From time to time on this blog, I have talked about my annoyance with my kids' schools. Sometimes the post was related to the special education bureaucracy. Sometimes it was about our choice to move to the suburbs, because we were worried about the city public schools. Sometimes it was about the mediocre education that Jonah was getting in the suburban schools.

I often get a lukewarm or even chilly response to those blog posts. Someone will sneer, "entitlement." Others will portray me as a shrill, humorless, privileged mom picking on the poor teachers. Weirdly, commenters on another blog criticized me for being a privileged mom, because instead of complaining about things, I was dealing with the inadequacies in education privately at home.

I can't win. And it's partially because there's so much discrimination against moms. Others can rally around about abortion rights, same sex education, the War in Iraq, and a million other political matters. But a mom with a political agenda is seen as shrill and entitled. Terribly annoying.

So, this morning, I'm going to rant. Harry and Megan have convinced me that we should care about high-performing schools.

I get a ton of e-mails (and not just from Amy P) complaining about a math program called Everyday Math. We don't have that program in our town; ours is more a hybrid between the old and new systems. Everything that I've heard about this math program is negative. Even with the hybrid system, Jonah's teachers have been terrible about math. They don't do enough repetition of math facts, and they just explain things really badly.

They don't do handwriting anymore, because the teachers tell me that all work will happen on laptops in the future.

Their time in specials (art, library, computers, health) is a complete waste of time.

They don't do enough writing.

They are not preparing the kids for good colleges. In fact, the head administrators seem to think that college consists of kids working in groups on laptop computers. They aren't preparing the kids for big lecture halls and blue books.

They assign book reports that consist largely of art projects that the parents complete.

They assign stupid homework like word searches and crossword puzzles.

They aren't even making sure that their curricula is lining up with the state standards. On state standardized tests, the kids are being tested on material that the teachers haven't covered yet. And in one case that I know about, a teacher coached the kids on the test.

Any criticism of school performance is rejected and blame is placed on the talent of the children. Or, in one very alarming instance, on the SES of the student body.

We're not in the highest performing school district in the state, but we're about at a B level for elementary and middle school. The high school is ranked in the top ten in the state, because it is a regional school district that brings in kids from wealthier towns. But I would not say that it is giving the students a high level education. A large proportion of the kids coming out of that high school are funneled into one of the substandard local colleges.

I love that you care about education and that you actively try to bring this debate into the open. I may not agree with everything you feel about particular programs or instructional techniques but I do believe they need to be debated and researched. Uncommon Misconception has an interesting post today about the lack of civil discourse and tolerance for differing opinions in our society today. In many ways your post relates to the same issues. I encourage you not to take comments which disparage your opinions and/or choices personally. The only way we can ever talk about these important issues is if we can talk about ideas without talking about people. I wish you the best as you work to improve education in the US and to achieve high performing high schools.

LikeLike

Very interesting. There’s a lot there, but here are a few thoughts.

1. When are you running for school board? (I’m not saying it’s possible to achieve anything as an individual on a school board, but the meetings will be much more exciting and better attended if you say this sort of stuff. That blogging politician (was she on school board?) would be a good model.

2. Get Willingham’s “Why Students Don’t Like School,” read it, and hand out highlighted copies to your kid’s teachers. It’s a deceptively simple, short book, but there are a lot of important insights there about the nature of learning. One of the biggies is that as human animals, we aren’t that great at reasoning. For us, “thinking” is generally just remembering, so any pedagogical that relies on too much naked reasoning on the part of students is going to be ineffective. I could go on, but bottom line–read the book.

3. How hard can it possibly be to explain arithmetic?

3. Aren’t there a lot of former art majors floating around who would be thrilled to pull down a public school teacher’s salary?

4. “Any criticism of school performance is rejected and blame is placed on the talent of the children. Or, in one very alarming instance, on the SES of the student body.” Wow.

LikeLike

Hey Amy P, nice to see your comment. The only thing I would like to add is that mathematics is very hard to explain – after all it is the basis for logic and philosophy. Computation and ‘math facts’ are easy but are hardly the most important part of math. One can use a calculator to do those tasks. It is knowing what, when, how, why, and what outcome is desired that is hard and that is what math is really all about. Most teachers do not, IMO, have the mathematical background to teach those skills adequately. They don’t even realize or values the importance of those skills. And, IMO, is one of the biggest reasons we do such a poor job of teaching math in our schools today.

LikeLike

There’s really only one proven solution: Nuns with rulers. (Morgan Freeman with a baseball bat will also work, but that’s not going to scale-up.)

LikeLike

I’m not sure math facts and computation are all that easy, actually. It just seems that way to us big people because we have absorbed it so thoroughly that we can’t imagine not being able to do it.

