The Most Important Component of Quality Teaching is …

What do you think the single most important part of effective teaching, in high school, is? Breaking down classroom management and teaching into a lock and step routine is impossible.  People are too variable.  And, especially in high school, we are talking about the interactions of 150 – plus people a day! It is because … Read more

Square Roots Part 1

Note:  Square roots are pretty tricky to teach and learn because the tendency is to seek answer-getting methods.  Patience at the onset, allowing for full development of conceptual understanding is key.  Do not revert to tricks and quick “gets” when first learning square roots.  Always revert back to the question they ask and how you … Read more

Where the First “Law” of Logarithms Originates – Wednesday’s Why E6

For a PDF of the following, click here. For a PowerPoint of this information, click here. rule 1 Wednesday’s Why – MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbeqcLbCaqa aaaaaaaaWdbiaa=nbiaaa@3804@ Episode 6 In this week’s episode of Wednesday’s Why we will tackle why the following is “law” of exponents is true in a way that hopefully will … Read more

What Do Grades Really Mean?

What Do Grades Mean The following is highly contentious.  Many of the situations discussed here should ultimately be considered on an individual basis.  The purpose of this is not to create a rubber-stamp solution to all problems that arise with grade assignment and student ability and or performance, but is to provide a general framework … Read more

How to Teach Exponents – Part 1

Exponents are one of the most difficult topics to teach because once you understand how they work, it seems so obvious.  And once you understand something to the point of it being obvious, your memory of how difficult it was to learn and what caused problems is almost entirely erased. To “Get It,” with exponents … Read more

Why Do Some Fractions Repeat as Decimals?

For a PDF of the following, click here. There’s a video of this material at the bottom of the page. If you’d like a PowerPoint that covers this material, email me at thebeardedmathman@gmail.com Why some rational numbers repeat as fractions Why Some Rational Numbers are Non-Terminating Decimals I’d like to explore the relationship between non-terminating, … 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

Adding and Subtracting Algebraic Fractions

part 2 Introduction to Algebraic Fractions Part 2 In the last section we saw both how to reduce Algebraic Fractions, which if you recall, are also called Rational Expressions, but also how the math works. Because of the relationship between division and multiplication, and multiplication’s commutative property, we can reduce Algebraic Fractions like the one … Read more