Maths Problem (Grade 3)

[p310don]

I had the opportunity today to go meet my daughter's teacher. In the meeting, I was given her recent maths test, for which she had received a C+ grade. I thought she was a bit smarter than that, so was a little surprised. I flicked through it, she made some dumb mistakes (gets that from her Dad I'm sure), but there was one question in particular that stood out....

An apple costs 45 cents.
An orange costs 30 cents.
Estimate how much an apple and and orange costs.

My daughter's answer was 75 cents.

She was marked incorrectly.

I queried that, seeing that 45 cents plus 30 cents does in fact equal 75 cents. Before querying it, I did re-check myself. I'm happy to question authority, but like to make sure I'm right (or at least think I am) before doing so. Yep, an apple for 45c plus an orange for 30c should cost 75c.

"Hey teacher. Can you look at this question?"

"Oh yeah, she got that wrong."

"What? 75c is the correct answer."

"Yes, but she was supposed to estimate..."

What in the actual F@#$#K??

I started boiling inside. If a mistake is made, then own it. My daughter made mistakes in this test. I don't believe she made a mistake here. The teacher's opinion is that an estimate shouldn't have a correct answer. She should have answered either 70c or 80c, or even $1.

To make matters worse, my wife is next to me. She is a grade 3 teacher. Not just a grade three teacher, but a teacher in the school my daughter goes to. In fact, the teacher in the room next door to my daughter's class. She and my daughter's teacher both went into defensive mode.

"Oh the test means she needed to round her answer. It's been removed for next year. We thought it wasn't right, so we're removing it next year. Lots of kids got it wrong."

What? Is it just me, or is a correct answer a correct answer?

I let it go in the classroom, it wasn't the right occasion to continue, and we had limited time. But the drive home, it continued. My wife wants it to be let go. I can let it go. Or can I? Should I?

Part of me wants to write an email to the principal, the school board, the local member, the minister for education; and whomever else should be fired from their jobs for letting this kind of indefensible mistake get through to the students. Part of me is livid.

On the other hand, part of me doesn't have the energy. And a (somewhat smart) part of me doesn't want to basically make this an attack on all the teachers defending this question, including my wife.

This question was written into the curriculum by some unnamed person or committee. That's the defence from the teachers I've spoken to. But, the blind follow, the visionaries make their own path.

I'm a teacher (of sorts, not in school). If I'm told to teach something that I know is wrong, I don't. Simple. Surely school teachers would do the same right? Not let 8 year olds think they're wrong when they're not.

I can feel this is devolving into a rant, but my final words. I know my own personality. If I'm right, and I know it, but someone tells me I'm not. I'll ignore them. I no longer have respect for them on that topic. Is that normal?

Anyway. curious on other's thoughts on this.

[rockedge]

I agree that it's really a bad lesson. Whats better than an estimate? That would be the exact answer.

In my job I was required to estimate as routine. Like how long will it take? What's it going to cost? The bosses really wanted details but an estimate is an estimate so I would have satisfied the crazy answer the teachers are looking for as follows:

An apple costs 45 cents.
An orange costs 30 cents.
Estimate how much an apple and and orange costs.

Answer: "around 75 cents"

My trick was even if I knew the exact answer I ALWAYS threw in the word " around" like this example: "around 75 cents" "seems like 75 cent plus or minus a few" or a favorite, "apparently close to 75 cents"

My ultimate favorite to silence the bosses: "only God knows...."

[wiak]

In my view, 75c is a pretty good estimate. In fact it is spot on, and no decimal point is involved. I spent four years of my life teaching mathematics in some international high schools, and in charge of maths department for one of these years. That question is useless for its intended purpose and no teacher worth their salt would mark 75 as a wrong estimate. Trying to justify marking that wrong is ridiculous and gives a bad name to teachers marking in such a blind to common sense manner. Becomes in fact difficult to trust the quality of the maths teaching there I'm afraid. Students sometimes give unplanned for unexpected answers that are actually correct alternatives to what was expected. Good open-minded teachers always recognise this and give the full mark. Question was at fault, not the student.

[rockedge]

Perhaps this lesson is for the Americans for when they go shopping........just because 2 items are listed that together they add up to 75 cents that is not the value displayed on the bottom line that one pays......got to calculate the sales taxes which can be a mystery as to what is what.

So basically anything for sale in America is "around" the price listed.

