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Parents' Math Anxiety Is Contagious to Their Kids (well.blogs.nytimes.com)
83 points by euske on Aug 25, 2015 | hide | past | web | favorite | 75 comments

Another thing is that even very basic math concepts can be hard to explain in a way that makes sense to kids. For example, if you have to explain why multiplying unlike fractions works one way whereas adding unlike fractions requires an entirely different procedure, lots of parents have no idea other than "that's just how I learned it."

The transcripts included in the research paper "Mathematics in the Home" (PDF: http://www.researchgate.net/profile/Nicole_Else-Quest/public...) are really telling. Parents who are comfortable with math will tend to ask their kids questions and give little hints when they're stuck, whereas parents that are uncomfortable with math will tend to just blurt out the solution whenever things are taking too long, or encourage strict adherence to one particular heuristic for finding a solution. Over the long haul, the result is that mathematics will start to look like just one long arbitrary list of rules. Of course, that's no fun, and so kids of mathophobes become mathophobes themselves.

Plenty of help available, though, for people who do want to help their kids: "Help Your Kids with Math: A visual problem solver for kids and parents", "Math Power: How to Help Your Child Love Math, Even If You Don't", "What Can I Do to Help My Child with Math When I Don't Know Any Myself?"

A deeper problem is that math is almost always taught as a list of rules in the first place, frequently by teachers who do not themselves understand the underlying concepts. Teachers who only remember the procedures can of course only teach procedures. Most adults don't even remember any procedures, since they have no need to in daily life.

This condemns children to repeat the cycle. They (completely rationally) decide that they're just 'not math people' because they can't follow lists of arbitrary seeming steps to do something that no one they have ever met ever actually does in daily life. And some of them grow up to be teachers themselves.

> A deeper problem is that math is almost always taught as a list of rules in the first place, frequently by teachers who do not themselves understand the underlying concepts. Teachers who only remember the procedures can of course only teach procedures

Sigh, your statement reminds me of one time when I was in 6th grade geometry and was asked to complete this one proof. The problem was intended to get us to apply a concept we had been taught verbatim, but I couldn't remember it well and so I completed the proof a different way by extrapolating other basic concepts we had gone over into a method we had not been taught. I remember feeling very proud of myself when I finished, as I had created something which in my 12 year old eyes was a "novel proof". I ended up being given 0 points on the problem because I did not complete my proof using cookie cutter methods we had been taught (even though my proof was correct and it was not specified that I use a particular concept in the instructions).

I remember complaining to my teacher about how this was unfair and she kept saying something akin to "well you didn't do the problem the right way". The incident pretty much killed any interest I had in math, which wasn't rekindled until I stumbled upon machine learning recently in my 20s.

That kind of story makes me irrationally upset. That's horrible — killing a child's interest in math because they didn't do the problem the "right way". It's completely antagonistic to the spirit of the field. Teachers shouldn't be teaching subjects if they don't understand them.

Its these kind of experiences that I want to learn to teach my child to make it through.

There are a lot of other people out there who will unknowingly be very discouraging, to both children and adults, but their opinions have no bearing on our ability to learn. I remember being in music class in grade 1 and it was my absolute favorite class. Near the end of the year I was told that I wasn't very good at singing by my teacher. I never tried to sing again, but I learned later that I have good pitch and a decent voice. I am not really interested in singing now, but I might have learned a different set of skills if I didn't avoid it.

Is there a way that I could have been prepared so that being told by the person I looked up to for validation, that I was no good wouldn't make me stop trying to improve?

I don't know about that, but if there's a way to teach that, it would definitely be a good lesson. It would certainly be nice if teachers didn't do things like that, but even if you could guarantee they didn't, you won't stop the bullies or the critics or anyone other hater as you get older.

As they say, don't let your schooling get in the way of your education.

To the grandparent: I don't think getting upset is at all irrational.

Same - I vow to make sure that never happens to my kids, even if I have to homeschool them.

We had to homeschool for a year because of this (substitute teacher just going through the motions). My son has been a year ahead in math ever since. We've had to supplement to keep him challenged.

This still happens to me when getting graded by peers on coursera. Makes me feel good about my job security :)

This itself explains the worship of the Standard Algorithm, and why people see a New World Order conspiracy behind every attempt to reform math education.

