
A ridiculous Common Core test for first graders - Steko
http://www.washingtonpost.com/blogs/answer-sheet/wp/2013/10/31/a-ridiculous-common-core-test-for-first-graders/
======
colomon
As the father of a five-year-old, two things puzzled me here:

1) "In the United States, students begin Grade 1 at the age of 5 or 6." Say
what? In our part of Michigan, kids begin kindergarten at 5 or 6, leaning
towards 6.

2) I see people here complaining about the math on the test, but what boggles
me is the reading! Are beginning first graders really expected to be able to
handle word problems? Maybe it's just been too long since I was there myself,
but I thought we were just learning to read "See Spot run" at that point in
school. For sure it seems like an insane amount of reading skill to ask of a
five-year-old.

~~~
mturmon
You make some good points.

People are put off by the jargon. The jargon in the test will have been
introduced in class by the teacher. For example, "number sentence" is
"equation". I support that one. It gets kids understanding the equal sign,
probably the most important symbol of mathematics, and making the connection
between story problems (in English sentences) and their mathematical
interpretation (in equations).

And the idea of a "related subtraction sentence" is good too. The related
subtraction sentences for 4 + 3 = 7 are 7 - 3 = 4 and 7 - 4 = 3. That's one
way to teach subtraction, as the inverse of addition. Understanding it this
way helps to remember the subtraction tables.

The problem is that the test itself is rubbish. (My third-grader has been
through this curriculum, in CA, but not with this test.) The worst one is
question 12, which asks for a subtraction sentence, but none of the choices
are subtraction. D'oh!

~~~
ktsmith
I'm curious, you say your child has been through this curriculum. Are you
saying your child was in a school using the Pearson curriculum or that your
child's school used a curriculum based on common core?

~~~
mturmon
Common core curriculum (in CA, not NY, but they seem to be similar), but not
Pearson tests.

Her tests and homework were reasonable.

I do have a problem with the attention her district pays to testing, but not
really with the curriculum per se. The testing does give teachers less
latitude with what subjects they teach, and when they teach it. They have to
cover certain concepts by the time the test is taken, which in her schools is
March or April. This means they have to re-order the curriculum to cover the
subjects to-be-tested in time for the test.

~~~
ktsmith
> Common core curriculum (in CA, not NY, but they seem to be similar), but not
> Pearson tests.

Yeah, the whole point is that if both states are implementing common core they
should be the same. If you look at the NY Common Core standard it's a word for
word match with what is posted on achievethecore.org and commoncore.org. Where
the differences lie is in the curriculums that each state, and even each
school district within a state, choose to buy and then how the schools
implement it. I'm seeing some schools being extremely strict and enforcing
scripted curriculum on teachers such as that provided by Success for All and
other schools allowing teachers leeway to teach how they feel is best for
their class each year so long as it's consistent across the grade level (all
teachers teaching the same concepts at the same times).

> I do have a problem with the attention her district pays to testing, but not
> really with the curriculum per se.

Has California, or specifically your school district, implemented performance
based pay or bonuses? That's in a trial run here and there have already been
complaints about increases in test focus at the schools in the trial. A big
part of the performance evaluation is based on test scores.

edit: I should note that there's the common core standards and then common
core curriculums. The curriculums should be compliant with the standards but
aren't the same thing. So NY and CA should both be adhering to the same
standard while they are free to use different curriculum (and almost certainly
do from district to district).

~~~
mturmon
Performance-based pay has been proposed and heartily resisted by teachers in
LAUSD (Los Angeles). This article
([http://www.huffingtonpost.com/2013/01/21/lausd-teacher-
evalu...](http://www.huffingtonpost.com/2013/01/21/lausd-teacher-evaluation-
utla_n_2517684.html)) says the union (UTLA) voted in January to allow
performance-based _evaluation_ , but I don't think this is linked to _pay_
yet.

Indeed, the superintendent of LAUSD is at this moment threatening to resign
([http://articles.latimes.com/2013/oct/25/local/la-
me-1026-dea...](http://articles.latimes.com/2013/oct/25/local/la-
me-1026-deasy-20131026)) because he and the school board (which is dominated
by UTLA) are fighting about this linkage.

The thing I just learned is that LAUSD has been forced to (eventually) link
evaluations to pay due to something called the Stull Act. And it looks like
that is a state-wide ruling that will eventually force all CA districts to do
this.

It's quite a situation. The outgoing mayor had made reform (a loaded word) of
LAUSD a priority, but his candidates failed to dominate the school board. The
charters and testing have the union grumpy. There were layoffs after the
recession and several idealistic and highly-motivated LAUSD teachers I know
were forced out under the union's last-in, first-out policy. They are now at
charters and private schools.

 __*

I'm actually pretty doubtful about the precision of these test scores; I think
they are noisier than most administrators seem to. And once you link pay to
the scores, things are going to go downhill fast.

------
ghshephard
Question 1 was bizarre. I'm not even sure what they were trying to ask.

Question 2 "There are 8 Jars. 6 Jars have Jelly. The rest have peanut butter.
How many Jars have Peanut Butter."

The first thing that occurred to me is that we didn't specify the Jars with
Jelly don't have peanut butter. Horrible question.

Question 3,4 I can live with.

Question 10 was greek.

Question 11 - Once again, nothing states that the others aren't red as well.
Reinforcing poor logical thinking.

Question 12 "Related Subtraction Sentence?" No wonder these kids are crying.

I couldn't read any further. This is how they are trying to teach kids math?

