Hello, reader! If you intend to post a link to this blog on Twitter, be aware that for utterly mysterious reasons, Twitter thinks this blog is spam, and will prevent you from linking to it. Here's a workaround: change the .com in the address to .ca. I call it the "Maple Leaf Loophole." And thanks for sharing!

Thursday, June 25, 2009

How Math Must Assess: a Post-Mortem

I am writing this now, instead of getting the heck up out of here for the summer like I should be doing, because I don't want to forget anything. In fact, I probably should have written it sooner.

For the uninitiated, read this first. Dan lays down his system.

What I Kept
Each skill considered, numbered, recorded as a separate grade, and tested twice. Unlimited opportunities for remediation, but outside of class. I would typically re-do the test items with the student and troubleshoot her misunderstandings or more trivial errors. Then if she could prove that she knew what she was doing on a different problem without assistance, I changed her grade to 10/10. I still gave assessments at times most teachers would be giving a quiz or a test: typically the middle of a unit and the end of a unit.

What I Changed
I made each question a maximum of 5 points. Sometimes I made half-point deductions, like for rounding errors. After the first assessment of a skill, it was recorded as a grade out of 5 points in my gradebook. After the second assessment, I changed the entry to be out of 10 points. If the student scored a 5 the second time, I made her grade 10/10, no matter what she scored the first time. If not, I recorded the sum of the scores from the two attempts.

I didn't use a stamp. I put a small sticker on each question earning a 5 on the second attempt, and it was up to the student to transfer the sticker to his checklist. Major instructional time saver.

What Worked
I tried this with both Algebra 1 (9th grade) and Algebra 2/Trig (10th and 11th grade). It worked really well for the older students. Every time I was available after school, I could count on anywhere from 2 to 15 kids wanting to remediate something. I have no doubt that spending more time on difficult topics benefitted these kids' enduring retention; the results of their state regents exam (administered almost 2 weeks after classes ended) bear it out. I received an email this afternoon which pretty much made it all worth it. This is the complete text:
I PASSED???????????????????!????!????? with a seventy five?? not just a
64.5?????? i see the numbers on my gradebook but seeing is not always believing.

That girl worked her tail off all year because she had a tangible incentive. If she did well the first time, she wouldn't have to stay after school. And if she didn't, she could change her grade.

What Didn't Work
Dan promises students excited about tests... I didn't see that. They were happy that they weren't stuck with bad grades and felt empowered to do something about it, but I wasn't feeling a big "Yippee!" on test days.

Since we are required to publish our grades on, which students and parents have access to, the concept checklists were mostly a flop. A handful of hyper-conscientious-types made good use of them, but students were more likely to go print out their scores before coming to remediation. I may do away with the checklists altogether next year. Not sure. I am not good at compelling students to keep a good notebook in general. I need to work on that.

Sometimes my grades felt a little inflated. I'm ok with that.

I think it worked better for older students because they have the maturity to take ownership of their grades and learning, they are invested in their performance because they are starting to worry about college applications, and they follow through by monitoring and coming to remediation. In practice, for me, the system relies at least partially on student initiative and how much he is motivated by grades. I did not have as much success with the freshmen, as much as I tried to sell what a good deal this was. They are much less likely to stay after school in general, and as far as grades go, they just want to do well enough to keep their parents off their backs. I'm not sure what changes I could make to do better there.

It's not perfect yet, but I'm sold on the idea. Much gratitude to Dan for coming up with and publicizing a better way. I thank you and my kids do too.

Algebra 2/Trig Concept List 08-09
(I can add to this, just ask.)

Thursday, June 18, 2009

Evolving Rational Expressions and Equations Unit

*update* The embedded file is not the original one that was posted. Improvements made 6/19/09.

To recap from comments in previous post, I have this for day 1, reviewing operations on polynomials and monomials.

For Day 1 homework, they will research a way to explain why dividing a number by zero is undefined and be prepared to explain it in class the next day.

For Day 2, we will start by explaining to partners our reasoning for a/0 is undefined. Then a few students will explain it to the class.

Then we get into this... I'm looking for feedback to make it better if you have any. Thanks Dan Greene for the idea and not minding me ripping you off.

Classwork 8 2

Wednesday, June 17, 2009

Rational Expressions & Equations

Started a little planning for next year...the other trig teachers and I have divvied up the units and are each planning three. We are to produce a calendar with daily assignments, assessments, a Smartboard Lesson for each day, and keys for all.

Was working today on Unit 8: Rational Expressions and Equations.

I have the calendar and assignments done and have started looking through the lessons I used this year.

They pretty much suck. This statement might preclude me finding employment for next year but I don't care: I am at a loss for how to make this concept interesting or relevant to 16 year olds. All we are doing is simplifying and solving algebraic expressions and equations. With no context. It's going to be a brutal 10 days of instruction if I don't get it together.

I can make it extrinsically rewarding by including lots of partner/group practice structures.

I can attempt to start off with some word problems of the type that one could, if one wished, write and solve a rational equation. Your standard Tom can paint a house in 3 days and Dick can paint a house in 5 days etc etc. I find that these are either easy enough to solve without an equation, or too difficult for this level.

I really don't want to get into the harmonic mean.

Ideas? Help?

Sunday, June 14, 2009


One of my favorite things about blogging is the emails I get out of the blue. Recently Amanda Glynn (glynna1030) sent me this nice description of a contingency to compel kids to stay on task. I used it on a review day when I really wanted kids to just sit and do practice problems for a half hour. That's tough during the last week of school, but it worked nicely. I used bonus points and plastic counting chips. Amanda agreed to let me share it.

