graphing calculators and their proper usage in high school mathematics courses math 511: trends in...
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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
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