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Interesting article on arithmetic


Ellie
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That is a very good article! I love it when smarter, healthier people selling expensive, bulky, time-consuming curriculum to mainstream homeSCHOOLERS say what I have been thinking and saying :lol: Go MP!  :driving:

 

If anyone is looking for some oldschool math resources, these are some of my favorites. You COULD put in a nice big order to MP right now OR you could do this entirely or mostly for free. 

 

Blumenfeld's How to Tutor was written to clean up the mess of kids taught the 1960's New Math and works just as well to clean up post-Y2K New New Math. I LOVE the math chapter of this book!!

 

Free printable pdf

http://blumenfeld.campconstitution.net/Books/How%20To%20Tutor%20(Arithmetic).pdf

 

Free read online version

http://blumenfeld.campconstitution.net/Math/index.htm

 

Harcopy for sale at Amazon

https://www.amazon.com/How-Tutor-Samuel-L-Blumenfeld/dp/0941995291/ref=dp_ob_title_bk

 

This book is pricey, but the section on arithmetic is excellent. A Guide to American Christian Education.

http://www.exodusbooks.com/guide-to-american-christian-education-for-the-home-and-school-the-principle-approach/ross/56469/

 

Ray's Arithmetic reprinted by Mott Media and splashed all over the internet for free. 

https://www.amazon.com/Rays-Arithmetic-Set-Joseph-Ray/dp/0880620501/ref=sr_1_2?s=books&ie=UTF8&qid=1473788302&sr=1-2&keywords=ray%27s+arithmetic

 

You will also find a ton of other "Practical Arithmetic" book at Google book by authors like Smith, Milne, Davies, and Olney. The 1857 version of Ray's Practical book, sometimes called book 3rd contains comprehension questions and more teacher help.

https://books.google.com/books?id=30wUAAAAIAAJ&dq=ray%27s%20arithmetic%20third%201857&source=gbs_similarbooks

 

Around 1900 the practical arithmetic books were replaced with graded books that were spiral and removed some of the rules and recitation. Opinions differ on whether that was an improvement.

 

Strayer-Upton

http://www.christianbook.com/practical-arithmetics-book-1/george-strayer/pd/545009?event=CBCER1

 

Free Wentworth and Smith

http://forums.welltrainedmind.com/topic/534083-free-strayer-upton-like-math-curriculum-complete-3-book-series-with-answers/

 

Be aware that these books are pretty rigorous and that when one room school houses transitioned from the Practical books, they often used the graded books "behind" schedule. Book 3 was seldom completed by 8th graders and the authors had different ways of attempting to accomadate this. Do not be afraid to fall "behind". Slow and steady wins the race.

Edited by Hunter
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The article is very true.

 

My son is taking Algebta 1 at the local public school. He finds it curious that the other students don't know their math facts. They have to think for a while to tell the teacher what 8x7 equals. They use calculators to do the quizzes for the arithmetic. The teacher asks them if a process he did on the board was correct, but they can't tell him because they can't follow the arithmetic.

 

My kids have practiced addition, subtraction, and multiplication flash cards (the packs that cost $1 each at Walmart) for years, but the kids at the local public school sure haven't. It does make me concerned about the future of our country.

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I don't even mind talking about 'why' something adds up, but this teacher ought to be smacked and the student commended, because the student was NOT wrong on how the basic algorithm works, and that skill is transferable to any other similar problem. Poor student :(. It is absolutely a valid math skill to do addition and subtraction by working to ten and adding the remaining quantities. And less error prone for many students, too!

 

This could also be why my second grader is better at mental math than a good number of adults - she hasn't yet learned that breaking apart numbers to work with them is apparently 'wrong' :huh:

In famous 1973 book Why Johnny Can’t Add, mathematician Morris Kline gave an example of how this worked out in the classroom of the late 1960s. The teacher asks, “Why is 9 + 2 = 11?â€

 

[T]he students respond at once: “9 and 1 are 10 and 1 more is 11.â€

 

“Wrong,†the teacher exclaims.

