
Afraid of Your Child's Math Textbook? You Should Be. - tokenadult
http://open.salon.com/blog/annie_keeghan/2012/02/17/afraid_of_your_childs_math_textbook_you_should_be
======
droithomme
It's silly to have churn in the publishing market with ever new approaches,
all of which are known to be less effective than proven methods of learning
math that have been known for hundreds of years.

Just use the Singapore Math series for K-6 and be done with it. Sound
pedagogy, known to work, has been debugged, no frivolous cutting edge theories
from M.Eds who have never taught math successfully.

~~~
Angostura
> all of which are known to be less effective than proven methods of learning
> math that have been known for hundreds of years.

[Citation needed]. The methods my kids currently use, seem more effective that
the ones I used at school. I am in my late 40s.

edit: I'm based in the UK, however.

~~~
droithomme
1\. My personal experience as a teacher.

2\. The average state of math knowledge of contemporary american high school
graduates, coupled with statistics on needed remedial education for college
entrants with high school diplomas.

Teaching math is easy. I can teach any kid math. It's not a problem at all
because we know how to do it. Many countries do it successfully. Observing
what schools are doing, the textbooks, the approaches, and the level of math
competency of elementary school teachers completely explains what is going
wrong. It's not a mystery. Also explains why kids homeschooled by parents,
even parents who were high school drop outs, end up with considerably better
math skills than most public school graduates, and even many private school
graduates.

Typical high school graduates don't understand fractions, percentages or
decimals. They can't do division. They don't understand algebra at all. We
know this is true because of college placement tests.

This is absurd. 100% of high school graduates should have passed differential
and integral calculus. That should be the minimal acceptable standard. That it
is not, and that graduates fail at even moderate arithmetic skills, shows the
complete failure of the system.

Downvote all you want while shouting "the dedicated teachers are not the
problem, the students and their parents are!" That won't change a thing.
Meanwhile, those who utilize proven approaches succeed and those who make
excuses and follow fads fail.

~~~
xiaoma
Out of curiosity, why is it that you would prioritize differential and
integral calculus? I studied calculus very early myself, but outside of later
classwork, I've only found it useful on rare occasions. I surely would have
used it more if I had gone into a research job or into material sciences, but
I estimate that very, very few careers are like that.

What would have been much more useful for me would have been a stronger
grounding in statistics.

~~~
droithomme
I didn't mean to prioritize it, I'm saying that level of understanding should
the goal of average achievement for high school graduates.

It is also really really far from what is being accomplished on average. High
schools have seniors who can't do division and don't understand operations on
fractions. Calculus is something anyone can understand, but it is seen by
teachers as some super advanced mysterious stuff for rocket scientists while
they struggle along to teach subtraction to 18 year olds.

Imagine a physical education fitness curriculum whose goal after 13 years of
training was for 18 year olds to be able to turn over by themselves and begin
to crawl. That's what we are doing, being satisfied with goals for graduates
that shouldn't be challenging even for 6 year olds. It shouldn't be tolerated
at all.

Schools that are graduating students with no math skills have had 13 years of
failed instruction with these students. Not just one teacher along the way.
All of them. The system should be burned to the ground and started over. That
will never happen though, it's too corrupt and incompetent. Myself I've given
up hope reform of the system is possible.

~~~
saulrh
Speaking as a recent high school graduate, please, _please_ don't give up. I
made it out of school knowing calculus and more because I had one physics
teacher and one math teacher that hadn't given up. They wrote their homework
themselves, used college textbooks and twenty-year-old texbooks they'd
collected from eBay, and railed constantly at the district's purchasing
people. They weren't able to change the system all by themselves, but they
still made - and continue to make - all the difference for dozens or hundreds
of students. You can do the same. Please.

------
meemo
I was the only person my cousin could turn to for help when he was taking math
in high school. When he asked me for help, my first instinct was to help him
find the relevant information in his textbook. But the textbook wasn't helpful
at all. First, he was often working with things that weren't indexed; even
though his homework was from the textbook's supplemental materials. Then, the
text was hard to understand. It just wasn't written very well. Finally, the
whole thing was just too busy, with many different fonts, all sorts of margin
notes, many footnotes, and colored boxes surrounding text. This made finding
information harder and just gave me a headache.