(I was giving my daughter one of her first sewing lessons last night and it was really interesting to see how effortless the various procedures (threading needle, forming short even stitches, pulling thread tight without puckering the fabric, tying knots) are even for an uncrafty person like myself and how effort-ful they are for a novice.)

LikeLike

whoa!

LikeLike

I love your school posts! Even if I don’t always comment.

I don’t hate Everyday Math. It’s grown on me a bit over the last 6 years of exposure.

LikeLike

I agree with Sandy, Laura. I suppose I rarely comment on the great school discussions that take place here–you have a such a wonderful comment pool for that topic, with Harry, Tim Burke, and others–but I learn a

lotfrom them. Keep it up.LikeLike

My big complaint about our schools is that I just have no freaking idea what’s going on. I do know we use Everyday Math. But I have no freaking idea what my kids are reading, writing about, studying, etc. Oh, they may tell me over dinner, but unless I email the teachers (and my son has 6!), I don’t know. I see assignments after the fact.

I know part of this is my own fault. But I don’t want all of my afternoon conversations with my kids to be “so, what assignment do you have in . . .” I’m frustrated by the fact, too, that the school does nothing about motivation. That’s our biggest problem in our house. My oldest aces the standardized test but is expected to cover the same damn material in class. He’s bored in every class except the gifted one and he has the grades to prove it (they’re not good). He often just doesn’t see the point. I won’t let this continue in high school, but I feel like I have no support from the school in helping him stay on track. It’s like there’s two different worlds–our house and school–and a huge gap between them. He’s lost in the school world thanks to large classes, boring material, etc.

I agree with you on the stupid assignments, especially at the elementary level. I’d rather see a more rigorous curriculum with no homework or better homework with a similar curriculum. In the first case, students would get more help with the hard stuff. In middle school, the assignments vary widely. Some are quite challenging, but they are interspersed with lots of busy work, most of which gets completed in study hall–another reason I have no idea what’s going on. Sigh.

Sorry for the rant, but I agree with you, and sadly, I’m afraid I’m just trying to deal with my own crap rather than change the system. I’ve actually offered to run for school board. Maybe I’ll do it.

LikeLike

I’m a math education researcher who studies children’s cognition in mathematics. I focus on middle school and high school kids, and am less familiar with elementary curricula, so I don’t have much of a connection to Everyday Math. That said, there is solid research supporting its use. For instance, a study in ’01 in MA examined demographically similar groups of students using Everyday Math versus traditional texts, and the Everyday Math students outscored their traditional-text counterparts on the state exam (difference was statistically significant). Similar studies in IL and WA found the same thing.

Understanding arithmetic, quantity, and especially things like place value, multiplication, and fractions is not simple to teach or learn. Curricula like Everyday Math emphasize developing an understanding of where these ideas come from and why the standard algorithms work. (For instance, why does it work to borrow and carry when subtracting?) The catch is that it is harder to properly implement these types of curricula without a lot of professional development support for the teachers. Elementary teachers sometimes have limited math understanding themselves, which adds to the problem.

LikeLike

That said, there is solid research supporting its use.There is also solid evidence supporting the fact that in schools where Everyday Math is used parents are doing the teaching.

LikeLike

“For instance, a study in ’01 in MA examined demographically similar groups of students using Everyday Math versus traditional texts, and the Everyday Math students outscored their traditional-text counterparts on the state exam (difference was statistically significant).”

I bet I wouldn’t like those “traditional texts” either. How does Everyday Math fare when compared to classes that have been working with Singapore Math and whose teachers have gotten the same level of professional development necessary for teaching Everyday Math?

My first grader is in a private school that uses Singapore Math (that was a major selling point for us). She just scored in the 99th percentile for math and science for children her age on the placement test she took for a gifted program. One element of Singapore Math’s philosophy is that they move very smoothly from the concrete to numbers. Somehow, the kids wind up with an amazingly strong sense of place value. They haven’t done formal carrying yet, but my daughter can do non-carrying addition in her head up to 4 digits from an oral problem. She’s not spooked by the fact that it’s a “big number.” I was doing some arithmetic practice with her last week (some stuff like 29 + 6, 26 + 5) and the interesting thing was that her response was to immediately reconceptualize the problems as 15 + 20 and 11 + 20.

LikeLike

albe,

The reason that EM students might outscore their traditional text counterparts is because the curriculum and the state tests are created with each other in mind.

In other words, the IL state test might ask a grade-schooler to write a paragraph describing how she solved a problem. EM teachers know this will be on the test and so will have spent oodles of time practicing writing skills explaining math procedures, as opposed to actually practicing them.

They also know that there will be lots of pattern recognition and estimation, while asking for little of those horrible “pencil and paper” algorithms, you know, the ones they’ll need for algebra.