 

“The correct answer is that by the definition of 2, 9 + 2 = 9 + (1 + 1). But because the associative law of addition holds, 9 + (1 + 1) = (9 + 1) + 1.

 

Now 9 + 1 is 10 by the definition of 10 and 10 + 1 is 11 by the definition of 11.â€

Edited by Arctic Mama
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Yes, interesting. I also agree kids need to just learn-to-automaticity arithmetic facts. My question though is how to do that in an age where 'novelty' is king & kids get easily bored with repetition. I've a 2nd grader & I'm serious in my quest for repetitive but 'seems new/interesting/fun' arithmetic activities. We've flashcards & card/board games but that only takes us so far--& we've still got quite a ways to go until automaticity sets in. Suggestions?

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Oh, I'm an ELL teacher & part of my day involves ELL math in a mainstream classroom. I also am astonished at the number of 'American' kids who don't know their basic facts! It's enlightening & serves as a warning to me--to get my 7 year old moving mathematically (& not entirely rely on PS's methodologies)!

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Yes, interesting. I also agree kids need to just learn-to-automaticity arithmetic facts. My question though is how to do that in an age where 'novelty' is king & kids get easily bored with repetition. I've a 2nd grader & I'm serious in my quest for repetitive but 'seems new/interesting/fun' arithmetic activities. We've flashcards & card/board games but that only takes us so far--& we've still got quite a ways to go until automaticity sets in. Suggestions?

You can train your kids to do math flash cards and other things that are "boring." It is good for kids to do some things that are boring so that they develop perseverance and learn how to do difficult tasks that don't strike them as novel or entertaining.

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You can train your kids to do math flash cards and other things that are "boring." It is good for kids to do some things that are boring so that they develop perseverance and learn how to do difficult tasks that don't strike them as novel or entertaining.

I agree. And flash cards and repetition don't have to take more than a minute or two daily. If they become part of the routine, they will just become accustomed to it. How long does it take to do say 20 flash cards daily and then a speed drill? Not long. And yet, if done consistently it can produce wonderful results in most children.
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I agree. And flash cards and repetition don't have to take more than a minute or two daily. If they become part of the routine, they will just become accustomed to it. How long does it take to do say 20 flash cards daily and then a speed drill? Not long. And yet, if done consistently it can produce wonderful results in most children.

With eldest we would drill on and off, mostly off for the last few years.

 

With youngest if we stop drilling, let's say multiplication for two weeks and focus on division, somehow several multiplication facts slip out of his head. So for him we just cycle through drill decks. He does about three minutes a day four days a week.

 

Eta: once a week he also has to do:

1 long multiplication question

1 long division question

1 large subtraction question

1 large addition question

1 fraction conversion question

1 fraction addition question

1 fraction subtraction question

1 find the perimeter question

1 find the area question

 

For him the list keeps growing. I find that with him, if he leaves any of those things off his list for to long then when he has to do it, it leads to frustration and tears. I also find that sometimes he becomes calmer and happier with math if I give him one of those review questions when he is getting frustrated with new stuff.

Edited by Julie Smith
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Yes, interesting. I also agree kids need to just learn-to-automaticity arithmetic facts. My question though is how to do that in an age where 'novelty' is king & kids get easily bored with repetition. I've a 2nd grader & I'm serious in my quest for repetitive but 'seems new/interesting/fun' arithmetic activities. We've flashcards & card/board games but that only takes us so far--& we've still got quite a ways to go until automaticity sets in. Suggestions?

We used Big Brainz/Timez Attack. The downside is my kids get a little overly into the video game aspect of it and get really tense :p. But in terms of retention and efficacy this worked beautifully. They also got much faster than they did with worksheets and flash cards alone.

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We used Big Brainz/Timez Attack. The downside is my kids get a little overly into the video game aspect of it and get really tense :p. But in terms of retention and efficacy this worked beautifully. They also got much faster than they did with worksheets and flash cards alone.