~~~
MBCook
I had the same experience. My little sister just finished HS a year or two
ago, and I helped her with her homework quite a few times.

The books were useless. It was nearly impossible to find concepts in it, and
when you did the description was often relatively short, relying on an example
that was often poorly constructed.

In the end, if the book didn't jog my memory I would have to Google the
concept to find a better page. The book might as well have been nothing but
problem sets.

I never met any of her teachers. I got the impression that at least one of
them wasn't qualified to teach math, but that was 2nd hand information through
the lens of my sister, so I can't be sure how accurate it was.

------
rcthompson
I guess if you ever try to fix a problem by throwing money at it, there will
always be someone there to intercept it. I think this has helped articulate
for me exactly _why_ "throwing money at a problem" is so bad: because it
attracts the kind of people who chase after large sums of money, not the kind
of people who fix problems.

(People always deride others in debates and arguments for "throwing money at
the problem", but they never stop to explain why it is a bad thing. Now I
know.)

~~~
nhaehnle
You make a very good point. Although I would add that money does play an
important role as well. The article mentions that qualified writers and
educators are leaving the field because the pay is so ridiculously low.

I suppose that what this shows is that simply "throwing money at the problem"
is not a good thing. You have to throw money at people who are genuinely
driven to solve the problem.

~~~
rcthompson
Yes the problem is when you "just" throw money at the problem without detailed
oversight by someone who cares about the problem and can get the money to the
right people.

------
tokenadult
Earlier Hacker News submission about teachers in Minnesota writing their own
textbook to state curriculum standards, by forking an appropriately licensed
online textbook series:

<http://news.ycombinator.com/item?id=3203857>

~~~
greenyoda
The link to that newspaper article says "story no longer available".

~~~
tokenadult
Thanks for letting me know. This

[http://minnesota.publicradio.org/display/web/2011/11/06/onli...](http://minnesota.publicradio.org/display/web/2011/11/06/online-
textbooks/)

appears to be a working link, from a website better about keeping links alive,
to the same AP news story.

------
DanBC
I met a 10 year old child with Asperger's[1] who was trying to do some math
homework. The book was wrong; they hadn't labelled a diagram but were asking
for those labels in the answers.

Maybe some children would have worked out to create their own key or to write
in the book, but this boy just stopped. An activity that he's good[2] at, that
he enjoys, is being slowly poisoned by poor quality materials.

It's not just math books either. Where's the Feynman quote about the horse
evolution?

[1] Proper diagnosis from a set of real doctors. [2] Got a scholarship to a
decent school partly based on his math ability.

~~~
nodata
I'm not sure that a kid with Asperger's stopping when they encounter a problem
leads to the conclusion that "[math] is being slowly poisoned by poor quality
materials."

~~~
DanBC
You're right. I meant to say that for him, his enjoyment is being slowly
poisoned.

------
joejohnson
_One math exercise in a chapter I was assigned called for students to use a
math formula to calculate their level of attractiveness, using a mathematical
ratio of 1:1.618 (otherwise known as phi or divine proportion), a formula
scientists have devised to set standards of beauty. Math can be tough enough
for some kids without having to learn that, on top of struggling to apply math
formulas to their face, they are also inherently unattractive. Talk about
installing math phobia!_

First, I think he meant _instilling_ math phobia.

And second, this "golden ration == attractiveness" myth is un-scientific and
an urban legend perpetuated by Dan Brown and similar authors.

