Memorizers are the lowest achievers

[SeaConquest]

In case you were feeling guilty that your kids haven't memorized their times tables yet:

 

http://hechingerreport.org/memorizers-are-the-lowest-achievers-and-other-common-core-math-surprises/

[clementine]

Where was this article 7 years ago when I needed it???  

[Momto4inSoCal]

Really good article. I like this - New brain science tells us that no one is born with a math gift or a math brain and that all students can achieve in math with the right teaching and messages

 

I had sort of pegged my older daughter as not being "mathy" but after watching her this year she really has blossomed and gets it way more than I ever thought. The article also solidified that I need to give my girls more time to work out a problem on their own rather than jumping in when they get stuck. 

[8filltheheart]

While the point of the article is good, I disliked the argument.  First of all, this is not new knowledge that CC has suddenly revealed to the world.  It has been talked about for ages. It was being talked about way before I was even born. Just one example.... Bloom published his taxonomy back in the 50s.  Those studying child development have long acknowledged that simple knowledge and  memorizing are the lowest possible levels in cognitive development.  I had an very elderly mentor in the 80s who lamented pre-school academics bc he believed that the reason he saw such poor thinking skills in his current (in the 80s ;) ) college students was because they had spent their childhoods being told what to think and what the right answers were and had been deprived of exploring and developing their own ideas behind things.  He believed that the educational crisis we were going to face was a generation of students who could do what they had been told to do, but didn't understand the purpose or whys behind anything they did.  (And those students went on to become the future educators of a new generation of students.)

 

I also cannot help pointing out the irony of the comments about CC valuing the objective of not needing to be rushed and allowing time for deep thinking and YET......what is the evaluation process for standardized testing student ranking (which motivates everything in ps and college admissions)?  A scenario where all students are compared to a bell curve based on how quickly they can answer the questions.  

 

And just another day where I am thankful for homeschooling and educating my children according to my own academic goals.

 

 

[idnib]

Hmm. To me there's a difference between memorizing multiplication tables and memorizing algorithms and how to plug things in without understanding them. 

 

The first, for me, is a given in order to perform calculations at a reasonable pace. And I sympathize with kids who take longer to memorize them. I was one of them and it truly embarrassed me in class.

 

Memorizing algorithms or how to simply enter data into a calculator without understanding why is a different animal, and I agree that those who understand the mathematical reasoning or even better, have been led to discover them for themselves, will fare better than those who have memorized without understanding or deriving.

[wapiti]

I agree with this: 

Mathematics is not a subject that requires fast thinking. Award winning mathematicians talk about their slow, deep thinking in math.

 

though it seems to me that she's setting up the old false dichotomy between procedural emphasis and concept understanding.

 

I both agree and disagree with this other part; however I think she's conflating a bunch of different issues (acceleration and fast workers and procedural math) and creating yet another false dichotomy, between acceleration and depth:

 

Geoff Smith, chairman of the British and International Math Olympiads warns that accelerating children through the system is a “disaster†and a “mistakeâ€. He, like me, recommends that high achieving students explore the mathematics they are learning in depth, instead of rushing forward.

 

Some school districts, such as San Francisco Unified, are trying to slow down the math experience, requiring that advanced students go deeper rather than faster. Students still reach calculus but the pathway to calculus consists of deep understanding rather than procedures and memorization. This is an important move. There is no harm in students being introduced to higher-level mathematics earlier, as long as the mathematics is enjoyable and ideas can be explored deeply. Third graders can be fascinated by the notion of infinity, or the fourth dimension, but they do not need a race through procedural presentations of mathematics.

 

Sure.  However, is the depth she's talking about really offered at the elementary and middle school levels?  What PS programs offer this type of depth?  There aren't many.  One size does not fit all and the least-worst alternative for bright math students to be challenged in a PS setting often involves some acceleration, ideally *with* extra depth.