[fredx181]

It's just plain stupid, if your daughter had said e.g. 78c, it would have been judged as correct ? And 75c is not an estimate, so something like" "too much exact" is "not correct"

This question was written into the curriculum by some unnamed person or committee

I think this person(s) should be fired, including everyone defending that your daughter's answer was *wrong*, what's *wrong* with some people nowadays ?

[Grey]

what's *wrong* with some people nowadays ?

Once again, we are convinced that little has changed since 1969. One and a half digger continue to dig https://forum.puppylinux.com/viewtopic. ... 245#p36245
PS. Only this time the teacher, not the student. But the point is the same.

[rockedge]

This question was written into the curriculum by some unnamed person or committee

My town has such a person. Highest paid position as well.......She is some kind of "doctorate" of something that puts her as the head of the school system's curriculum.

To justify her job which pays in the $250000 as base pay per year, she recommends changing the curriculum every other year which includes new books and new systems. Thoroughly confusing those who teach the children.

No one is one bit smarter. In fact the kid's lack of knowledge is astounding.

[Flash]

p310don, tell your daughter to smile ruefully, shake her head and move on to 4th grade, where the teachers will presumably be better.

Many years ago I used to take a kid from down the block with me when I took my dogs to the river. He was maybe 8 years old but he'd get up, on his own, before 6 on a Sunday morning and be waiting for me at the curb. One morning we're driving back from the river when he mentions that he couldn't understand multiplication. I said multiplication is just repeated addition. For instance, 4x3 is just 3 added together 4 times. He thought about that for a few seconds, then said, "that's all there is to it?" Every time I tell that story I get mad at his teachers all over again. What the hell were they teaching him?

I've mentioned this to a few teachers, and they all try to make excuses. There are no excuses for not teaching a kid the fundamental definition of multiplication. Or of anything, for that matter.

[williwaw]

Anyway. curious on other's thoughts on this.

perhaps best to let your wife go alone to meet the other teachers

[mikewalsh]

Heh. Reminds me of my own school days (this was the mid-to-late 70s). This, however, is a "positive" tale. Not ALL teachers blindly follow what they're told to do...

=================================

When I got into 'senior school' - this was 3rd year & upwards - I had terrible problems with long division. Others picked it up as natural as breathing, but I just couldn't get my head round it. This continued right through the 4th year.

Our deputy headmaster was a little Welshman. Mr. R.W.G. Jones (you never saw his name without full initials). An ex-Coldstream Guards RSM, he was also a former regimental boxing champion. Tough as nails, down-to-earth and didn't tolerate "nonsense". He was responsible for making sure everyone followed the school rules, was always smart and dressed tidily (including properly polished shoes. We were expected to give a good impression of the school if we had to go into town for anything). He took this duty very seriously, and it was common to see him tearing a strip off a student for not doing something right.

We were all terrified of the guy!

==============================

He was a maths teacher - a damn good one, actually - and taught the 5th (exam) year students. Quietly spoken in the classroom, he was one of the relatively small group of teachers that had "the knack" for making a subject - which he clearly loved - interesting, even fun.......and made you WANT to learn more. That's a rare gift.

I was reasonably good at maths; I wanted to get a good grade for this subject, but understood that my lack of comprehension would doubtless count against me. One day during the autumn term, I plucked up courage to ask him if he could help me with my long division "issues". He agreed straight away.

Over the course of the next 3 evenings after school, he spent an hour with me each time.....patiently explaining how it worked, showing me examples, giving me a short list of questions to work through each time. These would then be marked accordingly. If I got one wrong, he went out of his way to show me where I went wrong, and gave me a few 'tips' to minimize future mistakes.

During that short spell, I saw a totally different side of him that not many others did. His endless patience and true passion for teaching really shone through. Despite his somewhat fearsome reputation, at the end of those 3 days I thoroughly understand that aspect of mathematics......and in recent years have used the same technique to help one of my nephews with the same long-division woes.

I will always be grateful to that little Welshman. But that WAS 50 years ago.......and the education system has changed out of all recognition.

Mike.

[Flash]

Did he start by explaining to you that division is just repeated subtraction, the reverse of multiplication, then build on that definition?

[mikewalsh]

Did he start by explaining to you that division is just repeated subtraction, the reverse of multiplication, then build on that definition?

