College math for early childhood ed majors

Early Childhood Education Majors Can’t Do 3rd Grade Math, complains Captain Capitalism, who prints a math test from a “collegiate agent in the field.”

Most of this would have been fifth-grade math in my day.  I don’t think I could solve question 13 till eighth grade.

How much math does a preschool teacher need to know?

1. Bill says:

Here is a response to that:

How can you actually teach something you don’t actually know how to do (answer is, you can’t). The reason why so many kids today grow up hating math is due to the fact that they actually never learned how to do it correctly in the first place.

Get rid of all the fancy junk and go back to teaching it the way it was taught in the 1950’s and 1960’s. Emphasis on addition and subtraction facts, memorization of the multiplication table, use of the number line, place value, and
endless drills of these facts until the student knows the answer without having to think about it.

Is it any wonder why programs like singapore math and Kumon are so widely sought after for many students in
elementary and middle school?

UGH!

2. Some quick rummaging around the internet, and it looks like the first exposure to exponents is 5th grade. The calculation (not really “solving”) only requires that the student knows that 2 cubed is the same as 2 x 2 x 2.

But to teach something, you must be competent at a level well above what you are teaching. You have to know what is beyond that, what to leave out, what to leave open, and so on.

And if they are going to choose between educational approached based on anything but gut feel, rumor, and ideology, they need a course in experimental statistics.

3. therese says:

A friend of mine, a kindergarten teacher, noted the time a 4th grade teacher came in the break room asking if someone could fill her in on division of fractions since she had to teach it the next period. Scary!

4. Bill says:

Therese,

That is scary indeed, but multiplication and division of fractions is covered quite well in the yellow and black paperback known as ‘math for dummies’, and it does a plain, no nonsense way of explaining it 🙂

5. A better question is “How much math should a college graduate know?” Universities aren’t supposed to be trade schools, they’re supposed to turn out educated people–and none of the math on that page *should* be beyond a university graduate, especially if the university required Algebra 2 as a minimum entry requirement.

• Bill says:

Darren,

Back in 2009 I took a course in ‘introduction to informatics’ at the request of a local IT/IS trade group here, and in the 2nd exam, we had questions on basic
stats (mean/mode/variance/standard deviation) and some
probability/permutations/combination).

The average score (raw) of the class was 69%, I along with 3 other persons over the age of 40, and a EE major scored 90% or higher.

The average age of the students in this course was in their late teens or early 20’s, so I’d say that these students were actually looking to get into a IT career without a lot of math background, which in my opinion is a bad idea.

I recommended that the college beef up the minimal requirements to at least passage of pre-calc or higher
along with the addition of business and technical writing to the degree requirements.

That never happened, due to the fact budget cuts forced the closure of the program less than 2 years later.

It’s frightening to think that a college graduate has a complete lack of basic math skills, but as we make requirements easier and easier, we’re going to wind up with a nation of graduates who know absolutely NOTHING, except they they now have a pile of non-dischargeable debt from their student loans.

Sigh

• A better question is “How much math should a college graduate know?”

Everything on that problem set should be known by each and every student who enters 7th grade.  If I can do it in my head with barely a thought, they should all be able to do it with pencil and paper.

• Crimson Wife says:

I agree that arguing over whether the problems are 3rd grade level vs. 5th grade overlooks the bigger issue that these are high school graduates who are struggling with the problems. Clearly their diplomas are not worth the paper on which they are printed…

I went to what is still one of the most academically elite schools in the U.S. and we didn’t do order of operations or zero exponents in 3rd OR 5th grade. I think there’s a lot of hyperbole at the linked post. “Early childhood education” means preschool and daycare, and elementary school arithmetic is probably all that is reasonably necessary for such people — they will not be teaching finding common denominators, reducing fractions or factoring equations to 3-year-olds.

An interesting factoid from ETS (the last time I checked) was that the lowest performers on the GRE as a group were ECE applicants, closely followed by — wait for it — people going into educational *administration.* These future leaders of our school systems scored around 450 on the GRE Verbal, well below most teachers, and not suggestive of intellectual acumen.

I’d be more worried about the future school superintendent who can’t do the math in the given examples than I am about a future day care provider with the same limitations.

• Bill says:

Order of operations (aka operator precedence as we call it in programming) comes down to parens (), brackets [ ], and MDMAS (Multiplication/Division/Modulus/Addition and Subtraction). Anything to the power of zero is 1, as memory serves, so n ^ 0 = 1, which is one of those facts you just memorized (at least in my day in middle school, grades 6-8).