Only later do kids find out that constantly reaching for a calculator for single-digit operations while working an algebra problem is nothing if not cumbersome

The true test is to ask the middle school teachers if the students being sent over after years of EM are ready for middle school math, or even algebra.

I assure you that there are tons of high school and middle school math teachers who are tired of being blamed for their student’s massive gaps that were brought about by curriculums like EM.

So, at the end of the day, after you have blamed the parents, the students, and everything else in-between, you are going to have to finally take a hard look at the incoherence of the curriculum itself.

LikeLike

“My big complaint about our schools is that I just have no freaking idea what’s going on. I do know we use Everyday Math. But I have no freaking idea what my kids are reading, writing about, studying, etc. Oh, they may tell me over dinner, but unless I email the teachers (and my son has 6!), I don’t know. I see assignments after the fact.”

But, why would you expect to? Do you think your parents knew what you were doing in middle school, or would even think about emailing to ask about it? (yeah, I know, no email)? My parents certainly didn’t. And, I think that was true in elementary as well. I think we expect to know far more than we did in the past. I don’t know how right we are to want to know that, but I do know that it can be taken too far.

My child attends a private school, for which I have great respect. But, I don’t get a lot of information about what they’re doing either. I’m comfortable, but admittedly, because I know my child is learning, and I don’t care if she’s not learning the *max* that she could.

LikeLike

So, I’ve been trying to follow the everyday math stuff. I think my daughter’s school uses it, but don’t really know (see comment above; they don’t tell us things like which teaching methodology they’re using. They probably also supplement as needed). They’ve been taught multiple algorithms for multiplication, and I thought that was superbly excellent. What I fear with math education is that people learn rules and not concepts. My fear of rule learning is that rules get forgotten more easily than concepts. For example, if you’ve memorized that sin^2+cos^2=1, you’re less likely to remember it than if you understand that the equality is a result of the Pythagorean theorem (the people who are good at math re-derive those functions as they need them).

I think parents who say they don’t understand EM and thus can’t teach to their children are actually exhibiting the failures of math education in our past — that we were taught rules and not concepts. It didn’t take me very long to understand the multiple multiplcation algorithms, because, really, I do understand multiplication (I’m pretty good with the math I learned in high school, though iffy on some I learned in college).

Since I’m not a math educator, I really don’t know if the methods used in EM are better, but I do know that I don’t like the methods that were used to teach the non-scientists I now know.

I took the singapore math and EM math (our local math exam) for 6th graders. I could do everything in both, but I thought the SM math problems simplified down to about 3 different problems, when you thought about them (just with different numbers attached). The EM exam asked the kind of questions I actually ask when interacting with quantitative information (both at work, and in my regular life).

LikeLike

Using Amy’s daughter’s example, I think that people who are “good” at math (i.e. acquire it more naturally than others) develop the concepts from the rules in a way that people who are “bad” at math don’t. My husband, for example, who is truly mathy, doesn’t even see the multiple algorithms for multiplication as being different, because to him they’re obviously the same.

LikeLike

“(the people who are good at math re-derive those functions as they need them).”

My husband’s first PhD was in probability, and that’s exactly what he reports of himself–he didn’t memorize theorems. He not infrequently asks me for math facts. He also has trouble adding times, too (9:45 + 30 minutes, that sort of thing), although that may be unrelated.

LikeLike

Actually, having done a fair amount of work looking at the NCLB-mandated state assessments, they are more often than not in mis-alignment with reform curricula like Everyday Math. Most do not rely on students writing paragraphs about how they solved problems, as Susan described. Instead they are overwhelmingly multiple choice tasks that emphasize rote memorization of facts and procedures. Reform curricula like EM tend to emphasize conceptual understanding and traditional curricula (like Singapore Math) emphasize the facts and procedures most frequently seen on state assessments. That’s why it was encouraging that the EM kids did better on those traditional state assessments, because based on the curriculum alone, you’d expect to see the opposite.

I work with middle school teachers a lot, and our district uses EM at the elementary level and Connected Math at the middle-school level. Our middle-school teachers support EM because they see that their kids arrive in their classrooms with a solid foundation in multiplicative reasoning and rational number understanding, both of which are critical for developing an understanding of proportion, ratio, and rate in algebra. The key point, though, is that the district puts forth an enormous amount of resources towards professional development for the teachers. In absence of that PD, it’d probably be a different story.

When you review the literature base as a whole on the influence of curriculum versus teaching, it basically demonstrates that curricular influences are pretty minor in comparison to the teacher’s skills, attitudes, and knowledge base. I think people get all worked up about curricula because it’s tangible, but the teacher is far, far more influential than the curriculum.

