A Qualitative Synthesis of Algebra Intervention Research

Completion of a quality Algebra course by 8th grade is a prerequisite for successful entry into STEM majors; thus best practices in this critical course must be as equitable as possible to support STEM recruitment and retention. However, if the research base for Algebra is under-examines some populations of students, structural inequity may be unintentionally built into evidence-based practices. The purpose of this synthesis is to examine the ways in which qualitative Algebra strategy research did –or did not- account for equity issues including gender, SES, rural students, special education status, ethnicity, and native language through theoretical and participant choices. This synthesis used qualitative research integration techniques to provide a summary of fifty-eight qualitative investigations of Algebra 1 teaching strategies. The majority of studies specified constructivism, social constructivism, and situated cognition theoretical frameworks or did not specify a theoretical framework. The majority of research questions addressed the effectiveness of a particular pedagogical technique or intervention. Results suggest that the majority of study participants were Caucasian students from suburban localities and did not include sufficient detail necessary for replication.

Integrating Expert Knowledge in Cereal Food Manufacturing Processes

We present a procedure of knowledge representation based on a qualitative algebra, to predict the wheat flour dough behaviour from mixing settings. The procedure guarantees the consistency of the knowledge base and provides a concise and explicit representation of the knowledge. The qualitative model is implemented as a knowledge-based system (KBS) accessible and understandable by scientists and technologists in breadmaking. The KBS is a record of the domain knowledge, mainly know-how, and a tool to confront predictions of the dough condition with real observations. An example of such a confrontation about the wheat flour dough mixing process is shown; the results gives insight into ill-known relations between the process settings and the dough condition.

A constraint-based approach for qualitative matrix structural analysis

Qualitative physics, a subfield of artificial intelligence, adapts intuitive and non-numerical reasoning for descriptive analysis of physical systems. The application of a set-based qualitative algebra to matrix analysis (QMA) allows for the development of a qualitative matrix stiffness methodology for linear elastic structural analysis. The unavoidable introduction of arithmetic ambiguity requires the reinforcement of physical constraints complementary to standard matrix operations. The overall analysis technique incorporates such constraints within the set-based framework with logic programming. Truss, beam, and frame structures demonstrate constraint relationships, which prune spurious solutions resulting from qualitative arithmetic relations. Though QMA is not a panacea for all structural applications, it provides greater insight into new notions of physical analysis.