Why Does the Order of Operations Work?
Why does the order of operations help us arrive at the correct calculation? How does it work, why is it PEMDAS? Why not addition first, then multiplication then groups, or something else? I took it upon myself to get to the bottom of this question because I realized that I am so familiar with manipulating … Read more
Is Infinity Real?
How Many Primes are There Is Infinity Real Part 1 Teachers: The following is a discussion that can be had with students to create interest in mathematics by discussing two very easy to understand, but perplexing problems in mathematics. First, the nature of infinity. The second is the lack of pattern and order in the … Read more
Cube Roots and Higher Order Roots
other roots Cube Roots and Other Radicals Square roots ask what squared is the radicand. A geometric explanation is that given the area of a square, what’s the side length? A geometric explanation of a cube root is given the volume of a cube, what’s the side length. The way you find the volume of … Read more
Exponents Part 2
two Exponents Part 2 Division In the previous section we learned that exponents are repeated multiplication, which on its own is not tricky. What makes exponents tricky is determining what is a base and what is not for a given exponent. It is imperative that you really understand the material from the previous section before … Read more
Exponents Part 1
exponents part 1 Exponents Part 1 Reading Math One of the biggest things to understand about math is how it is written. The spatial arrangement of characters is syntax. Syntax, in English, refers to the arrangements of words to convey meaning. Exponents are just a way of writing repeated multiplication. If we are multiplying a … Read more
The Purpose of Homework and My Response
The purpose of homework is to promote learning. That’s it. It’s not a way to earn a grade or something to keep kids busy. It’s also not something that just must be completed in order to stay out of trouble. Homework is a chance to try things independently, make mistakes and explore the nature of … Read more
The Smallest Things Can Cause Huge Problems for Students
preemptive Pre-Emptive Explanation It is often the case, for the mathematically-insecure, that the slightest point of confusion can completely undermine their determination. Consider a beginning Algebra student that is learning how to evaluate functions like: f( x )=3x− x 2 +1 f( 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGMb WaaeWaaeaacaWG4baacaGLOaGaayzkaaGaeyypa0JaaG4maiaadIha cqGHsislcaWG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaGymaa qaaiaadAgadaqadaqaaiaaikdaaiaawIcacaGLPaaaaaaa@43D9@ A confident … Read more
Math Can Not Be Taught, Only Learned
Math is something that cannot be taught, but can be learned. Yet, math is taught in a top-down style, as if access to information will make a student successful, and remediation is rehearsal of that same information. Earnest students copy down everything, exactly like the teacher has written on the board, but often still struggle … Read more
