On page 81 in my book, there is a brief discussion of “feedback loops”. This teaching/learning strategy is so obvious and falls so easily out of any understanding of Polanyi’s tacit theory of knowledge that I am amazed to see it pop up in a recent research study as though a major discovery is being reported. Investigators at Florida State University claim that the “Mathematics Formative Assessment System” (MFAS) applied to kindergarten and first-grade students demonstrated learning gains of six weeks to two months worth of extra instruction. The technique calls for teachers to assess what the students understand, what they do not understand and then offer the right additional learning experiences to fix the missing or error-laden material in the students’ mind. Students are asked to explain their reasoning thus exposing to the teacher any misconceptions or procedural failures on the part of the students as they work on problems.

The real news here is uncovering the practical classroom management techniques needed to manage the formative assessment tasks. Since the MFAS process is different for each student, there is a challenge for teachers to deal one-on-one with each learner and develop the right instructional intervention to solve the cognitive problems experienced by each child. Perhaps a search for additional information on this could be found using the name, Mark LaVenia who was listed as the “methodologist” on the Florida State Team.

# Tag Archives: STEM

# Teaching to the Intuitive Side of the Brain with Kalid

Tacit knowledge is all about generating the “AHa” effect which embeds understanding into a more intuitive form of cognition than analytically encoded symbolic notation. I am always happy to see someone working hard to accomplish that as Kalid Azad does in his mathematics teaching blog. He complains (correctly) that most explanations for difficult ideas are offered in a logic based format (seems the best way by experts) rather than through a holistic approach. I recall as a former professor of physics the standard approach to teaching a topic in physics was to begin with an equation and show how that equation is derived. Students typically find the derivation quite baffling and may desperately memorize the steps. An alternative is to offer some exposure to examples of how the physical system behaves. Throw in a few problems, and then later work through the derivation when the learner has some grasp of what the topic is all about. Watch how Azad explains topics in mathematics to see an example of how this is done. He points out how a particular explanation may not work for you when a different one does so you might need to cast around looking for just the right kind of explanation to suit your own prior understandings. Kalid has several excellent books on Amazon to help anyone learning math develop an intuitive sense of what it all really means. Check out the calculus book here. His books make an excellent present for grandkids taking STEM in high school and college. The students themselves are not likely to realize they need his books but a parent and grandparent could help them get ahead by making sure the kids have these books to get them ahead in their education.