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The primary and secondary school educational system should be stable and any upgrading reforms should be made gradually and consistently. This is especially important in mathematics education, since the element of logical reasoning while learning is more prominent there. Inconsistencies in reforms generate deficiencies in the higher levels of young students’ reasoning skills and this situation continues on the university stage of education. We will report our findings about the reasoning of first-year university students on elements of geometry and associated algebra. We conducted an experiment where students’ understanding of the definition of dot product of two vectors, cosine function and linear (in)dependence of vectors is evaluated, and address their mathematical activity to provide insight into the key elements of the problem they are solving. We use Bloom’s and SOLO taxonomy as a tool for the assessment of our findings. We obtained the data from written exams given to vector algebra students and also from individual interviews.

Analyzing Educational Objectives that Include Critical Thinking: Dot Product Problems in Vector Algebra