Power from the Wind explains the importance of wind and the power that can be harnessed from it. Dan Chiras, the author of the informative book, helps those intrigued by the idea of wind energy by giving them a checklist of things to consider before setting up a windmill. The book covers all areas of study needed for a solid knowledge of wind energy. After reading this book, anyone can know what wind is and how it can be used to improve the world around us.
Monday, December 26, 2011
Thursday, December 15, 2011
This book is one of the main resources Covenant has been using for information about wind power. It goes into detail in the costs, the technology and plans for the future with wind technology. But in order to improve the future of this technology, we must understand the current technology. One of the current problems of wind energy is cost-effectiveness; the revenue made from windmills is not much more than creating one of the machines. Another difficulty being faced with wind power is the safety and size of the machines themselves. These machines are very large and many fatal accidents have occurred, but in the past 30 years there have been numerous improvements. We intend to improve other aspects of harvesting this power just as they have been improving the safety of it so that we may be able to have a resource that does little to no harm to the planet. The information from this book has allowed us to refine what our goals are and allow us to apply ourselves to the task of improving current designs.
Thursday, December 8, 2011
Thursday, December 1, 2011
Tuesday, November 15, 2011
With the knowledge that the future of our energy lies within the children of today, the U.S. Department of Energy’s Wind Powering America Program developed the Wind for Schools program in 2006. The main objectives of this program include: to encourage university-level wind education and training, to promote on-site education at the K-12 level by installing wind systems at schools unable to fund them on their own, and to support K-12 wind energy education in schools with installed systems and surrounding schools. This program is currently operating in eleven states, and is open for starting in other states. The most used and recommended product for schools wishing to participate is the Skystream wind turbine. When schools install this, they also get a full communication system which allows students to monitor the performance of their turbine and energy consumption. This is a great tool for the learning community.
Saturday, November 5, 2011
The following is a brief summary by Nick of Indiana's Consumer Guide for wind systems:
Wind electric systems are not only for the big businesses and important companies; they are also for the average homeowner. If a home is sitting on land that has enough empty cleared space and wind speed, then installing a wind electric system could possible to the best option for their energy needs. If it is unknown whether or not there is enough wind speed, U.S. Wind Resource Maps is a valuable tool. The cost of installing the system depends on the height of the tower and the diameter of the rotor blade. Also, a general rule of thumb is that the wind tower will cost anywhere from 1,000 to 5,000 dollars per kilowatt on initial installation. It is recommended that a wind electric system be installed by a company that specializes in it. This is not something that should be attempted without an expertise in electricity and manufacturing. For a home wind electric system, it is suggested to use a guyed system. There are three different types of guyed systems: balance, stand-alone, and grid-connected. All three have their own benefits and it is something that a home owner should look into before deciding to install a system.
Friday, November 4, 2011
The following video shows the set up and the experiment. A screen shot showing the analysis done to find work follows.
To find the work, the area under the P-V diagram, use menu Analyze, Integral. It is important that the work is negative. Why is it negative?
Wednesday, November 2, 2011
On the day of the egg launch, there was minimal wind, with maximum gusts of not much more than 1 m/s. Due to the size of the egg capsules, the wind likely had a negligible effect on the distance of the egg launch. But as a well struck baseball will only travel half as far as it would have it were to travel in a vacuum, air resistance does have an appreciable effect. Overall, out of 100 eggs, 21 survived with the maximum distance being over 60 meters. Obviously their grade wasn't based on the survival of the eggs. You can read more about the rules, parameters and grading of the Egg Launch at this site.
The AP Physics still participate in this event as an enjoyable review of collisions, conservation of energy and projectile motion. They do not need to write the paper again, but they do need to do the calculations. Their rules are there are no rules except to construct the protective container in the first five minutes of class.
Friday, October 21, 2011
God is in control of the wind. In Mark 4 (and parallel passages in Matthew 8 and Luke 8) the disciples were in a boat with Jesus when a great windstorm arose. They thought they were going to drown. Jesus got up, rebuked the wind and said to the waves, “Quiet! Be still!” Then the wind died down and it was completely calm. He said to his disciples, “Why are you so afraid? Do you still have no faith?” They were terrified and asked each other, “Who is this? Even the wind and the waves obey him!”