I think that many curricula like Singapore Math are pretty bad, especially in their lack of depth and rigor, but a good teacher can do so much to counteract that. I’ve seen students in Singapore Math classrooms do very well thanks to a mathematically talented teacher.

LikeLike

I think people get all worked up about curricula because it’s tangible, but the teacher is far, far more influential than the curriculum.Sorry: that is an ad hominem analysis of people’s motives as well as their state of mind (“all worked up”).

Dismissed.

Albe’s comment illustrates why the question of “reform math” versus Singapore/Saxon/Connecting Math Concepts/etc. is, ultimately, a question of politics and power.

Not to mention money.

“…the district puts forth an enormous amount of resources towards professional development for the teachers…”

No thanks!

LikeLike

I don’t think it is entirely correct to describe Singapore Math is “traditional.” Catherine?

LikeLike

I just put in my Amazon order for the 2nd grade Singapore Math “Challenging Word Problems” supplementary book. In a week or two, I’ll be able to see how lacking in “depth and rigor” it is.

LikeLike

I’m not quite sure I understand why you’d object to supporting teachers’ professional development? Ongoing (quality) professional development is good for teachers and good for kids…are you saying no thanks because the district supports it?

I do agree that politics, power, and money all play a role in the quality of education our kids get. I base my own research in urban, under-funded schools because I care about issues of social justice in math. I think it’s important that kids have access to quality math education regardless of how much money their parents have. Professional development that supports teachers and schools is one way to help kids whose parents cannot hire tutors or spend evenings teaching them. I would love to see the school funding structure changed so that kids didn’t regularly get denied access to quality schools just because they live in a poor neighborhood.

LikeLike

I think that many curricula like Singapore Math are pretty bad, especially in their lack of depth and rigor, but a good teacher can do so much to counteract that. I’ve seen students in Singapore Math classrooms do very well thanks to a mathematically talented teacher.Why do you maintain that Singapore Math is bad? What aspect of it strikes you as bad? The statement that Singapore Math is a function of the teacher and not the text is extremely misleading. Much of the strength of Singapore’s program comes from its sequencing of topics that help develop the skills and concepts that students need to solve complex problems.

I address the “it’s not the text it’s the teacher” conceit in my article on the piloting of Singapore Math in Montgomery County MD.

.

In another article I describe my experience tutoring my daughter and her friend using Singapore Math in order to escape the impending train wreck of Everyday Math that my daughter’s school was using.

You may find these interesting.

LikeLike

I’m afraid we’re going to have to agree to disagree, Albe. I’m actually in IL and I know for a fact that my district, as well as neighboring districts, have bought these curriculums to better align with state standards and to pass the state tests.

And, sacrificing procedural fluency for “understanding” is never a good plan. At best, you need both. Unfortunately, procedural fluency is something that parents are going to have to take care of on their own.

I also find it interesting that you denigrate Singapore Math as lacking in depth and rigor when the top scoring countries in math use it.

LikeLike

“I think that many curricula like Singapore Math are pretty bad, especially in their lack of depth and rigor, but a good teacher can do so much to counteract that. I’ve seen students in Singapore Math classrooms do very well thanks to a mathematically talented teacher. ”

I haven’t looked at the curriculum, only the placement exams: http://www.singaporemath.com/Placement_Test_s/86.htm. But, I thought that the SM test was repetitive and boring, and that I didn’t really care if people could answer those questions (that’s not to say the same thing as expecting that people who know math should be able to answer those questions — some of the problems took basic algebra and threw words around them. But, they did so in a formulaic way).

Here’s the math WASL (from Wash state):

http://www.k12.wa.us/assessment/WASL/Mathematics/PracticeSampleTests.aspx

I liked this test better. Why? Because it asked “real” questions. The math was different, though, and I’m not qualified to address the math itself, but what I want out of students is the ability to address quantitative information in the flexible situations in which they will encounter it in the real world.

(But, I say these things as someone who uses math, not as someone who teaches it).

LikeLike

Those of you who use the SM curriculum, can you have your kids take a EM math test (I think the Washington WASL is such, one that’s supposed to be aligned with EM math standards)? But, perhaps someone could suggest another test?

Someone asked the same of me about the SM math test, and I did have my daughter take the SM math placement exam. She did well.

LikeLike

“For instance, a study in ’01 in MA examined demographically similar groups of students using Everyday Math versus traditional texts, and the Everyday Math students outscored their traditional-text counterparts on the state exam (difference was statistically significant).”

albe — can you post a link to the studies you’re talking about?