------
Tycho
Why do we need more maths textbooks in the first place? I can't imagine
there's new branches of maths that we need to teach school kids about. (and
same goes for a lot of other subjects)

~~~
nhebb
I've wondered why there isn't a set of national texts available for core math
and science subjects. They're pretty stable subjects. So at one point I
decided to find out what the mission of the Dept. of Education is, and the
shocker (to me, at least) was the following little blurb from the ed.gov
website.

"In creating the Department of Education, Congress specified that:

No provision of a program administered by the Secretary or by any other
officer of the Department shall be construed to authorize the Secretary or any
such officer to exercise any direction, supervision, or control over the
curriculum, program of instruction, administration, or personnel of any
educational institution, school, or school system, over any accrediting agency
or association, or over the selection or content of library resources,
textbooks, or other instructional materials by any educational institution or
school system, except to the extent authorized by law. (Section 103[b], Public
Law 96-88)"

So even if we wanted to have national standards for math textbooks, the Dept.
of Education is prohibited by law from doing so.

~~~
keithpeter
Hello All from the UK

[http://www.education.gov.uk/schools/teachingandlearning/curr...](http://www.education.gov.uk/schools/teachingandlearning/curriculum/secondary)

The alternative is to specify the National Curriculum and then second guess
the changes each time the government changes.

School maths is a socially determined thing. It has little to do with
mathematics in University departments or the ways in which mathematical
reasoning is used in other areas of life. Definitions vary.

PS the new textbooks by pearson, stanley thornes, longman &c are relatively
error free.

------
spindritf
> That math homework you're trying to help your child muddle through might
> include problems with no possible solution. It could be that key information
> or steps are missing, that the problem involves a concept your child hasn’t
> yet been introduced to, or that the math problem is structurally unsound for
> a host of other reasons.

That sounds an awful lot like reality. Not that I think it's a great way to
teach maths (though maybe it is a great way to teach problem solving) but an
educated adult should have little trouble spotting the missing information or
contradictions and either guessing, pointing out, or assuming them away.

I realize that it wasn't intentional on the part of the authors (neither are
real problems), and that it's not the point of the article but merely a hook.

~~~
gatlin
Open-ended questions and problems are awesome. However, typically book work is
intended to be rote practice of an algorithm. Already it is not a simulation
of the real world - typically the real world open ended problems are cross-
disciplinary and much larger in scope than a context-free simple arithmetic
algorithm. That is not the point of book work, and when students go in
expecting problems to be internally consistent, sound, solvable, and to behave
the way the teacher told them, it can hamper learning as they have had the
proverbial rug pulled.

~~~
tokenadult
_Open-ended questions and problems are awesome._

Open-ended questions and problems are indeed awesome. Moreover, they are an
essential part of a sound education in mathematics, even at the K-12 (primary
and secondary schooling) level of learning. But open-ended questions used for
teaching purposes should be carefully written for sound teaching points, and
teachers using them should have sufficient background in mathematics to guide
student approaches to grappling with them. One of my favorite authors on
mathematics education reform (Professor Hung-hsi Wu of UC Berkeley) began
writing on that issue in 1994 with his article, "The Role of Open-ended
Problems in Mathematics Education,"

<http://math.berkeley.edu/~wu/open-role.pdf>

and he followed up on that article with a wonderful article in the fall 1999
issue of American Educator, "Basic Skills versus Conceptual Understanding: A
Bogus Dichotomy in Mathematics Education."

<http://www.aft.org/pdfs/americaneducator/fall1999/wu.pdf>

Since then, Professor Wu has written many more useful articles on mathematics
education, including guides for parents, teachers, school administrators, and
teacher educators on how to apply the new Common Core State Standards in
mathematics better to improve mathematics education in the United States.

<http://math.berkeley.edu/~wu/>

<http://www.corestandards.org/the-standards/mathematics>

A good example of a beguiling textbook by a world-famous mathematician with
lots of open-ended problems is Algebra, by the late Israel M. Gelfand and
Alexander Shen.

<http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773>

Some of the problems in this book are HARD, but they are generally well posed
problems of actual research interest to mathematicians, that just happen to be
accessible to pupils just beginning to learn algebra.

AFTER EDIT: answering the question kindly posted below, one example I had in
mind is that Gelfand asks students to figure out how many different ways there
are to group terms in an expression with parentheses as the number of terms
increases. This essentially asks the students to discover the Catalan number
sequence.

