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Instructional Activities on Calculus for High School
Level by Using a TI Nspire CX CAS Graphing
Calculator
Sayun Sotaro*, Sermsri Thaithae, Pisuttawan Sripirom Sirininlakul
Department of Mathematics, Faculty of Sciences Srinakharinwirot University
Bangkok, Thailand
*say@g.swu.ac.th
Abstract—The purposes of this study were 1) to study the
achievement and the efficiency of instructional activities on
calculus for high school level by using a TI Nspire CX CAS
graphing calculator and 2) to study students’ satisfaction toward
workshop learning with instructional activities on calculus for
high school level. The samples of this study were 16 students of
the second and third-year who were studying Bachelor of Science
and Bachelor of Education (Mathematics) in semester 3/2017,
Mathematics Department, Faculty of Sciences, Srinakharinwirot
University. The result of the study indicated that students had
educational efficiency to pass the criteria more than 60 percent of
the total students with a statistical significance level of .05. The
effectiveness (efficiency of process (E1)/efficiency of product (E2))
of the instructional activities on calculus for high school level by
using a TI Nspire CX CAS graphing calculator equal to
87.65/78.23. The students’ satisfaction toward instructional
activities on calculus for high school level by using a TI Nspire
CX CAS graphing calculator was at a high level.
Keywords—instructional activities, calculus, graphing
calculator, TI Nspire CX CAS
I. INTRODUCTION
Technological advancements in computers and calculators
have played an important role in human functioning. This
enables humans to perform tasks quickly and unlimitedly by
the calculators that play a significant role in Thai mathematics
teaching which is graphing calculators [1]. Graphing
calculators play a role in teaching and solving various
mathematical problems, which helps saving time in classes
such as algebra and conversion geometry etc. It's easier to
convey knowledge and thinking processes. Teachers can used
to organize a variety of teaching styles, giving learners a sense
of freedom to create conceptual ideas and help to quickly
calculate complex patterns. Graphing calculators are useful
tools for teaching mathematics at all levels including to help
solve problems and to develop conceptual skills. Another
important aspect is that learners can use graphing calculators to
help create knowledge, new ideas, and also help learners to
learn faster and easier.
The Texas Instruments model Nspire CX CAS Graphing
Calculator, briefly called TI Nspire CX CAS, is the latest
Computer Algebra System (CAS) graphing calculator of Texas
Instruments. The characteristics of this hardware were 1)
Graphing Calculator, 2) the convenience of data transferable,
3) rechargeable Battery, 4) English letter plastic keyboard, 5)
color screen, 320 x 240 pixels, 6) 100 MB memory for
recording and another 64MB for the operating system, 7)
calculate and yield both real number and complex number, 8)
algebra, calculus, and matrices can calculation by computer
algebra system (CAS), 9) geometric program, 10) function
graph, a graph of sequence, 3 dimensions graph, 11) find
values from the chart: highest, lowest, integral, slope,
intersection, contact line equation, 12) the statistics graph
includes histograms, box plot graphs, dot graphs, line graphs,
and regression equations. 13) matrices calculation, includes
inverse, determinant, transpose and row operation, 14)
calculate the logarithm, trigonometry, 15) can fit images into
the calculator, etc.
Calculus is an extremely important subject that forms the
basis of understanding nature and real-life phenomena. It can
be applied to natural rules. It is also the basis of almost every
field of science and is the necessary basis for modern science.
As such, learning calculus is fixed to be learned for high
school, and undergraduate level for almost every major.
Normally, teaching calculus is a lecture base and emphasizes
practice which enables students with a high ability to succeed
in studying. For students with moderate and mild ability, they
must try to put more time and effort into studying. The calculus
teaching development guidelines should allow students to learn
on their own. There should have media to practice according to
the learning abilities of each learner. The instructor is
responsible for guiding the learning path, suggesting the
importance and benefits of the learning, and can be applied
knowledge [2]. The study of Beth [3], observed and
interviewed mathematics teachers who used graphing
calculator to teach calculus, finding that graphing calculators
are very useful in teaching mathematics, such as graphing
calculators, making it easier and faster to calculate difficult
calculations. Students can use graphing calculators to check the
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graph that they create accurately. Graphing calculators also
help students to convert subjective visual to objective visual.
