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I will shamelessly plug my new book, only because I think its topic is important and relevant to people in the group. It contains ideas from philosophy, mathematics, and information modeling. It's also a fun read :)

First and foremost, this is a beautiful story about a girl who learns to count. However, most of us have forgotten how we became skilled counters, and few know that in doing so we also learn concepts from higher mathematics. If you are curious to know why you can count or if you want to do some exercises together with children to help them on their way to start counting, then this is the book for you. There is something for everyone in the book and you will enjoy it as an exploring kid or as a caring parent, as well as a seasoned mathematician. The book illustrates and thoroughly explains a number of key scenarios on the way towards counting, with pointers to anyone who wants to dig deeper into the presented subjects. It is time to learn how to learn to count!

My Little Big Math Book can now be ordered through Amazon!
There's a hardcover here and a paperback here

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Net of Pentagonal Pyramid (J2)
Розгортка п'ятикутної піраміди (J2)
Развертка пятиугольной пирамиды (J2)

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Howdy mathematicians :)  

I've made a short film about a lesson on taught on 2-step equations.  Lots of resistence from students on doing things algebraically.  In the film, I share some of my strategies on how I try to get them to see the beauty of algebra :)

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Remember being a student in math and the teacher made something you thought was simple into something really complex and you thought 'why would you ever do that.'  I'm on the other end of that conversation now.

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In the new episode of the Math Ed Podcast, I talk about a recent paper in ZDM that I wrote with Chris Engledowl and Vickie Spain. We focused on the discourse of attending to precision in secondary mathematics classrooms.

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Touch Integers ℤ (+ - × ÷)  (Basic operations and prime numbers)

I've started my reflections about this 20 years ago:
Is very easy add and subtract graphically. One can regroup the tokens of each order, regroup, carry or borrow tokens, and you can obtain the result in a simulation of abacus.

But not so easy to practice multiplication or division in this visual and interactive way:
Maybe is useful to look inside of the numbers:
Inside the numbers there are the components of the number: The prime factors.
To multiply two integers you must regroup the components of the two numbers.
To divide a integer, you must separate the components.

The program only works with integers. adds, subtract, multiplies and divides (but only exact division) 

Is my latest Android (free) App: 

More details and acknowledgements at:

(Tested successfully with borrowed nephews)
Animated Photo

Give examples of following functions:
1) f(x+a)= f(x)+b; 
2) f(x+a)= bf(x); 
3) f(x+a) = (f(x))ᵇ; 
4) f(ax)= f(x)+b; 
5) f(ax)= bf(x); 
6) f(ax) = (f(x))ᵇ; 
7) f(xᵃ)= f(x)+b; 
8) f(xᵃ)= bf(x); 
9) f(xᵃ) = (f(x))ᵇ;
a and b are constants

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Last week at PMENA, there was a working group on argumentation, justification, and proof (organized by Michelle Cirillo, +Karl Kosko, Megan Staples, and Jill Newton). Keith Weber gave a presentation on conceptions and conflict in the research literature and that presentation is now available as an episode of the Math Ed Podcast.

Coming soon... the panel discussion from the working group, featuring +Kristen Bieda, Anna Conner, and Pablo Mejia-Ramos.
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