## Posts tagged ‘NCTM’

### Blown Out of Proportion

In preparing a workshop about proportional reasoning for the 2011 NCTM Annual Meeting, I came across the following from “Learning and Teaching Ratio and Proportion: Research Implications” by Cramer, Post, and Currier, which appears in *Research Ideas for the Classroom*, edited by Douglas T. Owens. The authors discuss the following problem, which they presented to a class of pre-service elementary teachers:

Sue and Julie were running equally fast around a track. Sue started first. When she had run 9 laps, Julie had run 3 laps. When Julie completed 15 laps, how many laps had Sue run?

The authors claimed, “Thirty-two out of 33 pre-service elementary education teachers in a mathematics methods class solved this problem by setting up and solving a proportion: **9/3 = x/15**.”

I wanted to be surprised. Sadly, I was not.

Participants in my workshop (all current middle or high school math teachers) were asked to solve the same problem. Several incorrect answers were suggested, among them 3, 15, 27, and 45. Less than 40% of the attendees obtained the correct answer, 21.

This is frustrating, as proportional reasoning is extremely useful in analyzing real-world phenomena. In fact, it’s even applicable to language arts, as evidenced by the following graphic from my presentation:

The teachers in my workshop aren’t the only ones who have difficulty with proportional reasoning. Students have endless trouble, too…

Teacher: Today, we will discuss inverse proportion. Here’s an example: “If it takes 6 days for 2 men to finish a task, how long will it take 3 men to complete the same task?” The number of men needed is inversely proportional to the number of days required. Consequently, 3 men will be able to complete the task in 6 × 2/3 = 4 days.

Student: Oh, I see! I think I’ve got a real-life application of this. If it takes 6 hours for 2 men to hike to the top of a hill, then it will only take 4 hours for 3 men to hike to the top!

### An Open and Shut Case

Most mathy folks are familiar with the locker problem:

Every day, 1000 students enter a school that has 1000 lockers. All of the lockers are closed when they arrive. Student 1 opens every locker. Student 2 closes every other locker. Student 3 then “changes the state” of every third locker – that is, he opens it if it’s closed, and he closes it if it’s open. Student 4 then changes the state of every fourth locker, Student 5 changes the state of every fifth locker, and so on, so that Student

nchanges the state of everynth locker.Which lockers are open after all 1000 students have finished opening and closing lockers?

At the 2011 NCTM Annual Meeting, the following variation of the locker problem appeared in the Daily Puzzle Challenge on Thursday:

Every day, 30 students enter a room with 30 lockers. All of the lockers are closed when they arrive. Student 1 opens every locker. Student 2 closes every locker. Student 3 then “changes the state” of every third locker — that is, he opens it if it’s closed, and he closes it if it’s open. Student 4 then changes the state of every fourth locker, Student 5 changes the state of every fifth locker, and so on, so that Student

nchanges the state of everynth locker.One day, some students are out sick. Regardless, those present repeat the process and just skip the students who are absent — for instance, if Student 3 were absent, then no one would change the state of every third locker.

When they finish, only Locker #1 is open, and the other 29 lockers are all closed. How many students were absent?

The following applets can be used to investigate the original problem or to solve the variation.

### NCTM Annual Meeting — Indianapolis

The NCTM Annual Meeting will be held April 13-16 in Indianapolis, IN. On behalf of the Council, I’ll be presenting the following sessions:

**Using Free NCTM Resources to Promote an Understanding of Proportion**

Friday, April 15, 10:30am-12:00pm; Sagamore Ballroom 5 (Convention Center)**New Teacher Celebration!**

Friday, April 15, 4:45-5:30pm; Sagamore Ballroom 2 (Convention Center)

When not presenting, I’ll be hanging out at the Illuminations booth (#422 in the exhibit hall), letting attendees try their hand at floating plastic bears in an aluminum foil boat, distributing this year’s copy of the Daily Puzzle Challenge, and telling folks about all the great classroom resources they can find at Illuminations and Calculation Nation^{®}. If you’re in Indy this week, stop by to say hello — and to tell me your favorite math joke!

