Fung and coworkers have managed to do such as study and their findings are published in the International Journal of Education Research. No correlation is found between either a teacher's SMK or PCK and student performance in mathematics. It appears that knowing more mathematics may only be a prerequisite to teach mathematics effectively. In schools of high performing students, something additional seems to be required.
Fung and coworkers have found an additional teaching characteristic that actually correlates with learning outcomes for Hong Kong grade 4 pupils and teachers. They call this factor "pedagogic efficacy (PEf)". PEf is defined as "a teacher’s expectation that he or she will be able to bring about student learning". In this study, PEf is measured using a survey and sample questions are shown below:
Sample PEf questionsThinking about your present class please rate your ability to teach the following topics in mathematics at P4 level (circle the number that best corresponds to how you feel – leave the row blank if your class doesn’t work on this topic)PEf is about confidence, self-confidence. With sufficient subject matter and pedagogic content knowledge, a teacher can actually prophesy if his or her teaching will bring a positive outcome or not.
1very poor(I hate teaching this - most pupils find this difficult and so do I) 2not great(I don’t look forward to this – there are always problems for some) 3OK(I’m ambivalent – we just do it and no-one gets that excited) 4good(I quite enjoy this – most pupils get it and like working in this) 5excellent(I love teaching this – pupils get it, have fun with it and so do I!) 1 place value /num. systems 1 2 3 4 5 2 addition / subtraction 1 2 3 4 5 3 multiplication / division 1 2 3 4 5 4 Mental arithmetic 1 2 3 4 5