Culturally Aware Mathematics Education Technology

Culturally Aware Mathematics Education Technology

Erica Melis (German Research Center in Artificial Intelligence (DFKI GmbH), Germany), Giorgi Goguadze (University of Saarland, Germany), Paul Libbrecht (German Research Center in Artificial Intelligence (DFKI GmbH), Germany) and Carsten Ullrich (Shanghai Jiao Tong University, China)
DOI: 10.4018/978-1-61520-883-8.ch025
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Abstract

Education and learning take place in a situation that is heavily influenced by the culture. The learners’ cultural context affects cognitive processes in learning. Hence, to improve the conditions for learning, e-learning environments and their contents have to interact with the learner in a culturally appropriate way. Therefore, an e-learning system intended for cross-cultural usage has to adapt to the students’ diverse cultural background. For the enculturation of the European platform for mathematics learning, ActiveMath, a number of dimensions are adapted culturally. These are: presentation of system and learning material, terminology, selection and sequencing of learning objects, interaction, and learning scenarios. This chapter describes ActiveMath’ enculturation: computational model, computational techniques, and the empirical basis for the cultural adaptation.
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Motivation And Theoretical Background

One of the grand challenges in European TEL research focuses on technologies for learning that will be designed for culturally diverse and cross and intercultural settings.

Enculturation is not only important for tutoring systems that teach cultural relationship, geography, culture, and behaving appropriately in other countries, etc. such as the cultural training system Alelo1 but also for mathematics learning environments. At first, mathematics education may seem to be an unlikely field for enculturation.

However,

  • Mathematics education often follows the terminology (notions) of a particular book dominant in the region’s education or of a field that applies mathematics, e.g., electrical engineering

  • In the region’s or field’s mathematics education more often than not specific notations is used

  • Educationalists and teachers emphasize the cultural context and for teaching mathematics they follow the curriculum pre-scribed for their region and type of school

  • Educational psychologists and pedagogues emphasize the importance of posing authentic mathematical problems, which are relevant in the student’s life environment. This aspect is typical for a more constructivist-learning paradigm (Schifter, 1996; Fosnot, 1996).

Theoretical Background

In addition, at the level of cognitive processes Piaget’s theory of learning implies that learning heavily depends on the context and experience of the learner. Piaget’s influential theory of learning introduces two fundamental cognitive functional processes in learning: assimilation and accommodation (Piaget, 1947; Piaget, 1977).

Assimilation and accommodation are two complementary processes of adaptation in the learner’s mind through which awareness of the outside world is internalized. They are inseparable and exist in a dialectical relationship. In assimilation, what is perceived in the outside world (in the context) is incorporated into his/her mind without changing its structure. In accommodation, the mind accommodates itself to the evidence/context with which it is confronted and thus adapts to it.

An immediate implication of this theory is that the learner’s context including its cultural determination is reflected in the learning process (and in its adaptation efforts). Assimilation requires more effort when the external and internal (mind) features differ more. Accommodation can include adaptation leading to more correct mathematical schemes/mind structures but also adaptation to cultural differences that are mathematically not as deep. Both types of adaptation yield cognitive load, but the cognitive load for a mathematically rather shallow adaptation is extraneous and may hinder learning.

From a theoretical point of view it has also been defined which (different levels of) cultural groups are relevant for enculturation in (mathematics) learning. It isn’t only the region/country/language that requires enculturation but also communities of practice (CoP), which can be a group inside another or a group orthogonal to a region/country/language group, e.g., chemistry or electrical engineering students. Wenger (Wenger, 1999) acknowledges that (learning) practices are influenced by context(s) and that the internal dynamics of a CoP including its norms (part of a culture) are determined by the practices such as ’negotiation of meaning’ (i.e., understanding of mathematical notions and notations), ’learning’, as well as ’community actions’ (e.g., book publishing, conferences), and ’differentiation from other communities of practice’. Any CoP produces abstractions, symbols, stories, terms, and concepts that reify something of its practice in a congealed form. Note that even cultural variations whose nature appears to be linguistic such as notations and notions have a cultural (often historical) background. Reasons for such differences can originate from a dominant group of mathematicians in history and cultural ties to that group in certain countries, regions, and groups. A similar development (maybe not yet for mathematics) is observable today for communities of practice, e.g. users of email or SMS.

For cultural differences present in language-defined communities, a reason may be that in mathematics the history of schools, research, teacher education, popular books which influence the education culture go back to a language-defined culture that was present before today’s countries existed.

Key Terms in this Chapter

Student Model: component of a Learning Environment (or an ITS system) that collects information about student’s learning progress. In ActiveMath the learning progress is represented by mastery values for pairs “domain concept-cognitive process”. In ActiveMath, domain concepts are represented as nodes in the domain ontology and cognitive processes can be represented using different taxonomies of cognitive processes (e.g. PISA, revised Bloom).

Adaptive Course Generation: selection of learning objects according to the learning goal, which is represented by one or more domain concepts and pedagogical scenario to be used. Selection of learning objects is adapted to various parameters of the learner and his previous learning progress.

Enculturation of Learning Materials: the adoption of the content, way of sequencing, and presentation of learning objects to the local culture.

Automated Sequencing of Learning Objects: arranging learning objects into bigger learning items representing courses or learning paths according to an automated sequencing scenario.

Input Editor (or Formula Editor): refers to editor for mathematical formulas. Formula editors can be ‘inline’ using linear syntax (specific non-ambiguous 1 dimensional syntax like ones used in Computer Algebra Systems), or graphical (2-dimensional) and posses palettes with templates for mathematical expressions.

Semantic Knowledge Representation: In case of learning materials semantic knowledge representation refers to an ontology of learning objects annotated with metadata information allowing intelligent management of learning objects by search and retrieval tools of a learning environment. In some cases, the microstructure of learning objects also contains semantic information (e.g. Content MathML or OpenMath representation for mathematical formulas).

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