Blimey, Flash. We're talking here about nearly 50 yrs ago. He may well have done; it WAS a long time ago.

My point here, I guess, is "Never judge a book by its cover". But MY view is that, compared to MY school-days, kids nowadays have it easy. Multiple-choice questions; you're allowed to use calculators to solve your problems IN class itself.......everything is SO "dumbed-down". We have a generation of youngsters here who are probably AS intelligent - if not more so, given the steady upwards evolution of humans - than the rest of us. Yet their minds just aren't 'stretched', or given the chance to develop their thinking processes...

The bar is set very low. The obsession here in the UK is that every child must be made to feel good about themselves, even if they're as thick as two short planks......and every child MUST go on to university, AND graduate with high marks. So we end up with a whole generation of "intellectuals", and very few "doers". They think they're going to walk straight into a top paying job....and find that such are few & far between. So they try getting a job - any job, 'cos there's all those massive student loans to pay back (currently around the £45,000 mark; the highest any single student had to pay back was over £200,000!) - and what do they find? Nobody wants them....because they're "over-qualified"!

The general consensus now is that better than 70% of university students would be financially better off NOT going on to further education.......because the earning potential of those qualifications won't "balance out" and start to cover itself for more than 20 years after graduating.

At the end of the day, somebody has to sweep the streets. Somebody has to empty the bins. Somebody has to do the shitty, menial jobs that nobody wants to do, yet which are necessary to keep us all free of the kinds of diseases that used to kill people off at what we would consider a young age, 2-300 years ago. But the current generation consider this kind of work beneath them.....

And DON'T get me started on teaching standards.

Mike.

[bugnaw333]

At the end of the day, somebody has to sweep the streets. Somebody has to empty the bins. Somebody has to do the shitty, menial jobs that nobody wants to do, yet which are necessary to keep us all free of the kinds of diseases that used to kill people off at what we would consider a young age, 2-300 years ago. But the current generation consider this kind of work beneath them.....

That somebody is an imported college graduate from African/Asian countries.

[bigpup]

"Hey teacher. Can you look at this question?"

"Oh yeah, she got that wrong."

"What? 75c is the correct answer."

"Yes, but she was supposed to estimate..."

Your comeback should have been.

So, C+ is an estimate for a grade of A or A+?

Schools are no longer teaching anything useful.

But I guess there is no need, with all the cell phone zombies

[mikewalsh]

Heh. Yeah.......and in all likelihood, those 2 girls walking together in the middle of that picture are probably nattering. But they're not talking. They'll be doing so via a chat "app" on their phones..!

(*shakes head.....*)

Mike.

[muggins]

1 + 1 = 2

[superhik]

When they made women work they doubled the taxes and cut the salaries in half. And made the kids be raises by someone else. But they don't need smart kids, just the simple workers. Children are prepared for the job market not to be their competition. That means to work for someone else, pay taxes on money they earn, pay taxes on money they spend, pay taxes on things they own that they already payed taxes on with already taxed money.

[Flash]

Who "made" women work? (I assume you meant work outside the home, and for which they are paid.)

[stemsee]

Your daughter's answer isn't wrong, if it is her estimate. The defining aspect is whether the teacher taught 'estimating' before hand with clear instructions not to 'work out' a precise answer! Of course the fact that an estimate and a precise answer can be the same value is the problem that the teacher did not accommodate appropriately in her marking. In this case some kids would need the same time to come up with (work out) an estimate, as others would to calculate (work out) the actual answer! I was taught that a simple maths question should not be given only one point, but two. One point for the correct answer and one point for the correct methodology. So if this is a case of incorrect methodology, then the answer must be wrong.

[Chelsea80]

@p310don

Estimation in math is a technique used to find an approximate answer that is close enough to the exact answer for practical purposes. It involves rounding numbers and simplifying calculations to make them easier and faster to perform, especially when exact precision is not necessary.

So in your daughters example:

An apple costs 45 cents.
An orange costs 30 cents.
Estimate how much an apple and and orange costs.
.

Methodology

Sum the Numbers: Add all the values in the group together: 45 + 30. Total sum = 75

Count the Values: Determine how many numbers are in the group: 1 @ 45 and 1 @ 30. Total sum = 2

Divide: Divide the total sum of Numbers (75) by the total sum of Values (2) to find the estimate: 75 / 2 = 37.5
.

