Handheld Graphing Calculator in Color

As I was driving home the other day I heard a song on the radio that begins with, "Looking for a color in a shade of gray."

God created a very good and colorful world. Heaven will be a world of colors. However, many inventions in the past century or so started out in black and white.

The first permanent black and white photograph was taken in the 1820s. And although my favorite mathematical physicist James Clerk Maxwell made the first permanent color photo in 1861, black and white prospered well into the 20th century. I was interested to learn how many famous mathematicians and scientists were involved with the discovery of photography: Aristotle and Euclid described the pinhole camera in the 5th & 4th Century B.C., the name camera obscura is attributed to Kepler; Boyle and Hooke developed a portable camera in the 1660s.
Kodak came out with the modern color film in 1935, but due to expense color snapshots didn't become common until the 1960s and it became the norm in the 1970s.

Black and white television shows were first regularly broadcast in 1928.
RCA sold color TVs in 1954 for $1000. When Disney aired episodes of the Wonderful World of Color from 1961-1969, my Mom and her sisters enjoyed watching it even though they still only had a little black and white tube in the house. In 1972 the sale of color televisions exceeding that of black and white. I grew up watching the color test bars before the cartoons started.

Graphing calculators first came into my world in the late 80s. A little over twenty years later and it is now 2011. This is a historic year. Texas Instruments started selling a handheld graphing calculator that brings color to a world that was once only black and white (with some shades of gray these past few years).

WOW!

There were some things my students could enjoy with color only if they had installed the software that comes with the purchase of a handheld. Now, if they buy the TI-Nspire CX they will be able to enjoy the wonderful world of color in math and science wherever they are. A great thing is how much content is ready to use with color and more will be coming out throughout the summer. It will be a good year to participate in a summer workshop. In addition to being equipped with a lot of classroom-ready content, teachers will get a TI-Nspire CX or TI-Nspire CX CAS handheld and Teacher Software. If teachers choose a 'Connecting Math & Science' professional development workshop, then they will learn about all kinds of applications that will add relevance to what they are teaching. One of these workshop will be in Indianapolis. Click here for more details about this and others.

I've had opportunity to play with the CX recently. Look forward to more details about what I've discovered.

Why I Nspire? Part 4 - MathPrint

To recap the reasons already given why I use the TI-Nspire for teaching math and science:
#1 is because of the research,
#2 the value gained because the handheld comes with similar software,
#3 the TI-Nspire and TI-Nspire CAS are accepted on major exams.

Some of the first things I noticed and reasons for adopting the Nspire back in 2007, are the following:
#4) MathPrint. This has been a native feature of the TI-Nspire since it first came out that enables you to enter mathematical expressions they way they look in your textbook or homework paper. Students (and teachers) make fewer mistakes. You don't get lost in parentheses and carats. The TI-89 had what they called Pretty Print on the output so you could look to see if you typed it in correctly after you press enter. But the TI-Nspire has it on the input as well as the output. Instead of entering 'abs(((x^2-3x+2)/(x-5))^3)|x=-3' or 'int(sqrt(sin(x)),x,pi/2,pi)',

the Math Template palette can be used to select the desired template. The button to activate this looks like the absolute value and system of equation template. For helpful tips/reminders of what each template is used for you can use the Catalog. This button is just to the right of the Math Template button and looks like a book. Then press the number that corresponds to what you want to explore. For example, the image picture to the right is a screen capture taken from a TI-Nspire CAS software, so 1 is the alphabetical catalog, 2 the catalog by subject, 3 units (special built-in CAS feature), 4 symbols, 5 Math Templates, 6 Library.
For many of these there are short cuts: For the fraction template I would press ctrl obelus (the division symbol ÷). For exponents all you need to do is press the carat (^). Square root is the inverse operation of squared so it is activated by pressing ctrl squared. Seriously, I was so excited about this! The square root goes over everything it is supposed to. It had bothered me that the TI-84 even allowed sloppiness with parentheses. You did not need to close parenthesis. With the Nspire, if you ever open parentheses, there will automatically appear a close parenthesis.
Note that you typically enter characters as you would write them, instead of reverse Polish notation or RPN. So if you want to square x, first press x and then the x² button. For nth root, I would press ctrl ^. Euler's number raised to a power has its own button. Logarithm template is initiated by pressing ctrl 10^x. Some of the other templates can be found under menu. In fact, there are wizards that can help with fill in some of the syntax and pick the template. Press menu > Algebra > Solve a System of Equation, if you choose to solve a system of two linear equations with x and y as the variable, then you just press enter and everything except your equation will be populated.
To move from one equation to the next I like to use the tab button. With the TI-Nspire CAS, computer algebra system, you can solve all sorts of equations. As the third line shows this can also be done on a numeric Nspire with the numeric solve or nSolve. If I had wanted the decimal approximation, I could have also pressed ctrl enter as you can see in the keypad below.

