Tag Archives: Conceptual Understanding

Mathematics as Logic

by Mark Saul Maybe it is obvious, but it is something I’ve come to appreciate only after years of experience: mathematics is logic driven, and teaching and learning mathematics is centered on teaching and learning logic.  I find this to … Continue reading

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A Tale of Two Hats (Terrance and Lamar): supporting students in authentic mathematical inquiry

Terrance Pendleton, Drake University Students who have had me for at least one class are familiar with my alter ego, Lamar. If they were to describe him, they may say that he is the poster child for what not to do … Continue reading

Posted in Active Learning in Mathematics Series 2015, Classroom Practices, Faculty Experiences, Influence of race and gender | Tagged , , , , , , , | 2 Comments

Happy New Year(?)

Mark Saul, Editor Mathematics and mathematicians rarely make press.  So it was a bit sweet, but mostly bitter, to read in the New Yorker of the deaths of John Conway, Ronald Graham, and Freeman Dyson, three great losses to our profession.  … Continue reading

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Helping Students Gain Control in Developmental and First-Year College Mathematics Courses

By A. Gwinn Royal, Ivy Tech Community College of Indiana Currently, I am focusing on mitigating “learned helplessness” with respect to the study of mathematics. According to an article on the APA website (https://www.apa.org/monitor/2009/10/helplessness.aspx), newer research on learned helplessness suggests … Continue reading

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Comparing Educational Philosophies

I have recently heard several mathematicians claim that the educational philosophies of Math Circles and the Inquiry Learning Community are essentially the same. I disagree. I will contrast the differences between these two approaches, along with two other common educational … Continue reading

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My “First” Mathematical Problem and What It Means

I am inspired, by several previous blog entries, to write about my own mathematical awakening, and what I’ve learned from reflecting on it. I went to New York City Public Schools, in the Bronx.  I always enjoyed arithmetic and mastered … Continue reading

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Eating Our Own Cooking: What I’ve Actually Used or Shared

By Art Duval, Contributing Editor, University of Texas at El Paso A popular saying in business (or so I’ve read) is to “eat your own cooking”: Use the products your own company makes.  I suppose there are several motivations to … Continue reading

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Inverse Functions: We’re Teaching It All Wrong!

By Frank Wilson, Chandler-Gilbert Community College; Scott Adamson, Chandler-Gilbert Community College; Trey Cox, Chandler-Gilbert Community College; and Alan O’Bryan, Arizona State University What would you do if you discovered a popular approach to teaching inverse functions negatively affected student understanding … Continue reading

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The Second Year of “On Teaching and Learning Mathematics”

By Art Duval, Contributing Editor, University of Texas at El Paso Another year has flown by, and so it is once again a good time to collect and reflect on all the articles we have been able to share with … Continue reading

Posted in Classroom Practices, Curriculum, Early Childhood, Education Policy, K-12 Education, Online Education, Outreach, Student Experiences, Year in Review | Tagged , , , , , , | 1 Comment

A Framework for Integrating Conceptual and Procedural Understanding in the First Two Years of Undergraduate Mathematics

By Karen Keene and Nicholas Fortune, North Carolina State University One common instructional approach during the first two years of undergraduate mathematics in courses such as calculus or differential equations is to teach primarily analytic techniques (procedures) to solve problems and find … Continue reading

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