In this episode we're going to start our deep dive into the type of thinking we do when we combine numbers additively. I'll discuss the two words I use to describe what's going on in my head both when considering contexts and performing calculations, and we'll get a peek into where additive thinking fits in the larger framework of mathematical reasoning.

Shout out to Pam Harris for her extremely useful Development of Mathematical Reasoning graphic. Check out her workshops, (including a free one that expounds on the DMR graphic!)

And thank you, twitter user @Wparks91 (and perhaps many others) for generating widespread awareness of different mental math processes for 27 + 48 through this tweet.

You can find my video regarding the mental development of "conservation of number" here.

Also, as for the math joke at the very end...

There are 10 kinds of people in the world: those who understand binary, and those who don't.

...Binary refers to a base-two number system. It compares with our decimal (base-ten) system in these ways: while base-ten has ten digits (zero through nine), base-two has two digits (zero and one). Also, as you shift each place to the left when writing digits in a number, when in base-ten, the value of your digit is increasing by a factor of 10, while in binary, it is increasing by a factor of 2. So the binary system has the ones place, then the twos place, then the fours place, etc.; and the numbers we consider 1, 2, and 4 in our decimal system would be considered 1, 10, and 100, respectively, in the binary system. Hence, referring to "10 kinds of people", while using the binary system, is referring to precisely the same amount of people that our familiar digit of 2 is referring to.

As always, my hope is that your day is filled with freedom and power, and if understanding math better can contribute to that, may it be so!