Another fun tip I share with my calculus students is that you can quickly access the derivative and integral by pressing shift + or shift minus. Which one do you think does which? Why does that make sense, at least for polynomials? If you really didn't want a definite integral, do not fret, just leave it blank. How about if you wanted to do a second derivative? Once you have the first derivative template, you could change your mind and decide to make it I higher degree by pressing the carat ^ and then the number you want.
I've got a couple of tips for working with matrices too. Let say you picked a 2x2 matrix and you decided that you really wanted a 3x2 matrix, just press the carriage return button on the bottom right, ↵. To add more columns, first press shift and then ↵. To delete a row or column, I would select it by pressing shift and the arrowing left, right, up or down and then delete.

To get to know the Calculator page more and enjoy MathPrint there is a modified Scavenger Hunt on my school's website that I've used to help Calculus teachers and that could be used as an exploration for students.

This past year, the TI-84 came out with an operating system that adopted some of these popular capabilities. In addition to Math Print, one of the features is about how the history is preserved. Previously the 84 could remember the last 10 entries. These entries were retrieved by pressing 2nd ENTER. You can now up arrow to a previous line and press enter to copy and paste that text into the the entry line. On the TI-Nspire it remembers a history of 99 input and output lines for each Calculator page, up to a maximum of 50 pages in each of the 30 problems allowed in a single document.
In the image to the left, you can see that I have arrowed up three out of the eleven entries (see bottom right) that are stored in the history on page 3 of problem 1 (see top tab) of this 'Unsaved' document.

Perhaps part 5 of the series will be about the better resolution and the dynamic geometry capabilities.

Colorful Nspire Art

This year's J-term added a bit of color (or colour for my international friends) to their Graphing Art project. The picture to the left was done by Sarah who is quite interested in NASA. The stars are 'polar roses' translated vertically and horizontally using parametric and the truth that x=r*cos(angle) and y=r*sin(angle). The comet was animated. This may have partially been inspired by the brief NASA Now program we watched.

Since we became a NASA Explorer School we have also done a number of NASA activities including Exploring Space through Math's Weightless Wonder activity. The NASA Weightless Wonder Nspire file made it so they could do the activity paperlessly and with additional exploratory capabilities.

Another student whose brother attends Kettering did her picture of their mascot. Kettering is known for their co-ops which have even included co-ops with NASA. Besides the impressive quartic Kristen used for the head, I was also impressed with the oblique absolute value she used for the teeth - see the 22nd function f22(x). This activity definitely improves students' understand of transformations.

Kettering University mascot is the bulldogs.
As in previous years we did do a little data collection outside and may go out in the snow again tomorrow.

Why I Nspire? Part 3 -Exam Acceptance

There is a website that can visually display the frequency of word usage. I used Wordle.net to create the following word cloud for the TI website 'Top 10 Questions Parents Ask about Graphing Calculators".
The word cloud on the right was made by inputting this blog's website. This one appeals to me because it is like the fingerprint for this blog.

Now, for Part 3 in this series ...
One big reason that I made the switch from the TI-83/84 and TI-89 to the TI-Nspire CAS was because it is permitted on the AP Calculus exam. If it wasn't permitted, the decision would have been tougher. This question came up this past week on the AP Calc electronic discussion group.
I wrote that the TI-Nspire CAS's improved speed, math print or 'pretty print' on the input (and not just the output like with the 89), better pixels, and dynamic representations which make it easier to integrate graphical, numerical/tabular, algebraic, and verbal concept development are a few of the reasons we initially made the switch to the Nspire.

The TI-Nspire CAS can be used on all the College Board exams, like PSAT, SAT, AP (including AP Calc, Stats, Physics, Chem, etc.). The TI-Nspire is permitted on the ACT and IB tests, but CAS devices are not.

Today I learned of an exciting resource for IB teachers. "Written by Andy Kemp, a Head of Maths at an IB school in Somerset, the guide is specifically designed to help students understand how the TI-Nspire can be used as an aid to answering exam questions. The exemplar questions in this booklet are the author’s own work, and are written in the style of IB questions. Throughout there is as much emphasis on the mathematics as on the technology, as it is the author’s belief that without the focus on the mathematics, this guide would become little more than a button-pushing exercise."

I know from this website that the TI-Nspire is permitted on many state tests including TAKS. You could contact your local representative to get more info - for example for Texas see this link. Many state exams do not permit CAS.

Another summary of exam acceptance can be found at http://education.ti.com/educationportal/sites/US/nonProductSingle/assessments.html

There are a number of Test Prep resources and questions that can be used with the Navigator system to help students prepare for these high stakes tests.

