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Computer Algebra and Dynamic Geometry in Mathematics Education
7-10 September, 2016 Targu Mures, Romania
CADGME
2016
The Effectiveness of Kinesthetic Approach in Developing Mathematical
Function Graphs Recognition and Understanding at University Level
Mohamed El-Demerdash1, 2
, Pedro Lealdino Filho1
, Christian Mercat1
1
Claude Bernard University, Lyon 1 (France), 2
Menoufia University (Egypt)

Outline
1. Introduction
2. The Development of Kinesthetic Digital Resources
3. The Development of Recognition Test
4. Method and Procedures
5. Results
6. Conclusion
2

Outline
1. Introduction
5. Results
6. Conclusion
3

Introduction Main 3 Hypotheses
● Involving other senses, than the usual reading and listening, in learning
might lead to better learning, engagement and motivation of particular
subjects.
● The use of the kinesthetic approach would develop students’ recognition
and understanding of mathematical function graphs.
● Some students might need to use other senses as a preparation to
abstract and symbolic thinking at University and Undergraduate levels.
4

Outline
1. Introduction
5. Results
6. Conclusion
5

The Development of Kinesthetic Digital Resources
6

7

● Microsoft Kinect Sensor.
● Unity 3D Development Kit.
● Microsoft Kinect Software Development Kit.
● CindyScript: A programing language associated with Cinderella (DGS).
● UDP (User Datagram Protocol).
8

Outline
1. Introduction
5. Results
6. Conclusion
9

The Development of Recognition Test
10
Function Type No. of Items %
Constant function 2 10%
Linear function 2 10%
Quadratic function 2 10%
Cubic function 2 10%
Square root function 2 10%
Absolute value function 2 10%
Fractional function 2 10%
Trigonometric function 2 10%
Exponential function 2 10%
Logarithm function 2 10%
Sum 20
% 100%

Outline
1. Introduction
5. Results
6. Conclusion
11

Method and Procedures
1. Subjects
● The setting for the experimental study was at CFAI Savoie Chambéry.
● CFAI is a college training for careers in industry for young people, employees and
companies. It offers quality training to industrial companies.
● The enrollment of this college is approximately 280 students. The subjects of the
study were 51 students of the first year of Maintenance of Systems and Technical
Assistance engineers.
12

2. Experimental Design
● The pre-experimental one-group, pretest – intervention – posttest design was used
to investigate the effectiveness of the prepared kinesthetics digital materials in
enhancing the students’ recognitions of mathematical function graphs.
13

3. Before Intervention
● The researchers prepared two computers connected with two Microsoft Kinect
sensors in order to get kinesthetic feedback from the students. Cinderella and
Unity 3D Development Kit are also installed so that the software recognizes
students’ body gestures as input representations for mathematical function
graphs.
● The researchers met with the subjects of the study explaining to them the aims, the
nature of the study, what is required from them during the study (Starting from the
pretest, going through administering dancing as a “Function Hero” game, and
ending with the posttest) and what is expected from them by the end of the
experimentation.
14

4. Administering the Pretest
● The recognition pretest was administered to the study subjects as a pretest at the
beginning of the experimental study to assess their recognition of mathematical
function graphs. The subjects were informed that the duration of the pretest is ten
minutes.
15

5. Administering the “Function Hero” Game
● The class was divided into two groups of students according to their side in the
classroom (left or right). At first, as a warm up, two different sets of functions were
used and each group was subjected to a given set of functions. Each student got a
score according to his performance.
● Then the students edit the choreography and enter the functions of their choice.
16

5. Administering the “Function Hero” Game
● Students used their handheld calculators in order to propose functions to their
group. They tried to enter complicated functions that the other team would not
know or would not be able to perform. But it appeared to be complicated and
difficult to them as well, so most of them went back to propose simple functions.
● Afterwards, the first team perform their own choreography, then the second team
trying to get comparable scores. A comparison of the scores for the two teams
elected a winner team and an overall winner of the game. Small prices were then
distributed.
17

6. Administering the Posttest
● The recognition posttest was administered to the study subjects as a posttest at
the end of experimental study to assess their recognition of mathematical function
graphs after administering the “Hero Function” game. The subjects were also
informed that the duration of the pretest was ten minutes.
● We should have waited for the completion of the post-test before giving away the
prices because the students lost interest and were not eager to have their posttest.
18

7. Researchers’ Notes During the Experimentation
● As the subjects of this study are in a technical school, they are not particularly
interested in maths, but the playfulness of the activity proposed engaged them in
the action, even very weak students, usually very passive, tried to play and they all
enjoyed the game.
● The students have generally difficulties with abstraction, they are not used to
create mental representations. The challenge has stimulated their curiosity, they
explored new representations and they were happy to discover their algebraic
expressions, according to one of their teacher.
19

7. Researchers’ Notes During the Experimentation
● The subjects were not that interested in the posttest because they had their break
just one or two minutes before this test, they were in a hurry to go out. Then, they
confessed that they didn’t actually care for their answers, hence the results of the
posttest didn’t bring anything to the fore.
20

Outline
1. Introduction
5. Results
6. Conclusion
21

Results
22
● The pretest and posttest approach proved of no use in our context: the measured
learning gain is significantly negative, not correlating with the observation of their
great engagement in the game and the good game scores that even weak students
got. The anticipation of the graph of the function has to be anticipated from its
algebraic expression in order to get such high scores.
● The pre posttest comparison doesn’t prove this qualitative data we have collected.

Results
23
● Most elaborated functions were given by higher achieving students while lower
achieving students, were not concerned much with producing new algebraic
expressions but they were more concern in participating in the game and
performing the dance.
● A fourth result was the heavy use of hand-held calculators to propose
mathematical graphs that were then tested in the game.

Outline
1. Introduction
5. Results
6. Conclusion
24

Conclusion
25
● The game was very engaging for students, pleased and motivated them to
represent and propose some mathematical function graphs.
● The results are not conclusive, the experimentation needs to be repeated
in a context where the didactical contract ensures motivation for the
post-test.
● New experimental protocol is being considered in order to answer the
research questions including recognition and understanding.

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The Effectiveness of Kinesthetic Approach in Developing Mathematical Function Graphs Recognition and Understanding at University Level

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