Graphing Calculators and Their Proper Usage in

High School Mathematics Courses

Math 511: Trends in Math Education

By: Tessa Helstad

Scientific Calculators

Can be used in all 9th-12th grade classrooms

Graphing calculators might be more appropriate for 11th and 12th grades

Graphing Calculators Required Usage for Math Courses

Not required for Algebra I or Geometry, but could be explored

Algebra II, Pre-Calculus, Statistics, and Calculus - buying by students is recommended or teachers could have a classroom set

TI-83s or TI-86s are the most common TI-89s and TI-92s need to be monitored

more and are probably not recommended for assessments

TI-83 plus

(Silver Edition)

TI-86

TI-89

TI-92

GRAPHING CALCULATORS

Graphing Calculator’sRole in the Math Class

Classroom Discussions Assessment Usage Limited Assessment Usage Homework Use Exempted Use (homework/test)

– Teachers must also be aware of topics students might figure out, therefore not allowing use on assessments

ALGEBRA I & GEOMETRY

Should not be used . . .

Operations involving fractions

Graphing linear equations Order of operations Applying transformations

(TI-92) Solving linear equations

Could be used . . . Exploring systems of

linear equations Exploring lines that

best-fit data

Example on next slide

Algebra I Example (pg.1)

Finding the best-fit line

The following data relates the number of years of education (E) which a person completes and the average yearly income (I) in thousands of that person. Find the equation of the line that best fits the data. (I = mE + b)

Years of 12 15 16 16 18 20 22education

Average Yearly 32 40 52 46 55 85 62income (thousands)

Algebra I Example (pg.2) - Finding the best-fit line

This might be the first time these students have ever explored a graphing calculator.

Be sure to be patient and if possible have an aid to help out. With this grade level and this problem, I WOULD NOT show

the students how the calculator can compute the linear equation.– As the students are doing the problem on the calculator, have them

graph the points on paper as well. Discuss scales.– Then have them draw a best-fit line and choose two good points to

calculate the slope, y-intercept, and write the equation.– After the student has come up with the equation, then put the equation

in the calculator to check the computation on the linear equation and then allow thoughts on whether it is the best-fit line and how you could improve the line.

– Experiment with the equations of many students and show how more than one answer is correct. Discuss rounding of numbers and how it affects the graph.

Algebra I Example (pg.3) -

1. Turn plots on, with

scatterplot, and L1 and L2

as x and y values

2. Put data in L1 and

L2 table.

3. Choose a good window or let calculator fit

the data.

4. Select graph to view data

points.

5. After calculating good equations, try them on your graph. Discuss good equations and what changes might make the line connect to more data.

Finding the best-fit line

ALGEBRA II

Should not be used . . . Assessments should test the

students on the patterns created by transformation of quadratics.

Unit conversions Calculating with matrices Solving quadratic equations Assessing domain and range

Could be used . . . To explore quadratic

functions: translations and reflections.

Exploring domains and ranges

Example on next slide

Algebra II Example

1. Parabol

a reflects over x-axis or opens down.

2. Parabola

shifts left 5

3. Parabola

shifts down 6.

4. Parabola, opens down or reflects

over x-axis, shifts left 5, and down 6.

Parabola Transformations

PRE-CALCULUSCould be used . . . To explore quadratic and

cubic functions: translations and reflections.

Calculate with matrices Explore amplitudes, periods,

and shifts of sinusoids Solving quadratic equations Exploring complex rational

functions Finding actual zeros from a

list of possible zeros, when graphing with synthetic division

Should not be used . . .

To assess comprehension of cubic and quadratic functions.

Some curves’ sketches should be visually represented on assessments without calculator usage. (ie. asymptotes, x and y intercepts, end behavior of 2nd and 3rd degree functions)

Evaluteing trig ratios Graphs of y = 1/x or y = k x.

Example on next slide

Pre-Calculus Example

Radian Mode

I chose this window.

Sine Graph Amplitude

of 3

Sine GraphAmplitude = 3Phase Shift =

right п/4

Sine GraphAmplitude = 3Phase Shift =

right п/4Period = п

Sine Graph

Exploring Sinusoids and their characteristics

STATISTICS

Should not be used . . .

First introduction to mean, median, mode, box-and-whisker plots should be shown long hand.

Could be used . . . Can easily calculate

mean, median, and mode Can use tables and

matrices to display data Creating histograms and

box-and-whisker plots Computing two-variable

data analysis Calculate permutations

and combinations

Example on next slide

Statistics Example (pg. 1)

Use the following test scores: 80, 88, 91, 99, 100, 100, 79, 60, 75, 78, 82, and 88 to create a box-and-whisker plot. Label all statistics: quartiles, median, min, and max. Also note the values of the standard deviation, mean, and range.

» I would recommend doing this example by paper-and-pencil method first, but these high school students could use their calculators for further problems.

Statistics Example (pg. 2)

BOX-AND-WHISKER PLOT

ANALYZING 1-VARIABLE STATISTICS

Use TRACE to view stats.

1. Turn plots on

with whisker

plot selected.

2. Enter data in

L1 table.

3. Let calculator

fit the data. 4. Select

graph to view Box-and-

Whisker Plot.

5. View 1-variable stats.

CALCULUS

Should not be used . . .

Calculating areas under curves

Could be used . . . Explore tangents of

functions Find relative maxima

and minima of functions Learn simple

programming procedures

Exploring limits of functions

Example on next slide

Calculus Example

Calculating the area under a curve using limits of x=2 to x=4.

1. Lower limit of x=2 (Notice that

using trace we cannot get exactly 2)

2. Upper limit of x=4.

(Notice that using trace we

cannot get exactly 4)

3. This answer is approximate,

because 2 and 4 were estimated.

PROGRAMMING FEATURES

Some basic programming can be taught to students.

Be careful though, because what you teach them they can use against you.

Recommended to only 12th grade courses.

Examples of programs:– Distance Formula

– Midpoint Formula

– GPA computation

– Quadratic Formula (Advanced programming knowledge)

Example on next slide

Programming ExampleWriting, executing, and using

the distance formula.

Writing the Distance Formula

Running the Program and Computing Values

Additional Technology Link to transfer data between calculators

Link to connect to a computer and keyboard connection

CBLs and CBRs TI-Presenter - video adapter connects to a

TV or other projection device ViewScreen panel sits atop a standard

overhead projector

CBR

CBL

Additional Technology- Tools used to enhance

graphing calculator uses in the classroom.

TI- Navigator

View Screen TI-KeyboardTI-Presenter

Bibliography

TI website (online). http://www.ti.com/ NDCTM website (online).

http://www.sendit.nodak.edu/ndctm/ Advanced Mathematics: An Incremental

Development 2nd Edition. Norman, OK. Saxon Publishers. May 1998