Integrating Technology Years 5-8
Graphic Calculators in the Middle School
Stephen ArnoldDownload in PDF format
What is the one thing that no school these days can have enough of? Surely, for most schools, both Primary and Secondary, that would be true of computers. With new developments in hand-held technology over the past twelve months, however, the dream of having technology in the hands of every student may not be so far away. Even the prospect of having portable computer rooms for the cost of only three or four computers is now a very real and affordable possibility.
To most people, graphic calculators are expensive educational tools for senior mathematics (and perhaps science). While this remains true for most of these tools, Texas Instruments has put in enormous effort to ensure that the hand-held devices that they offer to schools are something much more. They now prefer the term personal learning tools(PLT) and this is a fair description. These devices are now capable of running software applications (called Apps) which provide the user with many of the features that might normally be expected from a personal computer
Imagine, for a moment, if students in your classes had access to high-quality interactive software tools for many of their subjects: mathematics, science, geography, history, languages and more – applications designed, not by computer programmers, but by teachers for real students in real classrooms. Imagine, too, that these devices also offer word processing (compatible with Microsoft® Word), spreadsheeting (compatible with Excel®) and even presentation software. Combine these features with a full-size keyboard and you may begin to see the possibilities for both primary and high school classrooms. For the cost of three or four computers, a school can have a portable computer lab of 30 such devices, with keyboards, and a teacher model with a viewscreen which sits on any overhead projector. Consider the possibilities!
The demands of new curricular documents are fast removing any options with regard to student access to technologies for learning. The new Mathematics curricula make clear that such use is mandated for both primary and secondary students, with a particular emphasis upon the use of spreadsheets, as well as other generic software types for mathematics, including dynamic geometry, graph plotters and interactive statistics packages. ALL of these required software tools are now available on graphic calculators, and these represent real value for money in a single package, since most Apps are freely downloadable from the Internet. When the expectations of the other KLA syllabus documents regarding technology are taken into account, no school will have enough computer rooms to fully service these needs. The ideal situation would involve every student having their own graphic calculator as a resource for many of their school subjects. In the short term, as suggested above, a class set of these tools will provide school computer facilities with much needed relief and offer a viable alternative from both educational and budgetary viewpoints
Tools for Learning MathematicsTop of Page
Students learn best when they are challenged and motivated. Good software tools offer learners opportunities to work at their own pace on well-designed activities which support them in acquiring new skills and understandings, while gradually encouraging independence. These are the essential principles of scaffolding: it is not hard to support students in their learning. The challenge comes in knowing how and when to remove that support: too soon and the learner becomes frustrated; too late and they become dependent
The free mathematics Apps designed for the middle school years offer examples of such features. Rational Rampage (pictured) and Decimal Defender involve a variety of game formats which are very effective in helping students to understand and acquire skills related to rational numbers (fractions, decimals and percentages) and operations involving decimals. What is my Angle? (pictured) is an animated guessing game which builds skills of estimation related to angle sizes and types. The wonderful Math by Hand app takes students carefully through the formal procedures for addition, subtraction, multiplication and division: first, in a step-by-step process (as shown), then with the option to move more quickly, and finally challenging students with missing numbers and requiring them to work backwards, checking that they not only can perform the skills required, but that they also understand the processes. Like most of the TI Apps, scores are kept for student and teacher benefit and improvements can be monitored. Each of these Apps fits perfectly into the requirements of the new syllabus: as greater demands for such skills with fractions, decimals and formal procedures are placed upon Stage 3 and 4 teachers, the need for software tools which allow students to progress at their own pace has never been greater. The personal nature of the technology (as opposed to the use of a computer) further encourages students to work in a non-threatening but well-structured way
Other apps offer even more creative opportunities for students to build knowledge, skills and understandings related to number, space, patterns, data and measurement. Number Curiosities is an excellent source of useful and sometimes quirky information about the counting numbers from 0 to 25. Problem solving tools may be found in Puzzle Pack, Logic Ladder and SMILE Mathematics. Some old favourites such as LOGO are available for students to investigate essential ideas of space, distance and angle as well as an excellent Probability Simulator (cards, dice, spinners, coins and more) for investigating chance. All of these Apps are built around the premise that we recognize as “working mathematically”, the essential component of our mathematics teaching and learningThe power of interactive geometry software to engage and empower students in their learning of geometry is now well documented. Tools such as Cabri Geometry II® and Geometer’s SketchPad® offer powerful teaching opportunities which are simply not possible using traditional static media (pens, paper, blackboard). Students are free to create and investigate shapes and patterns, transformations and constructions, establishing firm foundations for their future studies of mathematics. Such exciting tools are available as Apps also: GeoMaster and CabriJr (shown) which is available as a free app Finally, in addition to these marvelous open-ended software tools, there are interactive instructional packages for mathematics and science, such as the excellent Area Formulas App. Offering definitions, examples and explanations related to the areas of rectangles, squares, parallelograms, triangles, trapezoids and circles, this thorough teaching sequence then offers students the option to take quizzes and practise what they have learned
All the Apps for mathematics (and there are many more than what have been shown here) offer features additional to the already powerful facilities of the graphic calculator itself: not just function graphing, but tables of values and lists for studying number patterns, easy-to-use statistical capabilities for investigating and picturing data, as well as all that we would expect from a calculator which displays not just one or two lines, but a screen-full of steps. This is an example of technology designed by teachers specifically for the teaching and learning of mathematics. Teachers and students can certainly use these devices just for the Apps, without ever needing to learn how to access all the powerful mathematical features they offer. For many students, however, the Apps will be just the beginning
Tools for Learning Across the CurriculumTop of Page
The past twelve months has seen the development of a growing array of Apps designed for other curriculum areas. In my school, we trialed the use of these tools, not just for mathematics and science, but for geography, languages, PDHPE and religious education to name a few. The students were excited to find that they could use their calculators in so many new ways; the teachers were able to take advantage of this great opportunity to make use of available technology in all their classes. When coupled with the new TI-Keyboard, the possibilities expanded dramatically, offering effective note-taking facilities in all classroom contexts. Even laptop schools use their expensive computers most often for word processing. These tools are light, robust and will not run out of battery power after a few hours: they will run for months. And they can be used in external examinations for the School Certificate and for General Mathematics in the Higher School Certificate.
