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Recent Posts
 PreService Mathematics for Elementary (and Secondary) Teachers: a third essential element
 Some thoughts about epsilon and delta
 Understanding in Calculus: Beyond the “Sliding Tangent Line”
 Precise Definitions of Mathematical Maturity
 Everyone Can Learn Mathematics to High Levels: The Evidence from Neuroscience that Should Change our Teaching
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
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
Helping Students Gain Control in Developmental and FirstYear 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
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 handson 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
Reflections on Teaching for Mathematical Creativity
By Gail Tang (University of La Verne), Emily CilliTurner (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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SenseMaking 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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