The “Dichotomies Underlying Difference Stances in Mathematics Education” chart interested me a lot. I think both of sides are important, and I do not think that math teaching is either conservative or progressive. Even though understanding, sense-making, and exploratory are significant, fluency, absorbing and applying facts are also crucial. A student is not expected to do multiplication or division effectively if he or she is not able to memorize multiplication chart fluently. Also, some of the math concepts required by other subjects may be too hard for the students to understand at their current level, so the only way will be to present the topic and have them understand latter in advanced math courses. Another point that stopped me is that “rather than trying to cover a larger number of mathematical topics in a given time, Dewey advocated the development of high quality mental processes and a scientific attitude”. My inquiry topic is on how to foster mathematical thi
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