Balancing Ruler Problem – A surprising solution, Part I

So, if you tried to solve The Balancing Ruler Problem, I have a video that shows off the answer I got.

Be advised, this video is totally a spoiler, so if you are wanting to figure it out yourself, do NOT watch the video!

Now, this result surprised me a bit. The prism was located much closer to the center of the ruler than I was expecting. I am going to expand on my confusion and what I did about it next time.

Balancing Ruler Problem

For this problem, we want to see the effects of trying to balance two masses on a lever. (What class of lever would this be?) One of the masses is exactly double the other.

Here are some photos of the original configuration of the ruler and the wooden prism.

photo 1

A still from the video

photo 2

View of the ruler balancing from directly above the ruler

What inch or centimeter mark will the prism be under to balance the ruler once the pennies are added?

Vocabulary: Common Core Geometry’s first real hiccup

So, my student’s last Geometry unit test force a realization. Computational math classes, which my students have all had up until this point, generally are not focused on vocabulary.

I’ll give you an example:

Suppose a typical Algebra I teacher asks his or her students to solve 3x + 7 = 28. How would they do it?

Well, for the most part, they will probably add seven to both sides of the equal sign. Then, after dividing both sides of the equal sign by three, the answer would be x = 7.

Before this year, I would have been content to accept that as a “full-credit-answer.” My students would have never been expected to know that the reasons that those steps are effective. Namely, the subtraction and division properties of equality.

However, on this most recent unit test for Common Core Geometry, each of the six questions required written explanations. Written explanations require vocabulary. Sometimes a lot of it. And it needs to be used properly.

The first real hiccup in our version of the Common Core Geometry is that this math teacher is not used to having to facilitate the deep understanding of technical vocabulary. I’ve taught skills, procedures, and technical reading, but I’ve never required my students to need to know the vocab as well as they do now. Previous geometry courses that I’ve taught have still been so algebraic that if the students didn’t learn the vocab, they could still get by doing the crazy amount of algebra.

This year, the vocab has taken center stage… and the students aren’t the only ones needing to adjust.

Please add to the comments any tips or pointers you might have in helping develop deep and flexible understandings of math vocabulary.


Advice for the MEA, Part 2

This is part two of a two-part series. If you find yourself getting lost and need some background, then please go back one post and pick the story up from the beginning. And on we go…

So, in my last post, we established that the public face of the MEA is one that is dedicated to lobbying, healthcare, benefits, and otherwise interacting in the political and legislative process.

But, the new MEA, the right-to-work MEA, the MEA that has to sell its services to attract members should consider being able to answer one very important question:

What is the MEA going to do to help me become a better educator?

Education is what my job is all about and it is the “E” in the MEA. The MEA is fighting to help me become a better paid educator. The MEA is fighting to help me become an educator with a good healthcare plan.

But what if my main objective is to become a better educator? Can the MEA help me there?

I believe they can. If I were in charge of the MEA, here’s what I’d do. I would begin a major change. The MEA is dedicated to providing Michigan students with the very best educators in the world. So, we are going to cut our lobbying budget in half and instead, the dues that you pay us will be redirected to providing monthly professional development conferences. We will bring in the foremost educational reformers who will provide expert analysis and research-based techniques for improving instruction, assessment, scheduling, sequencing, community relations and instructional leadership.

Also, we will be altering the job descriptions of our building representatives. From now on, local EAs building representatives will be co-observers who will assist the administrators see to it that each member gets observed and evaluated by multiple sets of eyes. The building representatives will be thoroughly and continuously trained to ensure that they are of the highest quality.

Also, the MEA will continue to produce the legislative critique journal, the MEA Voice, but it will also be providing two top-notch professional educational journal for a modest $3 per month cost each. In either the elementary or the secondary version, this monthly journal will include an article from each of the 6 main core areas (math, science, ELA, social studies, fine arts, and foreign language) written by MEA members, approved by a board of 15- to 25-year veteran teachers.

Also, for far too long, the plight of the first-year teacher has been ignored, so in the new MEA, local officers will be personally responsible for the mentorship of the first-year teachers. They will meet weekly with the first-year teachers. The MEA will make sure that Uniserv directors’ offices have a room dedicated to creating a library of effective resources for consumption by first- and second- year teachers. Under the guidance of the local president, vice president, secretary, and treasurer, the first- and second- year teachers will be expected to read books quarterly and be observed by local union members who the staff elects as exemplary teachers to offer support and feedback to the young teachers. The MEA will sponsor a weekend conference that all first- and second- year teachers MUST attend in order to remain in good standing. The conference will be free to all first- and second- year teachers. It will include rap sessions with exemplary teachers, opportunities to observe master teachers, group sessions evaluating student work, and a keystone address by a cutting-edge expert in the field of education.

