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The Professor of Legend

The traditional mathematics professor of the popular legend is absentminded.

    He usually appears in public with a lost umbrella in each hand.

      He prefers to face the blackboard and to turn his back to the class.

        He writes a, he says b, he means c; but it should be d.

          Some of his sayings are handed down from generation to generation.

            • “In order to solve this differential equation you look at it till a solution occurs to you.”
            • “This principle is so perfectly general that no particular application of it is possible.”
            • “Geometry is the science of correct reasoning on incorrect figures.”
            • “My method to overcome a difficulty is to go round it.”
            • “What is the difference between method and device? A method is a device which you used twice.”

            George Pólya
            How To Solve It

            If you’re not familiar with Polya’s work, here’s a 4-page summary of his problem-solving method.

            Or check out David Butler’s wonderful Solving Problems Poster, which encapsulates Pólya’s system in a visual, easy-to-follow way that works with younger students, too.

            4 steps to solving problems

            CREDITS: “Professor” cartoon (top) by André Santana via Pixabay.
            THE FINE PRINT: I am an Amazon affiliate. If you follow the book link above and buy something, I’ll earn a small commission (at no cost to you).

            New Printable Puzzle Books: Diffy Inception

            The best way to practice math is to play with it—to use the patterns and connections between math concepts in your pursuit of something fun or beautiful.

            Diffy Inception puzzles have their own symmetric beauty, but mostly they are just plain fun. Students can practice subtraction and look for patterns in the difference layers.

            I just published four new activity books to our online store:

            Notes to the teacher include puzzle instructions, game variations, journaling prompts, and more. Plus answers for all puzzles.

            Available with 8 1/2 by 11 (letter size) or A4 pages.

            My publishing company runs this online store, so you can find all my playful math books there — including an exclusive pre-publication ebook edition of my newest title, Prealgebra & Geometry: Math Games for Middle School. Click here to browse the Tabletop Academy Press store.

            Have a Mathematical Thanksgiving Dinner

            With the pandemic still raging, most of us will have to adapt our normal holiday traditions to fit the new reality. We may not be able to have a big family gathering (except over Zoom), but we can still enjoy great food.

            So for those of you who are planning ahead, here is a mathematician’s menu for next week’s Thanksgiving dinner.

            Optimal Potatoes

            Green Bean Matherole

            Borromean Onion Rings

            Thanksgiving Turduckenen-duckenen

            And for Dessert

            May I suggest some of Don Cohen’s Infinite Cake?

            Click here for cake

            CREDITS: “Thankful” photo (top) by Pro Church Media via Unsplash.com. Food videos by mathemusician/doodler Vi Hart.

            Discern Patterns

            I’m almost done rewriting the Standards for Mathematical Practice into student-friendly language.

            They say mathematics is the science of patterns. So here’s…

            Math Tip # 7: Discern Patterns.

            • Look for patterns in numbers, shapes, and algebra equations.
            • Notice how numbers can break apart to make a calculation easier.
            • Number patterns morph into algebra rules.
            • Adapt math situations to make the structure clear. (For example, by adding new lines to a geometry diagram.)
            • Step back from a situation to see it from a new perspective.
            • Try to find simpler patterns within complex equations or diagrams.
            • Not all patterns continue forever. Test your patterns. Can you trust them?

            Continue reading Discern Patterns

            Exciting New Homeschool Math Program

            Homeschooling friends, check out this new homeschool math program that’s fun, rigorous, and engaging — a delightful, hands-on course that helps parents (and their children) understand math.

            Introduction to Cuisenaire Rod Structures Course

            I had the privilege of previewing this class as Sonya and Lacy put it together. I highly recommend it to anyone who struggles with math, or who wants to take a non-traditional approach.

            By focusing on making sense of number relationships, and by teaching algebra before arithmetic, this course provides a stress-free path to rich mathematical mastery.

            And for all they provide, including weekly live workshops and a slew of printable math journal pages that prompt deep thinking, the price is a steal!

            Continue reading Exciting New Homeschool Math Program

            Say What You Mean

            Continuing my project of rewriting the Standards for Mathematical Practice into student-friendly language.

            Here’s my version of SMP6…

            Math Tip # 6: Say What You Mean.

            • Words can be tricky, so watch your language.
            • Label drawings and graphs to make them clear.
            • If you use a variable, tell what it means.
            • Care about definitions and units.
            • Pay attention to rules (like the order of operations).
            • Use symbols properly (like the equal sign).
            • Understand precision. Never copy down all the digits on a calculator.

            Continue reading Say What You Mean

            Math as a Verb

            Here’s the full quote:

            I like to play games. Almost any type of game.

            I also like to play math.

            If you’ve known enough mathematicians, you may have noticed that this isn’t unusual. I’m not sure if a love of games and puzzles among mathematicians exceeds a love of music among mathematicians, but both are strong and intersect.

            Math in play is also a way of teaching mathematics. I think that as a metaphor, it best describes how I want to teach math.

            I am constantly seeking ways to get my students thinking about math as a verb. It is about doing, not just about having right answers or the end product.

            Games help set the culture I want to develop: Teaching students that multiple approaches and strategies are valued; trying is safe; and conversations about why, how, and discovery are the goals.

            —John Golden
            Yes, Playing Around

            CREDITS: “Football outside Jakarta” photo by Robert Collins on Unsplash.

            Master Your Tools

            As I’ve mentioned before, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

            Here’s my version of SMP5…

            Math Tip # 5: Master Your Tools.

            • Collect problem-solving tools.
            • Practice until you can use them with confidence.
            • Classic math tools: pencil and paper, ruler, protractor, compass.
            • Modern tools: calculator, spreadsheet, computer software, online resources.
            • Physical items: dice, counters, special math manipulatives.
            • Tools for organizing data: graphs, charts, lists, diagrams.
            • Your most important weapon is your own mind. Be eager to explore ideas that deepen your understanding of math concepts.

            Continue reading Master Your Tools

            FAQ: Playful Math for Older Students

            My students are so busy that time-consuming math projects are a luxury. How is it possible for older kids to play with mathematics?

            Too often, the modern American school math curriculum is a relentless treadmill driving students toward calculus. (Does this happen in other countries, too?)

            But that’s definitely not the only way to learn. For most students, it’s not the best way, either.

            Here are a few ideas to get your older children playing with math…

            Continue reading FAQ: Playful Math for Older Students