Addressing the incommensurability between state-administered, standards-based exams in mathematics, and the assessment-mediated problem solving exercises required to support coherent and progressive learning and teaching in the classroom

Seminar | November 17 | 2-4 p.m. | 2515 Tolman Hall

Speaker/Performer: Bernard R. Gifford, UC Berkeley

Sponsor: Berkeley Evaluation

I will be discussing a novel ensemble of enabling technologies, designed and built from the ground up to translate into practice the vision of assessment guided learning and instruction in the content area of mathematics articulated by the architects of No Child Left Behind (NCLB). These architects imagined that teachers, administrators, and policymakers would eventually learn to leverage the student performance data generated by State-administered exams to customize and target evidence-based instructional resources and interventions to those students most in need of this type of support. The ensemble, Learning Conductor: Mathematics (“Conductor”), incorporates a quartet of interrelated technologies:

1) Item Generator (I-GEN) employs sophisticated parameterization techniques to transmute the proven psychometrically valid but highly compacted assessments incorporated in State-administered end-of-year exams into the stream of similarly valid, but more finely tuned and less compact classroom oriented assessment items needed to evaluate the effectiveness of the finite sequences of instructional activities deliberately scored and orchestrated by teachers to help students achieve targeted levels of proficiency in specific strands of the mathematics curriculum.

2) Problem Generator (P-Gen) generates solutions to the mathematics assessment items generated by IGEN in the form of elaborated “Worked-examples,” a problem-solving format shown to be significantly effective in increasing student mathematical proficiency. P-Gen also dynamically generates geometrically mathematical representations to complement these worked-examples, another capability proven to be effective in increasing student mathematical proficiency.

3) Open Communications (O-Gen) is a collection of Open-Source communication and collaboration resources architected to make the assessment/Worked-example couplets (“Couplets”) generated by I-Gen and P-Gen accessible to students, teachers, schools, public libraries, public housing learning centers, and other education-minded community-based organizations on a location-independent basis.

4) Open Source relational database application (D-Gen) is architected and programmed to track the actions of individual students, as they negotiate the mathematical couplets generated by I-Gen and P-Gen. D-Gen can be used to produce progress reports that will make it clear to students the influence of their assessment-based problem-solving activities on their growth as capable mathematics learners. D-Gen’s report generation capabilities can also be used to provide teachers the kinds of data they will need to adjust their own teaching practices to take into account the assessment-guided learning activities of their
students.

I will discuss the origins and development of Learning Conductor, and more, importantly, the theory of assessment-guided learning and teaching that is beginning to emerge from these efforts to address the incommensurability of end-of-term and everyday classroom assessment items. I will also discuss how Learning Conductor can support the i) creation and evaluation of novel assessment items; ii) buttressed recent theories on “learning progressions” with empirical evidence; iii) support ongoing efforts redefine and reconstitute mathematics homework; and, iv) support the efforts of teachers working in educational settings characterized by a high degree of student heterogeneity.

Event Contact: dlsmith@berkeley.edu, 510-642-7984