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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.'"
Not just stupid, defiantly and proudly stupid. We've devolved into a culture that celebrates its own ignorance
No, we use 'x' over here, too.
I think that the () is supposed to be an unknown variable? 4+3+2=x+2; 4+3+2-2=x; 4+3=x; 7=x.
Support the EFF and Creative Commons. The war is coming, and they're supporting you...
I had to read it twice to get what they wanted done. An empty set of parens in proper mathematical expressions is valid and equivalent to (0).
"4+3+2=x+2 solve for x" is the correct way to state that problem.
Someone had to do it.
Ya, I've never understood why 1 + 2 = 3 = 4 - 1 isn't okay.
Technically it is as okay as it gets, both sides of each equality operator is equal which is exactly how the symbol works. TFA is about how people don't actually "get" that, if you look at the example in the summary it essentially says 9 = 11 which of course is plain wrong.
The reason "double equalities" might be wrong is if you're solving an equation while showing each step.
we used BOTH an x and a 'box' (as per my other post).
starting out, they taught us to fill in the missing value in the 'box' (square symbol). then, over time, when it was the right time to introduce letters as 'box symbols' they put an 'x' there.
made sense to me. a progression to get the kid up to that level of thinking. a box is empty and can be filled. makes good concrete sense. then later, we 'upgrade' the box to an x. same concept but more steps to get the kid there.
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"It is now safe to switch off your computer."
If you watch the video, they have pictures of the math questions, which makes things a lot clearer. The parentheses are TFA's way of trying to draw a blank space. In the original questions, it's an underlined blank space (so ___ would have been a better choice) -- the same sort of underlined blank space provided in grade school where they want you to fill in the answer. In mathematics classes before algebra, when they're trying to introduce you to algebraic concepts, it's common to use blank spaces for "figure out what goes in this space and write it", rather than writing an "x" and saying "solve for x", which would use a concept the students haven't yet been taught.
The actual notation used in math questions and textbooks is a blank space (e.g., an underlined blank space). The parenthesis are a poor attempt and rendering that in text.
No, we say "Maths IS hard", as in "Mathematics is hard" Not that it matters, I just thought I'd point it out. .
They will never know the simple pleasure of a monkey knife fight
Many, if not most public schools actively DISCOURAGE parents from "interfering" with their children's "education". Mostly, if you disagree with their policies or methods, you're kindly asked to SHUT UP. If you teach your child to read and count before kindergarten, you're yelled at. Essentially, you're supposed to just be a cheerleader and shout, "RAH RAH" while the school produces a herd of ignorant do-nothings with a ingrained sense of entitlement.
Gamingmuseum.com: Give your 3D accelerator a rest.
In most of the world we study Mathematics. I didn't realise that there was only one Mathematic studied in the US.
This is a dialectical thing about American English. We use singular verb inflections with collective nouns.
Queen's English: "Aerosmith are playing Wembley Stadium."
U.S. English: "Aerosmith is playing the Verizon Center."
This is why you hear "the data is" over here.
There's a perfect xkcd for my sig but I'm too lazy to look it up. sudo someone go find it.
"x = 1" is only a legal BASIC statement in the first place because interpreters have been relaxed for programmers too lazy to use "Let".
It's not really laziness. Mostly it's for historical reasons. My first computer (a TRS-80 model 1, "Level 1") had 4K of RAM. That's right, 4096 bytes. When you've got that little space for your BASIC programs, removing the requirement for "let" in your BASIC code freed up valuable bytes. (other similar shortcuts existed back in the day, such as "?" available as a replacement for "print".) ...and it wasn't just TRS-80s. Most computers of that era had similar restrictions. Today, space is virtually unlimited, but these legacy shortcuts remain.
Now get off my lawn.
If you consider North America and South America one continent, your opinion is automatically invalid.
Sice everybody seems to be too lazy to check, here's an excerpt from Wikipedia.
Etymology
The word "mathematics" comes from the Greek (máthma), which means learning, study, science, and additionally came to have the narrower and more technical meaning "mathematical study", even in Classical times.[9] Its adjective is (mathmatikós), related to learning, or studious, which likewise further came to mean mathematical. In particular, (mathmatik tékhn), Latin: ars mathematica, meant the mathematical art.
The apparent plural form in English, like the French plural form les mathématiques (and the less commonly used singular derivative la mathématique), goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural (ta mathmatiká), used by Aristotle, and meaning roughly "all things mathematical"; although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of physics and metaphysics, which were inherited from the Greek.[10] In English, the noun mathematics takes singular verb forms. It is often shortened to maths or, in English-speaking North America, math.
As Franky Boyle put it: "Who else could 'Scotch' an egg. Let's take an egg, cover it in meat and batter it!" That and the deep fried mars bar may explain some of the problem..
It's not a stereotype when it's true - yes there are fat people everywhere and thin people everywhere, but the US has more than 30% of their population obese. In the UK it's 22%. Italy, Austria and France are at around 10%. Up here in Canada we're hardly better than the US, and Mexico is nearly as bad. North America definitively holds the title for most obese continent, hands down.
I saw that in textbooks right on the cusp of learning algebra, to ease you into it. Only, it's not really "( )", it's, well...Slashdot doesn't support unicode so I can't show you...but, it's supposed to be a circle. TFA didn't use one either. IDK if it's because they're not using the same textbooks I've seen, or just because they don't know how to type unicode, either. At any rate, students would, from their earliest years, be used to seeing "2 + 2 = ( )" or "2 + 2 = [ ]" where those are supposed to be circles or boxes for them to put the number in. Or, perhaps "2 + 2 = ___" a blank line for them to put the answer in. The point was that, with no explanation of the equal sign, they come to the wrong conclusion about that circle. They see "4 + 3 + 2 = circle + 2" and they do what they've always done, by rote, and put 9 into the circle, then proceed on to the next little bit, which is +2, there, 9 + 2 is 11, they wonder why there isn't another circle, and make one.
At any rate, your solution of "just use algebra" is absurd, they haven't learned it yet. Algebra is what they're trying to teach them with this. And the point is, it doesn't matter. If they show them "x = 2 + 2, so x is 4", they just might get it. But, if they see "4 + 3 + 2 = x + 2" they would do the same as before "x is 9, so x + 2 is 11". They're just assigning too low a priority to equality in the order of operations, really...and also thinking in C I suppose, where (x = 9) + 2 does equal 11 ;)
ASCII stupid question, get a stupid ANSI