Yes, I don't understand why that's controversial.

Several people have explained exactly the skill that is being examined in the question, and it's surely a skill that most of the people complaining about actually use in their daily lives.

It's simply teaching something that is often done intuitively.

When did finding multiple solutions to a problem become an issue? Is it just because it's attached to "common core" that it's reflexively dismissed?

quote:

Originally posted by maladat:

The point of the area model thing is that it makes how to break it up really obvious - pick easy to calculate pieces that cover the whole area and don’t overlap.

It seems like the tool is far more complex than actually solving the problem. The student has to map an abstract concept of numbers into an abstract geometric visualization, then process that in an abstract way back into numbers.

Why teach them a method of breaking it up for mentally calculating an answer when mental calculations frequently result in errors? Written calculation is far less prone to errors.

It would be far more direct to teach the kids how to write it out on paper and do all the normal multiplication. Write 17 above 20 (or 20 above 17 if you prefer), and run the old fashioned system which teaches and reinforces the value of the position (1s, 10s, 100s, etc).

I expect many students struggle with the abstractness of this method, and many have difficulty with the geometric visualizations.

Our daughter is in 4th grade too and while she does understand the “new” math, my wife and I have ingrained times tables and she can run circles around her classmates with almost immediate, correct answers.

The new way just does not work with our old way of learning. It may have value somewhere but I don’t see it at the moment.

We reinforce to learn and understand the new way but Mom and Dad will show her the quick, simple, accurate methods almost all of us learned.

Another solution looking for a problem?

-Jeff

quote:

Originally posted by Fly-Sig:


It would be far more direct to teach the kids how to write it out on paper and do all the normal multiplication. Write 17 above 20 (or 20 above 17 if you prefer), and run the old fashioned system which teaches and reinforces the value of the position (1s, 10s, 100s, etc).

I have an elementary school kid in my house. I can tell you that they are teaching both methods. Having seen the entire progression over several months, I'm fine with how they are teaching math.

Seeing one single problem from the OP isn't seeing the entire picture. You have to look at the entire workbook of lessons, which I have.

quote:

Originally posted by Fly-Sig:

I expect many students struggle with the abstractness of this method, and many have difficulty with the geometric visualizations.

Yes they do, which is why it's being introduced much earlier.

I'll say again that the particular example in the OP was poor, but teaching the concept of number sets with geometric visualizations is introduced in the fourth grade. The concepts apply to algebra, geometry, and calculus. I'm sure it goes beyond calculus, but integral calculus, finding the area under curves, was the last math class I took.

Each grade builds on what was taught in the previous grade so the student will be prepared for the next grade. The commutative, associative, and identity properties of addition and multiplication are also introduced in the fourth grade along with the zero property of multiplication. I don't have a problem with that. My 16yo son started learning trig identies today, the inverse and Pythagorian ones, in his college trig course.

Teaching math isn't about getting the right answer. It's about teaching the process to get to the right answer. That boggles seventh grade minds. I can give them 2x=10 and all of them can tell me x=5. Nobody cares though and nobody is going to pay them to do that. The important part is that they know the process to divide both sides of the equation by 2.

We have a 4th grader in Spanish immersion. We are both older parents, and so learned math “tables” by memorization - now they’ve renamed that, and are starting to teach kids “how” to think. The troubling part is when you have a child that doesn’t think the same way that everyone else does- our son proved that to us on the way up to school one day when we had him figure out some math including different coins.. and when he was done explaining he proved us wrong. So I understand the new version and completely agree with Maladat, however I feel like this might lock out some kids who are thinking outside the box.. and potentially extremely creative.
My brother-in-law at Christmas time tried to show my son his way to solve a math problem; my husband and I had already shown our son “our” old fashioned way. My son’s teacher had shown him a third way, and I had to shut my brother-in-law down - because as we all know even if you come up with the right answer if you didn’t set the problem up the way the teacher wants to see it, you’ll get a zero mark. By the way, my young brother-in-law had never seen the way my son is being taught now (which is what the images are showing with the boxes and breaking it down) it makes great sense but I would like to come upon it on my own versus being shown that this is the only way to think..

quote:

Originally posted by Fly-Sig:
Why teach them a method of breaking it up for mentally calculating an answer when mental calculations frequently result in errors? Written calculation is far less prone to errors.