Eldest did great on times attack. He also has done fine with apps on my iPad.

 

Youngest did not. With youngest I have tried many different things but the one that is most effective in terms of time spent and retention is flash cards. Also for some reason it also has to be flash cards with me or his brother, never a computer app or game.

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Maybe it's the tactile nature of moving cards and flipping them? Or that it's black and white? Everyone is so individual!

I'm sure it is because he is able to answer outloud instead of having to type, or select the answer. I Switch up the cards often because he would otherwise just remember that the question with a blue shrimp in the top left corner has the answer of 49. But he also doesn't like plain ones, as in takes longer with them, gets distracted easier...

 

Now you know why I have so many different decks of flash cards. I think at one point I had eight multiplication decks.

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Oh, I'm an ELL teacher & part of my day involves ELL math in a mainstream classroom. I also am astonished at the number of 'American' kids who don't know their basic facts! It's enlightening & serves as a warning to me--to get my 7 year old moving mathematically (& not entirely rely on PS's methodologies)!

 

I was thinking about this. My MIL was educated only through the 8th grade in a poor village in a "developing" nation. Yet her math skills are impeccable and she gives my children wonderful arithmetic lessons using no materials other than her two hands. Her father gave all the children these lessons (in a house that had no electricity and no running water) before they even attended school, where I assure you there were not colorful manipulatives on every child's desk (another piece of the puzzle, I think-- that family culture of valuing math skills).

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I was thinking about this. My MIL was educated only through the 8th grade in a poor village in a "developing" nation. Yet her math skills are impeccable and she gives my children wonderful arithmetic lessons using no materials other than her two hands. Her father gave all the children these lessons (in a house that had no electricity and no running water) before they even attended school, where I assure you there were not colorful manipulatives on every child's desk (another piece of the puzzle, I think-- that family culture of valuing math skills).

Yes. My relatives were out on the Kansas prairie. Math was taught at home. The children did not solely memorize, they learned to make a ten, to visualize part/whole relationships, etc and knew the properties well when finished. The author of this article has not dug into the history of new math....like other programs, parts were left out when untrained teachers with no understanding of math attempted to teach new math instead of lead chanting or perform timed tests. There are papers written on how the implementation went poorly and why. I still remember 4th grade...timed test every single day. Kids would discover strategies and pass them on so they wouldnt be too slow and have to stay in for recess. That teacher did nothing that could be construed as teaching, just cracked the whip.

Edited by Heigh Ho
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I'm sure it is because he is able to answer outloud instead of having to type, or select the answer. .

There's something to saying it out loud. When we do Latin recitations, the curriculum says to make sure the recitations are spoken. Hearing the information as well as saying it makes a difference. I study Latin on my own and I do my recitations out loud instead of just reading it over in my head, even though it's just me.
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Yes. My relatives were out on the Kansas prairie. Math was taught at home. The children did not solely memorize, they learned to make a ten, to visualize part/whole relationships, etc and knew the properties well when finished. The author of this article has not dug into the history of new math....like other programs, parts were left out when untrained teachers with no understanding of math attempted to teach new math instead of lead chanting or perform timed tests. There are papers written on how the implementation went poorly and why. I still remember 4th grade...timed test every single day. Kids would discover strategies and pass them on so they wouldnt be too slow and have to stay in for recess. That teacher did nothing that could be construed as teaching, just cracked the whip.

Well, there will always be poor teachers and there will always be kids who game the system. However, I think the "old math" as well as other "old" ways of teaching took into account a child's developmental stage a lot better than the progressive stuff. My neighbor took her first graders out of PS due to the Common Core math. According to the Trivium, younger children, in the Poll Parrot stage should be memorizing, reciting,getting the foundations - not figuring out the reasons yet. And my neighbor's sons, in first grade, were being taught to find out the "whys" of addition. They didn't care, they didn't understand and it was very tedious. And these are extremely bright children.
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Yes, interesting. I also agree kids need to just learn-to-automaticity arithmetic facts. My question though is how to do that in an age where 'novelty' is king & kids get easily bored with repetition. I've a 2nd grader & I'm serious in my quest for repetitive but 'seems new/interesting/fun' arithmetic activities. We've flashcards & card/board games but that only takes us so far--& we've still got quite a ways to go until automaticity sets in. Suggestions?

