That all makes sense–sorry for misinterpreting you!
I will say one thing: I never actively memorized my times table. I went to a Montessori school. At some point along the way, after you’ve learned multiplication the long way with beads on chain and counting, you’d get to the point where you were supposed to use a physical times table.
All I did was use that for a while until I wound up remembering all the answers. And that seemed to be the way it was supposed to work. You didn’t use flash cards or anything. You just got your 10 problems, and you had to do them right (or be sent back to fix it), and then you got your 100 problems that you had to race to get done as quickly as possible. (I’m not sure that last part was part of the official Montessori method, and I think I may have already known my times tables by the time we got there.)
I’m curious how the times table is taught in schools now.
And sometimes kids can be less than fully reliable reporters. For example:
Yesterday my 6th grader came in and asked me about the difference between a dot plot and bar graph. This created drama for two reasons:
-I work with flow cytometery which uses the term dot plot to describe a graph that is more like what is commonly called a scatter plot(scatter means something else very specific, so that term can’t be used). But that was on me and once I looked at the book, I understood what was being asked.
-According to my son, in class his teacher had shown both graphs to be exactly the same, bars made up of dots. We looked in the glossary and saw that his math book did not show that. So either his teacher was wrong in here demonstration, or, what I consider more likely, my son wasn’t paying attention and misunderstood.
I’ve had this happen in the past as well with my son. And I couldn’t tell if the teacher was wrong or my son wasn’t paying attention, but since the teacher didn’t use the textbook to teach, there wasn’t anything to reference. It was highly annoying.
I think this thread got crazy lol
One of you said that (when referencing 7x3=21 being wrong because of 7+7+7) d you would have to see in context to be truly angry. I found hundreds of examples online of kids’ homework
Another used 47^2 by doing 50-3 x 50-3 etc… That is a shortcut to the answer that most people learn and call a trick. But it’s just using base 10 properties to work it out. While I love shortcuts. I don’t think kids should learn them until they understand the way you get the answer in a more logical way.
Yet another person said this common core argument is ten years old and been discussed before.
That may be so, however for people like myself whos first child just entered school 1-5 years ago then this is all new information and not old. And they are probably confused as most kids are.
Now before I start this I want to mention that my parents taught me the math I would be learning the Summer before the school year started.
Until recently I didn’t know that the way I learned 20+ years ago was something that has been around a while in other countries that people just recently (since internet got common in every home) learned about.
Having said that.
I was taught ones, tens and 100’s places. And that 2 tens is 20 so obviously 2 times 10 is 20
So by common core standards I would had the concept of base numbers like they want.
Everybody on the planet (unless they don’t know math) has the times table memorized by middle school. So some memorization is important. Otherwise what would you do, draw an array to figure out you money when paying a bill?
When I multiply 23 x 42 as an example I was taught to do the tens place first then the middle through cross multiplication involving ones and tens places then the ones a5 the end on the right.
It works using an understanding of round numbers (base 10 and base 100) like common core wants. It’s using an alternative way that most were taught in the u.s which also is visual.
They marked my child’s answers wrong also because it wasn’t done the way they wanted. (Box method) if my child can not only solve the problem fast and I’m there head and also show why and how it works, then I would say they have a clear understanding. Why man it wrong just because my child refuses to funny down to their way. I thought the idea was to see numbers in different ways and be more creative?
We had the same problem when he was leaving subtraction. There was a problem like 200 - 75.
My son said it’s 125. Can anyone say it’s wrong? His teacher did. Why? Because she wanted him to do some stupid subtraction by adding which was so backwoods confusing that neither my son not I could make since of.
So he said the teacher asked him how he got the answer. He told he just took 75 away from 200. She wouldn’t except it. So I went to the school and said excuse me? I can lay out 200 one dollar bills and take away 75 of them and there will only be 125 dollars left. How is my child wrong. She said because it was visual.
What??? Taking 75 dollars away from 200 dollars isn’t visual? This is insane. She said it’s common core standards.
Well I have read the standards. It says they need to understand it but does not mandate how they learn it. So why are so many schools using these dummied down ways of doing things.
From what I have seen a new method really was never needed. If kids were failing I’m math maybe it’s because of poor educational system as a whole and kids being allowed to have phone on the school. Or allowing them into the next grade without passing math.
