TEACHER PEDAGOGICAL AND CONTENT KNOWLEDGE FOR AUTHENTIC ASSESSMENT IN MATHEMATICS

Design based research methodology aims to enrich teacher and student learning through successive cycles of instructional design and planning, on-going analysis of classroom events and retrospective analysis. Often what gets designed is a whole "learning environment" with tasks, which include authentic assessment tools. The authenticity of the assessment has been defined as a multifaceted concept, which accounts: the authenticity of the task; the physical context dealing, with special importance to the technological one; the social context; the assessment as a result or a form and the criteria used for the assessment. These five facets have allowed identifying the critical elements that can be applied when analysing the authenticity of the assessment of a task. In this paper, the assessment tools considered are the teacher and student portfolios. The teacher portfolio includes the different designs and on-going plans of the authentic task, the materials and technological tools designed, the rubrics developed as a criterion-reference in coherence with the curricular guidelines and the teacher classroom diary. The student portfolio includes the paper and digital products of the students, which reveals the process of learning, including some audio and video recordings of individual and collaborative work. In order to retrospectively analyse the interconnections between the teacher and student portfolio, we consider the Technological Pedagogical and Content Knowledge. The Technological Pedagogical Content Knowledge has been enriched through the integration of its seven constructs with the five multifaceted concepts of authentic assessment. This theoretical integration has allowed to: (a) design the categorization matrix of Technological Pedagogical Content Knowledge for authentic assessment of teacher and students portfolios in mathematics education; (b) establish the correspondence between the criteria and requirements to design authentic assessment tools for mathematics and the technological pedagogical content knowledge needed; and, (c) present a list of heuristics to help mathematic teachers to evaluate the authenticity of the assessment tools designed.