 

Read this book, and don't worry about tit not being "fun". It's fun when you are good at it :)

 

https://www.amazon.com/Why-Dont-Students-Like-School/dp/047059196X

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So glad you posted this, Ellie! As you know, I LOVE this article. I HATE the trend now in schools to have "smart boards" and more computers and this that and the other thing. When we put a man on the moon using slide rules for heaven sake. Many very well educated people learned just fine with pencil and paper (or slates and chalk) and a well educated, involved teacher. Versus all this tech BS. 

 

And I'm not anti technology. I'm no lubbite. I prefer ebooks most of the time for my own pleasure reading, I think my Roomba is the best invention ever, and right now I'm typing on my macbook while my kids play gams on their kindle fire tablets. But to learn math? We don't need any of it. Just 10 fingers, and a pencil and paper. 

 

Bah humbug. 

 

I think it is the ultimate in narcissism to say that the old fashioned ways were no good, when they led to such amazing achievements! 

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Eh. The article is about one person who grew up in a very different time when it was easier to get jobs with only a bachelors degree. Some people intuitively understand math. He also is in a field where math is important but visual spatial skills are extremely important. It also does not have to be either or with lots of memorizing but not a lot of conceptual understanding or conceptual with not a lot if practice for those who need it. There are lots of ways to get more automacy with facts. They also use examples of bad programs or examples of conceptual math. Lots of countries have good curriculums and educate a lot of people with conceptual math. It is not like they did not have curriculums in the past where they learned how numbers work or the why. There are big differences in quality out there from things like Signapore math to Everyday math. I think the analogy they used that conceptual math was like making carpenters learn how tools were made or people learning to read how the alphabet system was develeped was really off. It is more like the difference of teaching site words only and memorizing or teaching the whys with good phonics instruction.

Edited by MistyMountain
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The entire article is suffering from a profound case of survivorship bias. His dad did well learning math this way, he can point to other people who did well learning math this way, ipso facto it must be a good way of teaching math.

 

Not shown: Any actual data proving this case. Are we to believe every student at his dad's one room school grew up to become a rocket scientist? Absurd! So what was the failure rate? We don't know, because he doesn't look and he doesn't tell us.

 

Here's some data, and you can look it up and confirm it yourself: Since the 1950s, when we first started keeping track, Americans have consistently underperformed citizens from other nations - including those which had just started to recover from WWII - in just about every mathematical measurement, including "how well students and/or adults understand basic mathematical principles" and "what percentage of students take higher math courses in high school or college" and "achievement on a simple math test".

 

Whenever I say this, somebody goes "Yeah, well American put somebody on the moon!" (or "invented computers" or whatever else they think proves the point) and, sure, that's true - but we're the third most populous nation in the world. It would be very surprising, with such a large pool to choose from, if none of our citizens succeeded. I'm not sure if repetition of "we put people on the moon" indicates a lack of knowledge of geography or a lack of knowledge about statistics, but at any rate, it doesn't convince me that the old school ways are best just because some percentage of people who learned that way eventually grew up to learn math I don't understand.

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I don't think we should neglect the why's of math, but I think we DO, as a society, now neglect the rote memorization of math facts. Hugely. It's just not done anymore. And I'm sorry, but more kids can memorize basic facts than can understand the convoluted mechanisms behind the math. Both is fine, but right now we just, as a society, teach why. And we do it poorly, at that. 

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What I think is being missed is that 'old school ways' did actually teach strategy and manipulation of quantities, anyone who has spent even a small amount of time with an older primer can see that. They absolutely teach parts and wholes, subitization, etc. The difference is not having kids get so bogged down in the definitions of the operations or procedural perfection to the exclusion of actually learning the facts cold.