### MJ4MF Review

I was delighted to open the April issue of the *Mathematics Teacher* journal and discover a review of *Math Jokes 4 Mathy Folks*. Reviewer Leah Evans had some nice things to say:

Math Jokes 4 Mathy Folksis a delightful read. The author has compiled a vast array of puns, quips, and jokes meant for people of varied ages and mathematical expertise.[…]

I highly recommend this book as a diversion from the rigor of mathematics. It allows us to have a good laugh (or a long groan) at a joke that only “math nerds” would get, and it points out that humor can be found in all mathematical applications, even a telescoping series.

I love the cliffhanger at the end! The reference to a “telescoping series” is — I think — in regards to this joke (p. 89):

If you’re interested, here’s a copy of the entire review. (Click on the image to view a full-size version.)

### To Infinity, and Beyond…

The table in the board room at NCTM headquarters contains an extended infinity symbol:

The design is based on the stylized infinity symbol that appears in the NCTM logo:

### Working at NCTM

I am the Online Projects Manager at the National Council of Teachers of Mathematics. I love my job — I’ve been here for 6 years, and I’ll stay here another 60, if they’ll let me; I love my organization — I’m not yet 40 years old, but I’ve been a member almost half my life; and I love my colleagues. But working at NCTM has its share of, um, *challenges*.

Take the equipment we have in the building, for instance. Today, I selected “single‑sided” on the photocopier, and all of my copies were printed on Möbius strips.

Of course, my mathy colleagues cause problems, too. There are three types of people who work at NCTM: those who can count, and those who can’t.

About a year ago, a small fire started in one of the hallways. An engineer, a scientist, and a statistician — who were at NCTM headquarters attending a summit about the merits of always including three related professions in the set-up of a joke — began debating the best way to extinguish the blaze.

“Dump some water on it!” the engineer suggested.

“No! Remove the oxygen!” said the scientist.

The statistician, however, started running around the building, starting fires in other locations. “What the heck are you doing?” the other two asked.

“Trying to create a decent sample size,” he said.

To put out the fires, a mathematician on staff brought them several buckets of water. The fires were extinguished one by one, but when they finished, there was an unused bucket of water. The statistician said to the mathematician, “Can you please get rid of that water?”

The mathematician proceeded to start another fire, and then he dumped the bucket of water on it.

“What’d you do that for?” the statistician asked.

“I reduced it to a previously solved problem,” said the mathematician.

More seriously, the following is a **true** story about NCTM.

The James D. Gates Building in Reston, VA, serves as the national headquarters for NCTM. In 1993, an addition to the building nearly doubled its size. In the area between the original structure and the addition, a courtyard was created, and a geometric design of circles and triangles was constructed on the floor of the courtyard with bricks and drainage pipes:

Long‑time members of NCTM might recognize the old NCTM logo:

Shortly after the building was expanded, however, it was learned that a number of publishing companies, eager to align themselves with NCTM after the release of *Principles and Standards for School Mathematics*, began placing the NCTM logo directly on their products. Cease‑and‑desist letters were sent to the publishers asking them to kindly remove the logo from their materials — and NCTM was shocked when they said, “No!” As it turns out, the publishers’ lawyers had done their homework, and they learned that the NCTM logo had never been trademarked. As a result, there was nothing that NCTM could do to prevent them from using it.

Consequently, the NCTM logo was revised to the version we have today:

In the courtyard, we have a constant reminder of a bureaucratic blunder. As you’ll notice, the current logo has the ® symbol — and no one’s taken this one away from us, baby! Personally, I think the new one is better, anyway, with allusions to the infinity symbol; the letter *x*, as an algebraic variable; and a small child, which is a constant reminder that our profession is not just about numbers and shapes but about the lives we touch.

### NCTM Regional Conference in Denver

The NCTM Regional Conference in Denver, Colorado, will be held October 7-8, 2010. I’ll be presenting two sessions at the conference:

**Developing Geometric Thinking**(Grades 6‑8), Thursday, October 7, 12:30‑1:30 p.m., Colorado Convention Center, Korbel 4C- Illuminations (illuminations.nctm.org) offers free resources that develop geometric reasoning skills. The Tessellation Creator allows students to explore patterns with polygons. Paper Pool requires students to consider similar figures in context. Several other Illuminations lessons in geometry will be examined.

