Proofs

EXAMPLE 3: REAL ANALYSIS

This example shows a criteria based assessment approach for a unit that has an emphasis on proof. Context: MATHS202 is a second year unit for students intending to continue their study of mathematics. The learning outcomes of the unit include developing an appreciation for rigour in mathematical proof and understanding the theory behind concepts like Riemann integration, which students will already be familiar with at a procedural level. The assessment of this unit includes six assignments with an emphasis on writing rigorous mathematical proofs, using theorems and definitions to justify arguments, and developing communication skills. The example under consideration covers most of these learning outcomes.

Juanita is the coordinator of MATHS202. After teaching the same subject in the previous semester, she realised that there are so many ways that students can write a proof for any question, that her marking scheme and instructions to her tutors needed to be broad. For MATHS202, the assignments were designed to build students’ ability to use definitions and theorems, and to apply conceptual understanding to construct a proof. However, many also included some questions that required students to do some calculations.

Juanita thought that criteria based assessment seemed very appropriate in this setting. Developing and annotating a solution, Juanita reflects on her process:

“First, I clarified the learning outcomes of the unit. Then I determined the aspects to be assessed (and their relative importance) and developed a marking/grading scheme. Finally, I communicated to the students how their work would be assessed (and let the markers know about this, too).” Read more about Juanita ’s process and the annotated solution for markers she created in Example 3: Real analysismathsassess guide [PDF – 6.2 MB]

Create your own rubrics by editing Example 3: Rubrics [Word – 20k]