LikeLike

I’m with Albe and BJ. My husband teaches calculus at a private high school, so he doesn’t deal with math in elementary schools, but we have 3 daughters in elementary school who are learning math the more conceptual way. I would have loved to learn it that way. I was talented at math when I was young but was burned by how I was taught–specifically because it was not conceptual enough and we learned to do things without knowing why we did them–and lacking that understanding I just tuned out.

I think that conceptual learning needs to be balanced with factual learning. The schools around here do that. But let’s not take away the progress we have made towards improving deep understanding. As my husband has noticed, my daughters (one a middle schooler) know far more math and understand it far more deeply than we did at that age.

I also want to say that there are great public school systems out there. I love our district. Even the specials are wonderful. The kids learn history in the art class–when I was in second grade, we just copied pictures of giraffes the teacher had drawn for us. In our school, the kids learn about Greece, China, Africa, etc., etc., and in depth too, and create artworks that really show knowledge of the styles of those different cultures. They learn Spanish from kindergarten, and their teacher is a native speaker. The middle school has to have separate orchestras for the different grades because so many kids play instruments, and in the gifted class they compose Gregorian chants and create operas in their special 6th grade humanities music class. And what’s more, the younger teachers are the best, and the oldest are the worst. Better educated, more knowledgeable, and much more creative about how they teach. Things are going to get only better over the next decade. I know this is money at work. I live in a very rich district, and the best and brightest want to work here. But money can have an effect if it is well-used.

LikeLike

Laura, I don’t think you’re shrill or humorless, but I do think you can be awfully hard on classroom teachers, who don’t make a lot of the decisions you’re complaining about. I also think sometimes you make broad claims like the one about laptops– I graduated from high school 12 years ago, and even then there were friends of mine required to buy laptops to go to college with– mainly engineering schools– but I think the idea has only increased since then. My husband just finished his first year of law school and was also required to buy a laptop. At a lot of “good” colleges, kids will be expected to have a certain degree of computer/digital literacy.

Also, the digital divide is a serious and real issue, and public institutions like schools and libraries are asked to shoulder the job of closing that divide, just as they are asked to do a lot of jobs that are really beyond their scope. There’s a lot of social work and counseling services that end up in the public school’s lap, for example. And while I’m sure you’re aware of that, I don’t often see much sympathy for classroom teachers in your posts on education.

I come at this issue from a lot of perspectives– I have two kids in an urban public school, I spend a fair amount of time actively volunteering at the school, I’m the daughter of a public school teacher and went to public schools for most of my life. I’m also a classroom teacher at an expensive private school. It’s not that I’m not interested in education. I also think part of it is the idea we have of teaching as not really a difficult profession. I’m honestly quite tired of hearing parents who have never taught in K-12 classrooms expound on all the things teachers do wrong, as if teachers are not qualified professionals dealing with difficult jobs with high stakes. Teachers need more professional development, teachers need more support, teachers need more education, but we also need, and don’t often get, respect from the public at large. There are more constructive ways.

LikeLike

“And, sacrificing procedural fluency for “understanding” is never a good plan. At best, you need both. Unfortunately, procedural fluency is something that parents are going to have to take care of on their own.”

I think I agree with this — that one must also be able to solve the problem, not just have a rough understanding of how one might go about solving the problem. But, I think procedural fluency that’s not linked to concepts will be quickly forgotten, and that we’re relying on false outcomes when we think that procedural fluency immediately after teaching means that the children have learned the problem solving in a way that lasts them through their lives, and not just through school.

LikeLike

I don’t think it is entirely correct to describe Singapore Math is “traditional.” Catherine?it’s not

LikeLike

Also, the digital divide is a serious and real issueevidence?

LikeLike

“…the district puts forth an enormous amount of resources towards professional development for the teachers…”I was referring to the fact that I am paying “an enormous amount of” money for teachers in my district to be professionally developed in teaching methods and curricula I don’t want foisted upon my child.

Learning stations in the high school, for instance.

LikeLike

I did not realize until reading this discussion that my 2nd grader’s class uses the Everyday Math curriculum. (Her teacher always refers to it as “the University of Chicago curriculum”.) I have to say I don’t share the experience of others here who think this curriculum is a train wreck. We have given zero support to my daughter other than checking her brief homework each night. She has never seemed to need it, and we have no time for it anyway. And she is progressing at a good clip, well advanced of where my husband or I were at her age.

Who knows if it’s the curriculum, but I will say this: her teacher is great, 15 years of experience and extra credentials as a math specialist. The classroom itself has relatively low variance between most and least advanced kids, and the structure of the program as delivered at her school is consistently enforced across the grade levels.

LikeLike

Laura- I also love your posts on education even those that deal with your frustration with the system. So keep it up! Us moms understand what you mean about being labeled “shrill” though…

Susan- my experience in an Illinois school is similar to yours. Our school uses EM and the emphasis on “writing out” how you solved a math prob is HUGE! But in third grade, they also do a lot of drilling of math facts to go with the more conceptual learning.