 

Balance - once you get the basic idea of what is being down, how, and why, that's where practice and memory should be kicking in. Basic math should be rote in application beyond the early years - that's where accuracy and speed to actually solve higher levels of math come in. My husband sees this in his workplace all the time. People with masters, oftentimes in science and math fields, struggling with basic calculations weighing down their more complex ones because they haven't internalized the foundational math skills and knowledge well. Watching someone with three or four years of thermo and calculus still slow to properly multiple 1.15*80 is painful, not to mention it actually affects their overall output and productivity in a time dependent schedule.

 

We use programs that are manipulative based and heavily conceptual, especially in kinder and 1st grade. But even Strayer Upton is fairly heavy on those in the basic manipulation of numbers. Once that's internalized though it's just a matter of getting all the common iterations of the expression (fact families) down, so that deeper and more comprehensive problem solving can be achieved with some degree of ease. The tel aren't mutually exclusive, but in a lot of the schools around here it seems the balance has shifted back, new math style, to ALL theory and very shaky actual understanding, let alone application and accuracy. And what I quoted above - criticizing a kid using a solid strategy because it didn't fit exactly what the teacher's manual required for 'knowledge' of addition? Ridiculous.

 

Balance is key, in my opinion :)

Edited by Arctic Mama
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What Arctic Mama said. Even CLE uses diagrams of base ten blocks, and advises using manipulative, etc. 

 

Teaching a kid tricks like making tens, etc etc is great. Requiring them to write an essay on them is dumb. Not every person will use the same mental math tricks. Let them find the one they like, and use it, without forcing it. 

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And what I quoted above - criticizing a kid using a solid strategy because it didn't fit exactly what the teacher's manual required for 'knowledge' of addition? Ridiculous.

 

Surely - but it happened in the 1950s too. And the 1940s, and the 1920s. There have always been teachers who are shaky in arithmetic and don't really understand what they're supposed to be teaching, and so don't like novel solutions to problems simply because they don't understand them.

 

it seems the balance has shifted back, new math style, to ALL theory and very shaky actual understanding, let alone application and accuracy.

 

Most people who throw around the term "new math" know what it was and how it is or isn't similar to what exactly they're criticizing about mathematics instruction today - and to be honest, I don't think any of us here is the exception.

 

The one real similarity between today and the days of the dreaded "new math" is that a lot of new teaching methods have been pushed down on teachers without giving them adequate instruction in these methods or getting buy-in from the teachers and families. That's a recipe for success all right.

Edited by Tanaqui
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Are you saying none of us have studied math pedagogy and how it has changed? Especially enough to make a basic evaluation of why some methods are more and less successful? That's simply not the case.

 

The current run of problems do seem more related to shaky math understanding in the teachers, themselves, and parents who aren't being clued in to why they're covering what they are - I agree with you there. But I'm also seeing massive overkill in our local district when it comes to strategy and theory - to the point where the kids don't actually know what to use and where because they've got four different ways to solve something and aren't fully comfortable with any one or why and when to choose a differing method. And yes, a plain lack of math drilling. This isn't universal but neither is it being made up whole cloth by ignorant parents on Facebook ;)

Edited by Arctic Mama
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Are you saying none of us have studied math pedagogy and how it has changed? Especially enough to make a basic evaluation of why some methods are more and less successful? That's simply not the case.

 

I'm saying that when people say the words "new math" they rarely seem to mean the same thing as each other, nor what I've seen from looking at actual samples. They also never really clarify what they see as similar between then and whatever they're complaining about now.

 

And yes, a plain lack of math drilling. This isn't universal but neither is it being made up whole cloth by ignorant parents on Facebook

 

LOL, no, there's definitely not enough drill. No argument here, and I hope you didn't think I said or thought that! Drill is boring, nobody likes it, and so everybody hopes they've found the magic formula to let them skip it. Well, unfortunately, you have to spend a certain number of hours to learn skills. You can either drill your way through over the course of a few years, or spread those hours over a lifetime, but sooner or later it has to be done - and in the long run, it's just easier to compact them into 20 minutes of drill every day.