 

Also, some of the comments to the article seem to indicate that the district in question has mostly done away with algebra being offered in middle school (presumably depending on the specific schools), which would cast doubt on the statement that there's a pathway to calc.

[wapiti]

I also cannot help pointing out the irony of the comments about CC valuing the objective of not needing to be rushed and allowing time for deep thinking and YET......what is the evaluation process for standardized testing student ranking (which motivates everything in ps and college admissions)?  A scenario where all students are compared to a bell curve based on how quickly they can answer the questions.  

 

I am so cynical that I've been trying to figure out what the CB's agenda is in making the SAT redesign more reliant on reading speed.  Some student group must benefit from this, but I don't know who that would be.

[Arcadia]

I do agree kids shouldn't be penalized for being unable to memorized the times table by a certain grade level in school but I am not for using the calculator early either.

 

In my district, the tables in K-5 has the multiplication table stuck onto the tables/desks. No kid need to remember the multiplication table.

Link is the desk name tag they use

http://www.superteacherworksheets.com/pz-desk-tags.html

 

The only depth I am aware of is math clubs which is run by PTA with or without volunteer teachers.

 

Also, some of the comments to the article seem to indicate that the district in question has mostly done away with algebra being offered in middle school (presumably depending on the specific schools), which would cast doubt on the statement that there's a pathway to calc.

San Francisco Unified is offering

9th - Algebra 1

10th - Geometry

11th - Algebra 2 or Compressed Algebra 2 and PreCalc

12th - AP Calculus or AP Statistics

 

from SFUSD

"All students will take CCSS Algebra 1 in 9th grade and CCSS Geometry in 10th grade once the full transition to the new course sequence is complete. In 11th grade students (with assistance from their families) will be able to choose from two course offerings: Algebra 2 or a compressed Algebra 2 and Precalculus course. The compressed course option would allow students to take AP Calculus in their senior year. Students could choose AP Statistics in 12th grade."

 

ETA:

What is ironic is that the top ranked countries for PISA 2012 mentioned in link probably had their multiplication tables down cold.

PISA is also a timed test, not a math Olympiad qualifying test.

[EmilyGF]

I would have been miserable if they had followed this path. In most schools, "slowing down to go in depth" works out to extra busy work without any extra depth - because most elementary school teachers are terrified by kids who get math quickly.

 

I skipped a grade of math in grade school and a grade of math in junior high. I majored in applied physics. 

 

Emily

[mom31257]

I don't know about the science finding you can't be born with a math brain, but I disagree wwith it. I have a math degree, and my brain works totally differently than my husband. It's the same with my kids. Ds understands a lot of math concepts before they are even taught.

[fourisenough]

It is NOT an either/or proposition. It should be both/and (conceptual understanding paired with fact/procedural fluency). Thank you BA/AOPS + Math Mammoth + Simple Solutions!

[wapiti]

San Francisco Unified is offering

9th - Algebra 1

10th - Geometry

11th - Algebra 2 or Compressed Algebra 2 and PreCalc

12th - AP Calculus or AP Statistics

 

from SFUSD

"All students will take CCSS Algebra 1 in 9th grade and CCSS Geometry in 10th grade once the full transition to the new course sequence is complete. In 11th grade students (with assistance from their families) will be able to choose from two course offerings: Algebra 2 or a compressed Algebra 2 and Precalculus course.

 

Interesting - so they offer to compress what is ordinarily two full years into one.  What was that about depth and not rushing?

[8filltheheart]

I don't know about the science finding you can't be born with a math brain, but I disagree wwith it. I have a math degree, and my brain works totally differently than my husband. It's the same with my kids. Ds understands a lot of math concepts before they are even taught.

 

I thought about this, too.  My math/physics geek definitely sees the world in patterns.  He sees sequences and patterns mathematically and has since he was tiny.  His thought processes are very different than mine.  He can also visually rotate objects in his mind..  I do not have ability.  (one of the reasons why I disliked calculus so much was that I could not mentally rotate an object.)  

