Sue VanHattum is a math professor, blogger, mother, author/editor, and fundraiser. She's a real powerhouse of motivation for making math fun and accessible to more of our young folks. Sue has teamed up with a number of writers to compile a book, "Playing With Math," which she is producing in partnership with Maria Droujkova in a community sponsored publication model.
Sue and I shared a delightful chat about what math is, what the book is about, and how we can all get more inspired to engage in math with our kids. And, Sue sprinkles the conversation with some interesting open-ended math problems. Think part coffee table conversation part math circle.
About Sue VanHattum
"I love teaching math, yet throughout my twenty-some years of teaching I've struggled with the fact that what I want to teach is problem solving but what I do teach most of the time is how to follow recipes (here’s how you find the slope or the vertex, here’s how you factor, and so on). Until recently, I never felt that I had made much progress in resolving this dilemma. In early 2008, I started reading Living Math Forum, an email group where participants discuss how to help their children learn math. In the years since that discovery, my life has been full of math-play adventures. I’m still learning how to bring that spirit into my students’ lives."
About "Playing With Math"
Why play with math? Because play is the best way to learn.
From the introduction of the book:
Math, more than any other subject, has to be approached by each student at their own pace, and in their own way. There may be one right answer, but there are more ways to think about the path from question to answer than you’d expect.
What is math?
Most people think it’s adding, subtracting, multiplying, and dividing; knowing your times tables; knowing how to divide fractions; knowing how to follow the rules to find the answer. Math is so much more than that! Math is seeing patterns, solving puzzles, using logic, finding ways to connect disparate ideas, and so much more. People who do math play with infinity, shapes, map coloring, tiling, and probability; they analyze how things change over time, or how one particular change will affect a whole system. Math is about concepts, connections, patterns. It can be a game, a language, an art form. Everything is connected, often in surprising and beautiful ways. The stories in this book will be full of examples that show math from these angles. More.
Reserve a copy of the book
Go to Incited.org
Other links of interest
Lou DiGioia, executive director of MATHCOUNTS, and I tried to do a podcast a couple of months ago. The audio had some serious problems and we produced a transcript instead. It was a great discussion although I asked way too much about the human Pascal's triangle that made a Guiness World record.
Anyway, the second time was a charm, and we produced a good audio discussing all things related to MATHCOUNTS and how the organization inspires kids to improve their relationship with Math. If you read the transcript, or even if you didn't, check out the podcast!
About Lou DiGioia
As executive director of MATHCOUNTS®, Lou DiGioia leads the largest nonprofit organization dedicated to extracurricular middle school mathematics. As a former Mathlete®, DiGioia is the first executive director to have participated the MATHCOUNTS Competition Series as a student. During his tenure, he led the creation of The National Math Club, which builds student enthusiasm for math by providing schools with free resources to hold afterschool math clubs; and the Math Video Challenge, an online competition that has teams create innovative teaching videos based on MATHCOUNTS problems. In 2013, he orchestrated the organization’s successful Guinness World Record attempt of the fastest time to create the first 25 rows of Pascal’s Triangle in human formation. DiGioia holds a BA from Georgetown University and an MBA from George Mason University.
[From the overview page.]
The MATHCOUNTS Foundation is a 501(c)(3) non-profit organization that strives to engage middle school students of all ability and interest levels in fun, challenging math programs, in order to expand their academic and professional opportunities. Middle school students exist at a critical juncture in which their love for mathematics must be nurtured, or their fear of mathematics must be overcome. MATHCOUNTS provides students with the kinds of experiences that foster growth and transcend fear to lay a foundation for future success.
For more than 30 years MATHCOUNTS has provided enriching, extracurricular opportunities to students and free, high-quality resources to educators. Every child is unique, but we believe all children are capable of seeing the beauty and joy of math, whether they come to us already passionate about math, or intimidated by it.
There are many paths to math. We work to ensure that all students discover theirs.
The MAA (Mathematical Association of America) sent me a review copy of their new book "Learning Modern Algebra: From Early Attempts to Prove Fermat's Last Theorem." I don't typically review textbooks but the title and then the contents of the book convinced me that I needed to interview the authors. Joe Rotman wasn't available but I was able to chat with the other co-author, Al Cuoco. I was really struck with Al's passion about teaching the teachers as well as the students. Al shared some great insights about the ingredients that I think should go into every math textbook to help teachers and students to develop the right habits of mind to succeed.