It would be far more direct to teach the kids how to write it out on paper and do all the normal multiplication. Write 17 above 20 (or 20 above 17 if you prefer), and run the old fashioned system which teaches and reinforces the value of the position (1s, 10s, 100s, etc).

First, they still teach "the old way" (long multiplication by hand), too. It's not an either-or.

Second, with this approach and others like it, they're trying to teach an intuition/feel for numbers that goes beyond just doing multiplication.

Third, long multiplication by hand, even though it is still taught, is almost totally irrelevant to present day-to-day life. Yes, it is absolutely something everyone should know how to do, but the reality is that barring exceptional circumstances, anyone who was born in the era of easy access to inexpensive portable technology is going to do arithmetic either in their head or on a machine (calculator/phone/computer).

I have master's degrees in mechanical engineering and computer science, which, believe me, required a lot of math. When I had to help my elementary-school-age kid with long division homework a few years ago, it took me a minute to remember how to do it. I don't think I'd worked a long division problem by hand since middle school. If I couldn't do it in my head or maybe scribble a quick shorthand step or two, I used a machine.

quote:

Originally posted by irreverent:
We have a 4th grader in Spanish immersion. We are both older parents, and so learned math “tables” by memorization - now they’ve renamed that, and are starting to teach kids “how” to think. The troubling part is when you have a child that doesn’t think the same way that everyone else does- our son proved that to us on the way up to school one day when we had him figure out some math including different coins.. and when he was done explaining he proved us wrong. So I understand the new version and completely agree with Maladat, however I feel like this might lock out some kids who are thinking outside the box.. and potentially extremely creative.
My brother-in-law at Christmas time tried to show my son his way to solve a math problem; my husband and I had already shown our son “our” old fashioned way. My son’s teacher had shown him a third way, and I had to shut my brother-in-law down - because as we all know even if you come up with the right answer if you didn’t set the problem up the way the teacher wants to see it, you’ll get a zero mark. By the way, my young brother-in-law had never seen the way my son is being taught now (which is what the images are showing with the boxes and breaking it down) it makes great sense but I would like to come upon it on my own versus being shown that this is the only way to think..

>My son’s teacher had shown him a third way, and I had to shut my brother-in-law down - because as we all know even if you come up with the right answer if you didn’t set the problem up the way the teacher wants to see it, you’ll get a zero mark

I remember getting zero points on a lot of math test questions in elementary and middle school for just writing down the answer and "not showing my work" - i.e., not performing the long multiplication process by hand on paper, or whatever.

I think the education system in general has always taught methods and required students to demonstrate the methods, not just the ability to produce a correct answer, it's just that some of the specific methods have been changed or added to over time.

Teaching long multiplication by hand isn't a great fit for the way everyone thinks, either. Teaching long multiplication by hand alongside "new math" may mean more kids struggle with some of the concepts taught in school (because some kids who understand one way easily may have trouble with the other), but may also mean more kids get out of school with basic competency in arithmetic (because some of the kids who struggle with one way may understand the other more easily).

With all that said, I have some experience with people who learn and think differently from the norm, and the educational system as a whole has NEVER handled that worth a damn and still doesn't. There are some exceptions here and there, but for the most part, those individuals are either forced to conform (often poorly) to educational expectations or end up excluded (kicked out, dropped out, quit, whatever).

I would assume many states do something similar, but Missouri has state level testing to determine how well the schools are teaching their students.

