Teaching practices aimed at promoting meta-level learning: The case of complex numbers

In this paper we seek to promote a conceptualization of “teaching toward meta-level learning” based on theoretical and empirical aspects. We adopt the commognitive distinction between object- and meta-level learning, and relate to meta-level learning as involving changes in the metarules that govern the discourse. Specifically, we refer to changes in the discourse on numbers emerging in the shift in discourse from real to complex numbers. We applied implications from the commognitive theory about meta-level learning to the planning and teaching of a lesson about complex numbers. Then, we analyzed the lesson to identify teaching practices that could promote meta-level learning. We found that these teaching practices can be clustered into three theory driven sub-sets: those referring to students’ current discourse on numbers, those referring to their new discourse and those referring to the transition between the two.