Studying Resources – Mathematical Association of America

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Open-Source Software Uncovers how Students and Instructors Engage with Textbooks

By Erin Moss Have you ever wanted a comprehensive understanding of how mathematics texts are really being utilized by college instructors and students? The NSF DUE-funded UTMOST project (Undergraduate Teaching of Mathematics with Open Software and Textbooks) explored just that, while further developing open resources for use in college mathematics classrooms. Readers may recall that...

Calculus for Teachers: Why Complex Numbers

By David Bressoud @dbressoud As of 2024, new Launchings columns appear on the third Tuesday of the month./ And now something else remarkable happens. If our function is differentiable at every point inside an open disc that contains x, no matter how small that disc might be, then the second derivative must exist everywhere inside that...

Curriculum Inspirations: Walking the Track

James Tanton takes viewers through this question from the 2011 MAA AMC 10 B Competition. Appropriate for the 10th grade level, this question covers the topic of the circumference of a circle formula in Geometry. Common Core State Standards (CCSS): A-SSE.2; 7.G.4 Read the Curriculum Burst essay that goes with this question here: Walking the...

Problem-Solving Strategy #10: Go to Extremes

It is fun to be quirky and push ideas to the edge! Taking the parameters of a problem to an extreme can give insight to the workings of the situation described. And such insight can often illuminate a path for success. Read more about this strategy here: Problem-Solving Strategy #10: Go to Extremes Find other...

Problem-Solving Strategy #9 Avoid Hard Work

No one enjoys hard computation or a tedious grind through formulas and equations. Brute-force work should be undertaken only as a last resort! Do what a mathematician does - think very hard first to devise a creative, elegant approach that avoids hard work! Read more about this strategy here: Problem-Solving Strategy Essay #9 Avoid Hard...

Problem-Solving Strategy #1: Engage in Successful Flailing

One can often identify to which topic a challenge belongs – this question is about right triangles; this question is about repeating decimals – but still have no clue as to how to start on the challenge. What should you do? Engage in successful flailing! Think about everything you know about right triangles or repeating decimals....

Problem-Solving Strategy #8: Second-Guess the Author

If a curriculum or textbook problem is staged, then use that to your advantage! Read more about this strategy here: Problem-Solving Strategy Essay #8: Second-Guess the Author Find other problem-solving strategies you can use on the MAA American Mathematics Competitions and other competitions here.

Problem-Solving Strategy #7: Perseverance is Key

What impression of the mathematical pursuit do we often give students? Answers are pre-known (they are at the back of the book or are in the teacher’s mind), all can be accomplished in a fixed amount of time (quizzes and exams are usually timed), and the goal is to follow a pre-set intellectual path (as...

Problem-Solving Strategy #6 Eliminate Incorrect Choices

Eliminating what cannot be right helps determine that which must be correct! Read more about this strategy here: Problem-Solving Strategy Essay #6: Eliminate Incorrect Choices Find other problem-solving strategies you can use on the MAA American Mathematics Competitions and other competitions here.

Problem-Solving Strategy #5: Solve a Smaller Version of the Same Problem

A large, complex task can be made comprehensible by examining a smaller, analogous version. This powerful technique applies to mathematics research too. Read more about this strategy here: Problem-Solving Strategy Essay #5: Solve a Smaller Version of the Same Problem Find other problem-solving strategies you can use on the MAA American Mathematics Competitions and other...

Problem-Solving Strategy #4: Draw a Picture

The upper-school mathematics curriculum tends to drill down to analytic techniques and visualization is put to the side. Visual thinking can unlock deep insight! Read more about this strategy here: Problem Solving Strategy Essay #4: Draw a Picture Find other problem-solving strategies you can use on the MAA American Mathematics Competitions and other competitions here.

Problem-Solving Strategy #3 Engage in Wishful Thinking

If there is something in life you want, make it happen! (And be then willing to handle the consequences of your actions with care and grace!) If there is an equation you wish to solve but wish there were a "+4" on the left ... make it happen! Add a 4 to the left, with...

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