However, students need to have an understanding of the rules,
formulas, or theories they learn to use graphing calculators
more efficiently. Ng Wee Leng [4] studied the use of graphing
calculators and calculus. It aims to determine whether the use
of TI Nspire can enhance teaching and calculus learning. The
results showed that TI Nspire graphing calculators are an
integral tool for teaching and learning calculus concepts in the
classroom. It was also found that the use of graphing
calculators was appropriate for the concept of algebra calculus.
Students enable better visualization of concepts and make
snapshots of relevant mathematical features. Also, students can
associate and show the results on the same screen, especially
algebra and graphics. The researchers were involved in the
development of mathematical and statistical instructional
activities including matrices [5], statistics in high school [6],
statistics for research [7], linear programming [8], relations and
functions [9], conic sections [10], and pre-calculus [11]
respectively by using TI Nspire CX CAS graphing calculator
and to study the satisfaction of teaching, which results in a high
level of satisfaction in teaching activities.
Based on research studied in Thailand and foreign
countries. It was found that the results of the instructional
activities using graphing calculator help students to create
subjective visual. It enabled students to observe, create
knowledge that will link to objective visual. The Graphing
calculator also helps to solve mathematical problems that
enable teaching to be more effective. Students have fun
learning environment. Therefore, based on the mention
reasons, the researchers agreed that research should be done to
create instructional activities using a TI Nspire CX CAS
graphing calculator in calculus for high school level to enhance
students' experience in the use of graphing calculator
technology for instructional activities on calculus for high
school level.
II. RESEARCH OBJECTIVES
To create and study the achievements of instructional
activities on calculus for high school level by using a TI
Nspire CX CAS graphing calculator.
To study the effectiveness of instructional activities on
calculus for high school level by using a TI Nspire CX
CAS graphing calculator according to criteria 75/75.
To study the student's satisfaction in the workshop of
instructional activities on calculus for high school level
by using a TI Nspire CX CAS graphing calculator.
III. SCOPE OF RESEARCH
A. The Population Used in Research
The population used in this study were 16 students of
undergraduate students who were studying Bachelor of Science
and Bachelor of Education (Mathematics). Department of
Mathematics, Faculty of Sciences, Srinakharinwirot University.
The samples used in this study were 16 students of the
second and third-year students who were studying Bachelor of
Sciences and Bachelor of Education (Mathematics) in semester
3/2017, Department of Mathematics, Faculty of Sciences,
Srinakharinwirot University.
B. Limitation
A primary limitation in the current research was the small
sample size due to the intensive care required for the students
thoroughly during the workshop and the limited number of TI
Nspire CX CAS graphing calculators which were supported by
Department of Mathematics, Faculty of Sciences,
Srinakharinwirot University. The total number of 20 samples
may lower the generalizability of results. The second limitation
concerns the selective content of calculus which covered only
15 topics according to the course syllabus. However, the
present study should be considered exploratory first step in
examining the achievement and efficiency of instructional
activities on calculus for high school level.
C. Variables
Independent variables were instructional activities on
calculus for the high school level by using a TI Nspire CX
CAS graphing calculator.
Dependent variables were activity performance, students'
achievements, and satisfaction of students toward instructional
activities on calculus for high school level by using a TI Nspire
CX CAS graphing calculator.
D. Research Tools
Instructional activities on calculus for high school level
by using a TI Nspire CX CAS graphing calculator
consists of 15 research topics : 1) Limit of functions 2)
Limit theorem 3) Function continuity 4) Average
change rate 5) Derivatives of functions 6) Formulas for
finding function derivatives 7) Higher derivatives 8)
Implicit differentiation 9) Slope of a curve or tangent
lines 10) Speed and acceleration 11) Increasing and
decreasing functions 12) Stationary points 13)
Maximum and minimum problems 14) Indefinite and
definite integrals 15) Area under a curve and area
between two curves.
The test measured the achievement of instructional
activities on calculus for high school level by using a TI
Nspire CX CAS graphing calculator.
Student satisfaction questionnaire on instructional
activities on calculus for high school level by using a TI
Nspire CX CAS graphing calculator.
TI Nspire CX CAS Graphing Calculator.