[Arcadia]

Interesting - so they offer to compress what is ordinarily two full years into one. What was that about depth and not rushing?

I rather the kids get the choice to do algebra 1 in 8th than the compressed 11th grade course which affects GPA. Weird policy considering that the neighboring school districts still have the algebra at 8th option.

I'm not in SF but this issue was in the papers since there are unhappy parents. My district still offers the option of algebra 1 in 7th.

 

I do think the issue is still the K-8 math teachers in my district. No consistency in teacher quality. I don't know any high school math teachers IRL.

[EmilyGF]

Having read the article (and others by Jo Baeler), I am really bothered by some of her writing. Understanding math as an interconnected set of big ideas is easier if you can do things without having to stop and think. You an see patterns easier if you know, for example, the 7s times tables.

 

 

Jo Baeler has some good points about American attitudes towards math. In Japan, for example, the attitude is generally that anyone can learn math (or violin) if they are just willing to work hard enough. Hard work is seen as a good thing. In the USA, generally, people brag about how little they work because, if they have to work, they aren't gifted. Kids who have to work hard in math should be praised for persevering and for diligence, and they may one day find that math "comes" to them.

 

This played out recently at my son's yoyo club. A good yoyoer had just mastered a hard trick and bragged, "And I didn't even practice!" I saw his mom a few minutes later and snarkily related the comment. "Huh," she said, "he's been practicing 1-2 hours per day all week."

 

I certainly agree that professional physicists and artists think differently, but I wonder how much is inborn versus learned. (Not claiming 100% either way.)

 

Scattered thoughts on a rainy afternoon,

Emily

 

[Arcadia]

Having read the article (and others by Jo Baeler), I am really bothered by some of her writing. Understanding math as an interconnected set of big ideas is easier if you can do things without having to stop and think. You can see patterns easier if you know, for example, the 7s times tables.

 

From another article on Jo Boaler

"And indeed, when you dig deeper into Boaler’s paper, she is a big fan of practice and repetition.

... ...

Of course, any sort of repetition will lead to memorization. You wouldn’t really be calculating 7 x 8 by picturing blocks every single time you need to make a quick calculation. The more you repeat it, the more natural it becomes to have the answer pop into your head. But Boaler is convinced that the student who memorizes through usage, not drilling, will be better off"

Link http://www.usnews.com/news/articles/2015/02/09/should-we-stop-making-kids-memorize-times-tables

 

Interpret it whatever way you want :lol:

[fourisenough]

I rather the kids get the choice to do algebra 1 in 8th than the compressed 11th grade course which affects GPA. Weird policy considering that the neighboring school districts still have the algebra at 8th option.

I'm not in SF but this issue was in the papers since there are unhappy parents. My district still offers the option of algebra 1 in 7th.

 

I do think the issue is still the K-8 math teachers in my district. No consistency in teacher quality. I don't know any high school math teachers IRL.

I totally agree; rush a year of elementary math/arithmetic if you must, so that ample time can be spent on the good/harder stuff in high school!

[amsunshine]

 

Sure.  However, is the depth she's talking about really offered at the elementary and middle school levels?  What PS programs offer this type of depth?  There aren't many.  One size does not fit all and the least-worst alternative for bright math students to be challenged in a PS setting often involves some acceleration, ideally *with* extra depth.

 

 

 

I highly doubt any public school in the United States teaches elementary or middle school math with depth, given the textbooks that are so widely used and the poor education of our elementary and middle school teachers.

[idnib]

Interesting - so they offer to compress what is ordinarily two full years into one.  What was that about depth and not rushing?

 

"More depth" may be referring to the amount of poop being shoveled, if you get my meaning.

[SeaConquest]

From another article on Jo Boaler

"And indeed, when you dig deeper into Boaler’s paper, she is a big fan of practice and repetition.

... ...

