Welcome to the 115th edition of the Playful Math Education Blog Carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.

In honor of Women’s History Month, this carnival features quotes from fifteen women mathematicians.

If you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Let the mathematical fun begin!

## The Women of Mathematics

They came from many countries and followed a variety of interests.

They conquered new topics in mathematics and expanded the world’s understanding of old ones.

They wrestled with theorems, raised children, published articles, won awards, faced discrimination, led professional organizations, and kept going through both success and failure.

Some gained international renown, but most enjoyed quiet lives.

They studied, learned, and lived (and some still live) as most of us do — loving their families and friends, joking with colleagues, hoping to influence students.

I think you’ll find their words inspiring.

“What I really am is a mathematician. Rather than being remembered as the first woman this or that, I would prefer to be remembered, as a mathematician should, simply for the theorems I have proved and the problems I have solved.”

—Julia Robinson (1919–1985)

“All in all, I have found great delight and pleasure in the pursuit of mathematics. Along the way I have made great friends and worked with a number of creative and interesting people. I have been saved from boredom, dourness, and self-absorption. One cannot ask for more.”

—Karen Uhlenbeck (b. 1942)

## Table of Contents

And now, on to the main attraction: the blog posts. A few articles were submitted by their authors; others were drawn from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, click one of these links.

- Talking Math with Kids
- Elementary Exploration and Middle School Mastery
- Adventures in Basic Algebra and Geometry
- Advanced Mathematical Endeavors
- Puzzling Recreations
- Teaching Tips

“I would like to encourage mathematicians, indeed anyone who has responsibility for the learning of mathematics, to model their own intuitive processes, to create the conditions in which learners are encouraged to value and explore their own and their colleagues’ intuitions. This seems to me to be a necessary step which provides a justification for, but is prior to, the search for convincing argument and, ultimately, proof.”

—Leone Burton (1936–2007)

## Talking Math with Kids

- Rodi Steinig highlights activities from a five-week course in Embodied Mathematics for 5–7-year-olds.

- The idea of Zero is a powerful math concept. Christopher Danielson and daughter discuss Cocoa Puff or Cocoa Puffs: The Language of Nothing.

- Megan Schmidt plays school with her daughter — who is always happy to do math if it means putting off bedtime — in Fraction Frenzy.

- For my carnival entry, I’ll share a recent guest post. Funville Adventures: Blake’s Story offers a great way to launch a math chat with your kids. And be sure to follow the rest of the Funville Web Tour!

- Conversation is an excellent tool for developing deep foundations in math. Lacy Coker explains 5 Keys to Math Narration for Improved Fluency and Conceptual Understanding.

“I especially want to thank the teachers, including my mother, who inspired me — those who awakened my sense of curiosity, showed me that there was ‘wow!’ in mathematics.”

—Doris Schattschneider (b. 1939)

“For me, mathematics is a part of Nature’s beauty, and I am grateful for being able to see it. Whatever mathematics I happen to teach, I love to communicate its beauty to my students.”

—Marina Ratner (1938–2017)

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## Elementary Exploration and Middle School Mastery

- Ioana suggests ways to get your students playing with (and creating their own) Mathemagic: Exploring Sudoku and Other Magic Squares.

- Paula Beardell Krieg and her students create images based on Fraction & more Fractions. I want to try these projects with my co-op math kids one of these days.

- How well can your children estimate fractions? Test their (and your own!) skill with Daniel Scher’s puzzle Deducing The “Mystery” Fraction.

- I love Don Steward’s resource blog! These from one fraction to another puzzles were a fun challenge.

- Ron King encourages middle-school-and-up students to think about their futures in his version of The Million Dollar Project.

“We had few toys. There was no movie house in town. We listened to the radio. But our games were very elaborate and purely in the imagination. I think actually that that is something that contributes to making a mathematician — having time to think and being in the habit of imagining all sorts of complicated things.”

—Mary Ellen Rudin (1924–2013)

“Aren’t truth and beauty enough? In fact, I have often reminded my students that the best mathematical achievements took place when the question, ‘What is it for?’ was not asked.”

—Bhama Srinivasan (b. 1935)

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## Adventures in Basic Algebra and Geometry

- Nicola Waddilove shares a free printable card-sorting activity for Solving Simple Equations.

- John Golden prompts math debates about relationships between integers and variables in Walk the [Number] Line.

- Don Steward will push your students’ understanding of linear equations to a new level with these radiating equations.

- Benjamin Leis’s students tackle a particularly tough probability question and a beautiful project from George Hart’s geometric sculptures: 3/20 Visible Math.

- James Tanton challenges us to try our own math/science experiment in Time Does Not Run Clockwise. Here’s Proof!

“Mathematics is a way of thinking. It requires no tools or instruments or laboratories. It may be convenient to have a pen and paper, a ruler and a compass, but it is not essential: Archimedes managed very well with a stretch of smooth sand and a stick.”

—Kathleen Ollerenshaw (1912–2014)

“When I was eight or nine, the thing I liked best when playing with my dolls was to sew clothes for them. It was fascinating to me that by putting together flat pieces of fabric one could make something that was not flat at all, but followed curved surfaces.”

—Ingrid Daubechies (b. 1954)

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## Advanced Mathematical Endeavors

- Patrick Honner proposes “a fun little exploration involving a simple sum of trigonometric functions”: sin(x) + cos(x).

