Y. KONGTHIP ET AL.
We get this picture, don’t we? Then, we can put it here. Is it
a rectangular? Well, let’s see our friend’s. At first, our friend
cut it like this. How many channels are there? There are six
According to the Episode in Item 393-398 as the above, in
Item 393, the teacher asks the students to explain why do they
get six channels the same. The student explain picture (d) as
Item 394, (cross the picture. Then paint it). The gesture is
iconic. As the Item 398, the teacher shows the Group’s per-
formance for their friends to consider again. According to the
above Episode, it could be seen that the student uses gesture in
concise messages in Mathematical Communication. So, the
participants have common understanding. It could be concluded
that it is Economically Mathematical Communication by stu-
dent’s iconic gestures.
Conclusion and Discussions
The research findings found that there were 7 kinds of stu-
dents’ Mathematical Communication by students’ Gestures
including 1) rigorousness by students’ beat gesture-Mathematical
Communication in which the students wanted to emphasize the
statements or pictures as their own ideas, or communicate with
their friends or teacher; 2) rigorousness by students’ metaphoric
gestures—gesture referring to content or concepts of the lesson;
3) economy by students’ deictic gesture—this kind of gesture
could be easily performed economically with common under-
standing; 4) economy by students’ iconic gesture—this kind of
gesture was to draw a picture to communicate economically
with each other for common understanding; 5) freedom by
stu dents’ deictic gesture—the students used various kinds of point-
ing, and had freedom to express their mathematical ideas; 6)
freedom by students’ iconic gesture—the students could use
many kinds in drawing picture as well as have freedom to ex-
press their mathematical ideas; and 7) freedom by students’
deictic and iconic gestures—the students used both of pointing,
and drawing picture to communicate their ideas as well as had
freedom in express their mathematical ideas, and the most
commonly used the characteristic of economically mathematical
communication by deictic gestures, and Students’ self learning
through problem solving while the teacher take notes students’
idea for later discussion in Open Approach. The teachers used
gestures for observing students’ learning in the classroom and
students had happiness in the classroom. Furthermore, the
schools in Lesson Study and Open Approach context, the stu-
dents had opportunity in learning based on their potentiality,
being able to think, perform, and express. They preferred to
express divergent think.
The teachers and Educational Staffs could use the behavioral
or gestures observation technique in learning of students during
they expressed Mathematical Communication with each other
meaningfully which was an evaluation from the students’
working process. In addition, their gestures could be able to be
used in reasoning, explaining, and analyzing their performance,
concluding their approaches, and evaluating their emotion or
feeling during learning. Specifically, under Lesson Study, and
Open Classroom situations, the students had freedom in ex-
pressing their ideas in various ways including both of verbal,
and gestures meaningfully with themselves. We implement this
result through pre-service teachers to bring this knowledge
working group with teachers in schools and teacher learned
these knowledge and I will write article to publish this result.
The studies of students’ Mathematical Communication by ges-
tures in other class levels should be studied further. And each
academic year had trained pre-service teachers about new
knowledge to bring this knowledge working group with teach-
ers in schools.
This study was fund by the Commission on Higher Educa-
tion, Thailand, and Graduate school, Khon Kaen University,
and was supported by Center for Research in Mathematics
Education (CRME) and Srinakharinwirot University.
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