Friday, January 30, 2009

Snow Days

God's voice thunders in marvelous ways; he does great things beyond our understanding.
He says to the snow, 'Fall on the earth,' and to the rain shower, 'Be a mighty downpour.'

So that all men he has made may know his work,
he stops every man from his labor.
- Job 37:5-7 NIV

So we had one of the biggest snow falls since the blizzard of 1978. This provided for two days off school. It worked out great for my daughter's birthday. She loves basketball. The water for our washing machine tends to not work when it gets too cold out, so we went to school and did a few loads while we played basketball in the gym. There is a nice sledding hill near the parking lot, so we had a great time with that as well.

Tip for playing in the snow:
- If you don't have great snow boots, tie plastic grocery sacks around your feet after you put your socks on. Hey, "reduce, reuse, and recycle" right. It also makes it easy to get the little kiddies feet into the shoe.
- Similarly, the reason kids can't stay out and play in the snow for as long as they would like is because of their extremities freezing. So use the plastic sacks as a layer for the gloves. When we can't find gloves that fit (or even when we can), I have the little ones use socks. First one sock, then the dry guarantee of the sack, then another sock. This avoids the other problem of the glove being too short. Snow on the wrist is not enjoyable.
- Dress in layers. Most of the kids have snow pants. But I just use a couple of layers. I also were layers of shirts instead of a big coat. If I get too warm, I can take off a layer. If that outer layer gets too wet, I can take it off before putting on my coat and driving home.
- Get a toboggan. At our school's annual auction a couple of years ago we invested in a nice lightweight wooden toboggan. This thing cannot be beat for distance and speed down a hill. It is always so satisfying to slide into undisturbed snow - boldly going where no one has gone before. (This heavier toboggan looks like it could really take some abuse and is built to last. Maybe we could get that to take the grandkids sledding.)

"By the breath of God ice is given, and the broad waters are frozen fast.
He loads the thick cloud with moisture; the clouds scatter his lightning.
They turn around and around by his guidance,
to accomplish all that he commands them on the face of the habitable world.
Whether for correction or for his land
or for love, he causes it to happen.
Hear this, O Job; stop and consider the wondrous works of God.
Do you know how God lays his command upon them and causes the lightning of his cloud to shine?
Do you know the balancings of the clouds,
the wondrous works of him who is perfect in knowledge" Job 37:10-16 ESV
My friend Heidi from Ohio sent me this tns file for the TI-Nspire. She has used something like this in the past with her geometry students when talking about rotational symmetry and the beauty of mathematics in the world. She also sent me this video where you can see the entire blue TI-Nspire. If you want the "snowflake" tns file, I posted it on the TI-Nspire Google Group with other tns program files and on my TI-Nspire site. You can get a 30-day free trial of TI-Nspire CAS and play too. What do you think? Cool, eh?

Thursday, January 29, 2009

Storage and traveling with TI-Nspire

The question has arisen, "How do you easily store the TI-Nspire in your classroom?"

I remember my grandfather and my dad saying, "A place for everything, and everything in its place." While I don't always live up to this standard, I think it is a wonderful idea. In fact, 1 Corinthians 14:40 similarly says, "Let all things be done properly and in order."

So earlier this semester I described to my wife what I was looking for. Using some of her superpowers, for under $10, she picked up a shoe organizer at Target for me. It is made of a nice canvas-type material with mesh pockets.

It holds 24 TI-Nspire's and I can look over and easily see if one is missing at the end of the period. Each student is assigned a number that corresponds to their book number. Some classes it is their book number minus 20 or some other number.

If you click on the above picture you may notice that I did not start with the number 1. Our school has a cart with 25 laptops in it. Students' TI-Nspire number corresponds with their computer number. The numbers of the laptops began with 11. I can see some value in having all the numbers be double digits. For example, no one will write a number in front of a 4 to make it seem like you have two number 24s. By the way, for reasons I can't go into right now, if I had to choose between laptop computers for my math and science students or TI-Nspire handheld technology, I would opt that each student have a TI-Nspire CAS.

As you can see, each student has a protractor and a ruler in their pocket too.

For traveling to give training with the TI-Nspire, a friend gave me a Top Rhino suitcase on wheels as pictured above. If you click that picture it will link you to a store that sells them. The model I have has special compartments for the blue TI-Nspire's 84 faceplate. It is like getting two different devices for the price of one. However, I prefer the computer algebra system capabilites of the TI-Nspire CAS for its scaffolding and exploring possibilities. (Check out the links at the bottom of this website for more info on CAS.)

There are other alternatives for storing and traveling with the TI-Nspire. It would be great to hear more about what you have tried. Okay, I'll share one more that I have enjoyed... The TI-Nspire Carry Case has captured the attention of several of my students. This canvas material is well constructed with a place for a business card (or other identifier) and a pocket that can be used for the TI-84 faceplate. I jokingly told some students the only thing I can think of that would make it any better would be if we were to sew a loop so it could sported around on a belt. Batman would definitely want this.

