Teaching Square Roots Conceptually

Teaching Square Roots Conceptually   teaching square roots How to Teach Square Roots Conceptually If you have taught for any length of time, you’ll surely have seen one of these two things below. 24−−√=62–√   or     4–√=2–√24=62   or     4=2 MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaacaaIYaGaaGinaaWcbeaakiabg2da9iaaiAdadaGcaaqaaiaaikdaaSqabaGccaqGGaGaaeiiaiaabccacaqGVbGaaeOCaiaabccacaaMc8UaaGPaVlaaykW7caaMc8+aaOaaaeaacaaI0aaaleqaaOGaeyypa0ZaaOaaaeaacaaIYaaaleqaaaaa@479C@  Sure, this can be corrected procedurally.  But, over time, they’ll forget the procedure and revert back to following whatever misconception … Read more

Try to Solve This Problem … without Algebra

Can you solve the following, without doing any Algebraic manipulation?  Just by reading and thinking about what it says, can you figure out what x is?  (The numbers a, x, and k are not zero.) Given:  3a = k And:  ax = 4k What must x be? If you’re versed much at all in basic Algebra you will be tempted to substitute … Read more

Vestiges of the Past Making Math Confusing

Something in Math HAS to Change Convention is a beautiful thing.  It allows us to use symbols to convey little things like direction or a sound.  We can piece those things together to make larger things, and eventually use it to create something like what you’re reading now.  There are no inherent meanings to these … Read more

Back in Session

I’m trying a few new things this year in math.  I will try to summarize how each week goes throughout the year and highlight successes and failures. This week I really tried to introduce the honors freshmen to “real” math.  That is, some basic proofs, how generalize things in math and expose them to some … Read more

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

What is Algebra?

This past month has been very busy here for The Bearded Math Man.  I’ve learned a lot about things I have merely taken for granted and have shared most of them with you here on my site.  And while I have a goal and a mission, the methods of achieving that goal are still forming. … 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

The Problem with PEMDAS

The problem with PEMDAS This problem has really stirred a lot of interest and created a buzz on the internet. I can see why, it’s an easy one to miss.  And yet, PEMDAS is such an easy thing to remember, the mnemonic devices offered make for a strong memory.  So people passionately defend their answers. … Read more

The Square Root Club

If you’re a teacher, I have a short story that you can share, adapted to fit your own style, that you can use to address the biggest issue with teaching … students learn what they want to learn.  Creating interest in mathematics for teenagers can sometimes be a challenge.  One of the easiest ways to … Read more

How Math Fixed Music

How Math Fixed Music Rational Exponents Sound GREAT Before we dive in, music is primarily defined by what we hear, not by the analysis and insight provided by math.  For example, an octave is a note whose frequency is double that of its parent note.  The mathematical relationship was discovered after the fact.  The following … Read more