The above assumes that the teacher has in fact taught the student how to achieve an estimate of a group of numbers.

A student can not be expected to understand how to achieve a mathematical outcome if the methodology has not been explained in the first place.

[stemsee]

@p310don

Estimation in math is a technique used to find an approximate answer that is close enough to the exact answer for practical purposes. It involves rounding numbers and simplifying calculations to make them easier and faster to perform, especially when exact precision is not necessary.

So in your daughters example:

An apple costs 45 cents.
An orange costs 30 cents.
Estimate how much an apple and and orange costs.
.

Methodology

Sum the Numbers: Add all the values in the group together: 45 + 30. Total sum = 75

Count the Values: Determine how many numbers are in the group: 1 @ 45 and 1 @ 30. Total sum = 2

Divide: Divide the total sum of Numbers (75) by the total sum of Values (2) to find the estimate: 75 / 2 = 37.5
.

The above assumes that the teacher has in fact taught the student how to achieve an estimate of a group of numbers.

A student can not be expected to understand how to achieve a mathematical outcome if the methodology has not been explained in the first place.

Isn't that sum you detailed, just the average?

[some1]

Intuitively kids know that 42 is the answer to most important things.
2 things is 42+42=84 - so rounding down to 80 seem a safe answer.

Check:
Estimating in school-classes is usually equivalent to rounding up/down.
Apple:35 ->40
Orange 40
Apple´+Orange is about 80

That'll be an A+ missus!

[p310don]

@Chelsea80 you have provided the answer to the question, "What is the average cost of each piece of fruit?"

The question was about the approximate total cost of the two pieces (my original post omitted the total part).

FYI, the "correct" answer in the teacher's eyes was either 80 cents or $1, with the actual correct answer being incorrect, because it was correct and they were after an approximate estimate rather than an accurate one.

There is confusion on the test between the terms estimate and rounding.

[Chelsea80]

@stemsee

Yes. It's just another way of putting it and easier for a young student to understand for a short cut to an answer.

Rather than trying to be taught:

An average is a statistical concept that represents a central or typical value of a set of numbers. It is commonly understood as the arithmetic mean, which is calculated by summing all the values in a dataset and then dividing by the number of values.

At a later stage in the students maths education the use of other terms can be explored and explained with the young student having mastered the basics I feel.
.

@p310don

The question was about the approximate total cost of the two pieces (my original post omitted the total part).

Thanks for the clarification.

[wiak]

Yes 37.5 would be average (in this case "meaning" the mean of the two numbers) whereas for apple + orange, I'd go for 80 as an estimate. But, yes, 45 is nearer to 50 than 0, as is 30, so 50+50=100 cents =$1 is another reasonable "estimate" (an apple plus an orange is going to cost around a dollar, albeit a "wee bit" under). All very well and good, but 45+30 is obviously 75, which is a pretty spot on estimate to me Marking that wrong is idiot extreme.

What is Wrong with the World!?
Rough Answer: WWW

[geo_c]

Yes 37.5 would be average (in this case "meaning" the mean of the two numbers) whereas for apple + orange, I'd go for 80 as an estimate. But, yes, 45 is nearer to 50 than 0, as is 30, so 50+50=100 cents =$1 is another reasonable "estimate" (an apple plus an orange is going to cost around a dollar, albeit a "wee bit" under). All very well and good, but 45+30 is obviously 75, which is a pretty spot on estimate to me Marking that wrong is idiot extreme.

What is Wrong with the World!?
Rough Answer: WWW

This all reminds me of my 7th grade math class taught by Mr. Webb. He had a few unorthodox methods of teaching. Like teaching us to meditate palms up, and marching around the room chanting all the prime factors of numbers up to 100.

But as we were doing a unit on estimating, at the end he addressed the class very precisely telling us that we could opt out of the test, and no points would be deducted from our grade, but if we chose to take it, we were stuck with whatever grade we got.

Well that was like a challenge, so I thought I understood the concept pretty well and took the test. Got a 70 I believe. I was ticked, I went to the vice-principal who listened but did not show much concern.

Lesson learned. Estimating is voodoo.

[cobaka]

@p310don

This question about "estimate" was inappropriate for a year-3 class for the following reasons, (reasons plural).