Wednesday, January 21, 2009

Box and Whisker on the TI-Nspire

I had some friends wonder about doing multiple box and whisker plots on the same screen.
So I put together the following to help explain the process. I figured others would be interested in how to do 'bnw' on the same screen with the same scale, so here is a description of what I did and what you see happening in the image to the left.

Last semester, my first 4 periods took a test. Like most of my multiple choice tests, students can score 110 out of 100. Our school has a pretty tough grading scale and some multiple choice questions can be tricky. Fourth period is an AP class that already receives a weighted grade, so they didn't get the blessing of 10 possible bonus points on their AP-like test.

I don't teach box and whisker graphs in any of my math classes, but I do use them for myself and for students to get a picture of how they are doing compared to their classmates. It enables you to quickly see things like what were the top 25% scores, or 3rd quartile, and what the median or middle score is. By moving the mouse around on this TI-Nspire Data & Statistics page, the top score, Q3, median, Q1, and lowest score appear. Q3 and Q1 stand for 3rd and 1st quartile.

If you click one of the sections, you see the data points appear. You can see that I added a movable line to show where the 100 point mark was. This can be done on the handheld by pressing MENU>Analyze>Add Movable Line.

The key to graphing anything on a Data & Statistics page is that the information in the list and spreadsheet needs to have a title. In other words, a variable needs to be assigned to the data. For multiple box and whisker plots with the same scale, use categorical data. I put the period in the first column and listed the grades in the class in the second column.

There is a nice shortcut to entering the same thing in multiple cells in this spreadsheet that behaves extremely similar to and Excel spreadsheet. On the handheld press CTRL+(Click), that is CTRL and the circle in the middle of the Navpad. There are more details about this shortcut in the "Tips & Tricks" section of the Spring 2008 Nspiring Times (page 14). Past issues can be found on the bottom of this page of the website.

These box plots can be graphed vertically or horizontally as seen on the last picture in this article. It is fun to watch the data move when the variable is changed by clicking on it. This is shown in a short video here.

Tuesday, January 20, 2009

Graphing a Picture

Beauty, creativity, mathematics.

I would say that beauty is part of what we were created to display.
"Your people shall all be righteous ... the branch of my planting, the work of my hands, that I might display my beauty." (Isaiah 60:21 ESV)

Several years ago I attended a T-cubed Regional Conference in St. Louis where a teacher, Pam Burke, gave a presentation called "Picture This!" (ppt) about a 'Graphing Art' project. She talked about how she would only give an assignment or project that had maximum educational value for the time spent. Her handout contained impressive examples of pictures students created with their TI-83 or TI-84. I modified this 'Math Art with TI' activity to serve as our final activity in my Exploring Math & Science with TI-Nspire CAS J-term.
The freshmen in the class probably hadn't done much beyond graphing linear functions, but I introduced, briefly explained and required at least 5 of the following different types of graphs:
  • linear (even inequalities)
  • quadratic
  • absolute value
  • square root
  • cubic
  • cube root
  • reciprocal
  • greatest integer
  • exponential
  • logarithmic
  • sine
  • cosine
  • tangent
  • semicircle
  • polar
Using transformations of the functions and equations, many of them created something that reflected their personality. The above picture was done by our school's top golf star. (Speaking of golf and the TI-Nspire, there is a mini golf course algebra activity at this link.)

Students learned how to limit the domain. They asked great questions and had an exciting time exploring. I had the students write out all the functions they had on their screen and I quickly collected their Nspire file using connectivity software.

