Sunday, April 17, 2011

And we're off....

NCTM, Day 1

1st session:     Differentiating for Gifted Learners
Craig Russell
University of Illinois Laboratory high School

He started out by telling everyone that it was "National Poem in your Pocket" day and gave us a little green piece of cardstock with a poem called "Mathematical Mind" on it (written by a former student).  Ok....

His take on gifted students:

NCLB has left behind the gifted students.
NAGC:  “Regular classroom curricula and instruction must be adapted, modified, or replaced to meet the unique needs of gifted learners.”
CCSS:  No references to what to do with gifted students.

What he does:  Daily group work; group work often differentiated; group assignments change at least once per unit; homework assignments include required and suggested problems, most include “alternative” problems (required for certain students if going to calc, etc.); assessments may be differentiated

How do you select the "gifted" students?
            Students self-select for “alternative” homework
            May be based on pre-test results  (determines groupings in classroom… ex. change focus from graphing linear equations to parametric equations, etc.)
            Students may be “re-directed”, both on in-class work and on homework
            Assessment: continual, with evidence for parents
            “open questions” and “parallel tasks” allow for self-selection and re-direction

Differentiation basics:
           1.  Product: gifted students may produce more sophisticated work with less structure in instructions
           2.  Process:  Gifted students learn through exploration, problem solving
           3.  Learning Environment: Different students have different learning styles and respond to different stimuli
           4. Content: Gifted students can learn more, at greater depth (not nec just moving faster)

1.  Product differentiation:
Student choice vs teacher choice (mandatory or suggested?) on projects
            Amazing Race – Roadblock.  Choose one of two options.  (Create or Crititque)
Smaller-scale activities may be more open-ended for some students
Tests/quizzes may cover enriched curriculum
Amusement park: students choose which ride, with knowledge that some are tougher  (design ride… basic is roller coaster, pirate ship is easiest, double ferris wheel, scrambler (toughest) – rates of change, parametric eq, accel, vel

2.  Process differentiation:
Problem-based learning
More open-ended problems, less clearly defined
Different resource materials
More emphasis on “why” than on “what”

3.  Learning Environment Differentiation
Flexible furniture locations – grouped or individual
Access to technology
Whole class vs small group instruction
Time allocation:  “sweep” or “anchor” activity/exploration

4.  Content examples
What product might be expected:
Modular arithmetic
Absolute value inequalities
Multi-variable functions
3-d conic sections
Hyperbolic functions
Partial fractions
Differentiation by adaptation
  • Math forum pow
  • QELP (from community college in nw) – environmental data sets keyed by math topic

Differentiation by unit:
We do this now:  What are the goals?  How much classroom time is devoted to each goal?  What lesson activities do you use?  How will learning be assessed?

We also need to think about:  With which of the unit goals are gifted students already comfortable?
What additional goals (enrichment? Acceleration?) related to this unit might be appropriate for gifted students?
Should (or could) the planned lesson activities be differentiated?

Materials (time?)
Peer/parent pressure
Balance:  time for pre-testing, de-emphasis on “routine”

Some lessons learned
Develop a “few” differentiated lessons per year
Study non-traditional textbooks:  COMAP, Core Plus, SIMMS, IMP, UCSMP, Discovering Geo, college texts (iffy?)
Use conferences to examine the literature
Look into NCTM Illuminations and math forum PoW
Find a partner

"Differentiating an insipid curriculum results in a differentiated insipid curriculum." – Carol A Tomlinson

Thinking about how to differentiate for gifted students actally caused us to think about how we challenge all students, and we have tightened our curriculum overall as a result.

Overall, I enjoyed this session - it gave me a lot to think about.  I'm not usually one who enjoys the philosophical-type talks, but this guy was entertaining and kept me interested.  I've tried to do a bit of differentiating in precalc this year by offering options for assignments, but there's obviously so much more I could do.  I'd like to incorporate pre-tests next year and differentiate based on those, but that's a big plan that will take a lot of work to pull together.

More to come: 

Trig Tricks You’ll Love
Ann Coulson

Supporting Productive Struggling in the Mathematics Classroom
Susan May and Kathi Cook

Student Centered Projects to Enrich a Precalculus Class
Masha Albrecht and Dan Plonsey

And this was just from Thursday!

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