Of course, any sort of repetition will lead to memorization. You wouldn’t really be calculating 7 x 8 by picturing blocks every single time you need to make a quick calculation. The more you repeat it, the more natural it becomes to have the answer pop into your head. But Boaler is convinced that the student who memorizes through usage, not drilling, will be better off"

Link http://www.usnews.com/news/articles/2015/02/09/should-we-stop-making-kids-memorize-times-tables

 

Interpret it whatever way you want :lol:

 

Thanks for the link. This part especially resonated with me:

 

The most compelling research evidence that Boaler presents is about how time pressure provokes math anxiety in many students. More than a third of students, according to one study cited by Boaler, experience extreme stress around timed tests.

A 2013 University of Chicago study found that that the working memory portion of the brain becomes blocked in stressed students and they cannot access the math facts that they know. Over time, the anxiety builds and their confidence erodes.

Boaler admits not everyone is harmed by timed math quizzes, but doesn’t see anyone benefitting from them either. “Some students are fine with them,†she said. “But when we combine those who are stressed with those who are turned away from math because of them, we have a large section of the U.S. population that goes across all achievement levels.â€

 

My son's brain shuts down immediately whenever a timer is involved. Times Attack, etc. are totally out for him, but he loves games like Prodigy. 

[Arcadia]

My son's brain shuts down immediately whenever a timer is involved. Times Attack, etc. are totally out for him, but he loves games like Prodigy

I like the long 3hr untimed format of the Cambridge A Levels math exams compared to the timed format of AP Calculus exam. You have time to panic and still finish the paper well.

 

ETA:

The smarter balanced (common core) tests are untimed.

[vonfirmath]

From another article on Jo Boaler

"And indeed, when you dig deeper into Boaler’s paper, she is a big fan of practice and repetition.

... ...

Of course, any sort of repetition will lead to memorization. You wouldn’t really be calculating 7 x 8 by picturing blocks every single time you need to make a quick calculation. The more you repeat it, the more natural it becomes to have the answer pop into your head. But Boaler is convinced that the student who memorizes through usage, not drilling, will be better off"

Link http://www.usnews.com/news/articles/2015/02/09/should-we-stop-making-kids-memorize-times-tables

 

Interpret it whatever way you want :lol:

 

Isn't drilling just a way of ensuring usage?

[Bluegoat]

Having read the article (and others by Jo Baeler), I am really bothered by some of her writing. Understanding math as an interconnected set of big ideas is easier if you can do things without having to stop and think. You an see patterns easier if you know, for example, the 7s times tables.

 

 

Jo Baeler has some good points about American attitudes towards math. In Japan, for example, the attitude is generally that anyone can learn math (or violin) if they are just willing to work hard enough. Hard work is seen as a good thing. In the USA, generally, people brag about how little they work because, if they have to work, they aren't gifted. Kids who have to work hard in math should be praised for persevering and for diligence, and they may one day find that math "comes" to them.

 

This played out recently at my son's yoyo club. A good yoyoer had just mastered a hard trick and bragged, "And I didn't even practice!" I saw his mom a few minutes later and snarkily related the comment. "Huh," she said, "he's been practicing 1-2 hours per day all week."

 

I certainly agree that professional physicists and artists think differently, but I wonder how much is inborn versus learned. (Not claiming 100% either way.)

 

Scattered thoughts on a rainy afternoon,

Emily

 

Yes, I was thinking along similar lines.  There was a study recently, IIRC, that suggested that memorization was actually an important step in conceptual understanding.  People seem to understand this more in other subjects - they know that if you don't know your facts in history or literature or biology that you will not be able to make connections and see relationships between ideas very effectively.  You especially won't be able to see new connections that no one else has made before.  You won't even be in much of a position to have doubts about whether the fact is actually true.

 

I do think that different people can be born with different ways of thinking, and perhaps some can be drawn to particular disaplines.  But i think - maybe part of that is a situation we create?  Maybe if math was taught in a different way, some people we don't think of as mathy would actually be able to contribute something a little different than the people who do well at it in more obvious ways.  I've found that in a lot of activities, people who think about things in a different way, maybe learn in a different way, if they have somehow got the expertise, can contribute a lot of insight.