Consider the World Geography app, freely available since late last year (and already updated once): every country in the world, with maps and pages of information for each. Not just useful for geography classes: I used this app with my Year 7 students studying the Old Testament for religion. We investigated the countries around the Holy Land, their locations and living conditions. The language teachers at my school were happy to make use of this resource for students to learn about the many countries that spoke French, or Italian, or any other language. In fact, some sixteen language localisers are available which transform the calculator itself into other languages, from French, German, Italian and Spanish to Chinese and Norwegian! All commands and menus are translated and students are practicing their language of choice every time they use their calculator!
What else would you like your students to have on hand? A dictionary, perhaps? As with most Apps, the quality of the development means that you rarely just get what you expect. In the case of World Geography, the option exists for students to take quizzes on any of the features of the countries or regions they have studies – and their score can be kept. The App called DAWG (Dictionary and Word Games) is a similarly diverse bundle. As well as the spell checker you would expect, this includes an anagram maker, word families and the best tool for doing crosswords: put in the letters you know, put question marks for the ones you don’t, and it will provide all the words that fit the bill! We love this one at home.Perhaps even more exciting, though, than these wonderful learning tools could be the truly open-ended software that we have come to expect from our computers: a full “office suite”: word processor (NoteFolio), spreadsheet (CellSheet) and presentation package (StudyCards). When used with the keyboard, the calculator truly becomes something much more. Many of the benefits of a laptop computer at less than one tenth of the cost.
Using a small freely downloadable plug-in with my computer, I am able to add a “TI-Tools” menu to both Microsoft® Word and Excel®. I can then create a document (word processor or spreadsheet) on my computer and at the click of a menu choice, send it to my calculator. As a teacher, I created my class notes and quiz questions in this way, then was able to walk into class and project them using the OHP. I could then move around checking student work and assisting while they got straight to work. There is literally no simpler and less expensive way for teachers to project their pre-prepared material for their classes in an interactive way.
Using the spreadsheet, my students recorded information from the World Geography App for half a dozen countries in the news at the time, then entered this data into the spreadsheet and were able to study and discuss graphs, such as Life Expectancy and Literacy, or Area and Population (as shown). Can Youpick the odd one out?
Finally, we come to StudyCards: based on the simple flash card idea (front and back) this is truly the App for everyone. Download the free StudyCards Creator and easily create stacks of cards with text and images on front and back. Just as easily, create them as multiple choice questions, for which scores may be kept, and teachers have the means of providing their students with instructional and assessment materials on any topic or subject of their choice. Dozens of StudyCard stacks are already freely available online, but it is so easy to create your own
Tomorrow’s Technology TodayTop of Page
Can you see the possibilities for such tools? Imagine them in the hands of every student at your school? At very least, imagine one or more class sets which can be taken to any room in the school. A portable, robust resource designed for schools
Do not forget that these tools link directly to data loggers, allowing the gathering of real world information on any number of different probes: temperature, light, voltage, pressure, heart rate, motion and many more. Add the idea of a portable science laboratory to that of the portable computer room
Finally, imagine if your room full of calculators were linked wirelessly to the teacher’s computer at the front of the room. The results of tests and assignments can be instantly gathered and displayed, so immediate checking of progress: how many chose option A? What proportion got this one correct? Why did so many students select C? The teacher’s computer could be connected to the Internet, allowing the calculators to be upgraded and new software installed easily. The Ti-Navigator is in the final stages of trialling in schools now. This wireless network facility will be available in the next few months, taking classrooms to new levels of interactivity, and inviting teachers to engage with their students in new and exciting ways! The classroom of tomorrow is not nearly as far away as many believeTop of Page
For comments & suggestions, please e-mail Steve Arnold.
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