I'm developing software that will allow learners to practice exam questions through a browser or their mobile phone. This is only the outside layer of the project though. What it is

*really* about is mapping learners' success at answering questions to their understanding of the concepts underlying those questions. By knowing with which concepts learners are struggling, the system can then do useful things like

- providing more practice on the types of questions with which the learner is struggling;
- recommending revision material to the learner from freely available educational resources (for example, see the Free High School Science Texts);
- providing feedback/reports to learners (and possibly teachers and parents) about their progress and about the specific concepts to which they should pay more attention.

All of the above is done per individual learner. In this sense the system is delivering a customised practice and revision schedule for each learner.

How will it work?
**Templated questions** Each test item (question) is described as a

*template*. A template is a generalisation of a particular question, where the details of the question -- such as numbers and some of the structure -- can be different in each

*instance* of the template. For example, a template for solving quadratic equations with integer roots might produce the following set of questions.

Solve for \(x\). Write the two solutions, separated by a comma. Example: 2,-3

- \(x^2 - 5x - 6 = 0\)
- \((1-x)(10-x) = -8\)
- \(x^2 - 21 = -4x\)

Note that the numbers and factorisation of each question are different, while the overall structure (quadratic with integer roots) is the same.

**Concept map** Test questions are designed to test subject-specific concepts. Furthermore, concepts typically require prior understanding of other concepts — covered earlier in the curriculum — for proper understanding. By incorporating the question-to-concept and concept-to-concept dependencies into the system, it can infer with which concepts learners are struggling based on their ability to answer test questions.

**Inference** This is where all the clever stuff happens. Based on the mapping of questions to concepts, the data collected of learners' responses to questions, and some mathematical modelling, the system estimates each learner's proficiency at each of the concepts in the curriculum. This information can be reported / visualised to give learners and teachers an indication of mastery and problem areas. More importantly, knowledge of a learner's mastery of concepts allows the system to provide targeted review material or additional practice for his or her problem areas.