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Statistics Uncategorized

A Day With Rick Wormeli – Redos and Retakes

Earlier this week, a handful of colleagues from my district and I experienced the educational whirlwind that is Rick Wormeli.  I have studied Rick’s writings for some time now, shared thoughts on redos and retakes and standards-based grading before, and incorporated some of his ideas into my own classroom procedures.  What I most enjoy about Rick is that he challenges your existing classroom practices, and breaks them down to their foundations:  if it’s not about achievement, and moving kids forward, then it’s not part of the plan.

The day began innocently:

Today will be a waste of your time.

Thanks?  But Rick’s point was that a single day of PD is simply not sufficient to synthesize these ideas.  Change only comes when we take what we learn back to our school, have discussions, think about our policies, and work as a team to do best for our kids.  Rick is correct when he states that “school is set-up to meet the needs of those who get it first”.  Let’s work on breaking down long-standing policies and  drafting new ideas which benefit all learners.

Climb That Tree

While the day was billed as a “formative assessment” seminar, the concepts really be-bopped from standards-based grading, redos and retakes, learning targets, and formative vs summative assessments.  I fear this blog post would be 10 pages long if I tried to summarize everything, so I’ll instead focus on one idea I have incorporated into my classroom routine this year: test retakes.

Rick WormelliHow do students react to the grades we give them on assessments?  How do our grading practices impede students reaching their learning targets?  Rick argues that many of our strategies cause students to wind up in “the pit”; further, many schools perpetutate practices (like losing lateness points, or not allowing corrections) disguised as “teaching responsibility” which cause students to fall deeper into the pit.  It’s our duty to lead students through strategies which will get them out of the pit, and professionally unethical to conflate evidence with compliance.

I have incorporated re-takes into every exam I give this year in AP Statistics, and have allowed re-dos in many Algebra 2 tasks.  I continue to evaluate the success of these methods, and I have been largely happy with both the results, and the attitudes of students in embracing the new procedures.  When should you allow redos?  To Rick, the answer is ALWAYS..it’s our professional responsibility to allow redos – unconditionally.  Here are some resources from Rick Wormelli which will get the conversation started:

Educational Leadership, “Redos and Retakes Done Right” – requires ASCD log-in, harass your principal!

“Fair Isn’t Always Equal” – Rick’s landmark book on assessing and grading in the differentiated classroom

Video on Redos and Retakes – Rick defends the redo/retake practice.

What’s the problem with allowing a failing grade?  Doesn’t that build character?  How do students react to a failing grade, as opposed to a different designator, like “not yet”…

HOW I MANAGE RETAKES

This year, my colleague Joel and I wanted to incorporate retakes into our statistics classes.  But there are certainly organizational challenges to be met, and our discussions challenged our beliefs on assessment and its purpose.  Here’s what we decided on for our classes this year:

  • Each unit test has two parts: multiple-choice and free-response, graded equally like they will be on the AP Exam.
  • There are always two free-response questions.  Sometimes they are actual former items from AP Exams, sometimes they are questions we write or adapt.  A free-response question is one scneario with multiple parts
  • After the exams are handed back, students may come in to take the “replacement question” for the exam.  The replacement question is a third free-reponse question, which students take on their own time during a daily directed-study period, or after school.  The grade on the replacement question replaces the score on the lower-scoring question from the unit test.
  • We don’t have a procedure for recovery for multiple-choice.  But we are kicking some ideas around.

Here’s why this procedure has worked for us.  Unit learning doesn’t end with the chapter test.  Students need to go back, reflect upon their misunderstandings, and develop a plan for doing better on the replacement question.  It’s great to see kids really reflecting about what went wrong on their test, and coming back to clarify what went wrong….that simply didn’t happen before.

The record-keeping is awkward.  But I am getting better at it, and figuring out the best way to manage this extra level of grading.  And Rick is now whispering in my head “Don’t drop the principle because you can’t handle the logistics.”

This is the first of what I am sure will be many posts reflecting upon this special day of PD.  Looking forward to sharing more ideas, discussions, and anecdotes!

To Rick: Thanks for the great day…and The Three Amigos was underrated

Categories
High School Statistics

My Favorite Teacher Circle: PASTA

Just got back from the fall meeting of my favorite local teacher circle, PASTA.  The Philadelphia-Area Statistics Teachers Association meets a few times each year to share best-practices in statistics teaching.  Many of this month’s presenters are AP Statistics readers, and the ideas are not specific only to stats…we just share great classroom action.  I gave a recap of our last meeting in the winter; enjoy the great ideas from our Fall meeting, and visit Beth Benzing’s website for materials from the meeting!

Daren Starnes, famous in the Stats-world as author of The Practice of Statistics, shared his first experience with Team Quizzes.  I have tried team quizzes before, mostly for quizzes where I knew students were having the most difficulties with material.  But Daren added some features I had not before considered:

  • Students are assigned to their teams at random.
  • Each team member received a copy of the quiz, and must complete the quiz.
  • In a quiz, one question is chosen randomly to be graded from each paper.  A student’s grade is a combination of the score they receive on the question, along with the average of the scores from the other papers in the team.