So, why should you join the MEA? Because, we are going to provide you the resources, the support, and the community to help you become the very best educator you could possibly be. Without us, you might be great, but you are doing it on your own. With us, you will become the very, very best.

How different a message would that be?

MEA, I know you didn’t ask for my advice, but there it is.

Now, let’s go have a great 2013.

Advice for the MEA, Part 1

I am a member of Michigan’s largest teacher’s union: The Michigan Education Association (MEA). (It actually represents several other groups of public and private school employees as well).

The last quarter of 2012 was a tenuous time for those actively involved in union activities. Proposal 2 (which would have constitutionally protected collective bargaining and union workplace procedures) was campaigned for the November election and the public voted it down more than 2-to-1. Then, during the lame duck session, the Michigan Legislature passed a series of “right-to-work” laws that give current union members the ability to remain employed in their current positions while ceasing to pay dues to a union. The reality of 25% to 40% of members accepting the new option is putting the MEA in a tricky position.

It has to sell it’s services.

MEA, I know you didn’t ask, but I have some advice for you. You provide a service to your members. No time would be better than now to begin to convince your members how vital your services are. I have spent some time trying to get a sense for what the mission of MEA is, not from reading the mission statement, but instead by looking at the publication: the MEA Voice. The journal that gets mailed to each member. THe contact that you keep with your members is contained within. In inspecting the MEA Voice, I have made a few observations.

1. The MEA Voice for December 2012 is a 24-page document (including the cover). In that document:

  • The cover is dedicated with a pretty cool picture of a rocket from a school’s rocketry program, which is competing against a quarter-page, bright red, “CRISIS” statement about legislation in the lower right corner.
  • The table of contents treats the rocketry program like a footnote to the huge picture of picketing, campaigning members in the middle of the page
  • The fantastic rocketry program is explained in a 2-and-a-half page article, which is split across the 5-page list of names of members who gathered at least 24 signatures for the Proposal Two petition drive.

All of this reveals one possible conclusion: The MEA is much more interested in the political side of education than it is about the academic side of education. At least that is what one could deduce from the organizations main publication.

But, I understand, 2012 was an election year. The lame duck session was very stressful and eventful. What about a non-election year. How about April 2011? That was 6 months past the 2010 mid-terms and a year-and-a-half from the 2012 elections. Surely if the MEA were going to publish some good academic articles, it would be then, right?

Well, here are some observations from that issue.

  • The cover shows a group of adults standing in a group looking up at the camera with the headlines “ENOUGH IS ENOUGH: ‘Ed Reform’ vs. Building Effective Schools. How to best help students.” A good start…
  • A letter to the members all about legislation and concerns about it.
  • A flash back to a 1934 essay about how public policy is conspiring against public education.
  • A top ten list in which the only item on the list regarding good teacher was a paragraph dedicated to an award-winning social studies teacher from Kalamazoo (which came in at #7… one spot below the save-the-date for the MEA member golf outing at #6.)
  • The first real article is a 4-page spread on the cover issue in which all of the pictures show protesting members with signs.
  • 3 pages about health care, 2 about retirement, 6 pages dedicated to officer elections, and exactly NO advice for a young teacher trying to get better. Also, there was no notices of conferences, workshops, or professional development (aside from some advertising space given to local university programs.)

In fact, I went looking through the rest of the available issues. Here’s what I found:

  • February 2011 – One page (out of 24) dedicated to a column on good ELA instruction. It was pg 22. Last of the whole magazine. For the record, it got the same amount of paper and ink dedicated to it as the one-page ad for the member golf outing.
  • December 2010 – One-and-a-half pages about an effective band teacher.
  • October 2010 – A notice of a instructional support PD conference appears on pg 3, and 2 pages dedicated to school improvement at Adrian High School. (This amidst the 6 pages dedicated to supporting Virg Bernero as Michigan’s next governer.)

You get the idea. A trip around the website says the same thing.

The MEA is a political organization that is now in the position of having to market itself to its prospective members. It is clear to me what the MEA does to support its legislative beliefs. it is clear to me what partnerships the MEA has for healthcare and retirement services.

But what if I don’t want to be a member of a political organization? What if my goal is to excel as an educator? What evidence do I have that you will support me in that venture?

In Part 2 of this series, I will complete my (unsolicited) advising of the MEA.