming up with another country starting with a "D". I was going for Dubai!

    At this point, I'm tired of seeing any set of standards. Just define the essential topics (terms, skills, procedures, concepts) that will be assessed and I'll be happy.

    No matter how many times I reiterate my point about how Calculus instruction changed when the AP Committee defined the curriculum and made it stand up on the AP Exam, my message has appeared to go unheeded. A Curriculum Guide, Syllabus, Scope and Sequence, whatever you want to call it does not stifle anyone's creativity! However a challenging exam that stresses conceptual understanding and application does impact instruction. Key topics cannot be covered superficially. Students still need plenty of mechanical practice and strong algebra skills, but that is no longer enough. Enough of the calculus metaphor for change.

    I am saddened to hear from you that many are not yet aware of the Common Core Initiative. However, they soon will be...

    Marcy said...

    Hi Mr. Marian,
    I did your little math puzzle and came up with a Koala in Denmark eating apples...does that still put me in the 2% and not the 98% or somewhere in between?!?I
    Melissa showed me your blog today...about chess. Very interesting :o) Hope all is well!

    Dave Marain said...

    Yes, Marcy, you are one of those 2%'ers!

    Thanks for the kind words, although I cannot claim to have invented that puzzle -- it was emailed to me and, apparently, it's been on the web for awhile. I always find it fascinating that some people who express a dislike for math or feel they are not "math people" get "hooked" on these puzzles! There are some mathematicians who consider all challenging math problems to be puzzles. Perhaps if we used the term "puzzles" in our classrooms in place of the word "problems" our students might be more eager to tackle them!

    By the way, I often write these posts with K-5 teachers in mind and you and Melissa in particular, since I value your opinions greatly.