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

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

Math is Hard

Math is Hard A typical conversation with a failing math student, with a failing math student’s parents, or with a counselor or administrator about a failing math student either directly sites this, or is pulled in a direction like driftwood in a tide by the fact that math is hard. A common conference would go … Read more

Accessing Prior Knowledge in a Way That Uncovers Misconception – A Lesson

Accessing Prior Knowledge in a Way That Uncovers Misconception – A Lesson If what we are doing in class today does not promote our understanding tomorrow, we have wasted our time. Click to download The order of operations and arithmetic with signed numbers combine to be the downfall of many high school math students.  As … Read more

Teaching Conceptual Understanding Flow Chart for Educators

Focus on Conceptual Understanding Flow Chart for Educators Teaching by concept alone will lead to inefficiencies in students.  They will, in effect, be reinventing a large part of the wheel at every turn.  (See what I did there?)  We have all witness what focus on procedure alone does.  It leaves students will a bunch of … 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

Confuse Them So They Learn

I recently did a lesson on the basics of reading and writing in Geometry.  You know, dry, dull stuff…what’s a point, line, ray, segment, how do you write an angle, what types of angles are there, and so on. While preparing all of this information I was thinking: How can I expose misconceptions about such … 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