Why Do We Learn Mathematics? - Calculation, Application, and Inspiration

I love this TED Talk by Arthur Benjamin on The Magic of Fibonacci Numbers. I particularly like the introduction. Here's how it begins.

"So why do we learn mathematics? Essentially, for three reasons: calculation, application, and last, and unfortunately least in terms of the time we give it, inspiration. 

Mathematics is the science of patterns, and we study it to learn how to think logically, critically and creatively, but too much of the mathematics that we learn in school is not effectively motivated, and when our students ask, "Why are we learning this?" then they often hear that they'll need it in an upcoming math class or on a future test. But wouldn't it be great if every once in a while we did mathematics simply because it was fun or beautiful or because it excited the mind?"

I've been a puzzle-solver and game player for as long as I can remember. I love to do math for fun. I wish more teachers saw the value of puzzling through non-traditional problems and the long-term benefits it brings.

Learn more about these ideas and the beauty of Fibonacci numbers in Benjamin's talk.

More Patterns!

Just a quick post today to share to new pattern sets, one for African animals and one for woodland animals. In each set you'll find 8 different pattern strips and pattern pieces. Patterns found in these sets include AB, ABC, ABB, AAB, AABB, AABC, ABCD, ABAC. Here's a sneak peak at a few of the pages from each.

Download African Animal Patterns.
Download Woodland Animal Patterns.

Enjoy!

Patterns, Patterns, Patterns!

I still find myself perplexed that patterns do not appear in the elementary portion of the Common Core Standards for Mathematics. Arithmetic patterns do appear in the upper elementary grades, but identifying, extending and creating patterns has disappeared altogether. This is a shame because understanding patterns is one of a number of skills that lay the foundation for algebraic thinking. Patterns help children make sense of the world around them. There are patterns in music, poetry, the seasons, life cycles, phases of the moon, tides, and more! Patterns can be used to solve problems. They can also be a powerful tool for helping children make connections across areas of math. Memorizing basic facts is so much easier when we teach children to recognize patterns and relationships.  

I know many elementary teachers that will be reluctant to give up activities related to patterning. Since I'm preparing teachers in Virginia, and since VA is one of the few holdout states in relation to adopting the CCSM, I am still focused on activities related to patterns. Perhaps teachers in Common Core states can sneak these activities in under the guise of the Mathematical Practice standards 7 and 8 which say that students will look for and make use of structure (7) and look for and express regularity in repeated reasoning (8).

For teachers helping students to recognize, describe, extend, and create a wide variety of repeating patterns, I have created a set of materials you may find useful. You'll find 8 different pattern strips and pattern pieces. Patterns found in this set include AB, ABC, ABB, AAB, AABB, AABC, ABCD, ABAC. Here's a sneak peak at a few of the pages.

Download Farm Patterns. Please let me know if you find this useful. I'm working on some other themed sets for repeating patterns, as well as a few for growing patterns.