kitchen table math, the sequel: Make a Teacher Crazy

Sunday, November 15, 2009

Make a Teacher Crazy

A recurring theme here is the interaction between parents and their schools and teachers. As a teacher who has parent conferences coming up this week I've been giving this some thought for selfish reasons but in so doing I've had a flash that it makes sense to toss around here. Here's the flash.

As consumers, parents have no idea what they are 'buying', i.e. there is no objective measure of what a 1st quarter, 2nd grade or 3rd quarter 7th grade (pick your own quarter and grade if you like) student should be able to do. Hell, truth be told, I'm not sure I know what a student should do either. You wouldn't go to the store to buy a dozen eggs without insisting on a definition of 'dozen'. Yet, with our kids we've created a mushy narrative for what we define as learning goals that leaves us talking around each other.

Here's what I mean. Below, I've extracted the Massachusetts standards that are relevant for addition. Before you read them, understand that you are looking at a spiraling standard and also, gulp, know that these are highly regarded in the educational establishment and have even been touted as a model for national standards. Also, ignore the creeping growth of the standard as it incorporates division and multiplication goals. Just focus on addition. Read them carefully and then be prepared for a quiz...

Grade 2:
Know addition facts (addends to ten) and related subtraction facts, and use them to solve problems.

Grade 3:
Add and subtract(up to four-digit numbers) and multiply (up to two-digit numbers by a one-digit number) accurately and use them to solve problems.

Grade 4:
Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently.

Grade 5:
Accurately and efficiently add, subtract, multiply whole numbers and positive decimals. Divide, whole numbers using double digit divisors with and without remainders

Grade 6:
Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers and positive decimals.

Here's the quiz.

1. For any grade of your choice, what speed should be used as a proxy for efficiency?
2. For any grade of your choice, what is the definition of accuracy?
3. For grade one, should students be accurate or efficient?
4. Why are grade 3 students required to be accurate but not efficient?
5. Are manipulatives, pictures, or fingers allowed in any grade to achieve the goals?
6. Are calculators or tables allowed in any grade?

What's your grade? Could you even answer the questions? This is mush and I submit that a sixth grade student whose addition facts come from his fingers is meeting these standards provided he consistently gets correct answers and doesn't use up a lot of paper to achieve a result.

Of course neither parents or teachers are going to change these standards. But, here's a thought to put some pressure on this part of the education puzzle. When you go to a conference, go with one simple question, "What should my student be capable of doing right now?"

This should provide a wonderful jumping off point for a more meaningful discussion than the standard fare. "Johnny's doing quite well" won't cut it, will it? When you get an answer, drill down and insist upon accuracy and efficiency parameters that pin down the objective goals. Don't settle for subjective answers. Find out how fast he should be doing things. Find out what the acceptable error rate is. Inquire as to the remediation Johnny is getting if he is not meeting the objective measures. Be ready for heavy spin. I'd be really interested to know what you get for answers.

And BTW, I really hope none of my parents are reading this right now because I'd have to make up stuff to answer this kind of interrogator and that wouldn't be pretty.


SwitchedOnMom said...

Paul, I am blown away by your honesty. Thank you.

Allison said...

Paul, as a comment to your aside about these standards,

What's your take on why MA is scoring so well? MA's a state miracle in education if you listen to the pundits.

What are they measuring that makes them feel so good? What, if anything has actually changed at the classroom level? What is it that has improved?

Cranberry said...

As a Massachusetts parent, I believe the state scores well due to the teachers. This is due in part to the high standards set by the teacher licensure test. When first introduced, in 1998, nearly 60% of the candidates failed. Many were the products of local ed schools. This was acutely embarrassing for those schools. I have heard that some (many?) ed schools now require students to pass the test before admission, raising the quality of the corps of prospective teachers. is a copy of an op-ed by John Silber, then Chairman of the Massachusetts Board of Education.

"It should not be thought that this examination was excessively demanding. In one section of the test, a short paragraph from the Federalist Papers was slowly read aloud three times as candidates wrote it down.

How could educated people fail to copy accurately what they had heard? It wasn't easy, but scores of applicants managed, recording broken sentences and curious new spellings like "improbally," "corupt," "integraty," "bouth" (meaning both), "bodyes" and "relif.""

A teacher who passed this test in 1998, and remained in teaching, is now a veteran. All the teachers since 1998 have passed this test.

The funding changes put in place by the Ed Reform process also helped. In brief, property tax imbalances are remedied, to some degree, by a complex formula of funding from and to the state.

Crimson Wife said...

What I don't get is why a distinction is made between 4-digit and 5-digit addition/subtraction. If a child has learned the algorithm for multi-digit addition/subtraction, then it really isn't any harder (just more time consuming) to solve problems involving larger numbers. Or am I just out to lunch here?

Anonymous said...

"Why does Massachusetts do so well?"

I really don't know and haven't studied any data outside my own district. My conjecture (and the areas I would probe if I had the time) would be; it's a relatively wealthy state so lots of helicopter parents are supplementing, we started from a low base line, our competition is not fantastic, and of course pundits are largely ignorant. In my school >60% of kids fail the MCAS. We have submarine parents.

Also, states test themselves. Each is free to create their NCLB measurement. Ours, in my opinion has gotten progressively easier every year I've been teaching. You can see for yourself by going to our DOE website. All of last year's questions and answers are available there.

The only significant change here is the relentless demand for teachers with more content knowledge. This is a good thing but I don't see it trumping the spiral and lack of demanding objective measurement.