I have definitely always thought the Illinois state test must emphasize “writing out” how you solve your math problems- I’ll have to ask my third grade daughter if she remembers what the test was like.

LikeLike

Evidence for Catherine on the digital divide:

What It Is

Where We Are Today

Three Stages of Digital Divide

LikeLike

“I think that many curricula like Singapore Math are pretty bad, especially in their lack of depth and rigor,”

Have you used these programs?

Singapore Challenging Word Problems (soon to be out of print) is far more effective & challenging than any elementary math program I am aware of. Singapore students out perform all other nations in math on international exams, which speaks directly to the effectiveness of the Singapore program. The bar graphing method used in this series provides students with concrete visuals of algebraic thinking.

Saxon Math may be out of style with many of America’s newer K-5 teachers, but it is enormously popular and highly effective with parents “after schooling” their children at home. There is a study at this link

http://www.nychold.com/report-wbwh-040619.p

(scroll down to view the graphs) that indicates that Saxon is far more effective than Everyday Math in both low and high performing students. (Saxon and EM were the programs used in this study)

I’ll put my son’s Singapore and Saxon Math skills up against any EM kid’s skills any day. My boy isn’t a natural, he got his ability through hard work, using an effective curriculum, and effective teaching provided by his mother.

The schools both public and private have failed to provide us the best and most effective math instruction. We had to do it ourselves.

Those of you who think the schools are doing a great job with your kids, may end up finding out in high school that wasn’t the case.

LikeLike

We also have to be careful not to confuse traditional math with traditional math taught badly. Many of us have experienced the latter and paid a high price for it.

And please know that no one here is advocating for one or the other in terms of conceptual/procedural knowledge.

But, it’s important to know what is meant by the word “spiraling” and why the word “mastery” is missing.

Spiraling, in regards to these new curriculums, means that if your child hasn’t learned some topic, or learned it very well, well, not to worry, he will get it the next time around. That’s the basic idea.

The problem with that is that there is no accountability since one can just spiral forever. Also, since math classrooms in most public grade schools are inclusive, you could have a kid 2 years ahead and another 2 years behind and everything in-between. Spiraling allows for this kind of classroom to exist and for everybody to feel good about it. That is, until the shock of junior high when certain kids will be tracked to algebra and others won’t.

Mastery means someone has to be held accountable. That doesn’t sound as nice as spiraling, but it is the anchor that kids need to do higher math.

An example was used about proportions and ratio. You could understand both deeply, but lacking mastery of division means you cannot solve a problem very easily, if at all.

I’m not sure if EM even teaches traditional division. I believe it teaches the partial quotient method somewhere around 5th grade. University of IL’s Math Trailblazers, another reform curriculum, does not teach long division at all. The teachers have to supplement it or it gets dumped on the middle school teachers. Yet somewhere down the road lurks polynomial division, irrational numbers and other such division-dependent topics.

Singapore Math, on the other hand, starts long division by the end of third grade, mastering it by the end of 5th. That’s the goal.

I think it’s pretty clear which kids would be able to understand rate, proportion and ratio the best and who would be prepared to tackle such problems when middle school begins.

Mastering basic math facts by the time kids are out of grade school is not beyond even a slower kid. Parents have a right to expect this to not be a part of any spiral. If anything should spiral, it should be conceptual knowledge since that might be linked to developmental ability in ways that procedural fluency isn’t. People understand things at different times. Gifted math kids understand math concepts earlier than others.

LikeLike

Just came from having a glass of wine with the neighbors. Coincidentally, they started a discussion about how much work they have to do with their kids after school. And both work, btw.

LikeLike

The trouble with EM and other “conceptual” reform math programs is that they give a false sense of achievement.

A classic example is my oldest daughter. She got all A’s and B’s in elementary school math (EM). In middle school though, her first progress report was failing.

Luckily, I happen to read an article at the LA Times about the reason kids struggle with Algebra was that the kids never master the basics like multiplication tables, division, etc… Factoring is especially hard since their is no shortcut, except for knowing the multiplication tables forwards and backwards.

We drilled and killed for two to three months, and she became an A student again.

The biggest problem is that EM doesn’t provide a foundation to these pre-algebra skills. Now many bright students (or students with parents who pay attention) will learn the basics despite the curriculum, but it’s the below average students who really suffer.

The real tragedy with EM is that it hurts the under-performing groups much harder than middle/upper class students who have plenty of home support.

Ironically, I think EM was designed to be an equalizer at the lower grades… talk about backfire.

