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Graphing Calculators

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Graphing Calculators

Using technology not as a crutch for basic calculations, but rather as a link to higher levels of understanding and to critical thinking skills

- Minnesota state standards require 8th graders to be introduced to such topics as algebra and statistics.
- Without bogging students down with complicated formulas and tedious construction of graphs by hand, the important mathematical concepts can be taught, rather than the potentially confusing computations.
- In a world saturated in technology, it is good for students to work with high-tech devices.

- Students may become calculator dependent; unable to do simple math without a calculator
- Students may become “button pushing monkeys”
- Not stimulated by the math problems presented
- Trusting whatever the calculator states, which presents a problem if they cannot tell when they have entered information incorrectly.
- Using, but not understanding, the foundations of the formulas they have been taught

- Teacher’s should create math problems that go beyond basic computation.
- Teachers should provide guided discovery of a rules and formulas, rather than giving students a jumble of letters and symbols to try to memorize.
- Teachers should remind students that calculators are precision machines
- you must type information in correctly to get the right answer. The order of operations becomes crucial.
- Use estimation to guess what the answer will be. If the answer you get is far away from the guess, it’s a tip you typed something in wrong.

- Graphing
- TI-84 allows you to enter in a formula, or several formulas, and graph them quickly and accurately

- Statistics
- TI-84 allows you to enter lists of numbers and then find the mean, maximum, minimum, standard deviation, sum, and more all with a few presses of the button.
In today’s media, it is very common to see a chart or to hear statistical figures used to support a claim.

Why not help to students understand and be comfortable gaining knowledge from these common-place presentations of information and data?

- TI-84 allows you to enter lists of numbers and then find the mean, maximum, minimum, standard deviation, sum, and more all with a few presses of the button.

- It is difficult to make an accurate graph by hand, especially if you’re not graphing straight lines.
- With the TI-84, you can
- make several graphs in a matter of seconds, change the equations to get a whole new set of graphs easily.
- Zoom-in and zoom-out.
- By a pressing of a few buttons, you can learn precisely where the intersections occur, rather than using algebra or (worse) eye-balling it.

Finding the intersection of two equations

(start at 0:32)

68/95/99 % rule:

t: population standard deviation unknown, use sample standard deviation

- In statistics, we use many complex formulas. Some are almost impossible to do by hand. If the data list is long, they take a long time to do even with a scientific calculator.
- The TI-84 does the tedious computations for you and lets you move on to interpreting the information – which is really the skill we want students practicing and mastering.

YouTube - TI 84 Finding One Variable Statistics

(start at 0:21)

- Calculators are an important technological tool to include in the math classroom
- Teachers need to create scenarios where calculators will be used effectively and where critical thinking, not just basic computation is needed to find the answers.
- The TI-84, with its graphing and stats features can help teach students to interpret charts and statistical figures that they frequently see in daily media.
- The TI-84 can do a lot! Don’t treat it like a mere substitute for paper and pencil.

- National Council for Teachers of Mathematics. (2008). The technology principle. Principles and Standards of School Mathematics (pp. 24-27). NCTM.
- Texas Instruments. (2009). Getting Started with the TI-84. (2009). TI-84 instruction manual. Appleton, WI: National Graphic Solutions.
- Davis, R.W. (Producer). (2009). Ti 84 finding one variable statistics. [Web-based video]. Retrieved from http://www.youtube.com/watch?v=UHpGzGGalx0
- TechPoweredMath. (Producer). (2010). Lesson: finding the intersection of two graphs on a TI-84. [Web-based video]. Retrieved from http://www.youtube.com/watch?v=u26O2uJ1uNg