And if you want a link from a government website as well as a major news outlet that specifically says common core isn’t working I’ll be happy to link it…
But to get you started here is what Harvard had to say about common core. Is Harvard a good enough source? What Happened to the Common Core? | Harvard Graduate School of Education
From what I have witnessed, while a few hardcore supporters will fight for common core. The majority of people want it gone.
You have my sympathy. Maybe you didn’t get a chance to read the entire thread, but you know, if someone pokes you with a pair of scissors, the problem isn’t that “scissors don’t work.” That person probably would’ve poked you with just about anything.
Maybe the poor educational system involved NOT TEACHING KIDS TO UNDERSTAND HOW THE MATH WORKS.
But you’re the expert. You can think of a single visual model that elides place value and doesn’t in any way require kids to justify their answer, so I bow to your abilities.
There, there.
Are you starting spring break now?
The problem is that either the teaching materials, or the teachers themselves, are failing to point out a simple but easy-to-miss fact: it is a convention of math representation that a 3 x 7 array is three rows of seven columns, while a 7 x 3 array is seven rows of three columns.
The trick is to let kids see two things:
[ul]
[li]The 3 x 7 array has exactly the same number of objects in it as does the 7 x 3 array, and that’s a graphic representation of the fact that 3 x 7 = 7 x 3, AND[/li]
[li]In math we have “ways of showing things” (i.e. representational conventions) that we all agree to use, and this is one of them. Rows first, columns second. And that will matter later in more advanced math, even though 3 x 7 still equals 7 x 3.[/li][/ul]
Depending on grade level, the teacher could point out facts such as:
[ul]
[li]One of the ways we all agree to show subtraction is that the first number is the total from which the second number is subtracted.[/li][li]One of the ways we all agree to show a fraction is that the bottom number shows how many parts something is divided into, and the top number shows how many of those parts we have.[/li][li]One of the ways we all agree to show the number “ten,” in our base ten system, is to show zero ones and one ten: 10.[/li][/ul]
In short, we all agree on some conventions even if they don’t get talked about or used right away, because we will use them later. For example, ‘first number means the x-coordinate and second number means the y-coordinate on the coordinate plane’ is another example of ‘order mattering.’
So the teacher should show a 3 x 7 array and a 7 x 3 array and show that though they look different, they each contain 21 objects----but it’s a convention to show the first number as the number of rows, and the second number as the number of columns. We all agree on this convention because it will be useful later.
Kids who understand that ‘we all agree to show fractions THIS way’ won’t find it odd or confusing that ‘we all agree to show arrays THIS way.’ It’s just the way a lot of stuff they learn in school works: we all agree to show things a certain way. In the northern hemisphere, anyway, we all agree to show maps with North at the top—it’s just something we all agree on, because it will be useful later if we all agree.
But to get to that point, their teachers need to understand that, too. And that may be the problem.
(my emphasis in the quote)
This is how stressed I am after a massage! Spring break is a month away, due to late Easter.
(Thanks for checking, and I hope you’re well).
I love your examples, but I quibble a little with the idea that “seven rows of three” is as conventional a representation of 7x3 as “One of two equal parts” is of 1/2.
When I teach multiplication, kids often solve a problem like “How many legs are on six normal cows?” with “4 x 6.” In whole class lessons, I pause, and ask for permission to write “6 x 4” because, “It’s easier for me always to put the groups first,” but I always remind them that their equation will get the right answer just as surely as mine will.
But I’ve been teach fractions this week, and one of the big errors is reversing numerator and denominator. This morning I graded a page with a problem like, “If you buy 2 gallons of juice for a party, and the guests drink 6/4 gallons of juice, how much juice is left, expressed as a fraction of a gallon?” One kid wrote “4/2” as the answer. I called her over and reviewed the problem with her, and this time I didn’t say, “Your way gets the right answer,” because it doesn’t: her way gets entirely the wrong answer, due to the convention of fractional notation.
Seeing as I am a civil engineer I would agree that yes I am an expert when It comes to using math and visualizing is a major part of my job As well.
I can think of many ways to visualize a problem. But what 3rd or fourth grader needs to use any more than if I have ten and you take away 4 I have six. Greater visual ability comes later with statistics, calculus, physics etc. Subtraction is the most basic concept next to addition. If you can think of a situation that a 8, 9 or 10 year old (or anybody) would need to count up the way they have been trying to teach… http://www.bipolarchildsupport.com/images/counting_up_method.jpg in order to simply subtract by taking away let me know. I’d love to hear it.