Daren also commented on the roles of introverts and extroverts in the teams, and how this method could empower introverted students to self-advocate.  He suggest the book Quiet: The Power of Introverts as a resource.

AdamAdam Shrager, famous as the social director and man-about-town at the AP readings, shared his movie-correlations activity.  This has become one of my favorite activities during the stats year.  Students are asked to fill out a movie-preference survey, which Adam then uses to compute peer-to-peer correltations in Excel.  (look for “correlation” in excel…you may need to activate the Stat Pack) Discussions regarding the interpretation of positive and negative correlations then occur.  Most importantly, mis-conceptions of the meaning of low or zero r-values are discussed with a context easily understood by students.

Table

Leigh Nataro shared her “Pacing a Normal Distance” activity, where students walked between 3 different campus buildings using “meter-long” steps.  The data is then entered into Fathom, and is used to discuss variability, the 68-95 rule, and normal probability plots.  Fun discussions of outliers and error as well!

Leigh

Our host, Beth Benzing from Strath Haven High School, shared a family income Fathom file which draws samples of various sizes from a clearly skewed distribution.  In addition to to having students record observations and work towards generalizations, Beth has worked to increase the rigor in her associated questions, using past AP items as her framework.  Some examples:

  • What is the probability that a sample of 5 families will have a combined income of over $500,000?
  • What is more likely: a sample of size 5 having a mean income of over $80,000, or a sample of size 25 having a mean income over $80,000?  You may recall a similar AP question from a few years ago regarding samples of fish.

Beth

Brian Forney shared ideas for bringing concepts from Sustainability to the AP Stats classroom.  In one example, Brian shared data on depths of ice sheets over time, with excellent opportunities to discuss cause and effect from scatterplots.  Check out Brian’s presentation on Beth’s website.

Finally, I was happy to share my recent lesson on Rock, Paper, Scissors and two-way tables.

The meeting concluded with some great ideas for making multiple-choice assessments more fair and effective.  There were a number of excellent ideas here, but I think I’ll look up some more info on alternate assessment methods and save it for another post…so stay tuned!

Categories
Geometry High School

A Math Teacher Ventures Into a Western Civ Class

During my prep period last week, I came back to my classroom after a trip to the main office and overheard some familiar language: Euclid, Pythagoras, The Elements.  What’s intriguing here is that my next-door neighbor isn’t a geometry teacher; rather, my colleague Glen is a social studies teacher, with 3 sections of Western Civ each day.  Excited, I popped my head into his classroom.  And after some good-batured ribbing out how he was advancing on my math turf, I went back to my prep.  But Glen and I later talked about our shared interest in the Greeks, which ended with an invitation to come into his class to share a brief math history lesson.  I’m no stranger to the occassional cross-curriculur lesson, so this represented a fun opportunity.

One on my favorite courses from my time at Muhlenberg College was “Landmarks in Greek Mathematics”, where I was fortunate to have William Dunham as a professor.  His enthusiasm for math storytelling has shaped my approach as a teacher, and his book, Journey Through Genius, was not only used in the course, but is a book I often come back to for inspiration and contextual reminders of math concepts.  The book both walks you through the mathematical landmarks (like Euclid’s proof of the infinitude of primes) and provides a backdrop of the places and people (like the fascinating battling Bernoulli brothers) which shaped the surrounding culture.  It’s a great resource for any math teacher.

For Glen’s classes, I chose an example which 11th graders could easily understand and which would provide a glimpse into the genius of the greek mathematicians: Eratosthenes’ approximation of the Earth’s circumference.

Eratosthenes observed that on the longest day of the year, sunlight would shine directly into a well, so that the bottom of the well could be seen.  But that farther from the well, in other towns, this did not occur.  The well was located on the town of Syene, which we now lies directly on the tropic of cancer.

Syene Well

In Alexandria, a known distance away from Syene, Erotosthenes measured the angle produced by the sun’s rays off a post in the ground.

SyeneAlex

Taking this further, we can use alternate-interior angles to use this same measured angle as one coming from the center of the earth.

earth

This central angle, along with the known distance from Syene to Alexandria, yielded an estimate of about 25,000 miles (or the Greek stadia equlivalent), an estiamate with an error of less than 1% of the actual circumference!  Both classes I visited seemed to enjoy this math diversion in the Western Civ class, with one student wanting to know more about how the Greeks approximated pi.

So find your local Social Studies teacher, and offer to bring in a little math!  There are some fascinating stories to tell.

Resources:

Excerpt from String, Straightedge and Shadow

From the Mathematical Association of America

From Jochen Albrecht, CUNY

Finally, from Carl Sagan’s landmark series “Cosmos”