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US Students Struggle With Understanding of the 'Equal' Sign
bickerd--- writes with news of research out of Texas A&M which found that roughly 70% of middle grades students in the US don't fully understand what the 'equal' sign means. Quoting:
"'The equal sign is pervasive and fundamentally linked to mathematics from kindergarten through upper-level calculus,' Robert M. Capraro says. 'The idea of symbols that convey relative meaning, such as the equal sign and "less than" and "greater than" signs, is complex and they serve as a precursor to ideas of variables, which also require the same level of abstract thinking.' The problem is students memorize procedures without fully understanding the mathematics, he notes. 'Students who have learned to memorize symbols and who have a limited understanding of the equal sign will tend to solve problems such as 4+3+2=( )+2 by adding the numbers on the left, and placing it in the parentheses, then add those terms and create another equal sign with the new answer,' he explains. 'So the work would look like 4+3+2=(9)+2=11.'"
I blame it on calculators where the evaluate button has "=" on it.
So I'm not being a curmudgeonly old jackass when I think this generation is stupid.
I think there's still a chance you are. Is it not more likely that rather than this generation being stupid, it is just being taught poorly by your generation? The article talks about the method students use to solve an equation. Why would a whole generation of students use a different method (and the same method) than the previous generation unless they were taught that method.
It should be: 4+3+2=x+2 (Solve for x) I don't see the point in substituting parenthesis for a variable. It just makes it more confusing for everyone.
This is one reason why we home school...public school systems fail in so many ways.
A better solution is to find a better school. A better public school, or a private school, or a charter school, or something.
Yes, home schooling can be used to impart better information. You've got a much smaller class size. You've got more attachment to your pupil. You can devote as much time and effort to educating your kid as you feel necessary.
But home schooling pretty much fails to develop a kid's social skills. And I've always felt that one of the more important things that public schooling does is develop social skills.
Home schooled kids don't generally have to put up with schoolyard bullies. They don't have to make friends. They don't learn about compromises and sharing and common interests the way you do when you're surrounded by other people all day long. They don't learn to file the rough edges off their own personality, so that they can get along with others. They don't learn how to put up with other people's quirks and issues. They don't learn diplomacy and tact.
Yes, you can supplement your home schooling with some good social exposures... Send your kid to the park for a good chunk of the day, or get them involved in some kind of sports or clubs... But, from what I've seen, an awful lot of folks who are doing home schooling aren't interested in exposing their kids to much of anything. They're more concerned about sheltering their kid either from harm, or from opposing viewpoints.
Some of the hardest people I've had to work with are those who've been home schooled. They're generally very smart, very well-educated, and completely unable to deal with other human beings.
"Work is the curse of the drinking classes." -Oscar Wilde
So I'm not being a curmudgeonly old jackass when I think this generation is stupid.
Oh hell. Generation N has always claimed that Generation N+1 is {stupid, lazy, amoral, immoral, bound for *insert cultural analogy to Hell*}. This holds inductively for all values of N. Strangely enough, they also happen to think that Generation N+2 is cute and cuddly.
I hate to tell you, but our parents' generation thought we were idiots too, I'm sure. I know their parents thought they were.
It's mathematics or math or math's. It's really dumb to remove the ematic and leave that trailing s. More so when you leave out the apostrophe which one is supposed to use when one leaves out letters. Plus it's much more in keeping with general rules for pronunciation of English words. Maths is just awkward.
Where are you from, so that I can make up a ridiculous name for your nationality?
Gamingmuseum.com: Give your 3D accelerator a rest.
In the elementary and middle-school texts standard notation is rarely used. I've got a doctorate, but helping my kids through their math often is a real stumper. It is very common to use a box, a blank, or a parenthesis to indicate something that they are to fill in in a "number sentence". The theory seems to be that you don't need to teach about unknowns and variables because that would be confusing. So this notation is somehow intuitively obvious to the least observant. As they may not cognitively be ready for the concept it becomes even more obscure. Have a look at the books sometime - you'll want to scream. I can testify that the methods used up until the mid 1960's were MUCH more effective in creating mathematical literacy. The Stanford Studies Mathematical Group (SMSG) series of math texts was, to my memory, the flying wedge of what was termed then "The New Math". The strategies like 4+3+2=()+2 come from that movement. Truth is, the "New Math" is a dismal failure and resulted in the destruction of the mathematical competency of two generations of American students. Unfortunately the math teachers now all came up through that system and have no idea that there is a better way to teach math.
Actually, people should be identified by their state--Texan, New Yorker, Floridian, etc. It's not the United State of America, it's the United States of America--indicating that each one has a level of sovereignty, and people should be identified by that smaller area. Similarly, people are Scottish or Welsh, and not United Kingdomian.
Battlemaster--Game with friends in medival realms
Are you nuts?
"Home schooled kids don't generally have to put up with schoolyard bullies. They don't have to make friends. They don't learn about compromises and sharing and common interests the way you do when you're surrounded by other people all day long."
All the homeschooled kids around where I grew up dealt with all that.
The asshole kids that bullied also bullied the home-schooled kids, granted they did not get to deal with the imported bullies from across town, but a bully is a bully. and they made friends with kids that lived near them.. Plus many were in sports programs with the public school kids. You can be home schooled and play football for your local public school at the same time. They joined lots of extra curricular activities. Many of us were jealous as they typically had a 4 hour school day plus got to take "classes" we never got. One kid was taking a class at the local motorcycle shop for learning small engine repair at 13 years old.
I know you guys love your twisted view of homeschooled kids as all living in basements and named "wolfgang" or "moon-unit-alpha" and are never let outside... but it's not reality. in fact it's pretty darn close to racism in being flat out wrong.
Do not look at laser with remaining good eye.
The students are the one who made up the =11 part. Try punching it the question "4+3+2= +2" into a calculator and you'll see why. To the students raised on calculators, "equals" doesn't mean equality anymore, it means "what do the numbers up to here add up to?" So they get to " = ( ) " and perform the "what do the numbers up to here add up to" operation, and write the answer in the blank provided. Then they're left with the +2 bit, so they add it again.
Left to right order of operations, for all operations.
If I have been able to see further than others, it is because I bought a pair of binoculars.
"Our youth now love luxury. They have bad manners, contempt for authority, they show disrespect for their elders and love chatter in place of exercise; they no longer rise when elders enter the room; they contradict their parents, chatter before company, gobble up their food and tyrannize their teachers." - Socrates, (circa 400BC)
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
While it's true that just because they thought it doesn't mean it's true, the opposite is likewise valid: just because many previous generations thought it, does not make it false.
It provides a burden for uniqueness that needs to be met, though.
It used to be that wisdom of age was respected and revered, even taken to heart.
When? When in living memory did the majority of young people actually respect their elders? Again, you're repeating things that have been said since the beginning of time. Hell, I've seen almost the exact same thing written in the bible. Kids were assholes then too. They still are. Time goes on.
We're talking about basic, first grade mathematics concepts here. How is this "not getting stupid"?
No, you're actually talking about pre-algebra if you look more closely at the example. Which kids have always generally sucked at.
The last couple generations, however, have been increasingly "stupid" in the "can't solve for x" sense. Test scores clearly prove this.
If there's a problem, it's not with the gene pool of the kids or their abilities. It's caused by well-meaning but catastrophically stupid policies that prevent the removal of problem students from classes, and the elimination of ability-based tracking. This means that normal kids are surrounded by juvenile delinquents and children who don't even speak English. If you remove those students (who would have not taken the test in prior generations) from the scoring, I wonder how the stats would play out.
In other words - it's not that the kids are getting stupid. It's that our schools are completely failing them.