<http://www.geometer.org/mathcircles/catalan.pdf>

~~~
psykotic
> Some of the problems in this book are HARD, but they are generally well
> posed problems of actual research interest to mathematicians

Could you share a few examples? I've looked through the books from Gelfand's
correspondence course (which are indeed excellent) but don't remember any
problems that fit your description. Some of them would certainly be
challenging for young children--I'm more interested in the second half of your
statement.

I'll volunteer one potential example. There was a sequence of problems that
dealt with the solvability by radicals of palindromic polynomials. That
certainly motivates some ideas of Galois theory in no small way, but it's very
basic and of no interest to research mathematicians.

Addendum: Now that I have looked it up in the book, I see it was a single
problem, Problem 270, not a sequence of problems. That sequence of problems
was from a mathematics competition for young children.

~~~
Drbble
Parent meant problems that were in the past of interest to research
mathematicians. Someone(s) published the first papers exhibiting Catalan
numbers underlying various counting problems. Obviously we don't expect
elementary students to be at the forefront of modern cutting edge research.

~~~
psykotic
If so, that's a much weaker and not terribly interesting claim. The concrete
example of counting with Catalan numbers is more compelling; it would be very
challenging for children who lack experience with recursive definitions and
inductive proofs. Systematic enumeration, albeit elementary, is distinctly
modern.

------
swang
Corruption in the "Text Book" industry is not new. Some of you may have read
the article written by Richard Feynman about his experience reviewing math
textbooks for California... in 1964.

<http://www.textbookleague.org/103feyn.htm>

------
mceachen
I've seen the horribleness of my children's text books, and completely agree
that they are not-good.

But now what? Who should we be talking to who can affect change?

~~~
gmichnikov
I don't think change in this area is going to come from within (unless the
reason for change is financial). If/when it happens, I think it will be the
result of external pressure that comes from things like Khan Academy and open-
source textbooks proving themselves to be better than paid textbooks.

I've thought about working on a free site to help parents/students locate the
best free online math resource that can help them with a specific question,
worksheet, homework assignment, etc. As a tutor, I've frequently heard from
parents that they know these types of things exist on the internet, but that
they have no clue how to find the right Khan video that will help with
tonight's homework.

If anyone is interested in this sort of thing, please get in touch.

------
joelhooks
My kids don't go to school, but we use the Saxon books for math here at home.
They are so well put together. Incremental development. Enough consistent
repetition of core concepts. All lessons back reference the
fundamentals/foundations with a simple indexing system.

~~~
joshkaufman
Do you use the original or homeschool edition? I'm planning to pick up a set
soon.

~~~
joelhooks
I always order the homeschool set, but I believe the actual textbook is the
same. We just get tests/answers.

------
WalterBright
Left unexplained in the article is why math books need to be reinvented every
year.

------
mattmcknight
I always find something a little ridiculous in these articles that blame the
textbook for errors (or a statewide test), when the textbook has been through
more review than an exercise that an individual teacher designs. That said,
math textbooks are becoming an anachronism. Adaptive individualized content is
already available up to high school level.

~~~
rcthompson
Did you even read the article? The whole point is that the textbooks are
written on an impossibly tight timeline by unqualified and underpaid writers
and undergo little to no review, either by the publisher or the school
districts buying them.

~~~
mattmcknight
Your comment is not related to the subtext of my comment. The guy has an
editor for his textbook contributions, but no editor for the material he gives
his own class. Therefore, the textbook material gets more review than
something he does on his own.

To your point, if he is unqualified to write exercises for a textbook, he
would also be unqualified to create these for his own class. If he is
underpaid...that is largely irrelevant- if he were really underpaid, he
wouldn't have taken the job.

The article was of the anti-corporate bias perspective, which is why it was on
Salon.com, that this is because of the "profit motive" of the publishers.
However, that perspective is also nonsensical. The examples do not change that
much from edition to edition- they are seldom created from whole cloth. Even
in his tortured example of complaining about the golden ratio problem was one
of textbook translation- pointing out that, as an author, he cared about
things other than the effectiveness of the text.

It is true that many textbooks are of low quality...but considering the bias
of the writer, the whole article is a bit self-serving, while also being
hypocritical.