🙂

Yes, I learned all that in middle school too. The point the blogger was making however was that this is “third grade math” which is a gross distortion of the facts. There is plenty of valid criticism to be made of math instruction and curricula, but the cause of reform is not advanced by the kind of wilful ignorance displayed in that post (and by some of its respondents).

Curricula and the spiral approach(not to mention the lack of emphasis on mastery) are key factors in poor math performance. Teacher preparation and skills are also important variables but even the most mathematically sophisticated teacher can do little with a very poor program that s/he is required to implement as prescribed.

Let’s address the real problems, not these fake ones. They are a distraction and cause real and meaningful critiques and suggestions for improvement to lose credibility.

• Mark Roulo says:

“Anything to the power of zero is 1”

0^1 is 0.
N^0 is 1 when N is not 0.
0^0 is undefined 🙂

• Bill says:

Chuck Norris says that 0^0 = GOD and
that only Chuck Norris can DIVIDE by zero 🙂

• Mark Roulo says:

*Any* mathematical expression is defined for Chuck Norris. If he wants it to be.

• Sean says:

Chuck Norris can remove non-removable discontinuities.. he can use Stokes Theorem on a non-continuous surface too!

All functions are integrable, for Chuck Norris.

Chuck Norris can move when the temperature is Absolute Zero – thus disproving the Third Law of Thermodynamics.

• Mr. T and Vin Diesel once got into an arm wrestling match. Chuck Norris won.

• Classics Mom says:

PEMDAS:)

• Ann in L.A. says:

N^0 doesn’t have to be memorized, and kids should probably see how it works at least once, even if they promptly forget it. You can show it by a simple example:

3^3 = 3 * 3 * 3 = 27
3^2 = 3 * 3 = 9 ( = 27 / 3)
3^1 = 3 = 3 ( = 9 / 3)
3 ^ 0 = 1 ( = 3 / 3)

The value for each reduction in exponent can be found by dividing the previous answer by the base number. Or in equation form: n^(i-1) = n^(i) / n

7. Cranberry says:

This is a real problem.

If this math at this level shouldn’t be required of early childhood education majors, why do they need a college degree at all?

That isn’t college level work. If the students were competent middle school students, they should be able to do these problems in their head. Giving college credit for work on this level is a waste of time and money–and makes me doubt that any of the other required courses do anything to produce good teachers.

“why do they need a college degree at all”

In many cases, they don’t. However, requirements vary from state to state. Some require ECEs to be certified elementary teachers, which means a bachelor’s degree. Other states accept an associate’s degree or diploma from a community college, such as this one:

Canadian provinces, so far as I can find out, train ECE’s via community college programs. The UK also provides preschool to children aged 3 and over (I believe it’s called the Early Years Foundation Stage) but I’ve not seen any description of the educational requirements for its teaching staff.

A community college program seems to me to be the appropriate model for most aspiring ECEs. It leaves open the possibility of upgrading to a BA at a later time if desired.

• Giving college credit for work on this level is a waste of time and money

You mis-spelled “fraud”.

8. lulu says:

If I remember correctly, early childhood ed is preschool teaching. As long as they can add and subtract, they should be fine from a teaching perspective. Elementary education majors should know how to do most of this, though. We use Singapore math and it has exponents in 5th grade, order of operations begins in 4th and continues in 5th. We’ve done fractions, but haven’t gotten quite that far with decimals yet (although we probably do this year).

• Sean says:

Saxon math introduces it in their Saxon 3 book and comes back to it in Saxon 5/4 – typically a 4th grade book. They don’t have decimal divisors at that level though. Zero exponents showed up once or twice.

Problem 13 is doable at the 5/4 level – they’ve got basic parentheses skills. 1,7&8 aren’t covered in 5/4- I expect them in 6/5 which my kiddos school is using in 4th grade.

9. Obi-Wandreas says:

What’s even worse is how many people either laugh at, shrug off, or are sometimes even proud of their ignorance at certain things (computer use, math, etc).

I can see someone being happy that they don’t know how to make crystal meth, or happy that they don’t know what it feels like to sleep on a cactus. To be happily ignorant of such basic useful knowledge betrays a fundamental lack of curiosity. Such people have no business being in a classroom, other than sitting in a desk taking notes.

10. Nels says:

With the pay for these jobs so low, they’re not going to attract many people who did well in school.

• cranberry says:

I’ve always heard openings for preschool teachers receive many applications. It’s like social work–the work doesn’t make nearly as much money as engineering, but there are many people who did do well in school who would love to enter the profession.