Not helping matters is the fact that most of the reformers are themselves ignorant chuckleheads who identify the heuristics that skilled arithmeticians use and codify them as a NEW set of rules to be memorized...

Standard algorithms are standard for very good reasons. They are 100% reliable and at least reasonably fast, if not the fastest.

Failure to learn the standard algorithms impedes progress. You are unlikely to do well in the next course if you are slow and can't handle numerous cases.

Learning alternate algorithms is great... once you have the standard algorithms down solid and are ready to prove equivalence.

Concrete illustrations based on things in your world -> procedural methods (your algorithms) -> formal proof seems to work in my teaching of basic maths to adults.

Have a look at the sample chapter from David Tall's book...


FWIW, this is certainly not what people who do research into how to teach math advocate. In fact, one of the recommendations for teachers is that they should try to get students to come up with the algorithms themselves, or to "guide" them to these algorithms, and then let students use whichever they prefer, because that's the only way to get students to really understand and use them.

That said, I've definitely seen some of that "let's just replace method X with method Y" – how harmful that is depends on whether it is just presented as a default or as The New Standard Algorithm, I guess.

> FWIW, this is certainly not what people who do research into how to teach math advocate.

Of course it isn't, because such lunacy wouldn't be supported by competent research. But the people who do education research, the administrators making curriculum decisions, and the concerned parents trolling about the dangers of "Common Core" on Facebook are distinct sets with little overlap.

The problem starts when the curriculum attaches needless importance to fractions. 'Mixed fractions', wth curriculum-authors? Similarly with adding and multiplying fractions. The emphasis is more on the procedure and getting the student to be able to implement certain procedures, rather than understand the underlying intuition. Let's take two examples: 1/2 + 1/4 and 3/4 + 1/7. For the former there is a heavy intuitive reason for kids to understand adding half to a fourth. If you think about the latter, you are just adding two mathematical entities with little physical relevance. Equivalent entities are 0.75 and 0.142857, there is no good reason why one should stick to fractions when you are dealing with hairy numbers like 1/7. Kids aren't told this, and it complicates issues. The answer that kids are forced to look for is -1-1-/-1-4- 25/28, which is as unintuitively clunky as 1/7. They are challenged to add increasingly hard fractions like 13/37 + 22/7, etc. At this point, kids who can grasp abstract concepts do well, and those that can't get discouraged.

I think physically intuitive math and abstract math should be explicitly identified and treated differently in curricula. Else, the result will be clumsy contrived attempts to find physical relevance to abstract concepts and weaker students falling behind. Dreary contrived problems must be replaced with fun puzzles. Puzzles share the attribute of abstractness-and-apparent-uselessness with portions of the math curriculum.

Somehow teachers and parents find it hard to accept that some topics in math curricula are purely in the abstract realm.

The other meta problem and perhaps a big cause of math anxiety is that the curriculum and system doesn't have much wiggle room to fail at understanding something. The most important quality for success in later life is perseverance when you're stuck or when you hit a wall. The education system teaches the exact opposite: "it is not ok to hit a wall or fail to understand something, you have to learn this right now, else you're done for!" There is very little flexibility to allow students to fail, persevere, and repeat. This is worsened by the needlessly frenetic pace of the academic year.

Edit: D'oh, got 3/4 + 1/7 wrong, it should be 25/28

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For the .co.uk links, concatenate: "amazon.co.uk/dp/",[10 character string in URL, aka ASIN]

So, your first link would be "amzn.com/075664979X"

That seems even less user friendly though. At least the original links give some clue to the text's title and subject.

Not much, but for your example I'd draw two circles (or bars), fill 1/3 of one, 1/2 of the other, and ask the child to sum those. Then, add the missing divisions to the circles, so that both are divided in 6, and ask the child to sum.

I don't know how to draw a multiplication (and I think I'm not alone), but get some physical tokens that you can divide in 2 or 3 (like matches), and you can do all kinds of fraction multiplication and division with them.

You could draw the multiplication of e.g. 1/2 and 1/2 by dividing half a pie into another half. But you're right, it's harder in many cases and impossible in some.

And, likely, vice-versa. I was struggling with modulo artihmetic in 7th grade, and came home and explained so to my mom. She said 'It's like a clock', and I got it immediately.