This has worked really well on review days and lets the kids get in an easy minor assessment grade.

First, they get into groups of 3 or 4 and assign someone the title of "Blockmaster" and some one else "Keymaster."

Then I review the rules: Everyone starts out with a 20 out of 20 points. If they have 5 blocks at the end of class, then that's their grade.

If they have less:
4 blocks = 19 points
3 blocks= 18 points
2 blocks = 16 points
1 block = 14 points
0 blocks = 12 points

There are 5 ways they can lose blocks:
1) Copying
2) All groups members not participating (leaving someone out)
3) Talking off topic (at this point, I remind them their topic is "This Review" not any math topic, "This Review" only)
4) Someone other than the keymaster looks at the answer key
5) Asking me a question before they ask their group

I make sure #5 is enforced by doing the following: Suppose Jim, Tyler, Kate, and Sam are in a group and Sam has her hand up. I walk over, looking at Sam, and then glance at Tyler and ask, "Ok Tyler, what is Sam's question?" And if Tyler can't tell me, i take a block.

Then they come and get their linking unit cubes (5 in a stack) and the answer key in a blue folder.

It works really awesome! You gave me an awesome idea, so it's only fair I give you one back!

Thanks, Amanda! And thanks for taking the time to share it with the world.

The Job for Which No One Is Qualified

Their Math Department needs to go knock some heads together in Human Resources:

/Redacted/ College is seeking Adjunct Instructors. Qualified candidates must possess a Masters Degree in the following areas: psychology, sociology, English, communication, library science, philosophy, information technology, natural sciences, economics, and math. Applicants are encouraged to submit a resume, cover letter, and official transcripts to:

Wednesday, June 10, 2009

The Homework Question

Sam Shah is trying to harness the power of blogs and readers to address The Homework Question (for 7-12 math). Not so much the "why" as the "how". As a service to the professional community, please go read his post and take the short survey. I am very interested in the results.

Tuesday, June 9, 2009

Target Practice

Ever see a student "graph" something by obviously just sort of copying the general shape he sees on his graphing calculator window? Come on, you know you have. Making a nice graph is a tedious procedure for an adolescent. Invariably someone is just going to wing it.

Exasperated with saying "plot points and draw a smooth curve" over and over, I hit on an analogy that sticks. I've never seen such pretty hand-drawn graphs as this year.

This is pretty famous on the Internet, and maybe you have seen it:

It is supposedly located in the men's bathroom in Amsterdam's Schiphol Airport. See the irregular black spot? That's a housefly painted on the porcelain.

Why on Earth would they do that? Because your aim improves when you have a target. The flies keep the bathroom cleaner for longer. In my search for images, I even found that a company is marketing a sticker called "the urinal fly."

What this has to do with graphing, of course, is in my exhortation for students to plot points before sketching a curve. After telling the story, now I can say, "Remember the urinal flies in Amsterdam? Give yourself a target." From my notes:

Now that is some explicit direct instruction! I'm a fan of the book Made to Stick, but aside from the six key principles simplicity, unexpectedness, concreteness, credibility, emotions and stories, I think they should add a principle for communicating with teenagers: grossness.

Ooh! Maybe next time I will find some housefly clipart in the Smart Notebook gallery and use them to plot points.

Sunday, June 7, 2009

What Can You Do with This: At the Gym

I have Definite Ideas for how I want to develop the supporting structure for this lesson, but I want to hear what you have to say, crowd. (You are supposed to be wise.) Directions here, if you need em.

Tuesday, June 2, 2009

How To Make a Facebook Fan Page

Hooray! This seems to work the way I want it. It is allowing me to send stuff to kids outside of class that they will actually see, but I don't have to deal with the potential over-sharing of friending them. I'm testing it out with one class for the remaining few weeks of the year. Here is what I did:

1. I explained the purpose to the class. They liked the idea and were very helpful with some setup decisions. I passed around a sign-up sheet for students to provide their email address, strictly voluntary. 15 out of the 20 students present signed up.

2. I went to Facebook and created a new page. I set it to Local:Education and called it "Dispatches from Ms Nowak" which I know is a lame title but it's descriptive enough.

3. I uploaded a picture and set some other settings the way I wanted. In the "about" section, I encouraged them to use the Wall for public communication with me and each other, but use my school email address for private communication with me. Then clicked "Publish Page".

4. I sent a mass email to the students who signed up (using Bcc: so they didn't all get each others' addresses) with a link to the page. It's up to them to go there and "Become a Fan."

5. Once they are fans, they will get updates in their news feeds when Wall posts are made on the page.

Ta da! I think this is everything I wanted. I can get their attention in their communication medium of choice, but all the interactions are publicly viewable, and the only pathway for private communication is the school-sanctioned one.

Monday, June 1, 2009

A Workable Teacher Facebook Scheme

I've been grappling with this: I'd love to claim a small fraction of the hours a day I know many students spend on Facebook, and be able to communicate with them through it. Kids, at least at my school, don't so much email. They Facebook and text. However, I would be uncomfortable friending students with my personal Facebook account. It's private space where I interact with my family and friends, and it needs to be separate from my professional life.

I don't know why I didn't think of this before, but over the past few days I'm liking the idea of a separate Facebook account for Miss Nowak, not for Kate Nowak, that I can use to friend students. Not that I would require it - some students don't even have a Facebook. But if they do, they will get updates from me like "Just posted grades from Trig unit test", and I can share interesting and useful links with them where they are most likely to see it. I also have to investigate the usefulness of creating Facebook "pages" or "groups" for classes, but I don't know much about them yet.

If you are using Facebook with your students, please let me know how you have it set up and how it's working for you.