- Introduce your students to hyperbolic geometry as One on Epsilon authors Clara Valtorta and Phillip Isaac discuss

Thinking outside the coordinate plane.

- Paradoxes are a great way to get students thinking. Murray Bourne challenges us to imagine The object with finite volume but infinite surface area.

- Do your young mathematicians have a favorite theorem? I bet they’d enjoy Mike Lawler and sons’ Simplified version of the Banach-Tarski paradox.

- And don’t miss the 155th Carnival of Mathematics.

“I remember when I took calculus in college, the only book I took home over the Christmas holidays was my calculus book. I wanted to do those word problems. I worked on one problem for the whole two weeks before I solved it. When the light dawned, I was so happy! I don’t believe I ever felt so rewarded. I was hooked. After that, to the amazement of my fellow students, I recall sitting on campus doing calculus problems for recreation.”

—Gloria Hewitt (b. 1935)

“I would like to win over those who consider mathematics useful, but colourless and dry — a necessary evil. No other field can offer, to such an extent as mathematics, the joy of discovery, which is perhaps the greatest human joy.”

—Rózsa Péter (1905–1977)

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## Puzzling Recreations

- Rob Eastaway plays around with dots in Thinking
*outside*outside the box.

- Jae Ess’s students love this new type of puzzle: Strimko Puzzle Review. This looks like a great opportunity for the “Now make up your own” extension.

- Kelly Darke reviews one of my favorite playgrounds of recreational math: This is Not a Math Book, It is a Magical Math Book.

- With only a few materials — scissors, paper, and maybe snap cubes — you can dive deep into the rabbit hole of math with Mike Lawler’s collection of 15 (+1 bonus) ideas for a 6th grade math camp.

- Malke Rosenfeld explores loops of hyperbolic crochet and quotes Margaret Wertheim on the Value of Embodied Knowledge.

- Sue VanHattum poses a twist on a fiendishly-difficult (at least to me!) Logic Puzzle – What Does Your Friend See?

“[Mathematical research] is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks — and with some luck you might find a way out.”

—Maryam Mirzakhani (1977–2017)

“Many problems from combinatorics were easily explained, you could get into them quickly, but getting out was often very hard. Finding the right problem is often the main part of the work. Frequently a good problem from someone else will give you a push in the right direction, and the next thing you know you have another good problem. You make mathematical friends and share the fun!”

—Fan Chung (b. 1949)

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## Teaching Tips

- Joe Schwartz points out that the learning process is messy when you let your students make Decisions — but oh, so valuable!

- Sonya Post wraps up a series of posts on number studies by showing how she and her son write Math Compositions. “What I am looking for is … his ability to apply the general principles of addition, subtraction, multiplication, division and fractions to a specific number, begin anywhere and transform what he knows into multiple expressions.”

- Do your students give up too easily? Jenise Sexton may have the answer: They Called Me A Murderer.

- Fawn Nguyen shares How I Use “Between Two Numbers” to get her students estimating and make them comfortable with large numbers.

- If you want something new to try, but you’re not really sure what, explore Sarah Carter’s series of Monday Must Reads — a weekly compilation of her favorite Twitter posts, featuring activities and puzzles for all ages. (Yes, I drew a few of this carnival’s posts from her collections.)

“I believe that math is in grave danger of joining Latin and Greek on the heap of subjects which were once deemed essential but are now, at least in America, regarded as relics of an obsolete, intellectual tradition. How do you teach the beauty of mathematics, how do you teach them to solve problems, to acquaint them with various strategies of problem-solving so they can take these skills into any level of mathematics? That’s the dilemma we face.”

—Evelyn Boyd Granville (b. 1924)

“We are surrounded with ever-widening horizons of thought, which demand that we find better ways of analytic thinking. We must recognise that the observer is part of what he observes and that the thinker is part of what he thinks. We cannot passively observe the statistical universe as outsiders, for we are all in it.”

—Gertrude Cox (1900–1978)

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## Credits and Carnival Information

Photos and quotations are from the MacTutor History of Mathematics archive. To learn more about the women who have influenced math history, check out Agnes Scott College’s Index of Women Mathematicians and Wikipedia’s Timeline of women in mathematics.

“Carnival 115” background image is by Fractal Ken via Flickr (CC BY 2.0).

And that rounds up this edition of the Playful Math Education Blog Carnival. I hope you enjoyed the ride.

The next installment of our carnival will open sometime during the week of April 24, at a blog location yet unknown…

** We need more volunteers!** Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math — if you would like to take a turn hosting the Playful Math Education Blog Carnival, please let me know.

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Want us to consider your post for next month’s carnival? Please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

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I have greatest respect to & I humbly bowed my head before all great Women-Mathematicians; they are all heroes of our humanity in man’s quest for truth, beauty & goodness that reside deep in their GOD’S Gift of Mathematical & Scientific Wisdom of Courage, of Value, as we see their true humanity @ the core of mathematics & science of the creation … of the Universe & Earth which possess mathematical formulae of life, love & symbols — especially those women-mathematicians who suffered most painfully in their lifetime on Earth because of inhumanity; yes, they all deserve our present modern human mathematical & scientific respect from our hearts — all of them past & present: yes, to all of them I have my soul-deep respect w/ the greatest admiration more than men of mathematics & science. All their mathematics achievements, in one way or the other, have had greatest impact to the present 21st Century Mathematics Level of Development, more than perhaps, do their contributions provide lasting value to our mathematics & science of today! My firm awe-filled Salute to all of them …