Jesus also spoke of our limited knowledge of the wind when he was talking to Nicodemus (in John 3). He said, "You should not be surprised at my saying, ‘You must be born again.’ The wind blows wherever it pleases. You hear its sound, but you cannot tell where it comes from or where it is going. So it is with everyone born of the Spirit.”
For the TI-Nspire STEM Project Challenge, students are to select a topic of interest that they want to investigate and explore, based on an issue or problem in the community (local, state or national) that they wish to change.
An interesting topic to investigate and explore is getting energy from WIND.
In the next weeks and months, my students will share laboratory experiments they have done with the TI-Nspire Lab Cradle and Vernier sensors and summarize their findings from the following links.
- Small Wind Electric System: An Indiana Consumer's Guide http://www.windpoweringamerica.gov/pdfs/small_wind/small_wind_in.pdf
- Purdue University's Windy Energy website
- Geographic Information System for Renewable Energy http://www.esri.com/library/bestpractices/renewable-energy.pdf
- Instructions to construct and Windbelt generator
- Kid Wind Project - Humdinger Windbelt kit
- Wind for Schools & Skystream
- Popular Mechanics - Windbelt
- Wind Power in Indiana
Recently an update about the potential for wind energy was published. This shows that Indiana could generate 443 TWh annually. For comparison, Indiana consumed less than 107 TWh of electricity in 2005. However, in 2010, the state only produced 1.24 TWh of electricity (which is better than many of our neighbors, but not in the top 5. Two of our wind farms did make the top 10 list.)
Thursday, October 13, 2011
Like with the NASA Student Launch Initiative we participated in years ago where Covenant Christian High School received a several thousand dollar contract with NASA, we wanted to come up with an idea that was truly worthwhile. See point#3 on this Covenant NASA-SLI website.
We began brain storming ideas. Some of these are recorded on this website. (There are also some fun pictures of how we are using the TI-Nspire in class, which sometimes means outside.)
I wonder which of the ideas listed, sound most interesting to you?
An idea the students got excited about that didn't make the list was to make a jet pack. In researching that, they came upon an impressive (and hilarious) water jet pack.
Thursday, May 19, 2011
- CAS stands for Computer Algebra System. This is great for exploration & discovery of mathematical concepts. It can serve as a ladder to help student reach new mathematical heights.
- Resolution – it has more pixels than any other TI graphing calculator.
- The grayscale was nice (color on the software), but now the TI-Nspire CX CAS includes color! This really is extremely helpful for engagement and enhances understanding. With color graphs I've seen freshmen exploring some advanced transformation, and seniors creating amazing 3-D shapes and animations.
- Images can be inserted.
- Geometry is integrated. No more going to the computer lab for those geometry classrooms. Now dynamic geometry can be in the hands of of every student! This also means lots of great simulations can be and have been made.
- Animation and sliders!
- Notes - makes it so much more of a teaching and learning tool.
- History preserved. Where did a student go wrong? Copy the history.
- Computer short cuts, like CTRL C, V, X, S, Z. (There are more shortcuts listed for "Dummies" here.)
- Content, content, content! There are many inquiry activities that have been written. See TImath.com or MathNspired.com. Also there are textbooks that integrate the use of the TI-Nspire, or as in the case of the Pearson/Prentice Hall textbooks for Algebra 1, Alg 2, and Geometry that now also address the Common Core Standards, the book is on the TI-Nspire.
- Incredibly easy to use data collection. There are so many Vernier probes that automatically work. There is no better way to learn slope or develop an understanding of derivatives and integrals than with real-world applications, like actually walking and seeing data in real-time with a CBR2 motion detector.
- Demonstrations – powerful visuals & multiple representations
- Graph function, polar, parametric, implicit, DE slopefields and more on the SAME screen at the same time!
- Exam acceptance. The TI-Nspire CX CAS is permitted on the AP, PSAT, SAT exam. The TI-Nspire is also allowed on the ACT, IB, and many state end-of-course assessment exams (including Indiana where I'm from). See part 3 blog entry.
- Don't forget all the research (part 1),
- MathPrint (part 4), and the
- software (part 2) that is included.
