Books
- The Humongous Book of Calculus Problems
W. Michael Kelley (author)
Grade Level: 12+
This book works through several calculus problems that cover every topic that is taught in a high school calculus and more. Textbooks can often seem dry, but this book provides comical commentary on every problem that makes math more approachable. I have used this book in my own calculus classes to provide another approach to confusing topics. This is a great book for anyone struggling in their calculus class or for those who would like some enrichment.
Larry Gonnick (author)
- The Cartoon Guide to Calculus
Larry Gonnick (author)
Grade Level: 12+
Gonnick is a mathematician who went to Harvard, but he has an excellent way of explaining the most difficult concepts in a simple way, especially in this book dealing with calculus. He uses graphics to clarify abstract topics, and he even throws in comedy to alleviate the stress!
- Calculus Made Easy
Silvanus Philips Thompson and Martin Gardner (authors)
Grade Level: 12+
Some people assume that calculus is hard because of its reputation, and it is hard if you are not mathematically prepared for this course. This book gives a short and sweet overview of the most important aspects in a high school calculus course. This could be a great book to assign for summer reading!
Students often struggle with the fact that the derivative deals with rates of change. The authors of this article show that using the calculus triangle may help students learn what information we can learn from the derivative of a function. It is a way to show students that the derivative is more than just another function. It shows how two values compare to each other at any moment in time, and the triangle visually shows the slope between two close points.
Websites
- Calculus-Help
Grade Level: 12+
This is one of my absolute favorite sites for calculus! My high school calculus teacher showed me the first two videos listed about limits, and I still reference them today. This site is owned by the author of the Humongous books like the one mentioned above. The video tutorials are basic but accurate, which helps start people off on the right track when they are being introduced to the early topics.
- Calculus Derivatives and Limits Math Sheet
Grade Level: 12+
Formulas need to be memorized, but a reference sheet can always be used to brush up those formulas that tend to be forgotten. This formula sheet has to be understood, so it may be a good idea for the teacher to walk through the sheet with your class. I have confidence that if students can read this formula sheet and understand it, they can read anything!
- Houdini's Escape
Grade Level: 12+
If students ever ask when they will use derivatives in real life, this is a great task to challenge them. Formulas are analyzed and derived to show students how calculus can be used to actually find the height of the concrete block Houdini should use to ensure he would not drown. This is a great project for a high school calculus class!
- Common Calculus Mistakes
Grade Level: 12+
A great way to assess students' knowledge is by having them point out the mistakes in people's work. This site gives intentionally wrong results so that people can try to find what went wrong. There are hints that can be seen by scrolling over the problem. The solution can be seen by scrolling over the answer section, and the correct piece is highlighted in blue. Students who really understand the material can really refine their skills with this site.
Articles
- Derivative of Area Equals Perimeter- Coincidence or Rule?
Rina Zazkis, Ilya Sinitsky, and Roza Leikin (authors)
Grade Level: for teachers
This article was written by questioning whether the fact that the derivative of the area of a circle is the circumference can be generalized to other shapes. Obviously, the derivative of the area of a square is not the perimeter of said square, but it is half of the perimeter. The authors provide several diagrams to show their findings, and I think this would be a fun read for math teachers at any level!
- Students' Exploratory Thinking about a Nonroutine Calculus Task
Keith Nabb (author)
Grade Level: for teachers
Have you ever wondered why points of inflection always seem to occur halfway between two critical numbers? Does this always happen? These questions elicit deep thinking about calculus and geometry together, and they can really enrich students' understanding. I think this article highlights what math is all about: asking questions and figuring out an answer using the skills you have acquired throughout your life.
- Understanding the Derivative through the Calculus Triangle
Eric Weber, Michael Tallman, Cameron Byerley, and Patrick W. Thompson (authors)
Grade Level: for teachers
Students often struggle with the fact that the derivative deals with rates of change. The authors of this article show that using the calculus triangle may help students learn what information we can learn from the derivative of a function. It is a way to show students that the derivative is more than just another function. It shows how two values compare to each other at any moment in time, and the triangle visually shows the slope between two close points.- Delving into Limits of Sequences
Beth Cory and Ken W. Smith (authors)
Grade Level: for teachers
The formal definition of a limit may not be fully appreciated by students who are seeing it for the first time. Limits are the basis of all calculus, so it is important for students to know what limits are and how to find them. This article shows a way that two teachers have introduced limits to their calculus classes. Students arrive at their own conclusions by looking at several examples and non-examples. This is a great read for any calculus teacher!
- A Close Encounter with Infinity: Inventing New Mathematics
Keith A. Nabb (author)
Grade Level: for teachers
Apparently, I like articles written by Keith Nabb (see above article). This article focuses on another nonroutine problem about infinite series. Nabb was brainstorming ideas about how to enrich this fascinating topic, and he decided to ask students open-ended questions that allowed them to create series with certain characteristics or state why one could not be made. I think these types of questions could be asked at any level, and they help to assess true mastery of this topic.
Online Articles
- The Calculus Trap
Grade Level: 12+
This article was very interesting to read because it obviously does not apply to every student, but it reveals the truth about the current high school curriculum. Students who excel through the curriculum quickly should not necessarily be pushed into calculus as soon as possible. There should always be more challenging problems that could enrich these students along the way.
- Masterful Teacher: How Calculus Became the Most Popular Class on Campus
Grade Level: for teachers
It is no secret that people need to be motivated to do something, and students are no exception to this rule. Jonathan Winn has found a way to get students excited about math, and his course is the most popular course on the campus of Crawford High Educational Complex in San Diego. He claims that it was very difficult at first to get students engaged, but he seems to know what can truly inspire students to want to learn math.
- Mathematical Firsts: Who Done It?
Richard H. Williams and Roy D. Mazzagatti (authors)
Grade Level: 12+
This is a fun read for anyone who is interested in the names of particular theorems or ideas. The authors take a look at several mathematical pseudoeponyms (Euler's formula, L'Hôpital's rule, and Pascal's triangle, to name a few). Each pseudoeponyms is accompanied by a description of why the person whose name appear in the title may or may not be the rightful owner of their discovery.