I think it is a grave mistake to decide academic skills and intelligence are not necessary for teachers at all levels. Parents and the system place a high premium on “warm and fuzzy” people for the early grades. So be it. On the other hand, intelligence should not be a disqualifying factor.

We know the gap between different kids is present at entry to the school system. Some children go home to parents who finished college and grad school. Other children don’t. Why should the public system not strive to give those children contact with educated, competent adults as soon as possible? People who entered high school able to do such math? Other countries do that. Why are we so anti-intellectual?

I do want to note that my children’s preschool and kindergarten teachers were well-educated adults. That is possible, but then they were in a desireable suburban system.

• Genevieve says:

I agree.

An important part of early childhood education (especially for children from disadvantaged homes) is developing children’s vocabulary abilities. Teachers that are smart and have the ability to speak clearly, with correct grammar and varied word choices are important.

• lulu says:

I think that there is a difference between academic skills and intelligence, and probably a big difference between what different people want in a preschool. I love my PhD engineer spouse, but was thrilled when my son had a particular preschool teacher who was (slowly and with struggling) working on getting a BA. Her ‘fun kid’ skills are amazing, she taught a class of 3 year olds to spell (and then read) their colors using songs, they did fantastic crafts, and they learned all sorts of things about various creepy crawlies. Requiring her to pass additional math classes wouldn’t have helped her teaching. My other child had a teacher last year who had a masters degree and had worked in other fields. She also had a great preschool year, but I’d be hard pressed to say that it was a better year.

I want my kids to do crafts, sing songs, and do the sorts of things that their STEM parents don’t really think to do. While I don’t want them to have teachers who don’t use correct grammar or teach them incorrect ideas, it doesn’t really require a degree to do that or pull together the fun units (farm animals, weather, bugs) that kids enjoy. And, as I wrote this, said spouse wandered through and said that the aforementioned preschool teacher was 2 orders of magnitude better of a teacher than he would ever have been.

• cranberry says:

Your children have a PhD engineer and a college degree (+?) at home. Before they entered preschool, they benefitted from your presence. You can look to the schools to provide crafts, songs, “and the sorts of things that their STEM parents don’t really think to do.”

Even many children of affluent college graduates don’t have STEM PhD parents.

My kids attended a public preschool staffed by teachers with a background in child development and special ed. They were able to spot potential problems in kids who were “typically developing.” They were also able to spot kids who were asking questions which showed a deeper understanding of math or the world than one would expect in a young child. The math test crossed out the negative numbers. I do think it is important that preschool teachers understand negative numbers, because some children may approach important concepts for later math understanding in preschool. Even the question, “what does zero mean?” is an important question. You and your husband could answer such a question in such a way as to lay the foundation for later math understanding. Someone who never “got” negative numbers will not.

The activities in preschool were enjoyable, but they also introduced the kids to things which made a difference later–letters, numbers, the concept of more or less, how to wait for your turn, how to work with other children on a task.

The teachers were warm and fuzzy, but they planned much of the school day with an eye to later success in school for their charges.

• lulu says:

It’s interesting that you brought up the 0 and negative numbers idea. My kid had a pretty good grasp of negative numbers at a young age, and the ‘struggling to finish a BA’ teacher did a big unit with zeros, saying that it was a really important concept for kids to understand. I’m not in any way saying that I want completely untrained teachers in the classroom. I’m asking what level of math they’re likely to actually need. That teacher had completed all of the early childhood classes and did yearly training to stay current in the field. She was struggling to fill in the ‘other’ parts of the requirement.

The teachers at both preschools knew their ‘early childhood’ milestones, did yearly assessments, and talked to the parents about possible motor, speech, or academic delays. They taught rhymes, letters, numbers, simple spelling or reading (if appropriate), and motor skills (cutting with scissors, hopping). I don’t want an bunch of untrained day care workers teaching at a preschool, but I don’t really care about whether preschool teachers remember ‘order of operations’ or exponents.

11. College Math should be a minimum requirement for all majors from any major University. Period.

• lulu says:

I tend to think that anybody with a 4 year degree should know a certain amount of math. I also don’t think that there’s anything wrong with a 2 year degree, and I’d rather people with those 2 year degrees spend the 2 years taking courses specific to their degree. We have a tendency to think that people should be fully versed in whatever we think is important…but there really isn’t any degree program that could include the 2 years of math and well-roundedness in bio, chem, and physics that the STEM types want, the American and international history/geography that we should all take to be knowledgeable about any potential constitutional or hot spot issues, the literature that we need to be able to read the right authors, the diversity requirements that most schools now have, and of course the many hours of education or childhood development classes that are actually practical must-haves for preschool teachers. Like I said to Cranberry, I don’t want uneducated people teaching preschool, but why we think that preschool teachers need to have 4 year degrees as opposed to a 2 year specialists program is a mystery to me.