If you want to know how well the kids are doing in math, go look it up. You may be surprised.

quote:

Originally posted by a1abdj:
I would assume many states do something similar, but Missouri has state level testing to determine how well the schools are teaching their students.

If you want to know how well the kids are doing in math, go look it up. You may be surprised.

Good idea. I looked up Texas' STAAR testing for 4th grade math as it was the example I started this thread off with:
2016: 28% did not meet (in plain English - didn't pass)
2017: 25% did not meet
2018: 22% did not meet
2019: 26% did not meet
2020: 42% did not meet (looks like a statistical anomaly)
2021: 31% did not meet

quote:

Originally posted by a1abdj:
I would assume many states do something similar, but Missouri has state level testing to determine how well the schools are teaching their students.

If you want to know how well the kids are doing in math, go look it up. You may be surprised.

I have looked it up in my area.

Only 1/3 of the kids are at grade level in math and English. What does that tell us?

quote:

Originally posted by maladat:

quote:

Originally posted by Fly-Sig:
Why teach them a method of breaking it up for mentally calculating an answer when mental calculations frequently result in errors? Written calculation is far less prone to errors.

It would be far more direct to teach the kids how to write it out on paper and do all the normal multiplication. Write 17 above 20 (or 20 above 17 if you prefer), and run the old fashioned system which teaches and reinforces the value of the position (1s, 10s, 100s, etc).

First, they still teach "the old way" (long multiplication by hand), too. It's not an either-or.

Second, with this approach and others like it, they're trying to teach an intuition/feel for numbers that goes beyond just doing multiplication.

Third, long multiplication by hand, even though it is still taught, is almost totally irrelevant to present day-to-day life. Yes, it is absolutely something everyone should know how to do, but the reality is that barring exceptional circumstances, anyone who was born in the era of easy access to inexpensive portable technology is going to do arithmetic either in their head or on a machine (calculator/phone/computer).

I have master's degrees in mechanical engineering and computer science, which, believe me, required a lot of math. When I had to help my elementary-school-age kid with long division homework a few years ago, it took me a minute to remember how to do it. I don't think I'd worked a long division problem by hand since middle school. If I couldn't do it in my head or maybe scribble a quick shorthand step or two, I used a machine.

1) Good! One of my big pet peeves is people not understanding the basis of what they're doing. All the new tools we have are nice, but are just tools.

2) Ok, but a feel for the numbers is different than understanding how or why it works. Actually solving a problem using the method in the first post is idiotic in the real world. If the person understands why the old fashioned method works, then they understand place values, and will have a feel for the numbers. As I wrote earlier, converting to abstract geometry is adding a layer of complexity.

3) Of course math by hand is almost irrelevant, but understanding the basis is not. That is what math by hand teaches. The method of doing math in one's head will depend on the person, but honestly I cannot see someone using this method in their head.

4) Ok we can measure dicks if you'd like. I have a degree in Electrical Engineering and all but finished a masters with a focus on speech recognition and synthesis. I expect I have taken as much math as you in the academic world, and used it regularly in the office. I worked 10 years in semiconductor manufacturing and testing. Then I went into aviation for the remainder of my career, which involved lots of math every day, much of which I did without electronic aid. That's where I saw so many who did not understand the basis of what they're doing. If the battery in their calculator died they were dead in the water solving anything. I carried and used a circular slide rule for decades. Many times I would do basic trig in my head to figure if we were within limits for crosswind or tailwind components, or use the slide rule if we needed a precise answer. The FO would be scrambling to put the numbers into a calculator or find the printed table of numbers, and have no idea if we were even close, because they'd always relied on electronics.

You'd be shocked at how reliant the younger generation is on electronics because they truly do not understand basics. Navigation, calculating reserve fuel, fuel to diversion airport, remaining fuel at landing, wind correction angles, effect of altitude changes on speed and fuel, etc.