LikeLike

Hi! Happy to have found your blog today (I see several familiar faces. Barry, Catherine…) I just wanted to say I feel like I could have written much of what you wrote, from issues with ostensibly “high achieving schools” to being a mom with an agenda. For a taste on the math front, see the discussion that was recently sparked on my blog at http://themorechild.com/2009/05/27/hagiography-alert/

I look forward to looking through the rest of your blog.

LikeLike

“I’ll put my son’s Singapore and Saxon Math skills up against any EM kid’s skills any day. My boy isn’t a natural, he got his ability through hard work, using an effective curriculum, and effective teaching provided by his mother.”

Please do — find an EM math test (like, I think, the Washington state WASL), and check out your kids knowledge. I’d love to hear how he does, after having experienced a different curriculum. I think “transfer” is the real test of learning.

And, I think I found the studies — the “What works” site at the department of education has reviews of different studies on math curricula. The Singapore series hasn’t been studied, apparently. The Saxon series has 1 study that the IES folks consider reasonable, and it ” . . . was found to have no discernible effects on math achievement.”

Everday math has 4 studies they consider acceptable, and it ” . . . was found to have potentially positive effects on students’ math achievement.” (average improvement index of 6%, range -7 to 14%)

(from http://ies.ed.gov/ncee/wwc/reports/elementary_math/eday_math/ and

http://ies.ed.gov/ncee/wwc/reports/elementary_math/sesm/)

I really hope to see more studies. I regard the answer of the best curriculum to be an empirical one, requiring measurement. We simply aren’t sophisticated enough about how children learn to be able to design the right “intervention” on theoretical grounds.

LikeLike

“We also have to be careful not to confuse traditional math with traditional math taught badly. Many of us have experienced the latter and paid a high price for it.”

The same, of course, is true for any curriculum, including reform math. I do think it’s meaningful if some curricula are more likely to be taught badly than others, but I don’t think the traditional forms that were used 20-30 years ago win on this accord. I guess it’s possible that a teacher who doesn’t understand the math, but knows the rules/algorithms could teach them to a student in a rote way, and the student could be sophisticated enough to uncover the concepts, even though their teacher doesn’t get them. But, I suspect that scenario could play out with any curriculum.

LikeLike

http://www.nychold.com/em-arith.html, for everyday math and division.

I’m trying to figure out why I care about this, and, I think it’s ’cause I was completely hyped by seeing the multiple methods of multiplication, which were then explained to me by the kids in the class, when I toured my daughter’s school.

Note that I suspect that the system is implemented well in my school, where the teachers are knowledgeable, and well supported, and the class sizes are very small. The kids also learn the “traditional” methods (which I think is conventionally done with ED math).

LikeLike

As someone currently outside of the issue, it’s still really interesting for me to read. I’ve been comparing Laura’s posts and the comments to what I know about some foreign situations.. The Japanese press occasionally posts stories on what’s seen as the problems in their educational system (falling behind Korea in math testing! Oh no!). The hot new things there are Indian math systems, and Finnish.

There the concern is about the education gap in those who can afford to send their kids to juku (the infamous cram schools) or get tutors to teach to the important entrance exams.

(The exams sometimes allow you to use 3 for pi, which I find somewhat hilarious.)

But please pardon my ignorance: what does SES mean?

LikeLike

I had a longer, kind of rambling comment, so I’ll leave a shorter, but probably still rambly one. First, to bj re: knowing what’s going on. I know I don’t necessarily need to know, but when your very bright kid comes home with failing grades, you feel a little blindsided.

In general, I think that some of the research, like any social science research on a complex topic with multiple variables, isn’t terribly definitive. And I think that different kids need different things when it comes to education. And different parents want different things. Some parents want a well-rounded type of education that teaches solid academic skills but also leaves room for art, music, socializing, etc. Others want just the academic rigors and still others want a more artsy kind of education. As a school, then, it’s hard to please and meet all those different needs and desires. Add to that the desire of state and federal government to assess progress without necessarily coming up with the best way to do that and you have a recipe for bad schools. Or at least schools that are very far from the ideal that many educated parents want.

The problem I run into is that of time. How much time do I have to advocate for me kids, both on a particular or a more general basis? Who do I complain to when things aren’t going well? In what ways can I help? I’m an informed parent, trying to figure out the best way to get involved not just with my own kids’ education, but with the system as a whole, and I have a hard time figuring out what to do. I can’t imagine what it’s like for so many others. And I just started getting more involved after I quit my job. Before that, I just couldn’t keep up with anything.

Okay, so that wasn’t any shorter, but I think this has been a great conversation.

LikeLike

“In general, I think that some of the research, like any social science research on a complex topic with multiple variables, isn’t terribly definitive.”

You should sent that to every newspaper editor in the country.