 

But I'm also seeing massive overkill in our local district when it comes to strategy and theory - to the point where the kids don't actually know what to use and where because they've got four different ways to solve something and aren't fully comfortable with any one or why and when to choose a differing method.

 

If I were to guess, this is at least partly due to shaky teachers and parents not knowing, themselves, why you might use this strategy or that one. They can't adequately explain it to their kids unless they understand it, and the best they get out of it is "some people prefer one strategy over another".  (Administration might not be much help either. Far better for a teacher to teach the only method they know than to spread their time over several methods they don't, but if they're required....)

 

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Well, personally I think drill has never been so thrilling and enjoyable, and my children who BEG for their math games agree. For them, some of these computer games and apps are definitely a magic formula...whether or not this will create superior thinkers and mathematicians is yet to be seen.

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I'm saying that when people say the words "new math" they rarely seem to mean the same thing as each other, nor what I've seen from looking at actual samples. They also never really clarify what they see as similar between then and whatever they're complaining about now.

 

LOL, no, there's definitely not enough drill. No argument here, and I hope you didn't think I said or thought that! Drill is boring, nobody likes it, and so everybody hopes they've found the magic formula to let them skip it. Well, unfortunately, you have to spend a certain number of hours to learn skills. You can either drill your way through over the course of a few years, or spread those hours over a lifetime, but sooner or later it has to be done - and in the long run, it's just easier to compact them into 20 minutes of drill every day.

 

If I were to guess, this is at least partly due to shaky teachers and parents not knowing, themselves, why you might use this strategy or that one. They can't adequately explain it to their kids unless they understand it, and the best they get out of it is "some people prefer one strategy over another". (Administration might not be much help either. Far better for a teacher to teach the only method they know than to spread their time over several methods they don't, but if they're required....)

I don't disagree with you there - but I think our instruction to math teachers is pitiful. I couldn't believe how much pedagogy and theory I was missing even as an intelligent and fairly adept product of the school system, especially compared to your average Hungarian grad, let alone their teachers. My friend with an MAT told me she didn't learn almost anything in terms of actual age appropriate teaching skills and real basics on how to teach and when to teach things. I was shocked, given that she has a bachelors in a science field to go with that teaching degree. I think that really fails our teachers, and doubly so when they're given new material to teach but not support or training in how to actually teach it.

 

It's kind of a mess, and I wonder if some success in homeschoolers is simply because many of these materials teach basic pedagogy in the parent/instructor side and we aren't locked into whatever some administrator decides is en vogue.

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You can train your kids to do math flash cards and other things that are "boring." It is good for kids to do some things that are boring so that they develop perseverance and learn how to do difficult tasks that don't strike them as novel or entertaining.

Yup, agreed. I am conscientiously building that tolerance in my daughter. She's learning to navigate through boredom spells & just accept doing some 'boring' things (i.e., teeth brushing & math facts). Nonetheless, the brain can process more effectively when novelty comes into play & so I'm also on the hunt to expand my repertoire of drill exercises. In this case, more is never enough.

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Yes, interesting. I also agree kids need to just learn-to-automaticity arithmetic facts. My question though is how to do that in an age where 'novelty' is king & kids get easily bored with repetition. I've a 2nd grader & I'm serious in my quest for repetitive but 'seems new/interesting/fun' arithmetic activities. We've flashcards & card/board games but that only takes us so far--& we've still got quite a ways to go until automaticity sets in. Suggestions?

Grab a ball - throw it to the kid who catches and can't throw back till they throw back with the answer. every time you drive somewhere make them work on whatever the latest is for a minute.

Don't make it long. 1-2 minutes often is enough.

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I read the thing about Singapore maths success and alongside the program they pointed out some of the strategies includes stripping back classrooms to just a clock and whiteboard - all the fun posters and decorations were distracting and also the emphasis on diligence as a virtue and quick response from the teacher for anyone struggling. Obviously we don't want a whole life in a super pared back environment but I think we have gone a bit overboard with cluttery decorations in class rooms.