If you want to learn more about this educational technology, this year the T^3 International Conference is in Texas. There is even a Calculus Conference-in-a-Conference track.

Technology tools

"Be still, and know that I am God..." Psalm 46:10
Two months ago an article appeared in our local paper. It was actually a devotion that was submitted by my pastor, Dr. Michael LeFebvre. I read a quote from this at a recent conference session that was focused on technology innovations in the classroom.

"A century ago, people thought that technology was going to make life less stressful. I have an old volume on my shelf called Achievements of Americans, published in 1859, that illustrates that optimism. Marvelling at the pace of innovation even then underway, the 19th century writers of that book exclaimed, “invention after invention crowd so thick upon us, that astonishment ... is only equaled by our wonder ... [at] the eventual result of all these ... upon our condition.” The hope was that improved technologies would bring greater harmony and peace to the human condition."

I know that peace and joy are not found in the latest piece of technology, but in the Lord. Teaching is hard work, especially striving to teach with excellence. I taught the topic of energy recently and I was reminded again of some encouraging words that Paul wrote in a letter to the Colossians, "...teaching everyone with all wisdom, that we may present everyone mature in Christ. For this I toil, struggling with all His energy that He powerfully works within me." Yes, that is where I want to get my energy. I pray that even though frustration may accompany the learning of anything new, that this article may bring some peace and encouragement to some.

So what is my philosophy/theology of technology? It is part of the dominion mandate in Genesis 1:28. I recently read Foundational Concepts of Christian Education that is on the Geneva College website. It discusses the implication of this for the school, student, curriculum, and discipline. But what is the implication for educational technology? The pros and cons of adopting an innovation ought to be weighed as part of considering the cost. Recognizing the sinfulness of humans, safeguards should be set up to protect and limit wrong use. The key thing to recognize is that technology is not the answer or goal, but is a tool to be rightly used.

The right tool for the right job. My grandfather used to say, "A place for everything and everything in its place."
If you need a tool for a certain job, it is a lot easier to find it if it is where it belongs. We did try to do some organizing of the garage this summer, which is probably why it wasn't too difficult to find these tools pictured on the left. The old pipe wrench actually belonged to my Grandpa Bird. It is large, adjustable to various sizes and provides the mechanical advantage you need to turn a pipe that is really stuck. Now, I don't really know that from personal experience, because I've never needed to loosen or tighten a pipe. But I love it and think it is really cool.

I actually have a slide rule somewhere too. But I've never used that to solve logarithms or get a decimal approximation of a trigonometric value.
Similarly, since I started working at Covenant Christian High School in Indianapolis, I can't remember using a chalk board until the last week when I was helping out an older public school as a math coach. They had recently acquired some great technology and wanted to be encouraged to better utilize it.

Within the past couple of years, my dad got me this handy little socket set. I have had occasion to use some of the ratchets.
It has some nice features. For example, the tool in the middle can act like a typical screw driver when the appropriate tip is put on the end, but it has a ratchet mechanism that can be easily adjusted to tighten or loosen.

Like a four function calculator, this tool cannot do everything. The adjustable monkey wrench on the left wouldn't open to the size of a large pipe. Similarly, you can't easily graph a function on a scientific calculator.

With any interactive white board you should be able to write on in it and save your work, but not all of these tools are designed to particularly enhance the math and science classroom like SMART Notebook Math Tools can. I have enjoyed showing this off at conferences and using this tool in my classroom from the time it was only available as a free download in its beta form. A couple of weeks ago I had a wonderful time showcasing SMART's Math Tools to an outstanding group of middle and high school teachers at a Christian school in Cincinnati.
One thing I especially appreciate about Notebook Math is that it recognizes its limitations and encourages teachers to be aware of the value of graphing calculators and TI emulators. The SMART Notebook on the computers I've used these past several years can be used to launch my TI-Nspire CAS Teacher Software with its built-in TI-SmartView emulator capabilities.

With some tools there is so much power and functionality that you may never use every piece. Even if I took a class to learn about the drill I have on the left, although I would learn more of what the different bits were for, I may not use them again. I really appreciate when a tool is intuitive and many things about it can be figured out without reading many manuals.

The sentiment that the TI-Nspire is intuitive to use has been the general impression I've seen in many students who have been introduced to it. A video that a friend from Scotland is in shows the engagement of the students, the formative assessment capabilities, and many of the other features that are gained by using the Nspire Navigator. I also appreciate that the operating system of the Nspire and Navigator have been improved over the years based on teacher feedback. These updates have come at no additional cost. This tip sheet says that it can take over 30 minutes to update the OS for every device in the classroom, but I've been able to do it many times in less than 5 minutes. The tip sheet is a bit dated, as there are now more ways to improve classroom connectivity.