My mom was the same way. I remember a particularly challenging (to me) elementary school word problem, involving a fictional system of currency. She went to a box of Trix cereal, we decided which cereal pieces corresponded to which fictional currency units in the word problem, and then we started doing transactions with the cereal, until I finally figured out the answer to the problem.

I found out later that she hated math, and thought she was bad at it (she really wasn't, but that's another issue entirely...). However, she never let me see that, which was fantastic.

I smell a Blank Slate Fallacy.

Math talent, like other intelligence, is inheritable. So until you've pried apart nature and nurture, the simplest assumption is that these kids are bad at math because they don't have much talent for it.

Google Turkheimer's Three Laws of Behavior Genetics for more on this often neglected field.

But what is "mathematical intelligence" or "math talent"? There's a big chunk of my family that didn't get any formal education in mathematics or anything else until very recently, and one of my most recent ancestors didn't exactly finish high school because of what I would retroactively diagnose as some learning disability. (Trouble with symbols & writing.) On the other hand, the same recent ancestor could visualize the way to build just about anything. So here I am, without a great love for algebra or analysis, but a great love for geometry (algebraic, differential, symplectic, etc) and a fine ability to create fitted knit garments and small pieces of furniture (and a PhD in pure math). Perhaps that's inherited, but due to the environment it didn't get anyone in my family past that far in higher education. I still screw up my face in frustration over subtraction problems, too, so do I lack "math talent" after all?

Did my recent ancestor who failed high school classes have math talent or not? And did my ancestors who didn't have a high school at all but could build a barn that still stands one hundred years later have math talent or not? How can we even talk about whether this thing is inheritable if we don't define it well and it manifests in such different ways in different environments?

The simplest assumption is that these kids are bad at math because math in our elementary and middle schools sucks! Look at the stats for immigrants to the US. If you came from impoverished places without educational opportunities, educational attainment rises over time. If you are a kid who comes from Hungary or Romania or Russia or South Korea, you'll be so much better at math than the US kids that it's not even funny. If your grandparents came from Hungary or Romania or South Korea and kicked ass at math, but your family has been in the US for a few generations, you'll suck as much as any other average American. If you're going to push heritability, you're going to have to face the conclusion that the water and air in America prompt genetic mutations that make people bad at math over a few generations. (I'm so glad I'm first-gen in part, but I fear for potential children.)

Also, why is it that when things like "illiteracy rates" come up, no one ever says "well, maybe they just don't have a talent for reading"? Reading and comprehension is a heck of a lot harder than multiplying fractions.

Doesn't the study control for this?

"The more the math-anxious parents tried to work with their children, the worse their children did in math, slipping more than a third of a grade level behind their peers."

The implication is that if the math-anxious parents did not work with their children as much, these children did better.

That just says that if you're bad at math, trying to teach it doesn't help.

That's useful "know your limitations" information, but I don't see how it separates nature vs nurture effects.

No, it says that if you're anxious about math, trying to teach it hurts the child's comprehension.

I don't think there is much distinction between "bad at math" and "anxious about math". The article certainly doesn't try to make one.

I was making a distinction between "hurts" and "doesn't help."

Then we agree.

Indeed, well said. Seems just as plausible, if not more so, that the anxiety is a symptom of poor familial aptitude for mathematics than the cause itself. But that's a thoughtcrime these days, so best not mention it ...

But until we know something provable about genetics and mathematical aptitude this line of thought is just hand-waving. You still don't know any better than anybody else why somebody is having a hard time with math.

That's why I said it seems "just as plausible" as the alternative. Its the article that's making the more definitive statements, not me. Besides, I think there's a reasonable amount of science that makes the argument for genetics over nurture quite compelling, but 20 years of malpractice and misdirection in the social sciences obfuscated that.

Ah, but it's only a thoughtcrime if you don't say it, and people call you an idiot for just thinking that.

I smell needless dichotomization. I'd rather teachers and parents didn't give up on students just because part of their mathematical aptitude might be genetically determined. Until you've pried apart nature and nurture, give people the benefit of the doubt.

I wonder whether there is anything specific to Math in this, or whether we're looking at a broader trend, which might perhaps be phrased as "Parents' academic anxiety is contagious to their kids"? Or maybe even "Parents' anxiety is contagious to their kids"?

Does this work the same way for parents who aren't comfortable talking or reasoning about (for example) history? Or literature? Or is math a special case that works differently from other subjects taught in schools?

