Thursday, April 16, 2015
Monday, February 17, 2014
Friday, April 6, 2012
I'm back!!
It's 2012 and a lot has happened since I debuted this blog. I am now well on the way to developing an electronic classroom. I started using TI nSpire calculators, with wireless communication capabilities at the start of the 2011-2012 school year. That has proved to be a tremendous help for my students. In addition, during the second half of this school year, I began using both Temple University's Calculus on the Web and the Khan Academy's Websites to help my students with their math.
It has been an eye-opener.
The biggest point: Giving students direct feedback on their work is one of the best motivators--especially if they can see a way to improve their performance and their knowledge. I think that's the real key: Give students a clear path for improving their math skills and, most likely, they'll put in the effort.
Some of my students are competitive and the Khan Academy's "energy point" setup is conducive to competition; students can rack up tens-of-thousands, even hundreds-of-thousands of points by cranking through the practice exercises.
But I created a couple of important "benchmarks" that are better measures than raw, total point scores. One of the most-important of these: Points per minute.
It has been an eye-opener.
The biggest point: Giving students direct feedback on their work is one of the best motivators--especially if they can see a way to improve their performance and their knowledge. I think that's the real key: Give students a clear path for improving their math skills and, most likely, they'll put in the effort.
Some of my students are competitive and the Khan Academy's "energy point" setup is conducive to competition; students can rack up tens-of-thousands, even hundreds-of-thousands of points by cranking through the practice exercises.
But I created a couple of important "benchmarks" that are better measures than raw, total point scores. One of the most-important of these: Points per minute.
Saturday, June 20, 2009
Calculus on the Web
Temple University has a fantastic instructional Website devoted to helping students learn as much as possible about math---everything from Algebra to advanced Calculus. I hope to incorporate "Calculus on the Web" into my Summer School and Fall teaching.
Will it work?
Stay tuned. . .
Will it work?
Stay tuned. . .
Sunday, February 1, 2009
DC Words and Numbers is up and running!
I've just created a new Website via Google, dcwordsandnumbers, as an instructional site. There's not much on the page yet, other than a couple of introductory videos and a sub-page listing my credentials and my curriculum vitae.
It's a start! My hope is to bring more of my teaching to the Internet community. The reasons are twofold: First, I think I'm an above-average teacher with something valuable to contribute. Second, I want to promote myself as a tutor (because I need to supplement my teacher's income).
So, stay tuned for more. . .
It's a start! My hope is to bring more of my teaching to the Internet community. The reasons are twofold: First, I think I'm an above-average teacher with something valuable to contribute. Second, I want to promote myself as a tutor (because I need to supplement my teacher's income).
So, stay tuned for more. . .
Saturday, January 24, 2009
Algebra II: Factoring is FOIL in reverse
My students at McKinley Tech are in the midst of learning quadratics. Most recently, we've studied the parabola and used the Vertex Form and the Standard Form to understand the main features of that geometric shape. One of the problems I assigned on the mid-term exam was to translate a parabola's equation from Vertex Form to Standard Form and then to graph the figure.
A day or so after the mid-term, a couple of my students asked: "Now that we can go from Vertex Form to Standard Form, how can we go back the other way?"
That question was music to my ears. "That's what we're going to learn next," I said, happy to have some of them ready to learn about factoring.
Translating a parabola's equation from Vertex Form to Standard Form involves what I call "unpacking" part of the equation and then multiplying and adding all of these unpacked elements until we arrive at a Standard Form equation. A main feature of this unpacking process is to multiply sets of numbers and variables in parentheses. For example, (x + 3) (x + 3).
There are two ways to do this. Here in the U.S., this multiplication process is known as FOIL, an acronym for First Outer Inner Last. Another, more-cumbersome method is known as the Double Distributive process. Suffice it to say we'll leave the Double Distributive process well enough alone.
Well, until last week, my students didn't realize that doing these FOIL calculations led them from Vertex Form through to another form of quadratic equation, the Intercept Form. I didn't bother to tell them about this, since it would have been a distraction from the final objective I had in mind: arriving at the Standard Form equation.
Now, however, as we embark on factoring quadratic equations in Standard Form, it makes to show my students some of the aspects of the Intercept Form.
I think of this as giving my students some perspective on what they're doing. Without this perspective to their studies, what they're missing is any understanding or appreciation of why they're learning. And with no understanding of "Why?" they're learning, students will become bored or disenchanted. And that's a recipe for disaster in the classroom.
A day or so after the mid-term, a couple of my students asked: "Now that we can go from Vertex Form to Standard Form, how can we go back the other way?"
That question was music to my ears. "That's what we're going to learn next," I said, happy to have some of them ready to learn about factoring.
Translating a parabola's equation from Vertex Form to Standard Form involves what I call "unpacking" part of the equation and then multiplying and adding all of these unpacked elements until we arrive at a Standard Form equation. A main feature of this unpacking process is to multiply sets of numbers and variables in parentheses. For example, (x + 3) (x + 3).
There are two ways to do this. Here in the U.S., this multiplication process is known as FOIL, an acronym for First Outer Inner Last. Another, more-cumbersome method is known as the Double Distributive process. Suffice it to say we'll leave the Double Distributive process well enough alone.
Well, until last week, my students didn't realize that doing these FOIL calculations led them from Vertex Form through to another form of quadratic equation, the Intercept Form. I didn't bother to tell them about this, since it would have been a distraction from the final objective I had in mind: arriving at the Standard Form equation.
Now, however, as we embark on factoring quadratic equations in Standard Form, it makes to show my students some of the aspects of the Intercept Form.
I think of this as giving my students some perspective on what they're doing. Without this perspective to their studies, what they're missing is any understanding or appreciation of why they're learning. And with no understanding of "Why?" they're learning, students will become bored or disenchanted. And that's a recipe for disaster in the classroom.
Welcome! Are you ready to learn?
Whether you need help with the Math and Verbal sections of the SAT, or with Algebra II/Trig and Geometry, I'm here. So, let's get started.
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