Abstract:

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 (Gulikers, Bastiaens, & Kischner, 2004). These five facets have allowed identifying the critical elements that can be applied when analyzing the authenticity of the assessment of a task [15] (Ashford-Rowe, Herrington, & Brown, 2014).

Those critical elements and requirements for authentic assessment are:
(R1) authentic assessment should be challenging for the student;
(R2) the outcome of an authentic assessment should be in the form of a performance or product;
(R3) authentic assessment design should ensure transfer of knowledge;
(R4) metacognition as a component of authentic assessment;
(R5) the importance of a requirement to ensure accuracy in assessment performance;
(R6) the role of the assessment environment and the tools used to deliver the assessment task;
(R7) the importance of formally designing in an opportunity to discuss and provide feedback; and
(R8) the value of collaboration. 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 (Mishra and Koehler, 2006). The model defines PCK in a consistent and similar manner to Shulman’s idea of knowledge of pedagogy and content; thus, it also characterizes other knowledge (such as: technological content knowledge (TCK) and technological pedagogical knowledge (TPK) with the aim of integrating the technological pedagogical content knowledge (TPCK)). In this paper we present how 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 present:
(a) the system of categories of Technological Pedagogical Content Knowledge for authentic assessment of teacher and students portfolios in mathematics;
(b) establish the correspondence between the criteria and requirements to design authentic assessment tools for mathematics and the technological pedagogical content knowledge needed by the teachers;
(c) present a list of heuristics to help mathematics teachers to evaluate the authenticity of the assessment tools designed.

Keywords:

Technological Pedagogical Content Knowledge, Authentic Assessment, Mathematics, Portfolios, Methodological principles.