How to Decrease Algebraic Mistakes – Part 6
This is Part 6 in my series for helping students make fewer mistakes in algebra.
In this post I show how — by using the double-slash notation — students can avoid mistakes when factoring by grouping.
This is Part 6 in my series for helping students make fewer mistakes in algebra.
In this post I show how — by using the double-slash notation — students can avoid mistakes when factoring by grouping.
Category:
Algebra, Double-Slash, Double-Slash, Factoring, Math Instruction Techniques, Tutoring, Uncategorized
My book, the Algebra Survival Guide, has just won an award from a student tutoring organization in Detroit, Michigan.
The “Front Porch,” of Detroit, Michigan, has given the Algebra Survival Guide its distinguished “Golden Porch Award” for helping “kids in Detroit through their first year of algebra successfully.”
Here is the notification about the award:
Category:
Algebra, Algebra Survival Guide, Award, Golden Porch Award, Uncategorized
This is the fifth in a series of posts on how to help students make fewer mistakes in algebra.
So far I have introduced a form of notation I have developed, the double-slash, which looks like this:
//
and I have described some of the ways that students can use it.
I’ll continue the conversation by showing how this notation can help students combine like terms with greater care.
Category:
"Scaffolding" in Math, Algebra, Double-Slash, Double-Slash, LIke Terms, Math Instruction Techniques, Order of Operations, Practice Problems, Pre-Algebra, Simplifying Expressions, Solving Equations, Uncategorized
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Combining integers … does any early algebraic skill cause more problems?
If so, I can’t think of one.
Fortunately, though, using the double-slash notation that I’ve been talking about this week helps students make sense of this tricky topic.
Even a problem as simple as the following can be made easier with the double-slash:
– 2 + 5 – 3 + 7 – 9
When we left off, we were talking about the double-slash, a form of notation I’ve developed that helps students attain greater focus when simplifying algebraic expressions.
With greater focus, students make fewer mistakes. With the double-slash at their disposal, students avoid the mistake of combining terms that should not be combined. In the following example, students use the double-slash twice to simplify an algebraic expression:
+ 8 – 2(3x – 7)
= + 8 // – 2(3x – 7)
= + 8 // – 6x + 14
= – 6x // + 8 + 14
= – 6x + 22
By cordoning off the section with the distributive property: – 2(3x – 7), the double-slash allows students to see it distraction-free. With this heightened level of focus, students are more likely to work out the distributive property correctly, then continue on, simplifying the whole expression with no mistakes.
When I left off yesterday, I pointed out a certain kind of algebra expression that tends to lead students to make mistakes. It was an expression like this:
8 – 2(3x – 7)
I pointed out that students often mistakenly combine the 8 and the 2, to get this:
= 6(3x – 7)
= 18x – 42
The theme of these posts is: how to help students avoid mistakes in algebra.
Anyone who has worked with students learning algebra knows the truth to the maxim: MISTAKES HAPPEN.
This is the first in a series of posts offering PRACTICAL SUGGESTIONS for decreasing the number of algebraic mistakes students make.
First, it’s useful to recognize a key fact: we can’t help students with mistakes if we don’t know what causes those mistakes.
Years of tutoring have taught me a lot about why students make mistakes. And one major cause of mistakes in algebra is that students combine terms that should not be combined. Not all their fault, though. Students are often confused about what they may and may not combine. And it is tricky!
Take a problem like this: 8 – 2(3x – 7)
Certainly some kids can simplify this expression with no trouble. But in my experience, many struggle with a problem like this (when first learning it), and quite a few stay befuddled for quite some time.
The biggest mistake is that students think they can and should combine the 8 and the 2 through subtraction, proceeding like this:
8 – 2(3x – 7)
= 6(3x – 7)
= 18x – 42
Q: How can we help students avoid this mistake?
A: Use a mark that show students what gets combined and what stays separate.
I will start to elaborate on how I do this in tomorrow’s post.
Extra, extra! I thought it would be interesting for you readers to send in comments on the kinds of algebraic mistakes that “drive you up the wall” the most. When I get a number of comments in, I will conduct a poll to see which mistakes people find most vexing. Should be “fun.”
A toy that educates … could it be a dream?
I recently found something that fits that category, educating students in concepts of GEOMETRY.
It’s called the Rubik’s Slide, created by Techno Source. I bought this Rubik’s Slide a few months ago because I needed another puzzle to keep my tutoring clients entertained while I grade their work, which I often do at the start of sessions.