Fibonacci and Fractals Links

I had the pleasure of being the co-presenter of a workshop called “Fibonacci, Fractals, and the Common Core Math Standards” at the VCTM conference at Saint Michael’s College on Friday. My partners were Professor Tim Whiteford of Saint Michael’s College and Laura Sommariva, a math teacher at Colchester High School.

The three of us shared what we’d done with students during a fifth grade field trip to Tim’s famous Penny Arcade. Here is Tim’s original write-up about that.

As promised, for the participants in our workshop and others, here are the resources we used to teach about fractals and Fibonacci numbers.

The Fractal Foundation Fractivities. How to draw Sierpinski triangles, do fractal cutouts and more.

Worksheetworks. Create your own graph paper and triangle paper.

On Being a Plant, Part 1, the 6 minute Vi Hart video we watched. She explains Fibonacci numbers, and demonstrates how to count the spirals on pinecones, draw realistic pinecones, and use graph paper to make a golden spiral.

Laura teaches summer math classes for elementary students in Switzerland. She has photos of her students here doing wonderful, related activities like building giant tetrahedrons out of mini marshmallows.

Have fun!

Fact Fluency

What is it about fact fluency that is so challenging for some students? It’s not uncommon for students to lack automaticity with their addition, subtraction, multiplication, and division facts into middle school and beyond. Struggles with fact fluency sometimes accompany low achievement in math, but that is not always the case. Sometimes struggling math students know their facts. Sometimes high-achieving students do not know their facts.

I am reading John Tapper’s excellent new book entitled Solving for Why: Understanding, Assessing, and Teaching Students Who Struggle with Math.  Tapper devotes a section of the book to students who face challenges in short term, long term and working memory. He weighs in on the fact fluency question there.

What students need to understand are underlying mathematics concepts. Multiplicative and proportional reasoning are, for example, critical to moving on from elementary mathematics. Fact retrieval certainly facilitates learning in these areas, but the inability to retrieve facts will not prevent students from reasoning at higher levels. Knowing math facts is important, but fact retrieval is to mathematics what spelling is to literacy: we want students to be proficient at the skill, but the skill is a small part of the overall picture. If a student is able to spell but cannot write a coherent essay, the spelling does them little good. The same is true with math facts. (p. 138)

This is interesting for students, parents, and teachers to ponder. Try spending ten minutes a day or less studying math facts. Learn them in a way that reinforces conceptual understanding and is fun. Enjoy higher level, rich mathematics. Like the Fibonacci spiraling Hurricane Sandy picture above.

Sugar and Ice book review

Phia Smith, a fourth grade mathematician at John J. Flynn Elementary School, read the book, “Sugar and Ice” by Kate Messner. Our school librarian told us it had some math in the story, including Fibonacci numbers. Phia and I had been learning about Fibonacci numbers together, so it seemed like a perfect book for her to read. She gave me permission to publish her book review here.

Sugar and Ice is a story about a girl named Claire. Claire is a skater and a mathematician at heart. She has a skating coach named Mary Pat. Skating on a cow pond she entered a skating competition and was so good she got offered a scholarship to a really nice skating group by Andrei Grosheva. With some troubles along the way she comes to a decision of what dream to follow. Read the book to find out.

I think it is a very good book. I enjoyed the bits of Fibonacci and math in it. I think it deserves 4 ½ stars. - Phia