As far as an array. It’s a matter of perspective. …
7 x 3
—
—
—
—
—
—
—
Is this 7 rows of 3 or 3 columns of 7? It’s all perspective or point of view. So to mark it wrong is ridiculous.
The CCSS is suppose to be designed to help kids reach certain goals. It’s clearly states that they won’t dictate how the goal is reached so long as it’s reached. Each school or district that adhere to the CCSS can decide their own curriculum.
So why are proponents so hell bent on forcing any certain way of reaching. Furthermore if a child comes up with their own way of figuring out a problem and can explain how they came up with the answer, regardless of how simple the solution, they should be praised not belittled or made to feel they are doing it wrong.
If I’m contacted to build a bridge or a dam or whatnot, believe me we look for the simplest solution to a problem not the most convoluted one.
Math is suppose to be fun.
I never intended on coming here for arguments. I just think that no matter the rational, too many states and districts are fighting the CCSS for a reason and instead of arguing maybe we shouldn’t be using all this energy to find a better solution.
There was a story I heard once and I truly don’t remember where I heard this but the story goes that a semi-truck got stuck under an overpass. Police, fire and even engineers spent the better part of a day trying to figure out how to get this truck out of there to no avail.
Then a young child who was watching from a corner shouted out, “why don’t you let the air out of the tires”. They did and it lowered the height of the truck thus solving the problem.
Sometimes the easiest solution is the best.
I personally think that most of these new lesson plans are more involved than they need to be when the solution to get a child mind to understand something can be much easier.
Just curious. If a non-engineer used that story to explain why a bridge or overpass you had designed could probably be built much less expensively, and suggested that you only made the design complicated and expensive because you had some sort of selfish reason, would you be inspired to chuck everything you’d learned in school and in your professional experience and accept that they probably understood what was going on better than you did? What if they cited their extensive experience looking at bridges and overpasses from cars, and the fact that they built popsicle stick bridges in high school physics?
ETA: there’s nothing wrong with a parent or observer to have questions and concerns and insights on these things. But please don’t insinuate that those of us that do this professionally are just too stupid or stubborn or selfish to do the right thing that is so obvious to you.
Bear in mind as well that you’re looking at some of these questions in isolation. It may well be that a particular method is being taught, even if it’s not the easiest, because it helps explain other concepts later on. Often the easiest methods hide the core mathematics and give you a shortcut to the correct answer, which doesn’t help when you need to adapt to new problems in the future. It also makes it more difficult to spot errors if you only how to follow the method without understanding why it works.
Obviously the effectiveness of this type of teaching will vary from school to school, as noted above some teachers haven’t implemented it very well, but the idea behind it seems sound, just different to how older generations were taught.
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First I don’t insinuate anything. I have utmost respect for teachers. And if you would like info have plenty of links in my browser history showing that it’s mostly professional teachers fromballnover the country, from elementary schools to ivy league schools that see a proble. With CCSS.
as for your question. I do nothing for greed or profit directly. In fact I donate my time and expertise for free anytime I can if it helps a poor community I’ve even been to Africa and installed water filtration without taking a dime. And if you’re interested I can give you a link where you can go and help out too.
If a non engineer came up to me and said my design was too costly and had a less expensive way to get the job done and it still followed all safety and environmental regulations and would be perfectly safe then I would say, “ease sit down and show me your ideas. I’d love to get this done.” I would never take offense like some people on here appear to get.
Insinuating that my idea is the end all idea just because I’m a professional engineer and the guy beside me who wants to help Is not, I would be arrogant.
I know that some teachers don’t like change. And that’s fine. Everyone has their own views. Just remember that the government decided what was best when creating CCSS not teachers. At least that’s my takeaway from what I have read from countless government sites.
And it’s actually mostly teachers trying to fight to get rid of this system.
I simply am fishing for a logical reason for my child getting a failing grade for doing the right thing. Something no one seems to be able to refute logically.
They were teaching a box method for multiplying. My child did ithe homework his way instead. Let me give an example…
24
X 22
Going from left to right (just like they told him to do when estimating)
20 groups of 20 is 400 (left side) 30 2’s plus 20 4’s add up to 120 (middle). Now he’s at 520 2 groups of 4 or 4 groups of 2 are 8. Add that to the 520 and you have your answer of 528.