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When you have a kid who has trouble memorizing math facts, the ability to use new math techniques to break things down and understand the concepts before you hand them a calculator in despair is extremely helpful.

Not only that, when you have kids who DO NOT learn through drill it is great to press on mathematically while not getting hung up on facts. Not only that, when my kids finally did have all facts down (through use, not through drill) they rock at math - not just computation but also problem solving and complex mathematical thinking. There's definitely something to take home from the article, but it isn't the end-alone-all way nor does it even work for everyone.
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I'm struggling a little with this at the moment - I made dd7 flash cards today, not + 0 or + 1 facts but all the others to 10.

I held them up and she answered. Better or worse if I add in subtraction facts to the pile, which we also need to memorize? Should she be counting to find the answer then eventually it will just sink in? Yikes my first time doing math facts and I'm a bit unsure of my self!

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I'm struggling a little with this at the moment - I made dd7 flash cards today, not + 0 or + 1 facts but all the others to 10.

I held them up and she answered. Better or worse if I add in subtraction facts to the pile, which we also need to memorize? Should she be counting to find the answer then eventually it will just sink in? Yikes my first time doing math facts and I'm a bit unsure of my self!

 

When we did flash cards I made triangle shaped ones.  I wanted the relationships to be shown no matter which corner I covered up. (and they doubled as addition and subtraction cards, so only one set! :D )

 

I think the counting is the first step, but if you can get her to see groups with manipulatives it might be easier for her.  For example, lay a 10 bar on the table.  Hold up the card with 7 and 4, she lays those two bars down in front of the 10 bar and can immediately see it's one more.  Eventually, the visual image sticks in their mind and they rely less on the manipulatives and eventually just know it.

Edited by HomeAgain
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Yes, it just takes a lot of practice with flash cards. The kids are very slow at first, but later they increase speed. I did flash cards or speed tests with my kids nearly every school day from 1st through 4th grades. It was one of the most tedious activities for both them and me, but now I see that the effort has paid off.

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Better or worse if I add in subtraction facts to the pile, which we also need to memorize? Should she be counting to find the answer then eventually it will just sink in? Yikes my first time doing math facts and I'm a bit unsure of my self!

 

I don't have time to pull up the citation just now, but research shows we retain more information when we mix it up - so yes, do addition AND subtraction at the same time (and then add in multiplication slowly when she gets to that point).

 

And yes, it's okay for her to count to find the answer now. I mean, she doesn't have them memorized yet, right? So she has to come up with the answer somehow. The options are: a chart, counting, or being told the answer by you. The last option requires the least active thought, so it's definitely the inferior choice.

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I'm saying that when people say the words "new math" they rarely seem to mean the same thing as each other, nor what I've seen from looking at actual samples. They also never really clarify what they see as similar between then and whatever they're complaining about now.

 

 

Awhile ago on the boards there was a big interest in the 60's New Math, and I found it interesting the big gulf between the impression of New Math I got from the (overall favorable) discussions here (emphasized the rigor and the mathematical precision and the conceptual focus), and the impression I got from people whose main memory of it is the Tom Lehrer parody (abstract and obscure conceptual understanding over practicality and actually getting the answer right), and the impression I got from my grandfather, who actually taught it and in fact was instrumental in getting his school district to adopt it (teaching the whys as well as the hows, and teaching how to *think* not just how to get the answer).

 

And it never made sense to me, how people were always saying the "reform math"/"new new math" of the 90s/00s was just like the 60s New Math, because my impressions of 60s New Math was formed by people who loved the mathematical precision of it, while my impressions of the Reform Math of the 90s/00s was formed by people who hated the *lack* of mathematical precision in it.  After thinking about it, I think of 60s New Math as an overhaul of school math written by mathematicians without enough input from educators, while 90s/00s Reform Math was an overhaul of school math written by educators without enough input from mathematicians.  Both were pretty "out with the old, in with the new", though - rejected the old ways and built up a new, better way from scratch - hit (fun) understanding over (unfun) memorizing - although I think the mathematicians of the 60s New Math assumed memorization would automatically happen (did for them, after all), while the educators of the 90s/00s Reform Math assumed memorization wasn't necessary.