~~~
Jach
I'm okay with questions 2 and 11. Admittedly #2 could be made more explicit by
adding the word "only" after "have", but I think in the absence of the word
"some" then it's a valid inference to conclude the writer meant "only". Same
thing with #11, it could have been made more explicit (in two ways!) by saying
"only 2 are entirely red" and asking how many are not entirely red. But again,
I think in the absence of a phrase like "at least two of them are partially
red" then inferring "only two are entirely red" is valid. I also think the
majority would have no problem making those inferences -- the person whose
test was uploaded didn't have a problem (they just failed with subtraction on
#11).

I think I get #5. The person wrote a 9 when they should have written a 4.

#6 is fine, but then it makes #12 not make sense. Shouldn't a subtraction
sentence have a subtraction symbol in it? Or is a "related subtraction
sentence" an actual thing, not just asking what the subtraction sentence is in
relation to the picture?

#7 is fine.

#8 introduces the "number sentence". (What's wrong with the word "equation"?)
But aren't all of the examples "subtraction sentences"? Bah! Apart from that
it's fine...

#9 introduces the "subtraction story". Guh?

~~~
ghshephard
"but I think in the absence of the word "some" then it's a valid inference to
conclude the writer meant "only""

The first two years of critical thinking were dedicated to trying to drive
that type of logic out of our head. "Six Jars Have Jelly" in no way implies
they don't also have peanut butter, it simply makes explicit that six jars
have Jelly. "The rest have peanut butter" doesn't imply the rest don't have
jelly, it simply makes explicit there are at _least_ two jars with Peanut
Butter. That entire sentence would have been perfectly applied to 8 jars of
peanut butter/jelly. By suggesting it does not, you are setting in place
logical frameworks in a child's head that become very difficult to remove -
even if it's clear they are invalid frameworks.

When you say, "I also think the majority would have no problem making those
inferences" \- you are just making my point - the Majority of people come to
conclusions that are in no way supported by the text, and, even worse, when
you point out their error, they instead suggest an inference has been made in
the text, when it very clearly has not.

"Some of the Apples in the barrel" in no way suggests not all of the Apples
are rotten. "A few people in the crowd acted out against the police" doesn't
imply they didn't all act against the police, etc...

The person whose test was uploaded is a six year old who is doing their level
best to come up with the "right" answer. In ten years, they are they same type
of student, who, in a chemistry exam, when provided with the question, "What
particle in an atom has the least negative charge" will answer, "Electron".

~~~
Jach
I wonder how many years of probabilistic thinking it would take to drive it
back into your head?

What's your prior for p1 = P(jars contain jelly and something else | you're
told "six jars have jelly"), and your prior for p2 = P(jars contain only jelly
| you're told "six jars have jelly")? Are they the same for you? For me,
they're quite different: p1 << p2. Why is that? As a first guess, I'm very
unused to seeing jars containing jelly plus other crap, even though I have
seen those strange peanut butter + jelly combo jars.
([http://www.americansweets.co.uk/ekmps/shops/statesidecandy/i...](http://www.americansweets.co.uk/ekmps/shops/statesidecandy/images/american-
smuckers-goober-grape-peanut-butter-jelly-combination-510g-759-p.jpg))
Furthermore I'm unused to being told "a jar contains X" when a jar in fact
contains "X and Y (and Z and ...)".