(1) According to Jean Piaget, the legendary child-developmental psychologist, humans develop skills in a recognized order and (generally) at identifiable ages. These are: (a) motor operation (eating, walking, catching a ball etc) then (b) concrete operations and (c) abstract operations. There are many demonstrations showing concrete operation (or understanding) on YouTube.

Link ->

This is a very good demonstration of a child who has not yet developed concrete operations according to Piaget's observations.

(2) The "correct" answer depended on understanding the word "estimate" but in a mathematical context. The answer "75 cents" was an accurate estimate. It wasn't wrong, 75 cents is certainly a better estimate than 76 cents;
Further, if the examiner expected the student to provide some measure of expected variation in the answer, then the language used in the question should suggest what was expected.
The question would be more appropriate in an English exam, not a maths exam. The marking of the question shows that the examiners (I imagine there was a minimum of two) failed to understand the question.
If you ask me to show an estimate of 300mm and I place my hands exactly 300mm apart - not 299mm or 301mm, then my estimate is accurate, not wrong.

(3) Repeating: The question is inappropriate because (in my opinion) a student in year 3 has not moved to understand abstract operations.

(4) In a past life a fellow called Ken Thompson worked for me. (Ken was somewhat of an imitation Thompson. He wasn't the Ken Thompson) He told me that some adults never get to abstract operations.
He said that there is a considerable range in capacity for abstract operations. Those with a poor ability (he said) program in BASIC, but struggle with C.
I can't see the difference myself (although Ken's observation depended on BASIC with things like "goto line 100" and variables A0 .. A9 etc.
But this posting is about the meaning of "estimate", not differentiation between understanding abstract concepts. I'll end here.

собака

Well I won't end there. An argument must have some benefit. Either you learn something or the person you argue with must learn something. Otherwise why argue?
I never argue with some people. (example - my sister).
She: Communism is a useful form of government.
Me: Really? Do you understand the underlying principles of communism? Have you heard about The Holodomor?
She: What's that?
Me: In the early 30's, the Communist Party induced a famine in The Ukraine to force collectivization of farming. Millions died. So many died we don't have an estimate of the dead to the nearest million. Death was so common that there are photos of people walking past dead bodies in the street. If you went to Kiev, somewhere in the city, there is a statue showing the generosity of Stalin at that time. It's called "The Girl with the Corn". You can see it today. The Holodomor was official Communist Party policy. And (at the same time) Stalin exported grain while people starved.

The_girl_with_the_cobs_of_corn.jpg (22.44 KiB) Viewed 512 times

She: Well, that was Stalin, not The Communist Party. Stalin was an evil despot. (That point was certainly true, but that does not negate the fact that the party, including Khrushchev and Beria, agreed to the plan).
Me: When Stephen Kotkin (historian -Princeton University) was asked for a summary of Joseph Stalin's life he said: "Joseph Stalin? He was a communist." Would you like to hear some of Kotkin's lectures on the life of Stalin? I'll send some. I heard Kotkin described as the man who knows more about Joseph Stalin than Joseph Stalin.
She: I'm too busy. Anyway there are lots of other communists. Stalin isn't necessarily typical.
Me: I have nothing more to say.

In contrast to that, I never argue with my daughter. I just sit back and listen. In an argument, at the beginning, she assembles her facts in a straight and very orderly sequence.
She can get to the focal point of an argument in approximately three or four sentences. (That's only an estimate - there may be some degree of inaccuracy here.)
I rarely argue with her, because (unfortunately) I'm often wrong. (sigh). But I learn a lot from my daughter, because she knows how to argue.
Probably got it from her mother, who was also clever. Her mother probably got it from her father, who was also clever.

o-o-o
My daughter told me, "Did you know that no-one living in Sydney can be buried in Rookwood cemetery?"
Me: What's going on there?
Kylie: It's against the law to bury someone while they're living.
Me: (thinks). Very logical. Can't argue with that.

(end)

More child development:
Link ->

[bigpup]

Good example of why home schooling is being done more and more in the United States.

[Grey]

@cobaka You choose strange topics to discuss with your relatives on a quiet, fine evening. It's better to discuss a trip to, say, Adelaide for the Fringe Arts festival or a cricket match

[fatdoguser]

An apple costs 45 cents.
An orange costs 30 cents.
Estimate how much an apple and and orange costs.

And and ... why two pears of course

Just wait for the human biology test results. What does one man and one woman make? There's no accurate answer, could be a him, her, it ... or many other potential results.