Mathematics Learning Instrument: A Correlation and Means Difference Comparison with Federal Accountability Algebra Test Scores

Abstract

Mathematics learning outcomes have specific cognitive development implications [2], [9]. Key contributions in ‘structure sense’ studies build upon a theoretical manuscript detailing a conceptualization of ‘thinking mathematically’ using symbols (i.e. ‘symbol sense’) [1], [6], [12], [13]. Likewise, from a theoretical basis, this manuscript reports and extends an initial conference presentation of the instrument: Algebra Concept Inventory to Measure Metric Sense (ACIMMS) [14]. This paper includes the complete instrument as well as developmental details, particularly; (a) a definition of ‘metric sense’ [9], (b) specific roles of mini-experts in Second Generation Instructional Design (ID2) [11], and, (c) creates a mathematics instrument using ‘metric sense’ to inventory five subject specific domain knowledge base items [5]. Selected applications of the instrument’s constructs are illustrated in equations conventionally found in trigonometry and statistics courses. Upper classmen from a United States high school form a sample for a correlation and means difference study between federal accountability exam scores and ACIMMS algebra instrument data. Confirmed are findings from a bounded literature review [9], that concurrent use of all five metric sense conceptualizations are not extensively utilized by secondary students in manipulating mathematical expressions [6]. Despite time discrepancies of up to three years between results of ACIMMS instrument data and independent federal algebra accountability exam scores, a significant positive correlation is found. Correct answers on each instrument question, which forms two respective groups of students’ independent algebra accountability exam scores, reveal a clear need for students’ persistent understanding of all five metric sense conceptualizations. Recommendations are made for teaching and further mathematics learning investigations.