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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.'"
Didn't they just fool the students with odd / non-standard use of symbols?
I presume that 4+3+2=( )+2 is supposed to mean the same as 4+3+2=x+2.
If they had presented the equation with x, surely (almost) everyone would have solved it?
I'm from the UK, is 4+3+2=( )+2 a commonly used / commonly understood way of presenting the problem in the US?
I have a friend who's a high school teacher. He's been predicting the downfall of society for a few years now, based on the fact the kids he teaches are - for the most part - useless twats. What makes it even worse is they also carry a strong sense of entitlement, as in "even though I can't be bothered to do the work properly or learn a single fucking thing while I'm here, I deserve an A grade from you, and when I graduate I am going to deserve an $80K starting salary somewhere just for showing up and playing FarmVille all day."
If libertarians are so opposed to effective government, why don't they all move to Somalia?
I also wonder how these kids cope when a second variable is introduced.
When I was studying multiplication, I just could not comprehend it. I was getting failing grades constantly, while my classmates were memorizing their multiplication tables and acing exams. I just couldn't understand it. Then, it dawned on me... multiplication wasn't some new mystery math, it was just addition in a new form!
Then I became better at multiplication than all my classmates, and stunned the teachers by how I went from getting 80% of my tests wrong, to getting 100% correct, and faster than my classmates. Unfortunately, it was at the tail end of the unit, so I still got a bad grade on my report card.
The teachers thought I was cheating, too. They had me take tests in front of them, during recess, to prove that I wasn't cheating. They then accused me of being lazy and not paying attention previously. No, I just didn't understand the mystery math they were trying to teach me, because they were expecting me to memorize things, and not actually teaching me to understand it. I don't think they ever accepted that truth.
So it is with addition and =. Children are taught to do this, then that. They are taught process, not meaning. They need to be taught from the bottom up, not from the top down. Teach them that = means equality, not evaluation.
Oh, and use standard notations, not this ( ) garbage that nobody uses.
I'm going to guess you're home-schooled, both because of your defensiveness and because of your lack of analytical skills (as opposed to memorization).
And you would be incorrect. Which means that I am a social paragon. Actually, just put me under the column of counter-example.
They made a comparison between two subject groups, which you did not address.
They didn't address it either except with some anecdotal evidence. Most of the socially maladjusted people I have met are products of the public school system. So, there is my anecdotal evidence. It cancels out. Care to bring any actual research to the discussion?
In fact, the existence of bullies undermines the argument, since those folks are by definition not socially well-adapted, and furthermore, they tend not to be "cured" by graduation.
In fact, let's roll with their thesis. Fire all the teachers, principals, etc. and just send the kids into a locked building with no adults for 6 hours a day. Of course, we shall expect them to not only master the social graces, but be experts in automobile engineering, medicine, mathematics, literature, composition, business, and pretty much everything else. Why not? They can learn all that stuff on their own, just like they can learn social skills in an unsupervised setting.
Who is lacking the analytical skills? Really?
That's the problem the students have. My reading has it going like this:
They're taking the blank as a "fill in the answer from the previous part", working the equation from left to right, instead of understanding that the right side is related to the left, and not "part B" of the problem.
This makes perfect sense to me. Helping my little sister with her homework just a few years ago, I would manipulate equations (like moving something to the other side or dividing both sides by two) and she would say you couldn't do that, so I'd have to tell her you could and then give examples that show it was correct. Her teacher didn't get the point that the equation is a whole across, she saw it as two separate things with a symbol in between. But she could usually get the right answers by memorizing the 3 or 4 steps for solving that kind of problem the teacher gave her. But if the problem has a trick in it or isn't formatted right... the students don't know what to do and intuit (incorrectly) how they are supposed to do it.
Comment forecast: Bits of genius surrounded by a sea of mediocrity.
Math education in America is pathetic. I went through my nephews High School textbook and there wasn't any MATH in it. There were lots of pictures of butterflies and "Why are we learning this?" columns and the whole thing looked like it was designed to be entertaining, rather than educational. The math was an afterthought, with hardly any problems, no explanations of those problems or how to solve them, and no answers. I was stunned, especially when I learned it was written by four math professors.
There is some argument, of course, that this is on purpose, and that we fail our duties to educate our children because an educated populace would be a danger to those in power. I'm not prepared to accept that, but I do think we've completely failed in our duty, and the uneducated masses of today is evidence enough of that.
My father has a saying, "There's no teaching if there's no learning. Until there is learning, you aren't a teacher, you are simply a presenter". I think we have far too many presenters, and not anywhere near enough teachers.
[citation needed]
Here I am. Cite me: I'm an original source.
My kids go to the public Montessori school in my city. It only goes to 3rd grade, though, and after that they have to transfer. We'd heard good things about another local public school and enrolled my daughter there. It was a fucking disaster.
Examples:
In 3rd grade, she was doing square roots. Her new 4th grade class was starting to learn 2-column addition.
The class had one hour to do math problems 1 through 20 (out of 100). She finished in about 10 minutes because it was remedial to her. For want of something to do, she went ahead and finished problems 21-100. Her teacher called her out in front of the entire class: "The assignment was 1-20, not 1-100. You didn't pay attention."
Since she wasn't allowed to work ahead, she pulled out a book to read. Again, from the teacher: "This is math, not reading. Put that away!" She was literally required to sit quietly in her desk for the remaining time.
Her weekly list of words to memorize for the spelling test on Fridays included "off" and "zoo". In 4th grade. I swear to God that I'm not exaggerating.
She'd cry in the mornings. "Please don't make me go to school today! I hate it there! Can't you tell them I'm sick and work from home and let me stay here with you?" I'd be sad if she was saying those things 6 years from now. Coming from my 4th grader, it broke my heart.
So I went to talk to the principal. He was a nice guy, and I'm a nice guy. We had a great visit and he said he'd work with the teacher to find more challenging work for my daughter to keep her busy and interested. We shook hands and I left.
Within the week, my daughter got detention for "looking bored in class". Shortly after that, she got a 96% on a test. Her teacher asked her (yet again, in front of the class) why she doesn't "get perfect scores on all her tests if [she's] so smart."
That afternoon, I enrolled her in a different local private school. They were doing cubes and long division in math class, and learning Latin and Greek word components in language class.
Sometimes it's not enough to talk to the teachers and administration.
Dewey, what part of this looks like authorities should be involved?
If you could get rid of all the religious wackos who use homeschooling as a way to indoctrinate their kids without having them exposed to the outside world, there would be a lot less stigma on the homeschooled crowd.
My blog. Good stuff (when I remember to update it). Read it.