There's a useful note in the article that maths-anxious parents didn't affect their children's reading ability. But it'd be fascinating to know whether (for example) poorly-literate parents have an effect on their children's reading ability, independent of other factors.

> Parents' anxiety

Really anything is - we've all seen it extend as far as prejudices. However, the degree of the influence probably varies wildly and I'd posit that "internal stress/stressors" (such as anxieties, fears) could have the largest overall influence.

Or what about "mathy" parents that show anxiety for the soft sciences?

Is soft science anxiety a thing?

Anxiety about writing or public speaking is. Not quite the soft sciences, but maybe close. (I think "outright dismissal" of the soft sciences is more likely than "anxiety" and maybe that's the point you were making.)

> Or maybe even "Parents' anxiety is contagious to their kids"

Definitely. As a parent, you have to be careful not to let your own fears or anxiety influence your children. I'm sure it's a good evolutionary trait -- children who afraid of the same things as their parents probably survive longer in the wild. But you don't want pass along any irrational fears.

> So much for good intentions. The more the math-anxious parents tried to work with their children, the worse their children did in math, slipping more than a third of a grade level behind their peers.

OK, assume they found a negative correlation between grades and the amount of help of the parents. I'm not buying this explanation. Sure, if your kid has worse grades then you help him/her more on the critical subject.

This is the study I believe they are referring to: http://cogdevlab.uchicago.edu/sites/cogdevlab.uchicago.edu/f... (PDF)

> we tested the interaction between parents’ math anxiety and the frequency of parents’ homework help while controlling for students’ grade, gender, beginning-of-year math achievement, and beginning-of-year math anxiety

So the study controls for baseline performance. It's definitely possible that some selection bias remains, but it looks like a reasonably well-executed study on a large sample (438 children) and I wouldn't discount the results out of hand.

Aren't practically all of parents' anxieties contagious to their kids?

My wife and I homeschool our kids. My wife and I were also both homeschooled. We both did Saxon math through highschool. For me it was hard, boring and great. After about 9th grade I basically just opened up the textbook and worked through the thirty or so problems every day. They were repetitive lessons with a short paragraph about the concept and how to do an example problem or two. There was not much detail or explanation in the textbook. This forced me to work out the underlying concepts myself and I knew trigonometry, algebra and basic mental math better than most of my peers by the time I went to college.

My wife is more of a visual hands on learner and suffered through the same text books. In college she had a series of bad professors (like, cancelling class because the professor had a hangover bad) and this just cemented her view that she was bad at math.

All that long exposition is to say that people learn different ways and a "bad" method may result in a good outcome. Learning is a complex interplay of teacher, student, material and presentation that can be different for every person.

When I teach my kids I like to have them all in the same lesson even though they are different ages and doing different levels of work. The primary purpose of this is to just talk about math, make it normal to think and reason about it and show that it's not scary. Math concepts are often taught as a series of ever increasing obstacles to be jumped over. You jump over them until you reach a ten foot wall that you just can't summon the mental power to leap over. Then you are bad at math.

But math is more like a hike. you start out in the foothills where even your 5 year old can keep up with the rest of the family. Each footstep is a little closer to the peak. You are making progress and learning even if you only make it to the first mile marker. You get fitter and accumulate some equipment and technical skills for the mountaineering sections higher up as you go. It's challenging but fun and you have a sense of accomplishment no matter how high you are. As you get higher the vistas opened up to you show you the world in ways you could never see lower down and give you motivation to go forward towards higher peaks and better views.

Saxon was a great math program. I worked my way through the Algebra 2 book in 7th grade, and coasted on that until I reached college. For some reason (ahem-one of the teachers helped write it-ahem) my high school used a different, much shittier math program. Until the second half of my senior year AP calculus class, I didn't have to cover anything that I hadn't done in the Algebra 2 book.

Particularly for things like manipulating and simplifying systems of equations, the Saxon program was great, simply because it was built on repetition and practice - you would work through dozens of problems of a particular category over time. The other thing that was very nice about the Saxon program was that it would revisit older concepts - the problem sets would not just be on the current chapter concepts, you'd also have to work through material that had been covered over the previous 15-20 chapters. My mother is a special education teacher, and she's had success even with children that have serious memory deficits, because the repetition will pound the knowledge through into short, medium and long-term memory.