 

 

[3andme]

I'm still struggling to understand how the author supports her conclusion based on the PISA results. She says "Yet data from the 13 million students who took PISA tests showed that the lowest achieving students worldwide were those who used a memorization strategy."  She also says that "The US has more memorizers than most other countries in the world."

 

I looked through the lengthy PISA report and cannot find any specific reference or support for that anywhere in the report. In fact, there's nothing in the report that specifically addresses memorization as a strategy. The report does define proficiency levels but the proficiency levels basically indicate higher mathematical performance on a range from simple to more complex problems.  So, the higher the score, the greater the ability to solve complex problems. Conversely, a low score indicates the ability to only solve simple problems. I can't see how this indicates definitively whether the poor performance was due to:  poor conceptual understanding, an inability to apply their conceptual understanding, or a reliance on memorization. 

 

I thought she might be trying to correlate memorization with one of the three subscore categories (Formulating, Employing, Interpreting) but looking at the definitions (see below) there's not one in particular that jumps out as favoring more of a memorization/procedural strategy.   Figure 1.2.37 (p. 63) compares the results of the mean total math score to the mean subscale scores, the US comes out slightly below the total math score in Formulating, at rough parity with the Employing score, and slightly above in the Interpreting score. So, it seems the only subscale in which the US outperforms its total math score is Interpreting but the report itself says on p. 61 that  "In fact performance on the interpreting subscale does not appear to be related to the overall math performance."  Maybe Interpreting is measuring a rawer form of analytic reasoning rather than a specifically mathematical one.

 

The same pattern holds for the lowest proficiency level students in the US - the Formulating score is the lowest relative to the total. So perhaps the author is equating low Formulating scores with memorization. Even then, it doesn't support her contention, that the US has more memorizers then most countries in the world as it clearly falls near the middle ranking in this subscale category (1.2.30).

 

If you look at the highest performing countries by total score, their Formulating scores are almost all the highest in relation to the total score and the Interpreting scores are the weakest. (Figure 1.2.37 on p. 63). So it seems like Formulating would be most closely correlated with strong overall math performance scores. If you look at the weakest performing countries, their strongest subscores seem to be in Interpreting.  Focusing in further on the lowest proficiency category for the lowest performing countries (see charts 1.2.30,1.2.33, 1.2.36), I still can't see how one can draw any more definitive conclusions.

 

Anyway, I fail to see how the author ends up where she does and I question whether her argument is more likely driven by her educational agenda then by the raw data. However, maybe she has access to other more detailed information or maybe I'm misunderstanding the report.

 

 

 

---Definitions of Subscale Factors---

 

Formulating - students must translate a problem into mathematical form. For example, in a problem about motion, students would need to translate the words into the components of speed, distance and rate and apply the formula for speed.(p.54)

 

Employing - to employ mathematical concepts, facts, and reasoning, students need to recognise which element of their " mathematics tool kit" are relevant to the problem and apply that knowledge in a systematic and  organized way to work toward a solution.(p.55)

 

Interpreting - students need to make links between the outcomes and the situation from which they arose for ex. careful interpretation of graphical data.

[jniter]

OK, I have to throw in my two cents, because this topic is something I have discussed often with my FIL,

 

He is a world reknowned mathematician. No kidding. The only reason he wasn't considered for the Fields medal is because was too old. He always jokes that he's really "slow".

 

First, I'm all for kids understanding *why*, but asking a 1st grader to "explain their process" for adding or subtracting in writing is too much, and that is the kind of assignment my son got a la Common Core. My son could barely articulate his feelings, much less translate his thought processes into words. I saw that as a sign of his youth, not as need to panic that he isn't a "deep thinker".