All points about the incompetence of textbook buyers stand though. They choose
for the worst of reasons, with effectiveness almost never even on the table as
a concept.

------
vacri
On the commission thing. one thing that's easy to overlook is that once an
author has written the book, there's nothing more to do, in an ongoing day-to-
day sense. Sit back and enjoy the royalties for years. Someone else does the
selling, and the author's efforts don't scale with the number of sales. The
salesperson has to sink effort into each sale, has to work it, or at the very
least do the paperwork.

Similarly the author gets royalties on all copies, but the salesperson only
gets commission on the books they sell. A thousand books sold by four sales
staff is 1000 books for royalty purposes, but only 250 books on average for
commission purposes.

There is some slight irony in assuming something is wrong with the number just
because they don't appear superficially linearly correct, when criticising the
quality of maths books...

~~~
Luyt
_Sit back and enjoy the royalties for years._

Apparently, that's not the case anymore for educational book writers. The
article states:

 _Today, royalties are a thing of the past for most writers and work-for-hire
is the norm._

...and during the article this new state of affairs is mentioned quite a few
times, and loathed.

------
kiba
One might thought that people incremental revise previous editions rather than
publishing whole new content, but it doesn't seem to be the case. At that
point, we might as well just use khanacademy math lecture and show them
according to a teacher's lesson plan.

~~~
droithomme
In most states math education is completely fad driven.

Textbook selection committees are usually staffed with people who do not
understand the subject, and when domain experts are asked to donate their time
to evaluate materials, their feedback is ignored as the only purpose of having
them aboard was to apply to the dog and pony show evaluation proceedings a
sheen of legitimacy.

Textbook publishers spend millions each year wining and dining members of
committees, providing them with gifts and trips and sometimes even setting
them up with speaking fees that are a masked form of bribery and kickbacks.
It's a well known problem and has been going on for decades. It's very similar
to the way the pharmaceutical rep industry works.

I strongly recommend everyone read "Judging Books by Their Covers" by Richard
Feynman for his experience in the process, which remains the standard modus
operandi to this day:

<http://www.textbookleague.org/103feyn.htm>

As the editor's postscript to that article summarizes:

"As a rule, however, state agencies don't want legitimate evaluations of the
textbooks that publishers submit for adoption, because the agencies are allied
with the publishers. The adoption proceedings staged by these agencies are not
designed to help school districts, to protect students, or to serve the
interests of taxpayers. Rather, they are designed to serve the interests of
the publishers, to generate approvals and certifications for the publishers'
books, and to help the publishers sell those books to local schools."

These dynamics are part of why I strongly oppose calls for national
standardization, the streamlining and centralization of would lead to a much
larger and more difficult to combat corruption as greasy palm edu-bureaucrats
rake in the dough for selling out the country.

~~~
r00fus
Fad driven, or politics/corruption driven? The textbook "industry" is one of
the most pernicious, that really should be put out of business... in today's
world, even if we were doing dead-tree based knowledge devices, they could be
tailored to the individual and printed on demand.

Of course, things like tablet-based (eInk or LCD) reading and khan academy are
the future of learning.

~~~
droithomme
There's two separate phenomenon. Pedagogical approaches follow fads rather
than solid principles known to work. Textbook selection is corrupt. Both are
problems that have not been solved at least since Feynman's experience in the
1960s despite much effort and an awareness of the problem.

------
edtechdev
This guy knows a lot about the textbook industry, but I'm not sure he knows
much about teaching and learning.

How you design texts can make a difference (google "conceptual change texts"
for example), but how much do textbooks really influence the quality of
instruction? If a teacher is just blindly following a textbook (and not doing
other things like supporting students, using interactive software, etc.), then
there are bigger problems.

Ironically, too, students would learn _more_ from a textbook with mistakes in
it if they were made aware of that fact and encouraged to find them. I know I
learned the most in geometry where I had a teacher who couldn't even draw a
circle and made mistakes every single day.

------
tsotha
How much has grade school level math changed over the years? Do we really need
new textbooks?