Simple, works on the same overall principle as the box method. He was able to do it in his head but still showed his work and described his process. It demonstrates an understanding of place values, does it not? And while I was standing there the teacher said it doesn’t work on all multiplication. So she wrote a longer 3 by 3 on the board and never even being showed by me solved it for her the same way. And behold the correct answer was given in less time and even explained. But she refused to acknowledge his ingenuity.
I am thinking of switching schools because I don’t feel this teacher should be teaching in my opinion.
Now I’m not saying that teachers don’t know how to teach. But can’t you admit that sometimes the teacher just don’t know best?
You’re the engineer, you work with calculus every day.
I’m the third grade teacher. I work with third graders every day.
What third grader needs to use any more than what you wrote? Every one. Whether they need to know something as simple as how many graham crackers to provide each student, if there are two boxes with 13 servings in each and a serving is 8 crackers and there are 18 students; or whether they need to be able to find the median of a set of results in their science experiments; or whether they need to be able to double a recipe; or whether they need to be able to subtract three-digit numbers mentally so they don’t have to do all the work of finding a calculator; there’s plenty of occasions for third graders to reason mathematically.
I trust you with bridges. Trust me with kids.
I agree completely. But just for fun let’s see if the way my son does it can be adapted easily to simplify an equation. My last post shows exactly how he multiplied the correct answer
(4x+3)(2x+4)
Write it as
(4x+3)
(2x+4)
Starting left 4x * 2x is 8x^2
The middle 4x * 4 added to 2x * 3 is 16 and 6 making it 22x
So far we have 8x^2 + 22x
Now just multiply 3 and 4 and we get 12
So we get 8x^2 + 22x + 12
All I want to point out is that I just did this the same way most teachers taught it when I went to school with the exception of me stacking each half. But the order of operations are the same. And it is also the same method of multiplying the 2 digit by 2 digit in the previous post. So it does adapt to a future step he’ll learn soon.
I tried to show his teacher that the similarity between her box method and my sons really isn’t that different just simplified.
And he was able to explain each step. That’s why I can’t wrap my head around her saying it’s wrong or that it wouldn’t work n other problems.
I don’t want to belittle any teacher but can anyone take a step back and see that the good teachers have years of experience and tend to focus on advanced students. At least at my son’s school. And less experienced teachers are teaching a new system that few grasp sometimes. I mean my son’s teacher is about 22-24 years old. She’s barely out of school herself.
Anyhow, my son probably has a better grasp of math than most seeing as I started his math education before kindergarten myself.
But they won’t place him in a more advanced class and she wants to fail him.
How is this right in anyomes mind?
No, they don’t.
But everything that’s been said to you, you’ve hand-waved away and said 'No, I don’t think it works like that" based only on your own memories of your own learning.
Everyone has concurred that often teachers mangle common core. But they mangled math before then, too: they mangle math because they are bad at math because almost everyone in America is bad at math. And when severe weakness in mathematical reasoning appears to be endemic, that’s strong evidence that the way we taught it to the last generation or two was fucked up. If anything, common core goes back to how math was taught before WW2, and honestly, people from that generation had better mathematical intuitions than people in my parents or my generation.
My most sincere advice as a teacher? Ignore your son’s actual grades. Grades are all bullshit anyway, and it keeps you focused on weird ideas like “technically right”. Don’t even look at his report card. Who cares? Focus on what he can do. You want him to be able to do everything the teacher wants him to be able to do in the widest possible number of ways and explain how each works–his own cognition–with precision and nuance. Don’t think “He knows THIS way, isn’t that enough?” The point is “He knows THIS way, can he learn another? And another?”
You really must skim a lot. My son does all that and more without a calculator.
You shouldn’t be taking offense. And instead of explaining how teaching subtraction by adding is more logical. Which I fear you can’t. At least not in the link I submitted. Instead you take offence
Maybe you’re a better teacher than my son has.
So teach me. Show me this way is really better. If I need to subtract 242 from 489. I can look at the 4 and 2 and say if I have four pencils and take 2 away that leaves me with 2. Same scario 4 away from 8 is 4 and 2 away from 9 is 7.
Teach me. First explain why a child in 3rd grade would not be around to grasp or visualize or even explain how that works.
But taking 242 rounding up to nearest 10’s then hundreds etc then circling those answers and adding it all up to get and answer creates better logic or reasoning or visualization then my example.
If you can do that then I might trust you teaching my kid. Because his teacher can’t even explain how that works. Just that it does