Using VNPS and VRGs in geometry

My extra set of whiteboards and the student presentation size I made have been my new favorite teaching tools.  A new document camera has been a close second, but nothing has compared to the change I’ve noticed in my classroom when I give students a task to complete in pairs on the whiteboards.

All the credit for this has to go to Peter Lildejahl, whose presentation I discovered from Dan Meyer’s blog.  I’ve also taken a ton of wisdom from reading how Alex Overwijk is using these.  But a day in class can go like this: we open up with some short problems, then I line up the students by some pseudo-random characteristic: height, birthday, etc.  Paired up the students get one marker per group, and then I share the task of the day.  I’ve done this in a huddle formation, it’s a great shift from what for me was typical.

This particular lesson was a discovery of the ratios of the 30-60-90 and 45-45-90 right triangles.  I had students create some examples of isosceles right triangles (and later equilateral), then use the Pythagorean theorem to find the missing sides and detect a pattern.  It was simple, within their ability, and established connection between similar figures and right triangles.

For the past few weeks I’ve been trying to do this almost every day.  I can tell it’s made my mathematics class more engaging.  The students work a lot more continuously, they don’t bail out as eagerly, and they have freedom to discuss the tasks.  I can walk around the room and listen to my students discussing mathematics, which has been probably the most incredible part.  Learning sounds awesome when my students are teaching each other.

It’s not been a perfect trial, Laura Wheeler has some fine rules that I need to use to refine the practice.  Some students can dominate the marker, some seem to work at separate ends of the space as their partner.  My tasks are the biggest shortcoming in this right now.  And I’m uneasy about there being a lack of “notes.”  So I encourage picture taking of work, or using a notebook to preserve important summaries.

I’m wondering if anyone else out there is researching this, because I may just have found my dissertation topic.


AP Statistics student whiteboarding with M&Ms

M&M AP Statistics lessons are usually popular, but throwing the student whiteboarding into the mix brought some student movement into play.  In pairs the students were creating confidence intervals for the true proportion of blues.  One half the class worked on the front boards, the other in back.  I’m hoping at least one group has an interval that misses the truth.

The student interaction in this lesson was awesome.  Having them all working in clusters created opportunities for them to get help quickly by glancing at a neighbor’s method or asking a direct question of them.  I’ll definitely be trying this again.

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The best advice that no one is taking

I read this NYT article by Elizabeth Green telling the story of two math educators and their roles in improving teaching.  Akihiko Takahashi and Magdalene Lampert have had unique experiences in studying American math lessons, and I was unfamiliar with both before discovering Dan Meyer’s blog reference to the article.

The parallels between modern Common Core math curriculum efforts and past top-down initiatives is striking.  We have no shortage of creative ideas or eagerness to try new things in our classrooms.  What’s missing most is quality teacher training and professional development, the author claims.

How would schools need to be restructured/supported to create this kind of change?

About Pearson, the Golden Goose State Standards, And Then Some


On December 13, 2013, Pearson, Inc., agreed to pay a $7.7 million settlement for allegedly using its nonprofit, Pearson Charitable Foundation (PCF), to assist its profit-making parent corporation in developing educational materials– including software.

In this post, I would like to offer additional discussion of Pearson the For-Profit, Pearson the Nonprofit, and some friends both have made along the Common Core way.

I’ve been reading tax forms again.

Allow me to begin with a word about nonprofits.

Nonprofits 101

Any corporation is able to start its own foundation– the idea being that the foundation provides an opportunity for the corporation to spend charitably– and garner a tax break for doing so.

Under the US tax code, foundations fall under 501(c)— tax-exempt organizations. The tax-exempt code specific to public charities and private foundations is 501(c)3.

The 501(c)3 nonprofit is limited in its ability to lobby since contributors are allowed to deduct…

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NYSUT Supports Districts That Opt Out of State Field Tests

Diane Ravitch's blog

The New York State United Teachers issued a statement supporting th districts that are opting out of state field tests.

