Counting With Kids

What makes a teacher of numeracy an effective teacher of numeracy? Askew, Brown, Rhodes, Wiliam & Johnson studied this question in “Effective Teachers of Numeracy: Final Report.” researchgate.net/publication… Their takeaway: “It was clear that those teachers with a strongly connectionist orientation were more likely to have classes that made greater gains over the two terms than those classes of teachers with strongly discovery or transmission orientations.” (pg. 28) What is a connectionist oriented teacher? “We characterise a connectionist orientation as including the belief that being numerate involves being both efficient and effective. […] Associated with the connectionist orientation is a belief that most pupils are able to learn mathematics given appropriate teaching, which explicitly introduces the links between different aspects of mathematics. Further to this is a belief that pupils come to lessons already in possession of mental strategies for calculating but that the teacher has a responsibility for intervening, working with the pupils on becoming more efficient.” What is a transmission oriented teacher? “The transmission orientation entails a belief in the importance of a collection of procedures or routines, particularly in regard to paper and pencil methods, one for doing each particular type of calculation regardless of whether or not a different method would be more efficient in a particular case. […] Since the transmission orientation places such emphasis on the ability to reproduce set methods and routines, what the pupil already knows is of less importance, unless it forms part of a new procedure. Methods that pupils have created themselves are not used as the basis from which to build more efficient and effective methods.” What is a discovery oriented teacher? “The discovery orientated teacher tends to treat all methods of calculation as equally acceptable. As long as an answer is obtained, whether or not the method is particularly effective or efficient is not perceived as important.” In summary: “In a sense the connectionist approach is not a complete contrast to the other two but embodies the best of both of them in its acknowledgement of the role of both the teacher and the pupils in lessons.” (See pages 35 and 36 of the report for a more detailed overview of each type of teaching orientation.)