• ns says:

lulu, I agree with you. It’s easy for people to armchair judge others and bash others for “lack of math skills” when really we should be asking, are these math skills really required for some one to be a great preschool teacher?

I am a STEM professional and I think the answer is no. I want my child’s preschool teacher to be loving an understand childhood development. I don’t care if she can (or cannot) do these math problems. Warm fuzzies are more important than passing this particular math test in IMHO.

I think it’s hard to define “competency” when it can mean different things to different people. If you can’t do this math test, does it mean you’re an incompetent preschool teacher? I don’t think so. But apparently to all the people here, who of course, are all above average, the answer is yes.

Good luck with your campaign to persuade the world’s top universities — Oxford, Cambridge, Harvard, University College — London, Johns Hopkins, Yale, Columbia, Cornell., McGill and myriads more. Few require math for non-STEM majors.

http://www.usnews.com/education/worlds-best-universities-rankings/top-400-universities-in-the-world

We have more important issues to worry about than that one.

• Bill says:

Elim,

Would you define ‘college math’, due to the fact that I’ve met college graduates who couldn’t even handle high school math.

As a side note, I don’t define anything below algebra II/trig (aka pre-calc) to be college level, that’s high school level in most developed countries in the world.

12. cranberry says:

Finland.

Apparently, teachers in Finland are chosen from the top 10% of the country’s graduates: http://www.smithsonianmag.com/people-places/Why-Are-Finlands-Schools-Successful.html

Kindergarten teachers (teaching ages one to six) complete a three year Bachelor of Education, specializing in early education. http://tinyurl.com/pyyhl4j

The gap in educational attainment between socioeconomic groups in Finland is much smaller than in the US: http://tinyurl.com/ov97wqn. Part may stem from making certain all students have well-educated, capable teachers from the first year of life.

13. Jim says:

To Mark Roulo – 0^0 = 1. This is not a convention. Rather the number n^m is the number of functions with domain a set A of cardinality n and codomain a set B of cardinality m. Such functions correspond to the subsets of the cartesian product AxB which are graphs of functions.
If n=m=0 then A, B and AxB are all equal to the empty set. The only subset of the empty set is the empty set. Thus we have to check whether the empty set is the graph of a function from the empty set to the empty set. The conditions for such a graph R are that for all x e A there is exactly one b e B such that (a, b) e R. This condition is satisfied for A, B and R all the empty set. So there is exactly one function with domain the empty set and codomain the empty set – namely the empty set. Thus 0^0=1 by the general defination of exponentiation for cardinal numbers.

• Mark Roulo says:

So 0^N = 0 for all values of N except for 0? And we have a discontinuity when N is 0?

*This* is math.

14. Jim says:

N^0 = 1 for all cardinal numbers N (including N=0) by the general definition of exponentiation of cardinal numbers. Continuity has nothing to do with it.

• Mark Roulo says:

I think we are talking past each other.

if f(n) = 0^n, then you are saying that f(n) = 0 for all n except for 0, where f(n) = 1? If so, then we have a discontinuity, no?

15. Jim says:

For N a non-zero cardinal let A be a set of cardinality N and let B be the empty set. Then AxB is empty so the only candidate for a function from A to B is the empty set. But the empty set is not a function from a non-empty set to the empty set because if A has an element a then for R a subset of AxB to be the graph of a function from A to B, R must have an element (a,b) so R cannot be empty
Thus if N is a non-zero cardinal then N^0 = 0 but nevertheless 0^0 = 1.

• Ann in L.A. says:

Kids get a kick out of the fact that you can create a 1 using nothing but zeros: 0^0 = 1. It’s like creating something out of thin air.

• Bill says:

Heh!

My Windows XP calculator in scientific mode
shows 0^0 as 1, which is correct, but very strange 🙂

16. Jim says:

To Mark Roulo – For x,y real numbers and x>0 one can define x^y by exp(y logx) and get an analytic function which extends the exponentiation of finite non-zero cardinals and satisfies (x1 x2)^y = x1^y x2^y and also
x^(y1 + y2) = x^y1 x^y2 . If y0 we can even extend this by continuity to y^0 = 1. But note that the resulting function is not C-infinity let alone analytic at any point (0,y) with y0. No value can be assigned at (0,0) which would even give continuity.
However the above is not relevant to the definition of exponentiation for cardinals. This definition leads to 0^0=1.