An example problem in physics.
The numbers used in the problem and memo were generated randomly by the system.
Click to enlarge.
The numbers used in the problem and memo were generated randomly by the system.
Click to enlarge.
Monassis does intelligent monitoring of learners' conceptual understanding while they practise curriculum-aligned problems on their computer or cell phone. The software can generate any number of questions with the same structure but different details, for example, numerical values in physics problems. This allows much more variety than a traditional question bank — to the extent that a different practise test can be created automatically for each student in a class. The system also generates a memorandum along with each test and tracks the learners' conceptual understanding through their success at answering different types of questions.
Monassis aims to discover the strong and weak points in learners' understanding as the learners are going through worked examples and drilling exam problems. By knowing with which concepts learners are struggling, the system can then do useful things like
The above is done for each learner individually, delivering a customised practise and revision schedule to match his or her pace and understanding.
Templated questions Each test item 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
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 practise for his or her problem areas.
The software and templated question database is currently being prepared for the 2012 South African school year. It will be made available as part of the support material for the freely available Grade 10, 11 and 12 FHSST text books in Mathematics and Physical Science. If you would like to try out the software or for more information, please contact Carl Scheffler at carl@siyavula.com.