Category Archives: testing

Understanding in Calculus: Beyond the “Sliding Tangent Line”

By: Natalie Hobson, Sonoma State University If you give calculus students graphs, they are going to draw tangent lines. As instructors we often encourage students to rely on tangent lines so heavily that discussions about rates of change become lessons … Continue reading

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Precise Definitions of Mathematical Maturity

[This contribution was originally posted on April 15, 2019.] By Benjamin Braun, University of Kentucky The phrase “mathematically mature” is frequently used by mathematics faculty to describe students who have achieved a certain combination of technical skills, habits of investigation, … Continue reading

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The Crisis in American Education

  The Crisis in American Education John Ewing American education is in crisis… I’m told. Want evidence? Look on the Internet. Search for “education crisis in America” and you will find millions of articles, essays, and (yes) blogs, all describing, … Continue reading

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Precise Definitions of Mathematical Maturity

By Benjamin Braun, University of Kentucky The phrase “mathematically mature” is frequently used by mathematics faculty to describe students who have achieved a certain combination of technical skills, habits of investigation, persistence, and conceptual understanding. This is often used both … 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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Interactive Images—Pictures for the Mind’s Eye

By Judah L. Schwartz, Harvard University a step in the direction of enhancing mathematical insight for teachers and the students they teach What is the real value of interactive manipulable mathematics software? Many educators see value in hands-on learning. To … Continue reading

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Teaching Mathematics Conceptually: An Example

By Roger Howe I have been worrying a lot about mathematics education for over a quarter century now. While many university mathematicians who get involved in mathematics education focus on the need for new teaching methods, I have been drawn … Continue reading

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MATHEMATICS: GATEKEEPER OR GATEWAY?

Some recent writers on mathematics education have been talking about mathematics as a field enjoying ’unearned privilege’ as a ‘gatekeeper’ in our society.  The more I think about it, the less sense this makes. For some writers, the reference may … Continue reading

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Reflections on Teaching for Mathematical Creativity

By Gail Tang (University of La Verne), Emily Cilli-Turner (University of La Verne), Milos Savic (University of Oklahoma), Houssein El Turkey (University of New Haven), Mohamed Omar (Harvey Mudd College), Gulden Karakok (University of Northern Colorado, Greeley), and Paul Regier … Continue reading

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Sense-Making and Making Sense

There’s an old slogan, probably due to Seymour Papert: “You can’t think about thinking unless you think about thinking about something.” Sense making is about the habits and practices used to understand mathematics, and making sense is about applying those practices to a particular structuring of mathematics itself.

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