Sometimes people do not use the best tool for the job. There are many reasons why this is true. If you want to see a variety of tools used for math and science education, the Teachers Teaching with Technology International Conference will be a good place to learn more. This has been one of my favorite conferences of the year.

More on the TI-Nspire Software

Recently on the AP Calculus electronic discussion group the question came up, "What software do you use for generating graphs. For example, for a limits test. How can I generate a graph with removable discontinuities, jumps, etc. Is there a good software program out there for generating graphs?"
There were several replies of programs that use esoteric nomenclature or fancy tricks.
One person replied "I don't have one that works well with piecewise functions (most will handle continuous pw functions with some cajoling and using logical operators (<, <=, >, >=, and, or etc) with Boolean (ie 1 or 0) output, but typically go bonkers when you have discontinuities)... I was just creating a diagram for f(g(x)) where f and g are PW functions for a precal class, and everything I have has come up woefully short (the TI's won't even evaluate Y1(Y2(x)) if you've used the logical operator kluge to get pw functions).
So I'm also all ears if someone has a graphing program that will handle PW functions in a reasonable way."

The most reasonable way I have found to do piecewise functions is with the TI-Nspire. Here was my response with some additional pictures and explanation included:
The TI-Nspire Software may be what you are looking for.
It will do piecewise functions in a very natural way - just like they look in a textbook. There is a math template for piecewise functions. Just press the button (highlighted in red in the first picture on the left) or you can find it in the catalog. The nice thing about the catalog is that it gives a verbal identifier as you can see in the picture on the left.

The Nspire will also do composite functions. You can even change the name of a graph from f1(x) to f(x) and g(x) and let h(x)=f(g(x)). I tested it with a composition of piecewise functions and it worked great too. This was really easy to do. Here is what I did: Open a graph page, arrowed over and deleted the 1 in f1(x) so it would say "f(x)=". Then I press the math template button and filled in the blanks. Next I arrowed down and made it g(x). Finally, I arrowed down one more time and entered h(x)=f(g(x)).

Also with the TI-Nspire CAS you can do many implicit/conics by entering, for example, f1(x)=zeros(x^(2)+y^(2)-25,y)

The graphs look really clean (not large pixels) if you use View > Computer. CTRL J is the shortcut for getting screen shots.

You can download the software that comes free with new purchases of the TI-Nspire Touchpad at http://education.ti.com/educationportal/downloadcenter/SoftwareList.do?website=US&tabId=1&paneId=6002#10
You could also get the TI-Nspire or TI-Nspire CAS Teacher Software for free from a Learn & Earn program http://education.ti.com/html/nspire/learn-earn.html

Yesterday in Physics First and in my AP Calculus class we studied the relationship between position, velocity and acceleration with graphs. We collected data with CBR2 motion detectors. Students plugged these into their handhelds and I could also plug it into my computer and begin collecting data automatically with the TI-Nspire Software.
Notice that the labels on the axes were automatically changed from x and y to Dist(m) and Time(s). These labels can be manually changed of deleted entirely.

On a Data & Statistics page the labels are the variable names.

The students then analyzed the graphs with menu > Trace > Graph Trace. It was fun to have the students predict what the corresponding velocity-time graph would look like and use a dynamic Data & Statistics page to easily who what the calculated solution would be. This is easily done by clicking the left side of the screen. I . I also enjoy just pressing tab to quickly change the variable. The default of the motion detector is to measure the distance every 0.05 seconds. At the same time it populates two other columns of data: dc01.vel1 for velocity and dc01.acc1 is the acceleration for data collection trial 1.

This was a graph of a ball rolling up an incline. At first it increased its distance away from the motion detector and then it came back down. The little imperfection near the peak was when it moves a bit horizontally near the top of the incline. Usually I use a nice racquetball but this time a used a larger less perfectly spherical ball we got from this summer's public library reading program. As you can see the acceleration was a component of -9.8m/s^2. Students who have at least had geometry may be able to even figure out what the angle of the incline was. This ball on an incline experiment is outlined at the end of an Xtreme Calculus activity. There is a link to this TImath.com activity from this site.

From the first time I taught algebra, I've always said that there is now better way for students to develop an understanding of slope than to walk it out and immediately see what kind of graph they are making because of how fast they are moving.

At the end of James Nickels explanation of projectile motion he wrote
"Such is one of the amazing revelations that mathematics gives us about the many nuances of the physics of motion, motion governed by the wisdom of God in Christ (Colossians 1:15-17; 2:1-3). These covenantal laws are treasures that man discovers by investigating the creation order (Proverbs 25:2). Classical physics, founded by men like Galileo, Kepler, and Newton, is a sequence of one fascinating revelation after another. This essay is only one example of these quantitative wonders."