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329
IV. RESEARCH METHODOLOGY
A. Creating and verifying the quality of the tool.
Instructional activities on calculus for high school level
by using a TI Nspire CX CAS graphing calculator, took
2 days, 7 hours per day, divided into 15 topics.
The test to measure the achievement of instructional
activities on calculus for high school level by using a TI
Nspire CX CAS graphing calculator, a subjective test
for 6 items, with two experts to validate the criteria of
Item Objective Congruence (IOC) guidelines to
determine the consistency between the content of the
test and the objective of behavioral learning, as well as
suggestions on questions. Use subjective criteria with
difficulty level between 0.20-0.80 and classification
power of 0.20 or higher, and the results of the analysis
of the confidence test using Cronbach's (-coefficient)
which equal to 0.610.
The satisfaction questionnaire on instructional activities
on calculus for high school level by using a TI Nspire
CX CAS graphing calculator. Researchers developed
the questionnaire based on the assessment of the
workshop program of the Department of Mathematics,
Faculty of sciences for 10 questions. The structure of
the questionnaire was 5 points Likert scale: 5 = the
highest, 4= high, 3= moderate, 2= low, and 1=the
lowest. The interpretation of the total average score,
which resulted from the satisfaction of the sample
students toward instructional activities on calculus for
high school level by using a TI Nspire CX CAS
graphing calculator. Based on the assessment criteria of
[12]: an average score of 4.50 – 5.00, means that the
students were satisfied at the highest level. The average
score of 3.50 – 4.49 means that the students were
satisfied at a high level. The average score of 2.50 –
3.49, means students were moderately satisfied. The
average score of 1.50 – 2.49 means students had low
satisfaction, and an average score of 1.00 – 1.49 means
students had the least satisfaction. The result of the
analysis of the confidence of the instructional activities
on calculus for high school level by using a TI Nspire
CX CAS graphing calculator using the Cronbach's (-
Coefficient) formula was 0.906.
B. Data Collection
The researchers conducted a workshop of instructional
activities on calculus for high school level by using a TI Nspire
CX CAS graphing calculator for the sample students by own
self for 2 days, 7 hours a day, and collected scores from
activities during the workshop and scores from the
achievement test to calculate a statistical value.
V. RESEARCH RESULTS
The researchers presented the results of the analysis as
follows:
Percentage, arithmetic, and standard deviations of
academic ability of the sample students are shown in
Table 1. According to table 1, the scores that students
got during learning activities, the achievement test, and
achievement of instructional activities on calculus for
high school level by using a TI Nspire CX CAS
graphing calculator has the average arithmetic 35.06,
46.94 and 82.00 marks, respectively, representing 87.66
78.23 and 82.00, respectively, and the standard
deviation was 5.23, 6.11 and 9.09 marks, respectively.
Instructional activities on calculus for high school level
by using a TI Nspire CX CAS graphing calculator had
performance value equal to 87.66/78.23 which was
effective according to criteria 75/75 that was set.
TABLE I. MEAN, PERCENTAGE, AND STANDARD DEVIATION OF
SAMPLE STUDENT’S ACADEMIC ABILITY.
Score
Number of
students
Total
score
Mean
Percentage
S.D.
During
Learning
Activity (E1)
16
40
35.06
87.66
5.23
After
Learning
Subjective
test (E2)
16
60
46.94
78.23
6.11
Total
100
82.00
82.00
9.09
The percentage of sample students who scored the
achievement on instructional activities on calculus for
high school level by using a TI Nspire CX CAS
graphing calculator of 70% or more of the total score
and tested the number of students who qualified more
than 60 percent of the total number of students as
shown in table 2.
TABLE II. PERCENTAGE OF SAMPLE STUDENTS WHO SCORED THE
ACHIEVEMENT OF BASIC KNOWLEDGE ON INSTRUCTIONAL ACTIVITIES ON
CALCULUS FOR HIGH SCHOLL LEVEL BY USING A TI NSPIRE CX CAS
GRAPHING CALCULATOR OF 70% OR MORE OF THE TOTAL SCORE AND
TESTED THE NUMBER OF STUDENTS WHO QUALIFIED MORE THAN 60
PERCENT OF THE TOTAL NUMBER OF STUDENTS.