Yes the repetition can be really boring and some of the problems, even the easier ones from previous lessons can take a while to solve. But I still remember the concepts from algebra 1,2 and trig and can pull them out and apply them in real world situations. I had to build a gaga pit[0] for my towns school just this past weekend and some basic trig definitely came in handy there.


That quiz at the end makes it almost impossible not to be classified as math anxious to some extent; answering even a single question (out of ten) with anything other than "Not anxious at all" (on its five point scale) gets one classified as "A little bit math-anxious" and told "Hey, who isn't? You don't panic over math, but perhaps you don't like it very much, either".

I'd assume parents X anxiety, or fear, or anger would be contagious to children in general. But this does bring back memories of my dad (general contractor) getting mad at my homework and calling for my mom (engineer) to come help hahaha. It was Calculus.

Contagious? Sure about that? Have you ruled out epigenetics?

Epigenetics isn't a magic wand; unless you really think people have "math receptors" in their body that will tune their epigenetics to be even worse at math in the future if they're frustrated today, and then pass it on to their children, it's a silly theory.

Moreover, most people have it exactly backwards... to the extent passing epigenetics to your children makes sense at all from an evolutionary perspective, it is passing adaptations, not weaknesses. If a parent has a hard time finding food, the stress of being hungry passes on to a child to make them smaller, i.e., less needing of food because they're not going to try to grow as much. Epigenetics is not "If you break a leg, your child will be born with a broken leg". That's just Lamarkianism, and Lamarkianism is still false.

> Moreover, most people have it exactly backwards... to the extent passing epigenetics to your children makes sense at all from an evolutionary perspective, it is passing adaptations, not weaknesses.

While I don't think epigenetic math anxiety is particularly plausible (for, basically, the "math receptor" reason you state earlier), an adaptation in general may turn out to be a weakness in a particular case. If, say, it was possible to epigenetically pass on stress triggers (an "adaptation", because having a stronger, quicker fight-or-flight response to a particular environmental condition that is a frequent stress source might generally be an advantage) this might manifest as a weakness in some particular cases. Now, because its hard to believe that there are "math receptors", it seems unlikely that even if this was possible in some general sense, that it would be possible in some way where "math" was the specific sensitized trigger, but if it was...

People are social animals. We get our social cues from others. If parents, teachers, etc show anxiety over something like math, it is entirely natural for youth to develop the same anxieties.

Related: http://www.psychologicalscience.org/index.php/news/releases/...

No need to go that far. Lots of behavior is heritable, so if one or both parents have "math anxiety", there's a chance their children will also have it.

"Math anxiety affects not only test taking and grades but also self-esteem and everyday computational skills. (How many gallons of paint for two coats of your living room? Can you convert a double-layer cake recipe into a triple-layer?)"

Is this really a thing? Are there adults (except for those in the < 2nd std dev range, who are near-but-not-quite-at mental disability-level) who cannot calculate the amount of paint needed to paint a room?

I wouldn't necessarily chalk it up to intelligence. I'm finishing a masters in statistics at the moment, quite a lot of math involved, and I'm mostly doing fine, however when I started the program after not having seen any mathematics in about a decade, I hardly remembered the difference between the circumference and the area of a circle. Now, calculating the amount of paint needed to paint a room might seem like more of a life skill than a math skill, but for some people it just doesn't come up, and when they do suddenly need math for something, they're not likely to trust whatever basic arithmetic they do think they still know.

For some people who are weak at math, it even becomes a badge of honor: "yeah, um, sure, we could calculate how we want to split the bill, but do we really want to be such nerds about it?"

Studies abound, too, showing that even grade school maths teachers often eff up when quizzed on pre-algebra.

What? Yes, of course it's a thing. I meet people like that every day.

A better example of following the rules without understanding would be percentages. Many people could tell you what buttons they push to answer "What is 37% of 240?" But many people would be lost if you asked them "What is 84 as a percentage of 270?"

Or "This product now costs £230. It has had a 20% discount applied. How much did it used to cost, before the discount?"

I think that "learning to regurgitate" information is partially to blame for these type of scenarios. Kids are encouraged to "do past-papers" and other such practice-based learning techniques; while these techniques may be a component of establishing knowledge they are most certainly not a singular solution. A person who has only done past-papers only knows how to be a parrot, and a parrot can't make the creative leap from "% of X" to "X over Y as %."