IMHO, it comes down to the method being taught in this thread wastes time and will needlessly confuse many of the students. It is not a practical problem solving method.

quote:

Originally posted by tatortodd:

quote:

Originally posted by a1abdj:
I would assume many states do something similar, but Missouri has state level testing to determine how well the schools are teaching their students.

If you want to know how well the kids are doing in math, go look it up. You may be surprised.

Good idea. I looked up Texas' STAAR testing for 4th grade math as it was the example I started this thread off with:
2016: 28% did not meet (in plain English - didn't pass)
2017: 25% did not meet
2018: 22% did not meet
2019: 26% did not meet
2020: 42% did not meet (looks like a statistical anomaly)
2021: 31% did not meet

2020 is not a statistical anomaly: it's called the "covid slump". Student performance across the board, but especially among adolescents, plummeted due to quarantine and periods of online learning.

The 2021 data is still follow-on from covid.

Our students were only (mandatorily) quarantined at the end of the '19/'20 academic year and have been on campus in some form ever since fall of '20.

It's now 2023 and they're only just now starting to remember how school works.

It's generally agreed that it will take about 5 years to undo the damage caused by online school and quarantine. The youngest kids may be even farther behind because of lost developmental skills.

Comparing 2020 and 2021 data to anything beforehand is anomalous because of covid.

quote:

Originally posted by Oat_Action_Man:
2020 is not a statistical anomaly: it's called the "covid slump". Student performance across the board, but especially among adolescents, plummeted due to quarantine and periods of online learning.

Potato/Potato. Statistical anomalies can occur for numerous reasons and one of the biggest contributors is outside forces. We're saying the same thing, but you're using a catch phrase and I'm using the mathematical term.

quote:

Originally posted by Oat_Action_Man:
Comparing 2020 and 2021 data to anything beforehand is anomalous because of covid.

What I didn't post was the STAAR results actually had dozens of pages of data sets backing up the simple table. It was easy to see if something was outside of a standard deviation. 2021 was within a standard deviation of 2016 to 2019. In other words, you made an assumption on data you have zero knowledge and you're talking out your ass.

quote:

Originally posted by Oat_Action_Man:
I'm 43. Not a math person in any way

Your posts have made this glaringly obvious. Not sure why you've been making inflammatory posts in a subject you're admittedly poor at?

Maladat and Fly-Sig,

I'm interested in both of your opinions on the teaching for the students who are exceptional (i.e. fellow math nerds). Is the multiple methods teaching the below average, average, and exceptional student? Are they risking the exceptional math students getting bored and in trouble?

quote:

Originally posted by tatortodd:
Maladat and Fly-Sig,

I'm interested in both of your opinions on the teaching for the students who are exceptional (i.e. fellow math nerds). Is the multiple methods teaching the below average, average, and exceptional student? Are they risking the exceptional math students getting bored and in trouble?

Exceptional primary students are definitely going to be bored with repetition. They master the concepts quickly, and even doing the homework that day might be boring, though some repetition is useful even so. I do think it risks boredom by introducing additional ways of perceiving the basic concepts once the student understands the concept. He is not going to be interested in another lesson on what multiplication is when he can already do it.

People learn in different ways. Some need context, some are visual, some spatial, some need procedure. Certainly the teacher can touch on all of those within the same lesson, and try to discern which methods work better with which students.

In general and not related to the specific method that started this conversation, teaching multiple ways of understanding concepts is wasted on the exceptional student once he grasps the concept. The average student may benefit from seeing a couple of different presentations of the concept in order to understand it.

quote:

Originally posted by Fly-Sig:
3) Of course math by hand is almost irrelevant, but understanding the basis is not. That is what math by hand teaches. The method of doing math in one's head will depend on the person, but honestly I cannot see someone using this method in their head.

If you mean literally imagining the rectangles, then I agree with you.

They’re using a visual aid to try to teach the concept of splitting up problems into easier mental problems.

