The paper reflects on the author’s experience of teaching mathematics education courses to teacher candidates using technology. It demonstrates both explicit and hidden presence of asymmetry among the topics included in the courses and shows what it brings to the study of mathematics for teaching by future teachers of the subject matter. Examples associated with asymmetry deal with pizza sharing, an irrational inequality, a quadratic equation with parameters the loci of which exhibit asymmetry, and asymmetrical modification of Pascal’s triangle leading to Fibonacci-like polynomials the roots of which alternate symmetrical and asymmetrical location within a certain interval on the number line. The examples presented in the paper are supported by digital tools including dynamic geometry programs, Wolfram Alpha, Maple, a spreadsheet and the graphics of Microsoft Word. The paper argues for the importance of the modern-day computational tools in revealing conceptually rich structure of mathematics, including the interplay between symmetry and asymmetry, to future K-12 teachers of the subject matter. Several reflective comments of the teachers on their learning experiences to teach mathematics conceptually in the technological paradigm are shared and analyzed.