Paul Ernest (1995) in his description of the many schools of thought of constructivism suggests the following implications of constructivism which derive from both the radical and social perspectives:
1. sensitivity toward and attentiveness to the learner's previous constructions;
2. diagnostic teaching attempting to remedy learner errors and misconceptions;
3. attention to metacognition and strategic self-regulation by learners;
4. the use of multiple representations of mathematical concepts;
5. awareness of the importance of goals for the learner, and the dichotomy between learner and teacher goals;
6. awareness of the importance of social contexts, such as the difference between folk or street mathematics and school mathematics (and an attempt to exploit the former for the latter) (p.485).