The TI-Nspire was such a superior learning tool for this activity compared to the TI-84 for several reasons
  1. The TI-Nspire has better resolution - more pixels
  2. The TI-Nspire is much faster. You don't have to wait anywhere near as long for the device to generate the picture. Along with this, I remember students doing this project with the 84 and by the time a modification was graphed they forget what change they made. With the TI_Nspire, the graph and function entry is on the same screen. When you scroll through the function, the corresponding graph is highlighted. (See the above video.)
  3. Teachers who don't have their students use a program on the TI-84 are limited to around 10 functions. There really isn't a limit on the TI-Nspire. It goes from f1(x) to f99(x). You can also use g(x), h(x), etc. You can backspace over the = and replace it with a greater than or less than symbol to do an inequality.
  4. With the TI-Nspire you can even graph polar on the same screen as functions.
  5. Again, unless doing this project as a program on the 83/84, you are locking up your resources. Students can't use their graphing calculator for anything else while working on the project. With the TI-Nspire you save the file and open up a new document if, for example, the science teacher wants students to do something with their handheld.
  6. Limiting the domain is much more intuitive with the TI-Nspire. Using a piecewise function template looks like the mathematics in textbooks. Whereas, multiplying or dividing the expression by a quantity including Boolean operators, may be mathematically educational, but fairly novel.
  7. Collecting their 'program' or screen shots is so much easier with the TI-Nspire. Any of the connectivity options work faster and better than what was used with the TI-84. If you want to get it from their handheld to yours, you don't need to go through 2nd Link-Receive-Waiting-Send. (I made up a handout called Managing your TI-83/84 to help students remember this process.) On the TI-Nspire, just connect the two handhelds and the one who wants to send something clicks Tools and Send and you have it. The Computer Link Software is quick and intuitive. The TI Connect-to-Class Teacher Software steps this up to enable mass distributing and retrieving files from students' handheld. Additionally, at this link it is announced that coming soon is a means of sending, collecting, and automatically grading wirelessly. It is called the TI-Nspire Navigator. This TI-Nspire TI-Navigator will be available Spring/Summer of 2009 in the UK according to this site.
  8. Since the purpose is investigating transformation, the TI-Nspire is impressively designed to dynamically facilitate this. E.g. graph f1(x)=x^2. Press ESC to escape off the function entry line so you can move the mouse to the graph. You can grab the graph in two ways: one will change the spread and the other will adjust the vertex, all while showing the effects of the equation.
  9. TI-Nspire CAS came in handy to at least one student. He wanted to use a hyperbola for the golf tee. He used CAS to confirm his algebraic manipulation in solving for y.
  10. Animation. (See the above video or another experiment in transformations - the US Flag.)
FYI, information about the TI-Nspire Summer Workshop that will be held out our school has been posted. I'm looking forward to that fun-filled week.

Thursday, January 8, 2009

J-term TI-Nspire in the Snow

Actually, the class that I'm teaching is called Exploring Math & Science with TI technology (especially the TI-Nspire CAS). J-term is a nice way to get back into the swing of school after the break. There are 3 hour morning and afternoon classes that students can take. Most of the upperclassman intern for the two weeks. I limited the class size since I knew I would have a diverse group. I have about 3 freshman, 5 sophomores, and a junior who are taking algebra 1, geometry, alg 2, trig & pre-calc. has been a great resource to give some exceptional differentiated instruction.

We have used some of the resources I put together back when I did the Physics of Toys J-term. (Check out our science of toys booklet. I need to edit it and fix the typos.)
So far we have investigated the terminal velocity of various sized bubbles, the distance a toy car goes when pulled back a certain distances, logistic curves from temperature data. We have also discussed diffraction, thin film interference, impulse-momentum, air resistance and other physics concepts.

More pictures of the good times with bubbles, snow, and data collection and analysis with TI-Nspire can be seen on this album.

After starting with the TI-Nspire CAS Primer, the students have done geometry investigations and SAT practice reviews. Next we'll do more with CBR motion detectors. I was particularly impressed with one student's unique depiction of his Fahrenheit and Celsius data today (see below). For other interesting graphs I've seen, check out this.
“It is the glory of God to conceal a matter;
to search out a matter is the glory of kings.”
Proverbs 25:2 (NIV)
Live as children of the King - explore and search out matters.

Thursday, January 1, 2009

New Year & Leap Second Costume Party

We had a number our children's friends come for an evening of good times with games, geography, missiology, sociology, physics, food, and fun. See pictures from the party.

They arrived by 6p.m. EST to celebrate the New Year in Madrid, Rome, Paris, Budapest, Geneva. They were dress up in costumes that represented people groups from anywhere in the world including China, Romanian Gypsies, England, non-specific island nations, France, Spain, Mexico, and Russia.

A highlight of the party occurred at 6:59:59 EST or 11:59:59 p.m. Greenwich Mean Time. We watched the atomic clock blink 59 seconds twice.

Food.................................... Game/Activity
cheese fondu ....................... Paper Tower competition (15 min, 8 1/2 x 11" paper, 20cm tape)
w/ apples, bread, etc. ........ Playdough sculpture

Fish & chips ......................... Jump rope
...............................(to leap into the new year with the leap second)
................................................ Pendulum competition
....................(washers & string to make pendulum with 2 sec period)
Laffy Taffy ........................... Jokes in British or some other accent
............................................... Watched Standard Deviants
. . . . . . . .. . . . . . . . .. .. . . . . . ."Russian Around Europe"

Smoothies ............................. Limbo
(planned but didn't get made)
Popcorn ................................ Make popcorn lei
................................................ Popcorn catching competition with a partner

Chips & Salsa ....................... Bubble Bowling (see page 335 of The Original Girls Handy Book)
'Fried' ice cream .................. Earth Toss with inflatable globes

We also had Mission Moments using Operation World were we read and prayed for various nations.

On the hour, the kids enjoyed counting down and blowing horns that I got from Kipp Brothers Toys. Everyone had left by 10:30, the time for Newfoundland's New Year. If you think having a half hour time zone is interesting, I found on a countdown clock site that there are a few places on a 15 min time zone - Chatham Island (part of New Zealand) and Kathmandu, Nepal.

Psalm 90: 12 Teach us to number our days aright,
that we may gain a heart of wisdom