Whenever I can find a memory trick that helps students get something straight, I use it. Students needs to remember so many things in algebra, so whatever help we can give them is well appreciated.
So recently I stumbled upon a memory trick that helps students tell which of two numbers is greater and which is less.
Let's Reduce Mistakes in Algebra!
You might be thinking: greater and less?! Why would any student have trouble with that? Well, before students hit negative numbers and absolute value, there is generally little trouble. The greater numbers are the larger numbers, the lesser numbers are the smaller numbers. And kids basically know what we mean by larger and smaller whole numbers, when they are dealing with positive numbers and zero.
But when students encounter negative numbers, some things change.
While 10 > 5, – 10 IS not > – 5. Instead: – 10 < – 5.
As if that were not enough, absolute vale comes along and makes things still more confusing, since it takes the value of any number and makes it positive. So now:
abs. value of – 10 > abs. value of – 5
No one would attempt to climb Mount Everest in a day.
But when we teach math, we often expect something similar from students. We expect them to learn a complex, multi-step process in one lesson, in one hour. We expect them to go from no awareness of the process, to awareness to competence to mastery. And we don’t take account of the fact that many math process requires a long ladder of thought steps. In edu-jargon, this process of taking all of the little steps into account — and teaching each step individually — is called “scaffolding.”
Like climbing Everest, doing Math requires many STEPS
I have long found “scaffolding” important in working with students who struggle with math in general and algebra in particular. (more…)
Over the past 10 -15 years, many states have mandated tough new requirements that ALL students (special education students as well as mainstreamed students) take and pass Algebra 1 (sometimes higher math courses, too) in order to graduate from high school.
While that may not sound very challenging for students who do well in math, these mandates have placed major hurdles before students who struggle with math in general — and algebra in particular.
New studies have been coming out on the impact of this so-called “Algebra-for-All” teaching push. I just found an interesting article on this topic at this site.
I’m now including a general link to this math news portal — in my blogroll — as it contains a wide range of articles for math educators. Its name on the blogroll is Math Education News. Feel free to check it out any time you drop by the blog — or any time at all.
And do feel free to share your comments on the current “Algebra-for-All” push. Do you find that it is working where you live and work? Or not working? Any suggestions on how to tinker with mandates to make them work? This is an important topic since algebra is the critical “gatekeeper” course to all higher math. And what’s more, major studies have found that success in algebra is one of the key predictors of matriculation into college.
So a lot is at stake when it comes to algebra. And a lot rides on how well we as a nation help children succeed in this course.
Share your thoughts; we’re all curious to hear what you think.
Here’s another interactive post for all of you blog readers.
It’s sort of the Pink Elephant that has landed in the living room, and I can’t just pretend it’s not here any more
The election of Barack Obama could portend significant changes in the system of public education in this country.
If you’re open to sharing, I’d really like to hear your thoughts.
What do you hope for in an Obama Administration, with regard to education? Research and new Grants? Changes to No Child Left Behind? Greater funding for urban and rural districts? Higher teacher pay? An end to vouchers? More accountability? Merit pay?
What are your concerns?
Do you have any ideas that you think Obama would do well to heed?
What might Obama ignore in the field of education that he would do well to pay close attention to?
I’m opening this up pretty wide. But with one restriction. All comments must be on the topic of education. Any that are not on education I will have to discard.
Your coments may be short, Just, what’s on the top of your your mind? I’d really like to know. And we can all benefit by hearing from one anoher.