Influential Teachers

Influential Teachers Teaching was never on the radar for me.  I loathed school, and didn’t hold much respect for teachers, or the profession of teaching.  When I went to college, not much changed along those lines, at first.  Now, I’m so passionate about the profession that I’m devoting a lot of my time and resources … Read more

Mathematical Literacy

Mathematical Literacy Integrating Literacy Development Opportunities in Your Instruction   A few years ago I attended a professional development seminar designed to help American math teachers integrate best practices and strategies required for their students to be successful with the Cambridge IGCSE program.  I was a guest “reference-source,” in the seminar because of the success … Read more

Favorite Technology

My Favorite Technology With the invention of the radio came claims that, “This will revolutionize education, forever.” Then came television, and more claims that, “This will revolutionize education, forever.” Then came the VHS player.  You guessed it, more, “This will revolutionize education, forever.” Then the internet came along, and louder than ever were the claims … Read more

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

This

Let’s talk about THE question in a teacher’s life … the baleful, “When am I going to use this in my real life?” Yeah, that one. The honest answer is probably, never… and they know it.  Why else ask, if not to subvert and diminish your role and purpose?  They don’t really want an answer.  … Read more

Our Youth Deserve Better – Computer Based Learning

There has been a push for computer-based learning in public education for about a decade or so now.  The thinking is that students can go at their own pace, have optimally focused and differentiated remediation and instruction, and thus, students will perform better.  That’s the sales pitch, anyway. I teach remedial math courses part time … Read more

Why Remediation Fails

Why Remediation Fails Students that struggle unwittingly do two things that ensure they continue to struggle with concepts and procedures.  Students can go to tutoring over and again, and sometimes it works, but it’s a long and frustrating journey. I’ve fallen victim to these two habits myself, we all have.  How students learn in school … 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

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