The Majority use probabilistic reasoning (even if they often suck at it) in
every day life. Rational agents (which humans approximate) use probabilistic
reasoning, see Cox's Theorem and the work of others. This is (part of) why
calling out a logical fallacy in an argument is often a mistake -- a lot of
arguments aren't small (or large) trades of deductive proofs, they're
probabilistic arguments where each side is trying to update the other side
with supposedly new information. Many logical fallacies can turn into
probabilistic theorems. For example, "arguments from authority" can become
valid in a probabilistic framework. How? While [expert said X is true] --> [X
is true] is a fallacious deduction (unless you assume as a premise that
whatever expert says is true, then it's just a tautology...),
probabilistically our everyday experience suggests P(x is true | expert said x
is true) > P(x is true | random nobody said x is true). We can find plenty of
cases where experts are wrong, but in general that pattern seems to hold, and
we're more willing to accept counter-intuitive truths from experts than from
people on the street.

To address one of your examples: [We're informed 'a few people in the crowd
acted out against the police'] --> [Not all of them acted out] is indeed an
invalid logical deduction without more premises, but let's treat this
probabilistically. (Fair warning: I tried my best to make sure there are no
errors in my math but I've been up all night writing signal processing
code...)

Let x="Not all of the crowd acted out",

let y="We're informed 'a few people in the crowd acted out against the
police'",

and let c=our general background context="We know an incident occurred with
the crowd and the police".

We have a prior belief about x: P(x | c) = P("Not all of the crowd acted out"
| "we know an incident occurred").

We receive a new piece of information, y: "We're informed 'a few people in the
crowd acted out against the police'". Now let's perform a Bayesian update:

P(x | y and c) = P(x | c) * P(y | x and c) / P(y | c)

Clearly if P(y | x and c) > P(y | c), then our updated belief about "Not all
of the crowd acted out" will go up, and the inference [y] --> [x] is valid.
(You would interpret the --> not as "therefore" but "increases our confidence
in". [Being informed the phrase 'a few people acted out'] increases our
confidence in ['not all people acted out'].)

I think it's clear that P(y | x and c) is in fact greater than P(y | c). If
you don't, then continue with this next section. Using marginalization we can
break down P(y | c) independent of x, then use the product rule to break it
down even further: P(y | c) = P(y and x | c) + P(y and not(x) | c) = P(y | x
and c) * P(x | c) + P(y | not(x) and c) * P(not(x) | c)

So, is P(y | x and c) >? P(y | x and c) * P(x | c) + P(y | not(x) and c) *
P(not(x) | c), subtract and factor:

P(y | x and c) * (1 - P(x | c)) >? P(y | not(x) and c) * P(not(x) | c), by the
sum rule:

P(y | x and c) * p(not(x) | c) >? P(y | not(x) and c) * P(not(x) | c)

P(y | x and c) >? P(y | not(x) and c)

Reminding what all the variables are again (temporarily dropping off the c for
brevity):

P("told 'a few' acted out" | "not all acted out") >? P("told 'a few' acted
out" | "all acted out!")

I don't know about you, but I think it's very unlikely to be told 'a few'
acted out if in reality everyone acted out. QED.~

To put my whole comment another way: try writing an AI and sick it on this
test. If it doesn't use probabilistic algorithms and instead insists when it
comes to question #2 that "I cannot know the answer other than it's between 0
and 8, the question isn't explicit enough!", it's going to perform very
poorly. Human language is not crisp, treating it as if it were is a bad idea,
that's why we use crisp math when we want to be crisp and if we can do
automated proofs so much the better.