 

My FIL says the "deep thinking" issue isn't about how creative or unusual the thinking is. He says American students are always "creative", but they have no TENACITY. They don't keep working at a problem until they understand how to do it. So they default to memorizing steps. I never taught math as "only" a set of steps, but I clearly delineated steps in order to *explain* what was going on. I often tried to used Socratic questioning to lead my students to answers and that was a COMPLETE disaster. I've witnessed my FIL sit and do nothing but think, not even scratch down ideas, for hours!

 

There are plenty of other studies that show students in other countries spend more time on difficult word problems than US students before giving up. And these students are from countries where they "memorize" math facts. My rusty brain says something about Comparitive Education research.

 

Edit: grammar

[8filltheheart]

 

 

My FIL says the "deep thinking" issue isn't about how creative or unusual the thinking is. He says American students are always "creative", but they have no TENACITY. They don't keep working at a problem until they understand how to do it. So they default to memorizing steps. I never taught math as "only" a set of steps, but I clearly delineating steps in order to *explain* what was going on. I often tried to used Socratic questioning to lead my students to answers and that was a COMPLETE disaster. I've witnessed my FIL sit and do nothing but think, not even scratch down ideas, for hours!

 

 

 

Check out Art of Problem Solving. :)

[Roadrunner]

Drawing division of fraction for six months is not depth. It is torture. Based on NY Engage materials visual strategy is the primary one in teaching math. Sometimes it is more convoluted than simple explanations. I question what they call depth.

[wapiti]

First, I'm all for kids understanding *why*, but asking a 1st grader to "explain their process" for adding or subtracting in writing is too much, and that is the kind of assignment my son got a la Common Core. My son could barely articulate his feelings, much less translate his thought processes into words. I saw that as a sign of his youth, not as need to panic that he isn't a "deep thinker".

 

Yes!   I think it's important not to misinterpret the writing output as necessarily representing the depth of thinking, particularly in a younger child.  (I can't imagine what CC would have done to my ds12, whose writing was on grade level in first grade but simultaneously had math skills several grades ahead.)

 

I think it's equally important not to misinterpret a process explanation as necessarily indicative of mathematical depth; it depends.

 

My FIL says the "deep thinking" issue isn't about how creative or unusual the thinking is. He says American students are always "creative", but they have no TENACITY. They don't keep working at a problem until they understand how to do it. So they default to memorizing steps. I never taught math as "only" a set of steps, but I clearly delineated steps in order to *explain* what was going on. I often tried to used Socratic questioning to lead my students to answers and that was a COMPLETE disaster. I've witnessed my FIL sit and do nothing but think, not even scratch down ideas, for hours!

 

Seconding the recommendation to check out AoPS and, at the elementary level, Beast Academy.

 

(As an aside, while AoPS is focused on its niche of high-performing math students, I see a rather large opportunity for the design of a CC-aligned program that's really high-quality, perhaps a second version of BA and AoPS where the challenge level is toned down in spots for average students.  I'd like to see what average 8th graders could do with the prealgebra text but so much relies on what came before.)

[jniter]

Check out Art of Problem Solving. :)

 

=) I've had the books for years. Used them in tutoring. I'll be using them when my kids get there. =D

[mom31257]

First, I'm all for kids understanding *why*, but asking a 1st grader to "explain their process" for adding or subtracting in writing is too much, and that is the kind of assignment my son got a la Common Core. My son could barely articulate his feelings, much less translate his thought processes into words. I saw that as a sign of his youth, not as need to panic that he isn't a "deep thinker".

 

 

 

I prefer a "classical" approach to math. Show them the processes, memorize facts and steps when they are young, but don't expect mastery of the why and the logical thinking/analysis of the why until they are older. 

[Stellalarella]

In case you were feeling guilty that your kids haven't memorized their times tables yet:

 

http://hechingerreport.org/memorizers-are-the-lowest-achievers-and-other-common-core-math-surprises/

 

I didn't see where Boaler was advocating that students should not master math facts in the linked article.  

 

I feel sorry for upper elementary, middle school and high school (neurotypical) kids who do not know their times tables.  Really sorry.  And I feel sorry for every higher level teacher that has to deal with students who do not yet know their times tables.  