Why I Nspire? Part 2 - software

I wonder how many of my students' parents read Good House Keeping. It was neat to see the positive review from the experts at the Good Housekeeping Research Institute lab for the kind of technology we are using in my classroom. Also of interest, that I've been meaning to link to, is a news release about the TI-Nspire Touchpad that came out about the time I was in San Diego for the large annual math teacher conference NCTM. Finally, here are answers to the top 10 questions parents ask about graphing calculators.

So back to the topic of ...
Why do I use the TI-Nspire CAS Touchpad in my classroom? Why would a parent want to get the TI-Nspire or TI-Nspire CAS for their child?

2. the SOFTWARE - When you buy a typical graphing calculator, that is all you get - a handheld device that is nice and durable (I wouldn't recommend subjecting it to extreme frigid temperatures). The batteries last a lot longer than a laptop. But if you get the new TI-Nspire, you also get the student software included. A few months ago you would have to buy it separately, retail price close to $100, and I suppose it is still available. But NOW it comes with the software. As TI's website says, it is a 3-for-1.

There are many schools now that are using laptops. I've heard of schools were the underclassmen are getting tablet PCs. The Nspire Student Software would be a perfect fit for this situation because they can use the emulator-like software and then when it comes time to take tests like the AP, PSAT, SAT, etc, then they are familiar and comfortable with the handheld Nspire that works just like the software.

More ways to distribute files
There are a lot of great activities that are ready to use that are available on sites like ti-mathnspired.com and timath.com. Teachers today also have ways to post them to secure school websites. Our school uses edline. I've also heard of schools that use RenWeb and Angel. When students check to see what the assignment is they can also click the tns (Nspire software file) that I have posted. If they are using one of the computers they installed the software on then it will open right up. In addition to the password protected website, our school also has a website where I have posted activities.

Collecting files
These files that students do can be collected or turned in for a grade via email or by sending the files to their handheld. No longer does a student need another piece of software (like TI-Connect for the TI-83/84 or TI-Computer Link for the Nspire). The TI-Nspire Student Software or Teacher Software makes the process of transferring files to a handheld connected to their computer as easy and drag and drop. Files sent to their handheld can be collected from students with TI-Connect-to-Class or with the TI-Nspire Navigator.

Pedagogical benefits
It has been my experience that students with the software explore mathematics more. This is huge! It is the dream of teachers that students would engage with the subject on their own. This additional opportunity to use mathematical technology empowers students to wonder 'what if' and then actually investigate it. I think this is particularly true for the TI-Nspire CAS (computer algebra system - for a comparison to the numeric Nspire check out this link).

It is easier for students to navigator the menu options and 'mouse around' with their computer. With the latest TI-Nspire 2.1 operating system larger files like those found on Math Nspired open so much faster and response with the Touchpad has improved as well, but when you use a computer to explore math and science topics with TI-Nspire technology then everything is extremely fluid and quick to respond.

I also think there are a number of pedagogical benefits of color. Students who use the software enjoy mathematics in color.

Sure there are reasons to use the handheld:
(i) It is useful on high stakes tests where a computer isn't allowed - you wouldn't want students looking things up on the internet or 'phone(text)-a-friend' to find an answer.
(ii) The handheld is useful for easily grading and keeping track of formative assessment when the teacher uses Navigator.
(iii) The handhelds are great for portable data collection with Vernier probes. You can go outside in the snow and use temperature probes or walk around in the hallway to learn about slope with the CBR2. It is nice not to be constrained to a computer.








Another feature of the software that students are likely to use include screen shots for lab reports. Stat
students will enjoy copy pasting data and easily porting it to their handheld. The software enables students to maximize the benefits of multiple representations of split screens. Currently I will not likely often use the computer view on the software for presentations in class or at conferences, but you get a lot more real estate with the smaller font of the software's computer view.

I am excited about so many improved features of the software that came about with the 2.0 OS.
The release notes do a nice job at explaining what new.

Why I Nspire? Part 1

TI-Nspire technology is the most intelligently designed and mathematically enjoyable technology ever developed for the classroom. It has been an important part of my math and science classes for the past 3 years. This will be the first in a series of blog entries that will help to explain why I made the switch to this 21st century technology. So, by request, here is the first installment. Enjoy (even if classroom technology isn't your thing, it may be interesting to see what is out there today ... and why). [Part 2: The software, Part 3: Exam acceptance, Part 4: Math Print, Part 5: The complete summary list]
Why do I use the TI-Nspire CAS Touchpad in my classroom? Why would a parent want to get the TI-Nspire or TI-Nspire CAS for their child? Or even more generally, why should middle school through college teachers and students use graphing calculator technology frequently?