E.g., in the original example, they want kids to understand that when they see “17 x 20,” they can do “10 x 20” and “7 x 20,” which are easier (and an obvious way to split up the area in the diagram) and then add up the results together, which is how many people do mental math.

As mentioned earlier in this thread, FOR THIS PARTICULAR PROBLEM, many people will instead do 2 x 17 and add a 0, but that approach only works when one number is a multiple of 10, while the splitting method works for any numbers.

quote:

Originally posted by Fly-Sig:
4) Ok we can measure dicks if you'd like.

I was genuinely not trying to start a dick-measuring contest or say I’m the ultimate authority on math.

I made some comments about some parts of traditional math education not being terribly relevant to day-to-day life, and wanted to make it clear that I was coming from a position of having done a lot of math and thinking math is important - rather than “I’m an underwater basket weaver and why does anyone need math for anything anyway?” or the like.

I also use mental math and estimation a lot and find it very valuable, which is why I think making it a teaching goal is a good idea (although I admit that while I can see the conceptual similarities, I have no idea how effective the specific teaching techniques discussed here actually are for imparting those skills).

quote:

Originally posted by Fly-Sig:

I went into aviation for the remainder of my career, which involved lots of math every day, much of which I did without electronic aid. That's where I saw so many who did not understand the basis of what they're doing. If the battery in their calculator died they were dead in the water solving anything. I carried and used a circular slide rule for decades. Many times I would do basic trig in my head to figure if we were within limits for crosswind or tailwind components, or use the slide rule if we needed a precise answer. The FO would be scrambling to put the numbers into a calculator or find the printed table of numbers, and have no idea if we were even close, because they'd always relied on electronics.

Around thirty or forty years ago, I was taking an old-timer to retrieve his repaired airplane from an airport an hour or so away. The old-timer was retired from either Pan-American or TWA, I don't remember which but when he retired, he held the record for the number of trans-Atlantic flights.

At the time that we made this trip, GPS navigation was not common in General Aviation; the primary radio navigation aid was VOR and we determined the correct WCA (Wind Correction Angle) by a process called "bracketing."

We were in a cloud layer and I was trying to pin down the correct heading for the crosswind. The old-timer glanced at the sheet of paper on which I had jotted down the weather at the departure and destination airports, thought for a few seconds, and said to me "Four degrees left."

I deferred to his experience, flew a heading that was four degrees left of the course, and the VOR needle stayed centered for the next 45 minutes or so of flight until it was time to initiate the approach procedure.

While sipping the post-flight coffee, I asked him, "How did you do that? Since we were flying from a higher pressure area to a lower barometric pressure, I know that the correction had to be to the left, but how in the world did you come up with four degrees?"

He then told me about how they navigated on trans-oceanic flights. I don't recall the exact numbers, but it was something like, take the difference between barometric pressure at the two end-points, and correct 0.5 degrees for each .01 inch of pressure difference, then multiply that by the estimated flight time in hours.

He did that in is head in a second or two, and nailed our heading for the flight. No calculator, no circular slide rule, no working it out on paper.

I remembered that "one weird trick" and used it for a few decades of flying. It always worked.

Helped my wife's friend's 5th grader with some math last night, from 4 states away (they're in CA).

Basic concept, you're given the area of a rectangle, and that the width is x of the length.
Method: Guess length x width & evaluate with the above measure. Then guess again & reevaluate, and keep on like that until you get x, and you have the correct dimensions.

Really annoying & roundabout way to do it, when some simple algebra got me there a lot faster.
I had to read the example a couple times to figure out how they wanted it to be done.

quote:

Originally posted by P250UA5:
Guess length x width & evaluate with the above measure. Then guess again & reevaluate, and keep on like that until you get x, and you have the correct dimensions.

This is how you do it when you are too dumb to know the correct formula (which is about as easy as it comes). This is what your tax dollars are supporting...to the tune of roughly $10K/year/student.