“ALBANY, N.Y. May 30, 2014 – As tens of thousands of students statewide prepare to begin vfield testing” questions for future state exams, New York State United Teachers President Karen E. Magee said today more time should be devoted to teaching – not testing – and called for an end to student participation in field tests.

The State Education Department is administering field tests from June 2-11 to try out prospective standardized test questions developed by the giant testing company, Pearson PLC. These tests do not count for students, teachers or schools and are solely used to “test the test.” Stand-alone field tests in English language arts and math will be administered in most schools to students who took the state’s 2014 Grades 3-8 Common Core ELA and math tests.

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My 100th post. So why not bash algebra?

Granted, and...

Hard for me to believe, but this is my 100th blog post. That’s the equivalent of a 300 page book – with much less pain, and lots more fun interaction: thanks to all my loyal readers and responders! And hooray for the Internet for permitting easy and rich discourse about one’s ideas.

To celebrate I thought I would return to my favorite educational whipping boy* Algebra I. There are so many reasons for dumping on Algebra but a timely one (on this blog milestone) comes from the fact that one of my blog posts on math was quoted in the recently-released Publisher’s Guidelines on the Math Common Core Standards!

Before I get into my rant, let’s be very clear about a few things:

I love math. I taught math – Pre-calculus and Geometry – and I am good at it, my best grades in school. I think non-Euclidean geometry is…

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Grading students: who’s it for?

As the school year comes to a close, students and teachers are playing a numbers game.  “What grade do I need to pass for the year?” is a question I’ve heard several students ask during the fourth quarter.  These students are not interested in learning for learning’s sake, but in satisfying their numerical obligation to earn the magic 65.  Very soon in New York, many mathematics students will sit for the first edition of the Common Core Algebra Regents on June 3, a summative (in-class final) exam, and perhaps also a soon to be phased out regents exam in mathematics.  If you’re a student with three “final exams,” plus a course grade, have you received enough quality feedback to inform your learning?  Consider that the three exams mentioned have similarities in content but also curricular, format, and duration differences.  What is a student left to feel about the meaning behind three exams in the same course?

What does a number from 0 to 100 really tell a kid about their performance?  Is 65 what we’d like the goal to be for many students?  I like the idea of standards based grading, but I wonder if that is improvement enough.  Students may receive more detailed measures with SBG, but they’re still asked to “put up numbers.”  Can’t we do better than this?

There are two reasons I can see why we’ve been so stuck with our traditional grading: it’s comfortable and it’s easy.  It’s been done forever, so there are no surprises when a report card comes home.  It’s easy because we establish a grading policy, parents and students are made aware of it, and from that point forward it’s enforced like a contract.  Grades are treated like objective measures when in reality they are anything but.  Do you know two teachers that grade kids the same way?  Me either.

This brings me back to the topic of the post.  We grade students not for their own benefit, at least not most of them.  We grade kids only to rank them, and increasingly to rank their teachers.  Feedback is an important part of learning.  But grades are not feedback.


What works in education – Hattie’s list of the greatest effects and why it matters

A laundry list of researched factors that all have a greater effect on student learning than home environment and socioeconomic status.

Granted, and...

I have been a fan of John Hattie’s work ever since I encountered Visible Learning. Hattie has done the most exhaustive meta-analysis in education. Thanks to him, we can gauge not only the relative effectiveness of almost every educational intervention under the sun but we can compare these interventions on an absolute scale of effect size.

Perhaps most importantly, Hattie was able to identify a ‘hinge point’ (as he calls it) from exhaustively comparing everything: the effect size of .40. Anything above such an effect size has more of an impact than just a typical year of academic experience and student growth. And an effect size of 1.0 or better is equivalent to advancing the student’s achievement level by approximately a full grade.

The caveat in any meta-anlysis, of course, is that we have little idea as to the validity of the underlying research. In a summary of…

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