On your last remark, I find it amusing that if I take your "it's not explicit
enough!" complaint seriously, I'm not sure whether you think the correct
answer is supposed to be "proton" or "neutron" or "electron". That's because
I'm not sure whether you mean "least negative" to mean to "furthest to the
right from negative epsilon (i.e. 'most positive')", implying the proton, or
"smallest member of the negative reals excluding 0", implying the electron, or
"smallest member of the negative reals and 0", implying the neutron. If I
wrote the question I think I would have meant "proton" as the answer. So given
that the answer is proton, however, the error the student most likely made is
just a parse error, failing to properly change "least negative" into "most
positive". Similar to answering "yes" to the question "the sky is not not
green?", or asserting -3 * -3=-9. It's a different sort of trick on the
student than what you insist question #2 could be tricking the student. In #2,
the trick would be "Aha, but we never said the jars were _entirely_ jelly!
Don't insert words that aren't there!" In this charge question, the trick is
"Aha, you didn't parse 'least negative' into 'most positive'! Read carefully!"

~~~
ghshephard
I don't disagree with you, that, if we have to make a "Best Guess", we need to
bring in our day to day context - but using the the one word, "only" \- not
only eliminates the guessing, it also helps to reinforce logical thinking.

Re: Electron - I was trying to use it as an example of a poorly written exam.
This particular question was on a Grade 10 final exam, and I thought it was
obviously, "proton." The "correct" (for some definition of correct?) was
"electron." I was using it as an example to demonstrated that "test creators"
\- are people, just like you and me, who make mistakes. Also using it to show
how the student who is always looking for the "correct" answer (as compared to
the correct answer) starts to lose their ability to parse and logically
communicate.

------
aspensmonster
>Take a look at question No. 1, which shows students five pennies, under which
it says “part I know,” and then a full coffee cup labeled with a “6″ and,
under it, the word, “Whole.” Students are asked to find “the missing part”
from a list of four numbers.

Wat.

Edit: [http://roundtheinkwell.files.wordpress.com/2013/10/the-
math-...](http://roundtheinkwell.files.wordpress.com/2013/10/the-math-
test.pdf) ; That's the actual test, apparently. I still think "Wat" is an
appropriate response though.

~~~
rallison
Some of those questions are fine. Some of those questions I hope have some
surrounding context. And some of them are pretty ridiculous.

I went in expecting (hoping) to see some above grade level questions that
simply let the really good students excel. I left disappointed.

That said, thank you for the link to the actual test.

~~~
ktsmith
Some probably do have surrounding context and in the case of #3 the kids were
probably provided with manipulatives so they could literally use cubes to
solve the problem. The test is still terrible.

------
BadCookie
This test is so, so bad. If this is how I had been exposed to math when I was
in the first grade, I hate to think how my life would have been different. (I
have two degrees in mathematics.)

I've heard stories of my first grader niece crying while trying to complete
her daily homework. I'm starting to understand why.

~~~
anaphor
I think grade school math curriculums are incredibly bad in most of the world,
though. I know it's awful here in Ontario. Everything I learned about
mathematics was from non-textbooks (e.g. Dover math books), lectures, papers
and blog posts. School didn't teach me a thing. I think the only decent
"textbook" I have is Concrete Mathematics, and that's not even close to most
textbooks. It's probably been posted a million times before on here, but
[http://www.textbookleague.org/103feyn.htm](http://www.textbookleague.org/103feyn.htm)

~~~
revelation
Wonderful article, but one verdict turns out to be wrong:

 _Translating from one base to another is an utterly useless thing. If you can
do it, maybe it 's entertaining; if you can't do it, forget it. There's no
point to it._

~~~
pmiller2
I'd say it's still a generally true statement. Other than base 2, 8, or 16,
there isn't much use for translating from one base to another.

~~~
impendia
The purpose of working in number bases other than 10 is to reinforce the
meaning of place value, and to implicitly teach students that the way we write
numerals is (1) very logical and sensible, but (2) an accident of biology.

What we should really do is make students add and multiply in Roman numerals.
Quick, what's LXXVII x XLIV? Attempting that will make you appreciate decimal
notation _real_ quick.

------
RougeFemme
One of my favorite stories regarding an elementary level Standards of Learning
(SOL) test in Virginia. . .Students are taught how to estimate relatively
simple sums, difference, products and quotients in their heads. Students are
required to select the "correct" estimate. One of the questions accidentally
(I guess) included the _actual_ answer among the choices. My son selected the
actual answer rather than the "correct" estimate and it was marked wrong.

OK, technically he didn't follow directions. . .the question asked for the
estimate. But. . .really. . .you penalize a kid for calculating the correct
answer and selecting that over the correct estimate??

~~~
Zancarius
First, I should apologize for relating a personal anecdote, because it doesn't
have anything to do with Common Core. It does provide something of a benchmark
for the state of education 25-ish years ago, and it's troubling to me that
we're continuing a downward spiral. Your story made me think immediately of
this.

When I was in 2nd grade sometime toward the late 1980s, I was subjected to a
science test with the following question:

"Which of the following is the closest star to Earth?"

The answers provided were "the sun," "the moon," "Venus," and "Mars."

I selected "the sun." I was marked off, and the teacher had returned the test
with "the moon" circled as the correct answer. I don't recall being bothered
so much by having marks taken off for providing an answer I knew with
certainty was the truth.

Following receipt of the test, I distinctly recall my mum heading off to the
school with me the following day to dispute this "fact." The teacher in
question and the school's principal both provided the bothersome answer "Well,
it's marked as 'the moon' in the answer sheet, so that's what we have to go
by."