Here are some of the questions we discussed.
1. What is your background and your experience teaching high school math to students and to teachers?
2. I attended the Ross program and you have a key role in a program that has its roots in the Ross program. Tell me about this program and your involvement with it.
3. There's something special about number theory and algebra that makes it accessible to bright students without a deep background in math. What do you think of that thought?
4. What is "Learning Modern Algebra" about and who is the audience?
5. How does Fermat's Last Theorem unite the book's chapters?
6. What are the challenges with how Modern Algebra is taught?
7. Why is exploration so important and how do you promote it?
8. Rigorous thinking about open-ended problems runs through the book. PODASIP (prove or disprove and salvage if possible) problems contribute to this. Can you speak to that?
9. Why is historical setting important in learning math and how do you weave history into the book?
10. Tell us about the importance of the "Connections" sections in the book.
11. Is there a next book or project?
12. The question I ask everyone: "What advice would you give to a parent whose child was struggling with math?"
About Al Cuoco
From the EDC web-site:
Al Cuoco is the lead author of CME Project, a National Science Foundation (NSF)-funded high school curriculum published by Pearson. Recently, he served as part of a team that revised the Conference Board of the Mathematical Sciences (CBMS) recommendations for teacher preparation and professional development.
Cuoco is carrying out several professional development streams of work devoted to the implementation of the Common Core State Standards for Mathematics (CCSSM) Standards for Mathematical Practice, including EDC’s Mathematical Practice Institute (MPI). Through the MPI, he and his colleagues have launched a new course for teachers and facilitators, Developing Mathematical Practice in High School.
He co-directs Focus on Mathematics, a partnership among universities, school districts, and EDC that has established a community of mathematical practice involving mathematicians, teachers, and mathematics educators. The partnership evolved from his 25-year collaboration with Glenn Stevens on Boston University’s PROMYS for Teachers, a professional development program for teachers based on an immersion experience in mathematics. He also co-directs the development of the course for secondary teachers in the Institute for Advanced Study program at the Park City Mathematics Institute. More
About "Learning Modern Algebra"
Learning Modern Algebra aligns with the CBMS Mathematical Education of Teachers–II recommendations, in both content and practice. It emphasizes rings and fields over groups, and it makes explicit connections between the ideas of abstract algebra and the mathematics used by high school teachers. It provides opportunities for prospective and practicing teachers to experience mathematics for themselves, before the formalities are developed, and it is explicit about the mathematical habits of mind that lie beneath the definitions and theorems.
This book is designed for prospective and practicing high school mathematics teachers, but it can serve as a text for standard abstract algebra courses as well. The presentation is organized historically: the Babylonians introduced Pythagorean triples to teach the Pythagorean theorem; these were classified by Diophantus, and eventually this led Fermat to conjecture his Last Theorem. The text shows how much of modern algebra arose in attempts to prove this; it also shows how other important themes in algebra arose from questions related to teaching. Indeed, modern algebra is a very useful tool for teachers, with deep connections to the actual content of high school mathematics, as well as to the mathematics teachers use in their profession that doesn't necessarily "end up on the blackboard." More
I love novel ways of looking at arithmetic. I'm fascinated with how computers compute in binary, with tricks for simplifying calculations and with how Vedic mathematicians handle difficult arithmetic efficiently. So, when Princeton University Press sent me a review copy of their new book "Count Like An Egyptian," I immediately fell in love with it. I was delighted to learn even more techniques and the ideas behind them to deepen my appreciation of the beauty of what most consider to be mundane arithmetic.
"Count Like an Egyptian" is a delightful book, full of color illustrations, fun stories, lots of hands-on exercises, and an appreciation for the power of simple but deep ideas.
David Reimer was a pleasure to interview. He is a brilliant mathematician who hasn't lost sight of the power and beauty of mathematics. He taught me and modeled that, despite the stereotype, the more advanced mathematicians are the ones who are more likely to communicate ideas well.
We discussed these questions plus some nice tangents!
1. How did you get interested enough in Egyptian computation to write a book about it? What is the book about and who is the audience?
