My 5th grader brought home her recent pre and post-tests on fractions. I can't fault the schools, teachers, or the typically lousy EM curriculum on this one. The topic is appropriate -- fractions in 5th grade requiring her to find the common denominator, add or subtract or multiply, and putting fractions in order, least to greatest. She's had plenty of classroom instruction and practice (she's also had a lot of afterschooling on this as Singapore Math's 5A and 5B spend a lot of time mastering fractions). The tests themselves were not particularly challenging.
So what's the problem? On a test she could easily have gotten 100% she got a 78. Why? Careless errors. She added when she was supposed to subtract, she failed to read the question properly, one she skipped entirely -- just missed the question. The one she skipped she got right on the pre-test. The ones she got wrong on the post-test she got right on the pre-test and vice versa.
So what next? Pedagogically, instructionally, what is the best way of getting kids to take their time and be careful? Is this just one of those 5th grade things? I'm tempted to ask the teacher for a copy of the test and have her retake it. Is there anything gained by having a consequence/punishment for carelessness?
Attention to detail seems critical in math. Am I overreacting? Anyone have success with this particular aspect of teaching?
My son (now 37) had a similar problem in fifth grade.
ReplyDeleteIn his case, he was just bored silly. He was being tested on material he'd found interesting when he was 5 years old.
I'd make sure your 5th grader appreciates that carelessness was the issue and then drop it.
Kids tend not to be careless about things they are interested in such as -- in my other son's case -- sorting his collection of baseball cards.
My math kid seems to do this with every new section he encounters. 9 times out of 10 his mistakes are the dumb ones.
ReplyDeleteAll I could think of to do was go over the dumb mistakes and teach him to check these particular things more closely before turning things in. It usually seemed to work.
My son gets bored very fast, too, but I've always told him that he gets to be bored when he is correct most of the time. Then he can complain.
I have her circle the + or - (or write it down and circle it for a word problem) before she begins to solve it-
ReplyDeleteDee
100% achievement is a wonderful teaching tool. It is only then can one truly conclude that knowledge has been obtained and you are not fooling yourself. In the future she could blame true misunderstandings on "stupid mistakes" and hence the erosion of ability.
ReplyDeleteThe best teachers I had would not accept scores less than 100. Less than that called for a do over.
After 16 years of school and letting lazy work and "stupid mistakes" slide, the working world may be a shock. This is a little dramatic I know but the attitude shouldn't fly.
Let me tell you a bit more about the son I mentioned in the first comment.
ReplyDeleteHe majored in math in college because he thought that would be the best preparation for being a software engineer. He's now a successful software engineer which is, of course, a field that doesn't tolerate mistakes.
I've always been happy that his boring experiences in the lower grades didn't dampen his love for mathematics and logic.
If you want to get across the idea that 100% correct is important, you can't do it with a bunch of unrelated problems; you need to do one problem which has several sequential steps. For example,
Step 1. Add 3 and 2
Step 2. Multiply the result of Step 1 by 8.
And so forth.
You want to reward two things: attending to all the problems and accurate work.
ReplyDeleteStart some kind of bonus system that rewards anwering all the questions (right or wrong) and also separately rewards correct answers.
Sometimes the bonus points are a sufficient motivator, other times you may need to permit the student to cash in the rewards for an extrinsic reward, i.e., more play time, some treat, etc.
This may be of some interest to you. It's the grading scale for 4,5,6th grade in Singapore:
ReplyDeleteUpper Primary (Primary 4 to 6)
A*: 91% and above
A: 75% to 90%
B: 60% to 74%
C: 50% to 59%
D: Below 50%
E: Below 25%
They don't expect 100% either...or even 94%. My guess is that they keep the kids engaged by giving them a few difficult problems to chew on rather than a hundred easy ones.
My son who is a fifth grader makes a lot of stupid mistakes too. I tell him that he's made the mistake but I expect him to find it and correct it. Sometimes telling him that if he makes a 90% on the odd numbered problems he can stop with that, but if he makes a lot of careless errors he has to go back and do the even problems as well.
There is an argument to be made about having the ability to focus even though the task is otherwise mundate and boring ..an ability necessary in the military, and a physician once told me that to be in the medical profession you also have to be able to focus on stupid little details when you are tired and don't feel like it.
I firmly believe that developing the skill/habit of paying attention to detail is critical.
ReplyDeleteThis is an issue that we face from time to time with our Meg (now an 8th grader). You might want to read the post about Meg and Algebra (titled "Math Story" and dated 3-24-07).
I like Ken's suggestion about using a positive reward system. For Meg, her carrot was that an A for the quarter was on the line; she was highly motivated.
I think there are some great suggestions here.
ReplyDeleteIf it were anything but fractions, I'd probably be inclined to relax about it, but I'm convinced that fraction mastery in the 5th grade is absolutely necessary for future math success.