While I don't recall what became of that particular test or my final grade, it
stands out as one of my earliest negative experiences in public education. I
can only imagine what these poor kids are feeling when faced with questions
that make no reasonable sense. It upsets me to think what memories they might
harbor in the years to come, because kids certainly do NOT forget.

And to think that education has only gotten worse since. Troubling times ahead
indeed!

~~~
greenyoda
_" Well, it's marked as 'the moon' in the answer sheet, so that's what we have
to go by."_

Or, in other words: "We were just following orders. We are not allowed to
think for ourselves."

It's tragic that these are the attitudes of the people entrusted to educate
children.

~~~
Natsu
> It's tragic that these are the attitudes of the people entrusted to educate
> children.

One person != everyone. Most of my teachers were good ones, willing to show me
things other people considered "too advanced" for kids like me. Such people
were the reason I could do things like purchase ethyl acetate as a child. Yes,
that gives off poisonous fumes. It's used in entomology and was recommended by
the books I was following.

~~~
Zancarius
> One person != everyone.

While true, and certainly many of the teachers I had when I was young were
quite good, some memories are punctuated by the inane.

------
carsongross
When I didn't have kids, I thought homeschooling was for nut jobs.

Hi. I'm a nut job.

~~~
tillinghast
Nut job here, too. Common core is terrifying. Glad it's getting some bad
press.

~~~
ktsmith
Why is common core terrifying?

------
tptacek
How much of this is the "backmapping" of 12th grade skills to 1st grade, and
how much of it is simply incompetent test and exercise authorship?

~~~
ktsmith
I showed the test to my wife who is a 2nd grade teacher in a school district
implementing common core. She was appalled both at the grading and the test
itself. Then I showed her that it was from Pearson and she exclaimed "That's
your problem right there."

~~~
mturmon
Exactly. The concepts are appropriate (maybe not for this age though, I was
unaware that NY first-graders could be only 5 in October), but the test is
crap.

~~~
ktsmith
> I was unaware that NY first-graders could be only 5 in October

That surprised me also. Here in Nevada the cut off is in September and so any
child in first grade would be at least six years old by October. A month or
two doesn't make a huge difference so perhaps their cutoff is in October or
November.

------
ryanhuff
I have an 8 yo going through the common core transition now. What I would
recommend parents do is teach the traditional fundamentals after school. Give
your kid regular work. Its not worth being an experiment.

~~~
ams6110
I'd recommend you send your kids to a school with a sane curriculum. The only
thing these public school morons will understand is when they start losing
students (and corresponding dollars that go along with that).

The public school system here is up in arms about a quite limited voucher
program, because their funding is based on the number of bodies in the
classroom. So they see it as taking "their" money, rather than thinking "I
wonder why those parents don't want their kids to go to our schools."

~~~
ryanhuff
That's a great idea, but with two kids in grade school, the local private
schools would cost me about $30k per year. I would rather invest 15 minutes a
day with augmenting what they are doing in the classroom. If you have the
resources to go private, more power to you.

------
gph
It seems like they tried to dumb down certain words like "equation" into
"number sentence", but only succeeded in making it confusing and ridiculous.

And on top of that these are problem solving questions introduced way too
soon. What's wrong with just asking a kid some addition and subtraction
questions without all the fluff? I know it's trying to tease out whether they
understand the fundamental concept and all that, but it's horribly done and
kids of that age shouldn't have to be self-aware of their own learning.

~~~
ktsmith
> And on top of that these are problem solving questions introduced way too
> soon.

While those questions weren't appropriate for a first grader at the beginning
of the school year introducing problem solving is a big part of common core.

------
NAFV_P
I was caught out by "number sentence" at first, I'm used to hearing the word
"expression".

Is this a re-emergence of _the new maths_?

~~~
bane
I agree, I've never heard that phrase and I have a degree in Mathematics.

~~~
NAFV_P
Cheers...

I am an amateur mathematician, but these days I focus more on imperative
programming languages. I tend to use the term _expression_ for both equations
and expressions, since in computing an expression returns a value of any type,
not just numerical types.

------
Aloha
oh god. I hate math, but I'm very very good at basic math, if I had had to
learn like this, I cant see how I would have learned anything except that I
didnt want to learn more.

~~~
anaphor
The only thing I ever learned from math in high school was "I don't care why
it's true, just give me the right answer" (the attitude of every single
student other than myself).

------
dancole
One penny-cup. That is the answer to the first question. The answers needed
units.