 

For a clear argument about why math fact mastery is valuable, please see Daniel Willingham's research compliation in "Why Students Don't Like School: A Cognitive Scientist Answers Questions About How the MInd Works and What It Means for the Classroom.  

 

 

I've been learning Latin as I've been teaching my kids.  If I don't have the facts, the grammar of Latin locked into my knowledge base, it's such a slog.  Yes, I can look up every other word in the dictionary, then consult the conjugation and declension charts in the back, I can chant every pattern for every word in my head--but translating one sentence that way takes forever.  Forever!  

 

Submit yourself to the discipline of learning, memorizing the basic facts and reap the benefits.  

[wapiti]

I didn't see where Boaler was advocating that students should not master math facts in the linked article. 

 

FWIW, from what I recall, the article was vague on whether "memorization" refers to learning the facts to mastery by any means or, in particular, memorization by rote.  She may have been referring to the latter and while I'm inclined to give her the benefit of the doubt, she could have made that a whole lot clearer.

[SeaConquest]

I didn't see where Boaler was advocating that students should not master math facts in the linked article.  

 

I feel sorry for upper elementary, middle school and high school (neurotypical) kids who do not know their times tables.  Really sorry.  And I feel sorry for every higher level teacher that has to deal with students who do not yet know their times tables.  

 

For a clear argument about why math fact mastery is valuable, please see Daniel Willingham's research compliation in "Why Students Don't Like School: A Cognitive Scientist Answers Questions About How the MInd Works and What It Means for the Classroom.  

 

 

I've been learning Latin as I've been teaching my kids.  If I don't have the facts, the grammar of Latin locked into my knowledge base, it's such a slog.  Yes, I can look up every other word in the dictionary, then consult the conjugation and declension charts in the back, I can chant every pattern for every word in my head--but translating one sentence that way takes forever.  Forever!  

 

Submit yourself to the discipline of learning, memorizing the basic facts and reap the benefits.  

 

It was here, which was linked in the article I posted:

 

http://hechingerreport.org/should-we-stop-making-kids-memorize-times-tables/

 

ETA: But, her position is obviously more nuanced than the headline implies.

[Stellalarella]

It was here, which was linked in the article I posted:

 

http://hechingerreport.org/should-we-stop-making-kids-memorize-times-tables/

 

ETA: But, her position is obviously more nuanced than the headline implies.

 

I cannot imagine a plurality of current elementary math educators handing kids a piece of paper with numerals on them and saying "Memorize These Equations.  You will be timed tomorrow."  

 

I have my kids work daily on untimed flash cards--but that's not how we start out.  It's all manipulatives, number sense, learning how to play with the numbers (8 + 4 = 12; Eight wants to be a 10 so it takes 2 away from the 4 to make a 10.  10 plus 2 is 12).  But at some point, after I've gone round the mulberry bush 57,000 times with all the number stories, number bonds, manipulatives and what not, I say--here are your facts.  Please learn them by heart. Honestly, I think in those classrooms where kids are lucky enough to have a teacher insist on basic facts mastery it probably goes much the same.   

 

It disturbs me that someone could read that article and the takeaway be that it's perfectly fantastic a kiddo hasn't learned the times tables.  

 

There are always outliers--I remember a story of some famous conceptual mathematician who never learned his times tables.  Apparently it didn't hold him back too much from putting together great number theory.  But for most of us swelling up the ole middle  bell curve of humanity, learning your times tables should just be a normal, expected, disciplined practice in basic education, a  mid product stemming from number sense and a pathway to easier stepping stones in more complicated mathematics.  

[SeaConquest]

I don't think the point is not to memorize math facts, but not to spend time drilling them at the expense of conceptual learning. I've never drilled my son on math facts, yet he somehow has managed to learn addition, subtraction, and multiplication facts (thus far) without the timed drills that I was subjected to as a child.