It means that students have the opportunity to grapple with mathematical ideas while being provided appropriate supports so that they may persist.
Two of my very favorite courses to teach are our pre-service elementary teacher courses. In these courses I get the opportunity to challenge (I think that's the right word) what the students know about mathematics or, well, what they think they know. Understanding representation of number in a Base-10 number system is a key understanding, and then there is how to "operate" within that number system that is also important. Well, my students have been working in Base-10 for 12 or more years, it's automatic for them and they would say they 'own' that knowledge. However, when I press them to demonstrate their ownership of that knowledge it becomes clear that many of them don't. Most know how to "operate" within the system but do so with little understanding. To eliminate the automaticity of working within Base-10 and to provide a context for the students to develop ownership of number representation and operations within a place-value number system we work in other bases, Base-2, Base-4, Base-5, etc. The students work collaboratively in groups of 3 and work with place value but within slightly different bases. It is such a pleasure to see the ideas "click" while they gain ownership of these concepts.Now enter COVID-19 and the shift to remote or online teaching. The cabinets on our campus are full of manipulatives that help these students make sense of elementary mathematics but they will not be available for use by my students in the fall as our campus has decided courses will be online. If I'm honest I admit that I will be challenged in teaching those courses during the upcoming year; especially in providing these students the same opportunities for developing ownership that my face-to-face students have had for years.
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