1. RESEARCH shows it to be beneficial (and is not harmful to basic arithmetic skills) to all aspects of mathematical learning.
Independent research firms and major universities have done studies to learn about the effectiveness of graphing calculators on math achievement. Their findings?
-- When teachers incorporate graphing calculators into curriculum more often, and when students have more access to graphing calculators, math achievement increases (1,2).
-- Students who receive instruction using graphing calculators perform as well or significantly better on key math skills(3). Students using graphing calculators during class instruction did as well or better on conceptual, problem solving and operational math skills than those who did not use graphing calculators.
-- Students using graphing calculators during instruction -- but not during assessment -- performed as well or better in all five math skills areas(3), indicating that student math skills did not suffer without calculator use specifically during assessment.
-- Students who use graphing calculators have significantly better attitudes toward math than those who do not use graphing calculators(3).
(1) "Impact of Handheld Graphing Calculator Use on Student Achievement in Beginning Algebra," Heller Research Associates, January 2006
(2) "Effectiveness of Graphing Calculators in K-12 Mathematics Achievement," Empirical Education Incorporated (EEI), November 2005
(3) "A Meta-Analysis of the Effects of Calculators on Students' Achievement and Attitude Levels in Precollege Mathematics Classes," Aimee Ellington, November 2003

Update: But what about specific research about the TI-Nspire? Since I first wrote this blog entry more research has been done. You can now find specific experimental research, case studies, qualitative research, and the research basis for the TI-Nspire. There is also research specifically for CAS (computer algebra system). Click the above links over the words to read more.

The following is a quote from another website [with some comments embedded]: "In fact, a substantial body of educational research now indicates that graphing calculators can have significant benefits for mathematics learning. Research shows that students using graphing calculators develop flexible strategies for problem solving and a deeper appreciation of mathematical meaning than students who do not use graphing calculators (Ellington, 2003; Khoju, Jaciw, and Miller, 2005). In addition, students who use graphing calculators are better able to understand variables and functions
[function notation is promoted by the TI-Nspire better than any other device I know. With the TI-81/82/83/84 you would graph y1, y2, but with the Nspire you graph or define f1(x), or even g(x), etc.],
solve algebra problems in applied contexts [There are a large number of these types of problems available on TI-math.com and coming soon there are some great NASA questions and activities with the TI-Nspire],
interpret graphs, and move among varied representations [multiple representation is the hallmark of the TI-Nspire] —that is from graphs to tables to equations—than students who do not have access to the technology....
Research from the National Assessment of Education Progress (NAEP) has consistently shown that at the eighth grade level frequent use of calculators is associated with greater mathematics achievement. Moreover, research shows that teachers and students who used graphing calculators most frequently learned the most. On the NAEP assessment, 8th graders whose teachers reported that calculators were used almost every day scored the highest (NCES, 2001). Similarly, in examining an implementation that aligned graphing technology with a comprehensive math curriculum, Heller found that daily use of graphing calculators is more effective than infrequent use (Heller, 2005).
[My 8th grade daughter has been enjoying her TI-Nspire CAS for some time now. It is true that our state end-of-course assessment for algebra doesn't permit the use of CAS, but the TI-Nspire is permitted. The TI-Nspire CAS is allowed on the PSAT, SAT, and AP exams. With the wealth of Math Nspired activities available (and more coming soon) that tackle the tough-to-teach and tough-to-learn topics, I'm certain this research will be even more true today. These activities are easy to use by teachers who do not have just about any experience with the Nspire.]Research shows that the association between frequent graphing calculator use and high achievement holds true for a wide variety of grade levels, socio-economic backgrounds, geographic locations, and mathematical topics (National Center for Education Statistics, 2001; Ellington, 2003)."

Added to all of these general things about graphing calculators, consider also what the TI-Nspire Navigator brings to education. Many schools are considering 'clickers for the classroom' or student response systems. I'm sure there is a lot of research that has been done to show the benefits of the enhanced engagement of students gained with clickers. These clicker systems are typically expensive and limited in their use. However, I've found that for a comparable price, the TI-Nspire Navigator and TI-Nspire handheld are more robust than any clicker system. This Navigator system is versatile at improving documented formative assessment through quick polls were students can enter mathematics in the way that it naturally looks, automatic screen captures, and sending and receiving files. It has enabled me to get feedback from a quiet class and get 100% involvement in the class where one student would often blurt an answer before others had time to think.