Saturday, May 14, 2011
Part of the inspiration for doing the research that these two freshmen pursued was the NASA Exploring Space through Math Weightless Wonder activity. They used the TI-Nspire and CBR2 motion detector to consider the parabola formed by a ball rolling on a ramp. I posted their PowerPoint presentation on our school's website.
Besides seeing the Endeavor, some highlights from the trip were hearing from the director of the Kennedy Space Center and former astronaut Robert Cabana, talking to astronaut and physicist Samuel Durrance, and hearing from a panel of NASA scientists and employees to encourage the students to pursue the challenging courses. The students got some great advice.
Update: I just got word about a Google Earth plug-in that lets you watch the space shuttle trajectory in real-time. It is similar to the what can be done with the calculus activity that was mentioned above, except this is LIVE. I think this will be particularly interesting when it takes off and lands. Endeavor is scheduled to land at 2:30 a.m. (Eastern time zone) June 1st, and the last shuttle should launch in July.
It requires the desktop version of Google Earth (free download here): http://earth.google.com/
Once you have Google Earth on your machine, just download the .kmz plugin below to your desktop and click it to start. It’s still in beta-mode so those involved in the development of it at the NASA Johnson Space Center in Houston would love to have feedback from teachers and students on what they think. Let me know and I'll pass on the feedback.
Wednesday, April 6, 2011
[Update: Videos about images on the handheld and what can be done with the TI-Nspire Navigator are now available on youtube. To transfer a file that you inserted an image on from the computer to your handheld, try this video tutorial. The basic insert image tutorial is here.]
Diagrams and pictures can help student engagement and exploration. The TI-Nspire Navigator 3.0 makes it easy to evaluate students in engaging ways. It encourages a new means for students to communicate their explanation of the relationship between their mathematical model and an image. This extends their learning beyond the normal rote problem set into an interactive investigation. Today in class I used the last image in this blog entry, the NASA Space Shuttle launch, to see how well students could write an equation of a line. They said they wish their previous math teacher could have used this. It would have helped them learn and understand slope and y-intercept so much better.
Images appear crisp and bright in vivid colors on the TI-Nspire CX. It comes with some images already loaded in the TI-Nspire, Images folder. But it is easy to import more jpeg, bmp, png, or clipboard (YES, copy/paste works) images. Any of these work just as well as the other from my experience. For more info about the file types you can read a recent google group conversation. I really enjoy copy/paste. It has been recommended to not use a several megabyte picture, but to keep the file size small. I've used images on a QuickPolls with the Navigator and it took it a second or two for the students to get the question to pop up on their screen rather than the normal nearly instantaneous delivery. But it was worth it.
So how do you insert a picture or image into a TI-Nspire document? It is essentially and easy and clicking 'Insert.'
From the software, images can be put into Questions, Notes, Graphs, Geometry, and Data & Statistics applications by clicking the 'Insert' button and choose 'Image...'.
Images convert from color into grayscale well on the Touchpad or Clickpad handheld devices.
The screen shots you see can be found in the 3.0 OS TI-Nspire document here.
All text and lines are mapped to black.
Here is an example from Data & Statistics page. Images can be modified by moving them, change the size but keeping the aspect ratio, squish or stretch vertically or horizontally. Again, on a D&S page select the image by pressing menu, Action, Select Image.So there is currently not a way to rotate an image or adjust the transparency. However, there is a way to make an image more transparent on a Graph and Geometry page with the following trick.
Note page 1.3 looks like the image is more transparent. Actually what happened is the image was inserted on a Geometry page, THEN the view (press menu>View) was changed to Graphing. This puts a somewhat translucent graph on top of the Geometry View. Similarly you could Show an Analytic Window on top of a Geometry page. This is what it looks like on a TI-Nspire Touchpad.For this OS we do have color, but we are limited to 9 vibrant choices.If you want to have images as part of a question, especially for doing Activity Center-like questions where equations are put on top of images, instead of doing a split screen, use the question type “Equation.” You can choose y= or f(x)= and change it later under ‘Response Type.’ Check the box for ‘Include a Graph Preview’ in order to make a question that will have some extra ease-of-use features. As the example below demonstrates, the student only needs to start typing in the equation and the graph appears and automatically updates. Again, this works when it is a Quick Poll or if it is part of a document.