People I went to school could definitely work out the paint or percentage problems, but for a really good majority of them: only because they faced those exact questions in exams/tests.

Yes. Not among engineers, of course, but among the general population? Yes.

I know what you're getting at but to be fair that probably is a slightly trickier question than it seems. You need to factor in how absorbent the walls are (are you using unfinished drywall?), what colour the walls currently are (Is it very different to the paint? You'll probably need multiple coats.), what's the brand of paint you're using (I've seen different brands range between 350 - 450 sqft / gallon).

The math version of the question would say "This little can of paint can give a single coat to 5 square metres of wall. How many cans would you need to give two coats to a room that is 4 metres by 3 metres by 2.5 metres?"

A number of people can't do this.

More importantly, why are parents doing their kids homework anyway? They're never gonna learn - how - to learn, if the answer is always to ask mum and dad.

The trouble with traditional homework is that you have to wait a long time before you get feedback, at the earliest it'll be the next day. This makes it hard to correct misunderstandings. So parents helping with homework is a great idea, not because pupils shouldn't learn to take charge of their own learning, but because homework kind of sucks as a tool for learning.

"at the earliest it'll be the next day."

One of the interesting hard mathematical results to come out of generalized learning theory, as used by machine learning, is that there is a fundamental relationship between the speed of feedback and the ability to learn. It is not merely a matter of "willpower" to learn from temporally distant feedback, it is fundamentally, irreducibly harder, and there's no way to "correct" it because it's not even wrong.

Homework grading (note the emphasis) as a learning mechanism has such a delay that its learning rate is effectively zero. And what feedback you get is often not even very much beyond WRONG!, which is not exactly rich with information itself.

Homework is only useful for the feedback and learning you get while doing it, and for the ability to assess the student because we live & die on assessments, give us a direct choice between assessment and learning and the system will generally prefer the former. So, I won't say "homework is useless" but we could save everybody a lot of time if we only checked that it was done and spot-graded it for assessment, rather than making the teacher laboriously, yet nearly entirely uselessly, grade stacks of homework.

Probably the most effective way to learn anything is to ask someone who knows and is willing to teach you.

Those people are called teachers. Generally somewhat expert in their topic. Usually more so than the parents.

If a kids approach to homework is to try everything and leave the answers he can't do for mum and dad, he'll be crippled in his learning. The point of homework isn't to get 100%, it's to learn.

I tutor people -- I use "tutor" to emphasize individual or small group instruction -- and the idea of mainstream teaching is horrific. I fully agree with the poster learnstats2.

For one thing (and this is probably most damning), classes are highly regulated by school administrators. Managers who try to hire obedient teachers. The few teachers who try to slip through are nevertheless horrifically constrainted.

Children want to learn; it's a deep human motivation that has to be beaten out of people. The adults I teach have to be scrubbed of so many educational scars and bad habits. If only I had time right now to go into depth of all the antipatterns, the symptoms.

I think I hear a blog post coming.... ;)

As mentioned in the article, even teachers can pass on their math anxiety to students (especially female elementary school teachers to their female students).


This rings so true for me. My 4th grade teacher took two weeks of "teaching" fractions. Afterwards, she breathed a sigh of relief and said we can now go back to decimals. I avoided "getting" fractions until I was in 2nd semester calculus in high school. I would change all fractions to decimals, solve the problems, and convert the decimals to fractions (since the teacher wanted answers in fractions). Crazy, right? When the lightbulb finally went on, suddenly everything got a lot easier just working with fractions. I took this so much to heart that my daughter was taught exclusively with fractions at first, and only later moved on to decimals. Believe it or not, she actually had trouble grasping decimals at first due to her fraction exposure.

This reminds me of a story one of the math professors at the university I attended told once. He said he was standing in a class teaching the Math for Elementary Educators class, when someone asked him why they needed to know 8th grade mathematics. Apparently the elementary school teachers in my state are qualified to teach up to 8th grade, and so he needed to make sure they actually knew 8th grade math.

Wouldn't it be great if the selection procedures we have for children teachers didn't make it almost certain that they suck at Math?

There is a huge difference between parents working on homework with their young children like a tutor would, and a child "trying everything and leaving the answers they can't do for mum and dad". Most parents who are actually interested in the education of their children are likely to do their best to fall into the first camp, though the article discusses that it's harder for parents with less expertise to act as tutors rather than answer-givers.

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