References:

Dick, Thomas P. (1996). Much More than a Toy. Graphing Calculators in Secondary school Calculus. In P. Gómez and B. Waits (Eds.), Roles of Calculators in the Classroom pp 31-46). Una Empresa Docente.
Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students' achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education. 34(5), 433-463.
Heller, J. L., Curtis, D. A., Jaffe, R., & Verboncoeur, C. J. (2005). Impact of handheld graphing calculator use on student achievement in algebra 1: Heller Research Associates.
Khoju, M., Jaciw, A., & Miller, G. I. (2005). Effectiveness of graphing calculators in K-12 mathematics achievement: A systematic review. Palo Alto, CA: Empirical Education, Inc.
National Center for Education Statistics. (2001). The nation’s report card: Mathematics 2000. (No. NCES 2001-571). Washington DC: U.S. Department of Education.
UPDATE April 14, 2011: Thanks to a recent discussion on the Nspire Google Group, I've been made aware of additional research with findings available online. These sites include a detailed mixed method long term study in Scotland and is available at http://www.abdn.ac.uk/education/documents/UofA_Report_Mar10.pdf. Another pdf files summarizing the finding of teachers in a manner that is approachable to other teachers.
The lead researcher "observed that teachers changed their teaching methods dramatically when using TI-Nspire, both the way they taught each topic and the way they teach in general. They found that the use of the Npires together with a move towards an investigative approach with more opportunity for questioning and discussion led to a deepening in students' understanding, an increased pace of learning and an increase in motivation and engagement across all ability
levels." A brief summary is available here.

Physics First - STEM

This next school year we will be officially starting Physics First. Freshmen will take physics, the foundational science, before they take chemistry and biology. I pray that God will use me to challenge these young students to think Biblically about all their studies. I appreciate the writings of John Byl in my efforts to do this.
Working with freshmen will be different than teaching upperclassman who perhaps have a higher maturity level. I will have high behavior expectation of these students just like they do at the Johnson Space Center (see the poster to the left).

Also I'm excited to see if this can positively impact PSAT scores. Freshmen who are taking geometry may be able to keep some of their algebra skills fresh because of various activities in my class. We will be using the TI-Nspire in class most every day for data collection, explorations, and formative assessment. We have a classroom set of TI-Nspire CAS so that even if students don't have an Nspire yet, they will be ready to participate. I think we'll even use our TI-Nspire Navigator to ask 'class opener' questions from PSAT practice and Indiana's Algebra End-of-Course Assessment (ECA) sampler.

Those students who are concurrently enrolled in algebra should find their education in one class complimented by the other. I know in my undergrad studies I frequently enjoyed learning and applying similar topics in both my mathematics and physics classes. Students who took algebra in 8th grade should find their study in physics to help them keep the algebra skills stronger than if they were doing a science that was more focused on memorization and less on data collection and solving relationships for the unknown. There are also some great NASA activities that I've been working with this summer that I will use in class this next year, including Exploring Space through Math and NASA's Math and Science @ Work for the AP level.

There is a real need for young people to take science, technology, engineering, and mathematics (STEM) courses. For example, a 2009 press release reports that “the current graduation rate from U.S. university electric power engineering programs is not sufficient to meet our nation’s current and future needs.” It goes on to say, "The bad news is that enrollment in electric power and engineering programs are not rising fast enough, and interest in science, math and technology is low in K-12 students. Enrollments are declining in electrical engineering in general. Among students, teachers, guidance counselors and parents, engineering is ranked low on the list of interesting and attainable professions. Furthermore, women are especially underrepresented in the industry and as students."

The following facts were listed at the start of a STEM video found here.
Additionally, recently I came across an article about the top 6 degrees ranked in terms of employment, by Chris Kyle. "Corporate consulting firm Challenger, Gray & Christmas polled 100 human resource professionals to find out what graduating students this year can expect from the job market in 2010, and, specifically, which degrees have the best odds of helping students get jobs....
#5 - Engineering Degree

It might surprise you to learn that engineering degrees are ranked fifth in terms of employment - and not first - but don't start feeling sorry for engineers just yet. According to a survey by the National Association of Colleges and Employers, eight of the top 10 best-paid majors are in engineering.

Desirable Degrees:
Biomedical Engineering
Civil Engineering
Electrical Engineering
Mechanical Engineering
Network Engineering and Administration
Programming and Software Engineering

Average Starting Salaries:
Petroleum Engineering: $86,220
Computer Engineering: $60,879
Mechanical Engineering: $58,392"

Of course, the real reason you pursue something isn't for the pay (note: I am a teacher), but because you have a passion for it, because you enjoy it, yea, because you recognize God has given you a talent with it. I recently heard a NASA engineer say, "Most jobs in engineering have higher pay but none are as cool as my job."

Even if you have a gift or talent with something, that doesn't mean it will be the easy for you to do that job all the time. Gifted musicians must practice hard and long. This is true of mathematicians, scientists, teachers, etc. For more about ability and 'talents' read this.

