The Trade-Off between Complexity and Accuracy. Preparing for Computer-Based Adaptive Instruction on Fractions

PS-I learning approaches with an initial problem-solving phase (PS) followed by an instruction phase (I) can be optimised by providing adaptive (individualised) instruction that builds on students' problem-solving products. A computer-based implementation of both phases offers the possibility of adaptivity at the transition from the problem-solving to the instruction phase. However, it also poses two challenges for the problem-solving phase, which should allow for (1) complex problem-solving processes (process validity); and (2) accurate diagnosis of problem-solving products. Increased openness of the learning environment can increase the process validity and decrease diagnostic accuracy and vice-versa (complexity-accuracy trade-off). Using two variants of a computer-based learning environment for fraction comparison with different extent of openness (O+ and O-), we investigate whether both requirements (complex problem-solving processes and accurate diagnosis of the problem-solving products) can be met simultaneously. To check process validity (complexity of problem-solving processes), we compare the problem-solving products with those from previous research on an analogous paper-based version. Our results show that valid and comparable problem-solving processes can be achieved in both computer-based learning environments (O+ and O-). Moreover, only the learning environment O- enables an accurate computer-based interpretation of students' products and thus resolving the complexity-accuracy trade-off.