Total
Number
of
Students
Number of students who scored
the achievement on instruction
activities on calculus for high
school level pass )Ratio(
Test
Prep.
Exact
Sig.
(1-tailed)
16
14 (0.9)
0.6
0.018*
*at a significant level of .05
According to table 2, after instructional activities on
calculus for high school level by using a TI Nspire CX CAS
graphing calculator, the test results showed that students
achieved the educational achievement of instructional activities
on calculus for high school level by using a TI Nspire CX CAS
graphing calculator, passing the criteria from 60% of the total
number of students at a significant level of .05.
The results of the analysis of students' satisfaction
toward instructional activities on calculus for high
Advances in Social Science, Education and Humanities Research, volume 520
330
school level by using a TI Nspire CX CAS graphing
calculator are shown in table 3. According to table 3,
students are satisfied with instructional activities on
calculus for high school level by using a TI Nspire CX
CAS graphing calculator as a whole with an average of
4.15, which is very satisfied. When considering in an
aspect, students are satisfied with instructional activities
on calculus for high school level by using a TI Nspire
CX CAS graphing calculator at the highest satisfaction
level which was 7. How much of the suitability of class
and audiovisual equipment during the training
workshop? 8 How much of the suitability of teaching
material? However, students have a moderate level of
satisfaction for 2. Before joining the training workshop,
how much knowledge do you have toward instructional
activities on calculus for high school level by using a TI
Nspire CX CAS graphing calculator? While other
aspects have a high level of satisfaction.
TABLE III. ARITHMETIC AVERAGES, THE STANDARD DEVIATION AND
SATISFACTION LEVEL OF THE SAMPLE STUDENTS AFTER INSTRUCTIONAL
ACTIVITIES ON CALCULUS FOR HIGH SCHOOL LEVEL BY USING A TI NSPIRE
CX CAS GRAPHING CALCULATOR.
Questions
x
S.D.
Satisfaction
level
1. How much of the suitability of the time
frame and pattern of the training workshop?
4.19
0.66
High
2. Before joining the training workshop,
how much knowledge do you have toward
instructional activities on calculus for high
school level by using a graphing calculator?
3.06
0.99
Moderate
3. How much ability the lecturer have to
answer your question?
4.25
0.58
High
4. To join a training workshop, make you
have ability and confidence. How much
ability do you have to share knowledge with
the lecturer?
4.12
0.72
High
5. After joining the training workshop, how
many levels of knowledge do you have
toward instructional activities on calculus
for high school level by using a graphing
calculator?
4.19
0.54
High
6. Do you think you can apply the
knowledge that you got from the lecturer for
yourself?
4.44
0.63
High
7. How much of the suitability of class and
audiovisual equipment during the training
workshop?
4.31
0.79
Highest
8. How much of the suitability of teaching
material?
4.38
0.50
Highest
9. How much satisfaction do you have from
the overall training workshop?
4.19
0.66
High
10. Do you think the training workshop
should be held in the future?
4.38
0.50
High
Total
4.15
0.50
High
VI. SUMMARY OF RESULTS, DISCUSS THE FINDINGS AND
SUGGESTIONS
A. Summary of Results
Students had achievement toward instructional activities
on calculus for high school level by using a TI Nspire
CX CAS graphing calculator passing the criteria from
60% of the total number of students at a significant
level of .05.
Instructional activities on calculus for high school level
by using a TI Nspire CX CAS graphing calculator had
performance value equal to 87.66/78.23 which was
effective according to criteria 75/75 that was set.
Students were satisfied with instructional activities on
calculus for high school level by using a TI Nspire CX
CAS graphing calculator as a whole with an average of
4.15, which was very satisfied.
B. Discuss the Findings
The results can be discussed as follows:
1. According to the study, more than 60 percent of all
students have the ability for instructional activities on calculus
for high school level by using a TI Nspire CX CAS graphing
calculator. The instructor arranges the content and activities
from basic to more advance and reviews the basic knowledge
that the students have studied. The instructor explains steps in
detail by using a TI Nspire CX CAS graphing calculator for
learning calculus for the high school level. Students have a
chance to practice on their own. They are eager to study and
don't feel tired of studying and doing activities. All learners
focus on the graphing calculator monitor or focus on the large
screen in front of the class showing the instructor's graphing
calculator monitor. This allows students to concentrate on the
subject and the skills of using a graphing calculator on calculus
for the high school level. This enables students to learn non-
studied content and have better graphing calculator skills than
in the early stages of teaching.