2. You're a math professor. What courses do you teach and at what level?
3. You researched the Rhind Papyrus to figure out how Egyptians did computations. Where did you get a hold of the Papyrus? How much time did you spend unraveling its secrets?
4. I'm fascinated with the idea that children can learn to do multiplication and division by just learning to double and add numbers. How did we develop such a cumbersome system of multiplication that requires memorizing tables?
5. I find it interesting that computers doing multiplication (and all other arithmetic) in binary equates to Egyptians doubling and adding numbers. Can you connect the dots for our listeners? (Nice video here, btw: https://www.youtube.com/watch?v=EDLLPnfpMfU)
6. Tell us about how Egyptians worked with fractions and why it was so novel.
7. One reviewer said this: "Of course our system is more apt for us (or for machines) to do calculations just following recipes, which need no insight or wit, but what we lose is that the Egyptian system keeps the practitioner sharp, forcing him or her to think about the problem and the result of the calculations." What do you think of the statement?
8. In addition to exploring Egyptian computation you also write about other mathematical systems. Tell us about those.
9. Is there a next book or big project?
10. The question I ask everyone: What advice would you give to a parent whose child was struggling with math in school?
About David Reimer
In high school I was a mediocre student at best. But I did far better on my SATs than was expected. I passed a number of AP exams never having taken any AP courses but learning from published study guides. This got me into Colgate. I started as a computer science major but quickly found that I knew more than my professors, at least in practical computing. I toyed with becoming a physics major, winning the school’s award for the best freshman physics student. I eventually settled on math as everyone in my family did.
Over the summers I worked at Creative Computing, which was then the largest computer magazine in the world and for Prudential Insurance, where I wrote the database for the central office’s purchasing department. I passed two actuarial exams and was offered a job but decided to take a try as a freelance programmer. On one project, which we spent six months on, the company cancelled and refused to pay us. Desperately needing money I taught night school calculus as an adjunct. I immediately knew that this is what I wanted to do for the rest of my life.
I got into the graduate math program at Rutgers. While most grad students taught recitations and graded papers, the department noticed my teaching skill and gave me my own higher level classes even giving me a 300-level course. I finished up my Phd. thesis while making some money as a full instructor first at Rutgers and then at Middlesex Community College. While there I was told that my proof of the Vandenberg-Kesten conjecture won the Polya Prize in Discrete Mathematics which is given every four years to what is considered to be the best work in discrete math during that period. The conjecture is a generalization of a probabilistic proposition often used in percolation, the theory of how things like epidemics and fires spread. Being overly simplistic it basically says that given two events that can happen anywhere but not in the same place, the probability of both happening is less than what would be expected if they were independent events. Based on this theorem I got what most would call a post doc at the Institute for Advanced Study in Princeton (where Einstein worked) and then a job at the College of New Jersey where I am today.
About "Count Like an Egyptian"
(From the Princeton University Press book page)
The mathematics of ancient Egypt was fundamentally different from our math today. Contrary to what people might think, it wasn't a primitive forerunner of modern mathematics. In fact, it can't be understood using our current computational methods. Count Like an Egyptian provides a fun, hands-on introduction to the intuitive and often-surprising art of ancient Egyptian math. David Reimer guides you step-by-step through addition, subtraction, multiplication, and more. He even shows you how fractions and decimals may have been calculated--they technically didn't exist in the land of the pharaohs. You'll be counting like an Egyptian in no time, and along the way you'll learn firsthand how mathematics is an expression of the culture that uses it, and why there's more to math than rote memorization and bewildering abstraction.
Reimer takes you on a lively and entertaining tour of the ancient Egyptian world, providing rich historical details and amusing anecdotes as he presents a host of mathematical problems drawn from different eras of the Egyptian past. Each of these problems is like a tantalizing puzzle, often with a beautiful and elegant solution. As you solve them, you'll be immersed in many facets of Egyptian life, from hieroglyphs and pyramid building to agriculture, religion, and even bread baking and beer brewing.
Fully illustrated in color throughout, Count Like an Egyptian also teaches you some Babylonian computation--the precursor to our modern system--and compares ancient Egyptian mathematics to today's math, letting you decide for yourself which is better.