P. Salcedo L. ; M. del Valle L.

R. Contreras A. ; M.A. Pinninghoff

Universidad de Concepción

Chile

Chile is located onthe south of SouthAmerica.

Previous ideas

It is a good choice to becompetent using ourlanguage in differentfields orally, writing, ortalking to each others.

Students are in the processof learning the language.Step by step they increasetheir language in terms ofaccuracy.

All the words describing aparticular area ofknowledge are namedLexicon.

It is possible to quantifythe lexical units of alanguage using statisticsindicators.

Each word is a lexicalunit.

LexMath is a tool to study the available lexicon inmathematics (oral and written, not symbolic)

LexMath is created to establish an innovation in theway in which the available lexicon for a group ofstudents is collected.

About LexMath

Using LexMath you can study the latent lexicon of agiven population and to present easily the mainindicators.

tabs

The center of the screen displayinformation about a specific center ofinterest, e.g. geometry

Aboutdescribes LexMath

Surveyallows 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, modifyor delete informationin the platform.

Fig. 2. Semantic structure as a graph.

LexMath allows to visualizesemantic relationships, taking intoaccount the frequency of differentexpressed sequences, when testinglexical available.

Nodes in thegraph are thewords.

The size of each node increases as the number of

time that a word appears in the

answers of a group increases.

Edges indicate thesequence in whichwords are written.

The edge’s thickness increases as the words connected by these edges are written in the same

order.

LexMath allows to delete relationship that are not relevant because it

appears with a low frequency.

STUDENT MODEL

Lexicon in general center (1 to 3)

Lexicon in specificcenter (1 to 7)

DOMAIN MODEL

Teaching activities

EXPERT MODEL

Rules fordetermining

activities accordingto student’s lexicon

Rules for detectingnon available

lexicon

Strategy InferenceEngine

INTERFACE

Lexical Availability Test

Lexical AvailabilityReport and Lexical Availability Index

(words)

Didactic Activities

Report: SemanticRelationships

Models

About the Adaptive Hypermedia Model

Fig. 3. Adaptive Hypermedia Model

Using LexMath you can have access to Gephiand the graphs which enable the study ofsemantic relations between them.

Gephi is an interactive visualization andexploration platform for all kinds of networksand complex systems, dynamic and hierarchicalgraphs.

http://www.gephi.org

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

Instead, you can see strong edges between number -equation - unknown.

We didn’t find words as letter or function or othersrelated to Algebra.

We have a question for the future: Why do studentsremember these words when they are requested towrite words in relation to Algebra?

In the previous slide youcan see that the mostimportant word isnumber.

However, number is nota main word in this area.

Lexmath’s applicationsIn Concepción (Chile) was conducteda research about lexical analysissupported by LexMath.

The hypothesis is that there existdifferences in the vocabularyassociated to the field ofmathematics, according to thedifferent socio-economical levelpresented in the EducationalInstitutions

The goal of this research was toanalyze the lexicon and semanticnetworks on a sample of high schoolstudents.

ConclusionsLexMath is faster than others statisticsprocedures.

The mentioned hypothesis wasconfirmed: there exist differencesin semantic networks for identicalcenter of interest when consideringsocial-economical background instudents.

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.

Acknowledgement

This work is supported by the Chilean National Fund for Scientific and Technological

Development, FONDECYT, through research project number 1140457