Notice the ‘Data View’ options on the bottom right of the Quick Poll. If Graph is chosen, the image appears and students’ contributions are shown when they press enter.
Gray is the default color for students and green is the correct answer. Under the Review Toolbox is a wrench and hammer. By clicking this Tool and choosing Graph Tools, Individualize Student Responses can be activated.
I know the summer workshops will give more hands on experience with images and tips for the use of color. The Connecting Math & Science workshop in Indianapolis (among other places) will also share some updated colorful files to help encourage students toward STEM careers. They will also have colorful 3.0 Nspire files for some NASA activities.
Monday, April 4, 2011
This is an exciting time. I would say that with the use of the TI-Nspire Lab Cradle the number of probes/sensors that can be used nearly doubles. According to a Vernier website the number of available sensors if you are using the Easy Link or Go Link are 50 and with the Lab Cradle it is 58. However, let's say you have some old sensors in the stock room that you thought you would never get to use again. With the right adapter, I have now tested an old accelerometer, pressure sensor, a microphone that was designed for the CBL, and just today I received the Motion Detector Cable MDC-BTD and got the original CBR to collect data as shown in the picture. (Thanks Grant, a top AP calc & physics student, for having your camera and taking the pic.) So the $145 TI-Nspire Lab Cradle can be a really good deal if you have some older equipment. Potentially hundreds of dollars of resources can now be used again and you won't need the approximately $60 Easy Link.
[Update: I've used the Easy Link with the older equipment with great success. Note that there are several data collection sensors like the microphone, photogates, and motion that will not work with the EasyLink's one 'BTA' port, but need the Lab Cradle's 'BTD' ports. The Lab Cradle also has 3 places to plug in 'BTA' plugs so you can, for example, measure temperature of 3 things at the same time like we've done with this evaporation lab.]
Now to the question about 'what data collection equipment should you get?'
If I was consulting your school and helping you develop a plan that fit your teachers, I would begin by asking several questions. But since we aren't having that dialogue, I'll give a general response.
If you don't have any sensors, and you have less than $150, the two data collection probes that all schools ought to have for science and mathematics would be the temperature probe and motion detector - Easy Temp and CBR2.
Neither of these require an additional interface. You can plug them directly into the mini USB on the top of the TI-Nspire. Similarly, if you have have a $5 mini to standard USB adapter, then you can plug a Easy Temp ($38) or CBR2 ($93) into your computer and the Nspire software will auto-detect and begin collecting data.
The gas pressure sensor is another one that (along with Easy Temp) is especially useful in bio, chem & physics.
I was recently asked what sensors I would recommend for an environmental class. Take a look at the recommended probes with the lab book "Investigating Environmental Science through Inquiry." Instruction are provided for pH, conductivity, soil moisture, O2, UV sensor (this appeals to many classes), light sensor (I bet you have that one from your CBL days), etc.
Most of these work with the Easy Link. But you cannot use the microphone with the Easy Link.
That is why I'm so excited about the Lab Cradle: multiple probes, extended battery life and help to power probes with the built in rechargeable battery, AND more sensors that I have been wanting to use.
I think math and physics teachers will be especially excited by the microphone. With a tuning fork you get real-world sinusoidal data that gives audible significance to the general equation y=A*sin(B*x)+C, where B=2pi*frequency or 2pi/T, the period. In mathematics they tend to call the coefficient in front of the x-variable B, but especially when dealing with rotational motion, like a Ferris wheel, I prefer to call it omega, the angular velocity. We used a 512 Hz tuning fork to get the data shown in the screen capture. The curve fit gave a value of 511.7 Hz. I love it!
[Update: Microphone lab with the TI-Nspire and many more are now available from Vernier.]
In addition to the microphone, with the Lab Cradle the 3-axis accelerometer, photogate, nuclear radiation monitor, and rotary motion sensors are new comers to the Nspire family that will be useful for mathematics and science classes.
