Extending example spaces in topology to aid undergraduate students’ transition to generalization and abstraction

Stimulating students to construct knowledge by themselves helps them to experience a more successful transition to the next educational step. Research in university mathematics education suggests that it might be beneficial to introduce undergraduate students to theoretical objects by engaging them in the autonomous construction of example spaces. This approach is generally fruitful, but students sometimes have difficulty in providing counterexamples to false conjectures. Inspired by the “boundary examples” construct, we investigate its potential to overcome these obstacles, through “bridge page” tasks. We present the first findings on the role of bridging examples in reaching generalization and abstraction in topology.