Comparative investigation of cognitive and pragmatic thinking modes linear algebra

The analysis focused on the presence of different thinking modes found on the interview and responses to questions related to linear independence, span, and spanning sets of two students taking their first linear algebra course at the college level. The findings provide insight on how first year linear algebra students move from one thinking mode to another. The focal point of this research was to document and discern the similarities and differences between student thinking modes displayed on their interviews and class assignments. Based on the analysis, it was concluded that the level of exposure of the two students to all three different thinking modes types (Analytic-Arithmetic, Analytic-Structural, and Analytic-Geometrical) during their interviews are about the same, but responding to the questions of the assignment are not following the thinking mode types that Sierpinska (2000) established. To measure the influence of the grouping of responses from the two students, we added the frequencies of responses for assignments and interviews for both A24 and A25 for the common categories. Then we performed another frequency analysis using the regression test between the combined assignment and interview categories. The correlation between assignments and interviews was improved compared to the individual test analysis completed between assignments and interviews of each student separately. This increase in correlation is attributed to the increase in the size of the data set by using the responses of combined students in the analysis