"Under God the People Rule"

This is the official state motto of South Dakota. I came across this as I was looking at the map as we crossed the state on our travels back from an amazing vacation in Wyoming. I was reminded of the Godly dominion spoken of in Genesis 1:28 and Psalm 8:6. Also the motto "Under God the people rule" testifies to His sovereign rule (see Proverbs 21:1, Psalm 96:⁹Worship the LORD in the splendor of holiness; tremble before him, all the earth! ¹⁰Say among the nations, "The LORD reigns!"). There are other states with motto's that reflect our dependence and trust in God. Florida's official motto is the same as the United States motto, "In God We Trust." It was on their state seal since 1868, but it wasn't until July 1, 2006 that it became their official motto. I really like the license plate option we have in Indiana, it is also nice to know that it is constitutional. Ohio's motto "With God All Things are Possible" was, of course, challenged by the ACLU in 1997, but Ohio's motto was shown not to violate the First Amendment of the US Constitution.

The reason we journeyed up to South Dakota was to see the National Parks. I had never been to Mount Rushmore. Aw we were driving there we saw a dark rock. I wondered how they got the name Black Hills. We learned it had nothing to do with the color of this rock, but because of how dark the hills can look with the rich ponderosa pines. Especially when a cloud would come, I clearly understood why they were the Black Hills. We got there just in time for the last park ranger walk of the day. The sun was getting low as the kids worked on the Junior Ranger workbook.















It was a beautiful site, a monument to democracy (that was one of the answers we had a hard time finding in the workbook). Around 9 o'clock they started a lighting ceremony. We soon discovered that they wouldn't turn the lights on until the end of the hour long ceremony. We hadn't reserved a hotel room for the night and we had already been driving all day, so we hit the road before illumination.

Before we left we learned about some great mathematics involved in the construction of Mount Rushmore. They made a model with the scale ratio of 1:12. One foot on the scale model corresponded to 12 feet on the mountain, or as the picture below indicates, 1 inch = 1 foot. This reminds me of an activity I have my students do when they are learning about vectors and, depending on the spring scale they use, 1 newton is set to equal 1 centimeter. Scale comes up in many math classes as well. Similar triangles is taught in geometry and the last year I worked on a cool activity to help students explore a topic in the Prentice Hall Algebra 1 text.
The monument was made using protractors, plumb bob, distance measuring devices (and some explosives). To read more about the mathematical details of Rushmore, check out this site.
Do you get the irony/humor in the picture on the right? ... "Math Rocks!" ... Washington, Jefferson, Teddy Roosevelt, and Lincoln are rocks. I read that 90% of Americans can't name the faces on Rushmore. After my kids had the interview with a ranger at the end of searching all the exhibits to find answers for the Junior Ranger workbook, I'm certain they will remember which president is which for quite some time.

We have learned so much by doing the Junior Ranger Programs all over the country, including FL, KY, MO, IN, DC, and now SD. Here is a picture of adventures in the past.

Press-to-Test

[Update: I have posted a new video to youtube, click here]
Writing a good test is a challenging task. Helping students obey Leviticus 19:11 - "Do not steal, do not lie, do not deceive one another" - can be an even more challenging objective. As teachers, we want to assess what students know so we can help them learn, provide accountability, and see what it is that we need to teach better next time. Therefore it is of no values if a student steals a neighbor's answers and plays it off to be their own work and knowledge.

The TI-Nspire CAS now has an LED. So what is so interesting about that?
Teachers can use the Nspire's built-in Press-to-Test feature to clear out any 'cheat sheets' and make it so that they don't carry all their calculations with them out of the classroom when they leave. For teachers who have a class set of these learning tools, they would probably prefer for all the answers to NOT be on the screen when the next student comes in and gets their graphing calculator.
This becomes an even more important issue with the new Scratchpad Calculator and Graph. The only easy way to clear Scratchpads and current document is to use Press-to-Test.

Here are pictures of the LED blinking. These videos will be linked to in a powerpoint (4MB) that explains how to use Press-to-Test.

With the TI-Nspire Navigator or TI-Nspire Teacher Software, use Transfer Tool (end class if needed) to send "Exit Test Mode.tns" (this can be a blank tns that is called Exit Test Mode) to the Press-to-Test folder.
1. Click ‘Add to Transfer List’ and find Exit Test Mode.tns
2. Click that file, then click the ‘Edit destination Folder’ field
3. Click the ‘Change’ button and then ‘Start Transfer’.

For more details, check out the Press-to-Test Guidebook. Similarly you can use the TI-Nspire Computer Link software to transfer any file called "Exit Test Mode" to the "Press-to-Test" folder.

Update regarding the TI-84: To enter Press-to-Test hold down both left and right arrows while you press ON. With OS2.55MP and 2.56 (when the 84 keypad is on the Nspire), there is now the ability to disable logbase() and summation.
See this link for 84 screen shots and explanation.