Examples of commands, limit of function, and area
between two curves used in TI Nspire CX CAS graphing
calculators of Instructional activities on calculus for high
school level by using a TI Nspire CX CAS graphing calculator
were shown in Figure 1, 2, and 3 respectively.
2. The results of the development and effectiveness of
Instructional activities on calculus for high school level by
using a TI Nspire CX CAS graphing calculator showed that
Instructional activities on calculus for high school level by
using a TI Nspire CX CAS graphing calculator created by the
researchers was as effective as 87.66/78.23, with a threshold of
75/75, when considering an inter-study score (E1) above the 75
threshold set, as the researchers conducted the process of
Instructional activities on calculus for high school level by
using a TI Nspire CX CAS graphing calculator by exploring
the structure of the content, dividing the course content. Create
activities that use a TI Nspire CX CAS graphing calculator in
detail. Researchers provide class material and students can act
on their own, and post-school test scores (E2) are not much
higher than the 75 threshold set because students have limited
time to review content and activities using graphing
calculators.
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331
3. Students who attend training workshop are satisfied with
Instructional activities on calculus for high school level by
using a TI Nspire CX CAS graphing calculator at a high level
as a whole which may come from the content of Instructional
activities on calculus for high school level by using a TI Nspire
CX CAS graphing calculator. Students can apply the content
for their research and the lecturer can also convey the content
and develop activities on Instructional activities on calculus for
high school level by using a TI Nspire CX CAS graphing
calculator. The lecturer conveyed the content with TI Nspire
CX CAS graphing calculator to help for calculation, students
have a chance to attend a workshop at the Department of
Mathematics, Faculty of Sciences, Srinakharinwirot University
for 2 days. There is one TI Nspire CX CAS graphing calculator
equipment per person.
Fig. 1. Example of commands used in TI Nspire CX CAS graphing calculators
Advances in Social Science, Education and Humanities Research, volume 520
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Fig. 2. Example of limit of function used in TI Nspire CX CAS graphing calculators
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Fig. 3. Example of area between two curves used in TI Nspire CX CAS graphing calculators
VII. CONCLUSION AND SUGGESTIONS
A. Conclusion
The result of the study indicated that students had
educational efficiency to pass the criteria more than 60 percent
of the total students with a statistical significance level of .05.
The effectiveness (efficiency of process (E1)/efficiency of
product (E2)) of the instructional activities on calculus for high
school level by using a TI Nspire CX CAS graphing calculator
equal to 87.65/78.23. The students’ satisfaction toward
instructional activities on calculus for high school level by
using a TI Nspire CX CAS graphing calculator was at a high
level.
B. Suggestions
1) Recommendations to implement the findings: The
results indicate that Instructional activities on calculus for high
school level by using a TI Nspire CX CAS graphing calculator
can improve the calculus ability of the high school level for
sample students. Therefore, there are important suggestions as
follows:
Students who attend Instructional activities on calculus
for high school level by using a TI Nspire CX CAS
graphing calculator should have preliminary knowledge
of the using a TI Nspire CX CAS graphing calculator.
Instructional activities on calculus for high school level
by using a TI Nspire CX CAS graphing calculator,
instructors should allow learners to learn definitions
and/or process of solving without using graphing
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334
calculators first. Once the learner understands, the
graphing calculator will only be introduced to help
students to make calculations faster. But the process of
solving the problem, graphing calculators can't create
their troubleshooting process. Learners will only enter a
command for graphing calculators to process. The
learner does not lose the concept of problem-solving.
2) Suggestions for future research
There should be a study on the effects of using graphing
calculators for calculus teaching at the high school
level, by adding more practical training and spend time
teaching at normal times or inserting in the contents of
one of the courses.
There should be a study on the effects of using graphing
calculators for calculus teaching at the high school level
with high school students in the form of classroom
research or future research.
ACKNOWLEDGMENT
The empirical research for this study was funded by a grant
from Faulty of Sciences, Srinakharinwirot University. Thank
you so much for all Department of Mathematics for your
supports including equipment’s, places, and facilities.
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