Careless errors will sink her eventually. So maybe I'll try some of the reward ideas -- as long as she knows before she starts that there is something on the line, she'll be inclined to be more careful (I hope).
BTW, I can't count on any help at the school. They've moved on. Apparently whether you master the fraction or not, it is onward to geometry and measurement, then more data and probability. I doubt she'll see another fraction until 6th grade at school.
ReplyDeleteIt's times like this that heterogeneous grouping is such a disadvantage. Without worrying about getting into a higher level course, there's simply no down side at school for careless errors and low grades.
My son is also a 5th grade EM math student. He also makes careless errors. It doesn't add up to much, so I'm not overly concerned. On his homework last night on "cash" and "debt" for adding negative numbers (He had to cut out these little pieces of paper for cash and debt.), there were two errors. I told him that he had to find and fix them. I told him that he has to be very careful on tests because others might think that he really doesn't understand the material. He also doesn't like getting lower grades because of silly mistakes. Something has to motivate them to be more careful, even if it's external.
ReplyDeleteAs a side issue, EMs use of "cash" and "debt" to teach adding negative numbers doesn't do much for me. It may be useful on a superficial level, but I don't think it holds up very well as the problems get more complicated. EM seems to make a distinction between a negative sign and a minus operation. At least my son thinks they are quite different animals.
When I tell him that there really is no difference, this bothers him.
7 + (-2) = 7 - 2
Is is a sign or is it an operation? Is this changing the negative sign to a minus operation? This confused him.
I think that trying to teach understanding with real world analogies can get in the way. Kids will have a hard time generalizing the concept. He did come up with this saying: "When two different signs go walking, the negative does the talking."
I told him that it doesn't matter how you add things together:
A + B = B + A
He said this doesn't work for the minus operation:
A-B does not equal B-A
I told him that if he thinks of the minus sign as being tied to the number, like this:
A + (-B)
Then he could do this:
A + (-B) = (-B) + A
But "B" could be a negative number itself. How do you explain this (easily) with cash and debts? What happens when you multiply or divide signs? When reform math programs talk about understanding, they mean this sort of superficial understanding, and not any sort of mathematical understanding.
I like to think of signs as operations. A negative number is really just -1 times the positive value. The -1 is a unary operator. I have found this very useful in manipulating algebraic equations. "Cash" and "debt" only go so far.
Distinguishing between a minus sign and a negative sign must be a daunting task for someone just starting algebra. At least I found that distinction difficult to grasp a first. It took me a while to understand that in an operation like 8 - 3 the three is positive. It helps to know the rule for rewriting this operation in algebraic form: add the opposite 8 + (-3). It clarifies that the three is positive in 8 - 3.
ReplyDeleteI have the same problems with pretty much all of my kids... in all subjects.
ReplyDeleteBesides for a good old fashion lecture (which hasn't helped terribly much so far), I always make them redo the test at home. If nothing else it makes them aware of their mistakes.
I think that trying to teach understanding with real world analogies can get in the way. Kids will have a hard time generalizing the concept.
ReplyDeleteEM's cash and debt project only goes so far. It won't show on the state tests though, because those things really like money problems, so until high school, a kid could remain pretty confused about negative numbers and still pass the state testing easily.
I like the algebraic explanation -5 = -1 * 5. That was something that made sense to me back in algebra I.
Steve, your son is very smart! He's correct that a unary minus sign is not the same as a binary minus sign.
ReplyDeleteProving that a-b which means (+a)-(+b) is the same as (+a)+(-b) requires some sophistication.
Great question. I was the same way all through school until I hit the workforce where--as many other commenters suggested--I started to care more about what was going on and did just fine. Pedagogical fixes though? I think helping kids slow down, take their time, and--as painful as it seems to a kid rushing through life--re-check their answers when they're done. I'd suggest repeated conversations with your daughter about slowing down and double-checking, and make sure it's a habit she develops early rather than leaving it too long. Good luck!
ReplyDeleteJohn Saxon constantly comments on the fact that human beings are prone to error. It's a theme with him; he believes it's natural to make errors and unnatural -- unnatural as in requiring vigilance -- to be error-free.
ReplyDelete(I think that's a fair summary. I've been surprised, at times, at the vehemence of his statements about this.)
fyi, in behavioral programs mastery is typically defined as 80% to 90% correct.
I think some psychologists put the figure as low as 70%, though that wouldn't sit well with me.
Quite early on -- perhaps in Saxon 6/5 (??) -- Saxon has a lesson on algebraic addition.
ReplyDelete6 - 7 = 6 + (-7).
This is the one area in math where I have bragging rights. I'm pretty sure I was never taught the concept of algebraic addition -- I remember discovering (yes! discovering!) it for myself.
I always liked the idea of the minus sign as being -1 times, too.
(I may have figured this out on my own, too. I had a lousy math education.)