Tuesday, March 29, 2011
Some of the participants were excited to learn about the new Vernier DataQuest application and wanted to know more about the TI-Nspire Lab Cradle, like how much it costs. For the participants who were familiar with Vernier's Logger Pro, they felt right at home with the DataQuest. They were pleased with the options available, like the built-in Motion Match, along with the versatility of the functionality.
Regarding connecting sensors, to use one CBR2 or an Easy Temp you do not need any interface device. Plug it in and you are ready to go and have students make discoveries and connections about slope, sinusoidal cures, parabolas and more. Two of my students won a trip for themselves and me to the Kennedy Space Center for their research and presentation regarding parabolas with the motion detector. (Here is the press release from last year.) Teachers will appreciate that you can just plug in the motion detector and click the green start collection button to get the position-time and corresponding velocity-time graph simultaneously.
Update: With OS 3.6 in December 2013, you don't need to move your cursor or press TAB to get to the green start collection button. It is active and ready for you to press Enter to begin collecting data.
By pressing menu, Analyze, Tangent (derivative) or Integral, calculus classes will find themselves easily making real-world connections.
The Easy Link, an interface between one probe and the TI-Nspire handheld, enables you to plug into a good number of sensors. It costs $59. However, you are still limited to one sensor unless you plug into a computer. You can connect as many sensors as you have USB ports and Go! Links.
Data collection is extremely fast and easy when you do two sensors at the same time. Currently this can be done with the old TI-Nspire Navigator Cradle or with the software.
Now with the TI-Nspire Lab Cradle you can connect the mini-USB port on the top to the USB of your computer (no TI-Nspire handheld required) and enjoy demonstrating data collection with the 3 analog (for most sensors, including voltage, pressure, etc) and 2 digital (like for the CBR, microphone, rotary motion sensor, etc) channels.
Some examples of data collected with two sensors include:
- Magnetic Field Sensor, current probe, and a slinky to get great linear data
- magnetic field sensor and motion sensor for distance for an inverse relationship
- light intensity and distance - an inverse square law relationship
- voltage and current - the slope of this linear data is resistance, based on Ohm's Law.
With the Lab Cradle you will even be able to plug in two CBRs if you have a mdc-btd cable. Students can then investigate motion parametrically. One motion detector can be oriented in the x-direction and the other in the y.
YES, you read that correctly. With the Lab Cradle you can use the old Vernier probes and sensors you've had in a science storage room or mathematics teacher's closet. This includes the CBR! I'll try to share more on this and include pictures this next week.
Also, the TI-Nspire Lab Cradle is like getting 3 Easy Links plus a lot of things you couldn't get or do with the Easy Link. So in that regards the $145 doesn't seem so bad. Especially if you got the 5-pack bundle that comes with a 5-unit charging bay, that would be enough for just about any class size. With the experiment set up, every student could collect the data on their own Nspire.
In a similar price range is Vernier's LabQuest Mini. It is $149. With that you will need a computer with Logger Pro or Logger Pro Lite. Of course with the Lab Cradle you need a TI-Nspire OR a computer with Nspire software (http://www.vernier.com/calc/
Vernier's stand alone device is LabQuest. This impressive colorful touchscreen device is $329, but it comes with the emulator software.
So if your school, or even if it is just you using the TI-Nspire Software, or if you have some students with the TI-Nspire, what should you get?
I'll try to answer this in more detail next time...
