The Group Theory Concept Assessment (GTCA) is a multiple-choice measure designed to capture conceptual understanding at the introductory group theory level.

The GTCA covers: binary operation, associative property, commutative property, identity, inverses, groups, order of elements, subgroups, homomorphism, isomorphism, kernels, normal groups, cosets, quotient groups, cyclic groups, Lagrange’s Theorem, First Isomorphism Theorem.

The GTCA is available online. Additionally, for interested instructors, there is a companion website containing:

• national results for each question
• a breakdown of what your students may be thinking for each multiple-choice option
• links to relevant research on student thinking to learn more

If you are interested in using the GTCA for your class or your research, contact: melhuish@txstate.edu.  

The GTCA was developed and field-tested through a rigorous multi-stage approach:

(1) A panel of experts identified the most essential topics in introductory group theory
(2) The most commonly used textbooks were identified and analyzed in terms of these relevant topics
(3) The mathematics education literature was searched to identify any established ways students think about this topics
(4) A set of relevant open-ended tasks were developed, analyzed by experts in the field, and refined
(5) Open-ended tasks were piloted, refined, and administered to nearly 400 group theory students + 15 students were interviewed about their responses
(6) Open-ended tasks were converted to multiple-choice versions were options reflected most common student responses
(7) Multiple-choice version was piloted, refined, and field-tested with hundreds of additional students + 15 students were interviewed about their responses