The document discusses lexmath, a tool designed to analyze and collect lexicon in mathematics among students in Concepción, Chile. It highlights the effectiveness of lexmath in measuring lexical units and semantic relationships, revealing differences in vocabulary associated with mathematics based on students' socio-economic backgrounds. The research confirms that students from lower socio-economic levels demonstrate less lexical availability, with gephi used for visualizing semantic networks.

1. P. Salcedo L. ; M. del Valle L.
R. Contreras A. ; M.A. Pinninghoff
Universidad de Concepción
Chile

2. Chile is located on
the south of South
America.

3. Previous ideas
It is a good choice to be
competent using our
language in different
fields orally, writing, or
talking to each others.
Students are in the process
of learning the language.
Step by step they increase
their language in terms of
accuracy.

4. All the words describing a
particular area of
knowledge are named
Lexicon.
It is possible to quantify
the lexical units of a
language using statistics
indicators.
Each word is a lexical
unit.

5. LexMath is a tool to study the available lexicon in
mathematics (oral and written, not symbolic)
LexMath is created to establish an innovation in the
way in which the available lexicon for a group of
students is collected.
About LexMath
Using LexMath you can study the latent lexicon of a
given population and to present easily the main
indicators.

6. tabs
The center of the screen display
information about a specific center of
interest, e.g. geometry

7. About
describes
LexMath
Survey
allows the students to
write the words they
think, related to an
interest center in a time
interval of two minutes
Activities proposes
the activities that
are more suitable to
the lexicon the
students holds (in
an adaptive way)
Reports permits to display a
table for showing the lexical
availability (list of words
ordered according to the LAI,
related to a specific question)
Administration
(a restrictive option)
allows to add, modify
or delete information
in the platform.

8. Fig. 2. Semantic structure as a graph.
LexMath allows to visualize
semantic relationships, taking into
account the frequency of different
expressed sequences, when testing
lexical available.

9. Nodes in the
graph are the
words.
The size of each
node increases as
the number of
time that a word
appears in the
answers of a group
increases.
Edges indicate the
sequence in which
words are written.
The edge’s thickness increases as
the words connected by these
edges are written in the same
order.

10. LexMath allows to delete relationship
that are not relevant because it
appears with a low frequency.

11. STUDENT MODEL
Lexicon in general
center (1 to 3)
Lexicon in specific
center (1 to 7)
DOMAIN MODEL
Teaching activities
EXPERT MODEL
Rules for
determining
activities according
to student’s lexicon
Rules for detecting
non available
lexicon
Strategy Inference
Engine
INTERFACE
Lexical
Availability Test
Lexical Availability
Report and Lexical
Availability Index
(words)
Didactic Activities
Report: Semantic
Relationships
Models
About the Adaptive Hypermedia Model
Fig. 3. Adaptive Hypermedia Model

12. Using LexMath you can have access to Gephi
and the graphs which enable the study of
semantic relations between them.
Gephi is an interactive visualization and
exploration platform for all kinds of networks
and complex systems, dynamic and hierarchical
graphs.
http://www.gephi.org

13. Fig. 4. Semantic relationships for the center of interest Algebra.

14. Instead, you can see strong edges between number -
equation - unknown.
We didn’t find words as letter or function or others
related to Algebra.
We have a question for the future: Why do students
remember these words when they are requested to
write words in relation to Algebra?
In the previous slide you
can see that the most
important word is
number.
However, number is not
a main word in this area.

15. Lexmath’s applications
In Concepción (Chile) was conducted
a research about lexical analysis
supported by LexMath.
The hypothesis is that there exist
differences in the vocabulary
associated to the field of
mathematics, according to the
different socio-economical level
presented in the Educational
Institutions
The goal of this research was to
analyze the lexicon and semantic
networks on a sample of high school
students.

16. Conclusions
LexMath is faster than others statistics
procedures.
The mentioned hypothesis was
confirmed: there exist differences
in semantic networks for identical
center of interest when considering
social-economical background in
students.
It is important to note that students with a lower social-
economical level show less nodes and edges.
Gephi is an important tool to describe semantic relations.

17. Acknowledgement
This work is supported by the Chilean National
Fund for Scientific and Technological
Development, FONDECYT, through research
project number 1140457