Tuesday, March 15, 2011
C is for color or colour for those outside the U.S. And what might the X stand for? Well,
eXtra color obviously. Or perhaps it suggests that it is
eXciting and new. As you can see from picture, it is
eXtra thin. It is flatter than many cell phones. I put it on the table next to a blackberry and they were about the same thickness. It is
eXtra bright. With the backlit screen it makes it so much easier to read then its predecessor. The screen is so crisp and clear, students have commented that it is a better screen than their cell phone. Many teachers will especially enjoy that it has
eXtra battery life. No longer will teachers or students need to replace the AAA batteries. It doesn't use any. It can run for weeks without needing recharged. When it does need recharged, this can be done with the wall charger that comes with the purchase, or the mini USB can be connected via a wire to the USB of a computer, OR it can be docked into a CX docking station, OR it will be charged from the Navigator cradles. Another extra is
eXtra memory. When I turn on my TI-Nspire CAS Touchpad and look at the status it says it has 27.8MB; the TI-Nspire CX CAS has 115.2MB. Maybe the X stands for
eXpandable. There is a special CX TI-Navigator Wireless Network Adapter that is yellow and sits atop the CX. This plugs into the new port on the top and has little metal 'grips' that are secured in the groves on the side. Our school has purchased through a couple of distributors over the past years, including Bach Company and School Mart. The latter says the CX Navigator hardware will be ready to ship in May. Another way to expand the TI-Nspire CX is with the Vernier Lab Cradle. This tool which will be available in April will enable data collection in ways that were not previously possible. Finally, I suggest that the TI-Nspire CX is
eXtra nice, because it plays well with others. The Lab Cradles work on any TI-Nspire. If you already have the TI-Nspire Navigator, those cradles fit really well on the CX and you can have a mixed class of Clickpads, Touchpads and CX. However, I would recommend only having a class of Touchpads or CX because all the buttons are in essentially the same location. I've heard many teachers and students who first get their hands on the CX exclaim how much they like the button on the new CX. They also quickly notice the responsiveness of CX's touchpad. That's right, it still uses the touchpad and is not a touchscreen. This means that it is still allowed on all the major tests. The TI-Nspire CX CAS is permitted on the PSAT, SAT, AP exams like AP Calculus, AP Statistics, AP Physics, AP Chemistry, etc. In addition to the above, the numeric TI-Nspire CX is permitted on the ACT and IB exams.
For those wondering, 'What is this information about a graphing calculator doing on a Godly Dominion blog?' I would answer both you and myself that technology, especially educational technology that seeks to "inspire all students to achieve to their potential and become innovators of tomorrow," is an integral part of the cultural mandate, or the dominion mandate, in Genesis 1:28.
And in the words of one of history's greatest mathematical physicists,
Saturday, March 12, 2011
Inserting images makes mathematical modeling a lot more fun. I was showing the picture of the Alamo with the equations on it to a TI-Nspire Online User Group (The next meeting is April 14.), when someone asked about how the circle was draw. When you are on a Graphs or Geometry page you can press menu > Shapes > Circle.
After the circle is draw, you press menu > Actions > Coordinates and Equation and click the circle to show the equation of the circle. I like to move my cursor over the circle and press ctrl menu for right-click and choose Coordinates and Equation. Showing the coordinate or equation is a feature that can be turned off by teachers who do not want students to have access to this. To do this they would use Press-to-Test.
Not that too many high school teachers use 3D by graphing z(x,y), but there is definitely a lot of excitement about this functionality on the TI-Nspire. It is so much more powerful than what was available with the TI-89. When z1(x,y)=x^2+y^2 is entered in the 3D graph view, a paraboloid is almost immediately rendered. This used to take a lot more computing time on the 89. Then something the 89 couldn't do, graph another 3D graph on top of that and z-trace. Auto-rotate by pressing A or just use the arrows.
Here is a video of a 3D graph that is rotated. I guess I need a better video camera if I want to do any future videos like this. To the right is a much better picture of what the heart looked like on the TI-Nspire CX handheld. (Here is a link for more graphs of hearts.) I was showing this to some middle school students last night. My oldest daughter was begging me to show her friends the CX. Some of her basketball teammates were spending the night on Friday before they went on a service project on Saturday morning. This group of girls said they had never heard of a z-axis. By easily changing the orientation of the axis by pressing x, y, and z or rotating using the arrows, it was fun to watch the 'light bulbs' turn in in their minds. They were so excited about math and learning some things their teachers hadn't taught them. They were exploring and explaining to each other what the z-axis was. With color, images, and fun 3D shapes, math becomes a lot more cool, even for 8th grade girls at a sleep over.
Yes, 3D and the new differential equations graph type, now enabling the drawing of slope fields from anywhere - even the Scratchpad, will be features that are available for the CAS or numeric TI-Nspire or TI-Nspire CX when they upgrade to 3.0.
Saturday, February 26, 2011
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).
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.
Saturday, February 5, 2011
#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.
Thursday, January 13, 2011
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.