# The Learning and Teaching of Linear Algebra Through the Lenses of Intellectual Need and Epistemological Justification and Their Constituents

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## Abstract

*Intellectual need* and *epistemological justification* are two central constructs in a conceptual framework called *DNR*-*based instruction in mathematics*. This is a theoretical paper aiming at analyzing the implications of these constructs and their constituent elements to the learning and teaching of linear algebra. At the center of these analyses are classifications of intellectual need and epistemological justification in mathematical practice along with their implications to linear algebra curriculum development and instruction. Two systems of classifications for intellectual need are discussed. The first system consists of two subcategories, *global* need and *local need*; and the second system consists of five categories of needs: *need for certainty, need for causality, need for computation, need for communication,* and *formalization,* and *need for structure.* Epistemological justification is classified into three categories: *sentential epistemological justification* (*SEJ*)*, apodictic epistemological justification* (*ASJ*), and *meta epistemological justification* (*MEJ*).

## Keywords

Intellectual need Epistemological justification## References

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