**New and Preservice Teachers Workshop**, Thursday, October 7, 10:30 a.m.‑12:00 p.m., Colorado Convention Center, Korbel 4B

If you happen to be in Denver the same weekend, please stop by and say, “Hi!”

### Math Talk

I have to admit, I’ve never been a huge fan of the books of Theoni Pappas. They don’t excite me in the same way that a collection of Martin Gardner’s problems or Ian Stewart’s math essays do. But I greatly respect the huge impact she’s had in making mathematics palatable to so many people. She’s written over 40 books, many for kids, and they’ve been very well received.

A brief biography of Theoni Pappas appears on the NCTM website, because the Theoni Pappas fund sponsors an award through NCTM’s Mathematics Education Trust. Teachers in grades 9‑12 can apply for awards up to $4,000 to develop materials under the Connecting Mathematics to Other Subject Areas grant.

So, what made me think about Theoni Pappas? It turns out that some folks on Amazon who bought my book, *Math Jokes 4 Mathy Folks*, also bought her book, *Math Talk*. And though I’m not a fan of most of her books, I do love this one. It’s a collection of “mathematical poems for two voices,” and it contains quite a few gems. One reviewer at Amazon said, “This is a delightful, engaging introduction to the world of mathematics, giving children and adults alike a glimpse of the wonderful adventures that lie beyond simple (and boring) drills.”

A review in the NCTM journal Mathematics Teacher said, “*Math Talk, *in its novel approach, would make an interesting addition to the mathematics library for any age group.”

Below is a poem from the book. I’m surely violating copyright laws by posting this, but you can see this same poem by choosing the “Look Inside” link at Amazon, so whatever.

I applaud her attempt to mix math and language, and I’m honored that my book gets to share a page with hers.

I hope you enjoy her poems as much as I do.

### Success at NCTM Annual Meeting!

**Math Jokes 4 Mathy Folks** sold out at the NCTM Annual Meeting! It was offered in the NCTM Bookstore, where members received a 25% discount off the cover price. Officially, the conference started on Thursday morning, but the bookstore was open on Wednesday, and all 250 copies were sold by Wednesday afternoon. Thanks to everyone who bought a book! (Members who weren’t able to get a copy at the conference can call (800) 235-7566 to order a copy from NCTM. For large orders, call Robert D. Reed publishers at (541) 347-9882 to inquire about bulk discounts.)

I did a book signing yesterday afternoon — my first ever. It was a lot of fun! It was both exciting and intimidating to see a long line of fans waiting when I arrived, but I had a great time talking to them and sharing jokes (full story on NCTM.org). One woman shared a joke I’d heard before:

What type of lingerie does a mermaid wear? An algae-bra!

But she had a follow-up that was new to me:

What type of lingerie does a little mermaid wear? A pre-algae-bra!

It was great to get some new material.

Thanks to everyone for your incredible support! A big thanks to anyone who shared a joke with me, and an especially huge thanks to members of the NCTM marketing department who made this all possible!

### Make Your Own (Math) Joke

Here’s my favorite joke (even though it’s not a math joke):

Two cannibals are eating a clown. One turns to the other and says, “Does this taste funny to you?”

It’s beautiful in its simplicity. Just 19 words, none of them extraneous. It’s a triumph of humor, and I tip my hat to its creator.

I love this joke, and I would have included it in *Math Jokes 4 Mathy Folks*, but it’s not a math joke. But it got me to thinking — could it be altered so that it could be a math joke? That is, can you put two different words in the blanks below so the joke is more mathy? And can you do it so that it’s still reasonably funny?

Two cannibals are eating a ________. One turns to the other and says, “Does this taste ________ to you?”

I offered this challenge to attendees at the Math Joke Hour that I hosted yesterday at the 2010 NCTM Annual Meeting. They came up with quite a few that are worth sharing, though not all of them are mathematical:

math teacher… chalky

statistician… normal

Kenneth Appel… fruity*

actuary… bland

angel… heavenly

mechanic… greasy

Iowan… corny

pot smoker… mellow

Warren Buffett… rich

old seafarer… salty

bodybuilder… strong

Got another worth sharing? Leave it in the comments section.

* Kenneth Appel is the mathematician who, along with Wolfgang Haken, proved the Four Color Theorem in 1976.