 

And all the "new math" approaches of the past 50 years - where "new" means a self-consciously different-from-the-old-not-so-good-ways (so includes 60s New Math and 90s/00s Reform Math, as well as today's Common Core) - all faced significant pushback from parents and teachers who didn't understand the new approach and were unwilling to take on faith the experts' assurance that the special all-new all-better way of approaching math (which made no sense to them) was in fact genuinely better than what they had learned.  Honestly, I think a lot of problem with the various "new maths" is how they presented themselves as breaking with the old, bad past - instead of showing how they were an extension and improvement on the past.  They made it into an either/or thing - accept all the shiny new and reject all the old bad - and so if you didn't see the past as all bad, thought it was basically solid, you were effectively forced into rejecting the "new math", because the "new math" overtly set itself up in opposition to the old ways.

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I am no expert, but I have always thought the problems with the new maths is first treating average children like gifted children, and secondly expecting elementary school teachers to teach this stuff without training, and forgetting that some of them even with training, just might not be capable of teaching the stuff.

 

I lot of average kids, moms, and teachers ARE capable of doing back-to-basics type math. They get it done. They get something done. Something is something.

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It is really easy to practice math facts. You can do that alongside any math program. You can do apps, 2 plus to does not equal 5 and the multiplication version of that, flashcards, worksheets etc.

 

Conceptual math is not super complicated or meant for only gifted kids. A curriculum focusing on traditional algorithms can be just as bad for kids that are average or who have a math weakness with any cognitive profile. All programs have some explanation but a program can spend a little bit of time on explanation and the explanation can be more on what to do not on numeracy skills. Right start math teaches addition and subtraction from left to right and really shows through what you are doing with pictures. Other programs teach you borrowing and carrying from the right and really hammer in how to do that process with less time on place value.

 

You do not need to be gifted to understand tens frames and how to manipulate numbers in your head. It is not abstract to learn what numbers really mean. There is so many different programs out there and they are all a little different. I think the weak conceptual programs come in when they cobble things together too quickly before really testing out what works. I read about the program for my district and it was just thrown together really fast by one teacher for the new standards. The standards are fine if you look them over but the standards themselves are not going to solve the issue and throwing something together too fast does not work.

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Math major who had a regular job, had to tutor his kids and neighbor kids because of poor math teaching, now teaches math and writes education articles, an interesting history of math education in the U.S. He likes Saxon amd Singapore and is not a fan of poorly designed "fuzzy" math, explains why common core math is a problem, especially for less intelligent kids who cannot make the jumps, according to him it is not incremental or well designed.

 

https://www.amazon.com/Math-Education-U-S-Still-Crazy/dp/1523928204/ref=sr_1_1?ie=UTF8&qid=1474012233&sr=8-1&keywords=barry+garelick

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Well, there will always be poor teachers and there will always be kids who game the system. However, I think the "old math" as well as other "old" ways of teaching took into account a child's developmental stage a lot better than the progressive stuff. My neighbor took her first graders out of PS due to the Common Core math. According to the Trivium, younger children, in the Poll Parrot stage should be memorizing, reciting,getting the foundations - not figuring out the reasons yet. And my neighbor's sons, in first grade, were being taught to find out the "whys" of addition. They didn't care, they didn't understand and it was very tedious. And these are extremely bright children.

 

I don't know -  I really think the whole not worrying about understanding thing is about the weakest link in the whole neoclassical approach.  And who really does that, has a child memorize 3+2=5 without actually showing them what it means by some method or other, as if it is just a bunch of words without meaning?  I've never been convinced that Sayers really thought anything so improbable.

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