As for John Silber, I've taken that test. The quote is regarding one part of a language comprehension test and it is decidedly not trivial. The quotation cited is not a short paragraph. Mine was all about Cuban cigar making. It's a very long paragraph and you are expected to capture every word with correct punctuation. When I took it I could barely get it done. My fingers cramped up and I was in physical pain trying to keep up with the reading. It just shows how pundits can get things wrong I guess. John and friends have taken over a failing school system (Charlsetown I think) to show us the way. It's performance is no better than the rest as far as I know.

As for the state's funding fun. Money is doled out according to rules that are byzantine to say the least. Districts with all the helicopters get disproportionate money from those populated by submarines. My (very poor) district had its state funding cut by millions this year. I have 30% sped students and a like number of ELL kids. All that extra state funding has provided me with 0 sped support and 0 ELL support. You only get the money if you don't need it.

re: "Four and five digit distinction"

That's a great catch. You get extra credit on the quiz :>}. I provided an extract. There are other 'standards' that are exquisitely synchronized to these. One of them is place value. For some bizarre reason, I've never fathomed, place value 'learning' is spread out over 6 years. So four digit addition is occurring in the year when you are learning place values to 10,000. Five digit addition happens in the year when you learn place value to 100,000.

This particular bit of nonsense makes me crazy because it ensures that kids never see place value as a continuum with repetitive rules. They never see addition as a continuous extension of single digit addition facts. The slavish adherence to the spiral lays the hierarchical beauty of mathematics on its side, chops it into little chimneys, and dispenses it like M&Ms. All of this is done without ever demanding mastery. I suppose it makes no sense to demand mastery because you never have all the parts of a strand until its over and it seems that some things are never over.

I've actually had kids come out of this elementary puzzle that could not count. They get to one of these arbitrary thresholds in a counting sequence and instead of overflowing to the next place they go back to 1. Ooops! Missed that lesson!

Cranberry said...

I forgot to add, in the last decade, the state offered financial incentives for teachers to retire early. Reportedly, for many teachers near retirement age, it made no financial sense to remain in the classroom. Our district lost many good, experienced teachers through this program, so I don't see it as a positive measure for our district. If the teaching body had a certain number of inadequate teachers near retirement age, though, that might have made a difference, on a statewide basis.

Another factor that might help is the lack of funding for, or interest in, gifted programs. I wish our state had some support for kids who are above grade level! It doesn't, though, and the few districts I've heard of which had small gifted programs have gradually lost them, due to budget cuts. (The only exceptions in the public sphere would be the few exam schools, such as Boston Latin.) I do admit that it puts an end to the "gifted dance" in other states, whereby the name of the game is to qualify for the gifted program. This would seem, logically, to lead to systems offering different curricula, within the same schools, which is a division of effort. I don't know if we lost the very high end to support the middle. I suspect that it's so, but the gifted kids would score "advanced," and there's no way to distinguish between "advanced" and "really advanced."

Our affluent district doesn't get money from the state, on the whole. The only moneys we get are "circuit breaker" funds, paid out, with a year's delay, on significant sums expended for sped outplacements. They don't match the whole sum, only a percentage over a fairly high base amount. The state cut the allotment for this year, which led to cuts after the budget cycle. More cuts are forecast for this year. Sped and ELL are mainly the province of individual districts.

I suspect our affluent district meets the budget by shorting the "general ed" kids. Until recently, the state broke out the per pupil spending by "sped" and "general ed." The difference between the two was staggering. They have stopped that practice. For several years, parents have been supplying basic classroom supplies, paper, pens, kleenex, paper towels, water. We haven't reached toilet paper yet, but it's coming. The district does supply early reading tutoring to children who don't have IEPs yet, but might qualify. Part of the game is heading off Sped identification. (In my cynical estimation. You could see this from the other side, that some kids shouldn't be in sped at all. I just believe that it postpones the day of reckoning for a few years.)

I think the affluent districts look better because the parents supplement, either by tutoring themselves or paying for private tutors. Huntington, Kumon, Sylvan, and other companies all have little centers in strip malls in every direction. Sylvan sends tailored ads to our house.

We're "older" parents, in that our eldest is in high school, and our youngest in elementary school. I've noticed a rising emphasis on test prep, which I find unhealthy. The "younger" parents, though, seem to expect and demand it. Many begin drilling their own children in preschool, which I think is too early, for a child who comes from a literate family.

Cranberry said...

A third grader should be able to multiply, but will need more practice to become efficient, perhaps? My personal milestones for my children are different, and not spiraling. By the end of third grade, the child should have mastered the times tables, up to 10 at least, preferably up to 12. Knowledge of the algorithm for multiplication allows the child to multiply further numbers on paper. By the end of fourth grade, the child should have learned the standard algorithm for division. Knowledge of the times tables means that there's no need to look for "friendly" numbers. Also, by the end of fourth grade, the child should grasp the concept of fractions, and know how to go between simple fractions, 3/4 and the like, to decimals, without memorizing a table (as called for in Everyday Math), nor using a calculator. So, no, neither calculators nor tables should be used through 6th grade. (We're known by the math teachers as the odd parents who object to calculators. Our eldest came home at times saying, "the teacher said, 'tell your parents that you must use a calculator for this assignment.'")

Lisa said...

I have an answer to this one. My child's school has 'child led conferences' in September and May. They are pointless so I asked my dd's kindergarten teacher what she would be learning since she can already read and do simple math. The poor young thing's answer was work on her scissor skills. To my credit, I did not laugh.

SteveH said...

"My child's school has 'child led conferences'"

They don't do that until 7th grade at our schools. We have one for our 8th grade son at the beginning of December. We go to the different classrooms, our son shows us his portfolios, and he tells us how he will be a better student. We talk to and teach our son on a daily basis. We want to talk to the teachers, not our son. They do provide a chance to talk with the teachers, but our son is there in the classroom along with other parents and kids. I think their goal really is to avoid one-on-one meetings with parents.