SES = socio-economic status

LikeLike

Why shouldn’t parents know what’s going on in their kids classes? If my kid is learning about recycling in their social studies class, then I will make a point of showing what we do with all the paper products in the house and how I recycle plastic bags and all that. It’s nice to continue the discussion at home. Maybe some kids volunteer that kind of information. Mine don’t.

The wealthier districts around here have all the curriculum on-line, so parents can see what’s going on. They also have open gradebooks that can be accessed by parents from home at any time. That way there are no nasty surprises.

LikeLike

This is a very interesting discussion. I’m not terribly familiar with either ED Math or Singapore Math (although I think I get the general idea of the main differences). However, I’d like to address in a general sense the comment above about procedural fluency vs. understanding (I’ll take the quotes off of “understanding” and assume that we’re talking about genuine understanding).

I am a chemistry professor, I sometimes teach freshmen, and I’ve often thought that the biggest math-related problem some of my students have is that they can’t

usemath to solve problems…not that they can’t solve math problems (if that makes sense). Those at the “top” do just fine…the ones that are the most comfortable with math have both the fluency and understanding. Those at the “bottom” have problems, but in my experience some of them get through because they recognize that math is an issue for them and they work extra hard and seek out the needed help.But those in the vast middle…they can solve equations for a variable, convert between units, make graphs, etc. if they’re told what to do and it’s all set up for them, but they have a heck of a time really understanding how to use math as a tool. I’ve also found that the students that struggle the most seem to never have been asked to really think through how to solve a problem, rather than using an algorithm to solve it.

I, for one, would be willing to sacrifice a bit of procedural fluency in my students in exchange for more understanding of concepts as they relate to using math to solve problems and an (accompanying?) willingness to do the mental “heavy lifting” of figuring out those solutions. One problem in which a student is asked to apply concepts in a complex way to an unfamiliar situation is better than 10 plug-and-chug problems, in my opinion. FWIW.

Also, I was a math minor in college, was definitely taught the “old fashioned” way K-16, and I can say that, while I did pretty well in math because I worked hard at it and could follow directions, I still don’t “understand” it as well as I’d like. And much of the advanced calculus that I no longer use is just…gone. Whereas if I’d been taught with more of an eye toward conceptual understanding, I might have retained more. Who knows?

Sorry for the overlong ramble…

LikeLike

Daniel T. Willingham has a chapter in his book “Why Don’t Students Like School?” entitled “Why is it so hard for students to understand abstract ideas?” He relates the story of a geometry student who successfully calculates the area of a tabletop, but is then stumped by a problem where he needs to calculate the area of a soccer field, not realizing that it is essentially the same problem. Willingham says that while “Abstraction is the goal of schooling,” “the mind does not care for abstractions.” “The mind prefers the concrete.” “The surest way to help students understand an abstraction is to expose them to many different versions of the abstraction–that is, to have them solve area calculation problems about tabletops, soccer fields, envelopes, doors, and so on.”

LikeLike

Louise makes a great point about applicability and making connection between concept and reality. This, IMHO, is where my kid’s great teacher really makes the difference.

It also strikes me that this may be a critical difference when it comes to the whole SES thing. Although we don’t ever help our daughter with math homework, and are in fact not familiar with the approaches she uses, we do apply math to life every day. Just a few days ago we were in a conversation about how many paving bricks we needed to get for our back yard patio project, and my daughter sat at the dinner table and asked questions about that.

LikeLike

It appears that our school district has been using Investigations for math instruction and is now switching to enVision. However, it also appears that principles have a fair amount of control to tweak the curriculum — it seems pretty clear after 3 years and 9 teachers that there’s a lot of on-the-fly improvisation happening in the classroom, and none of the kids’ math homework has ever been of the “photocopied workbook” variety.

I had breakfast with another parent of a second-grader just before spring break and we both bemoaned the lack of instruction in what we called “basic math facts” (by which we meant, memorizing addition/subtraction of the numbers 1-19) and column addition. We were feeling very frustrated with all the strange methods that the kids were being taught for reaching math answers. Lo and behold, our kids all came home with photocopied addition/subtraction flashcards THAT EVENING and the weekly class newsletters for the next month emphasized that kids wouldn’t be able to keep mastering concepts without being able to rattle off those addition/subtraction facts within a second or two.

I feel blessed to have teachers with the experience and intelligence to comprehend (a) their target audience of hyper-concerned parents and (b) the fairly straight-forward concept that math is not an either/or proposition.

Now our three kids are doing the “transition-to-third grade” multiplication stuff, and we’ve been encouraged by all the conceptual tools they’re deploying to figure this out. (For example: 9×7 can also be 10×7 – 9.) It’s fascinating for spouse and I to watch three second graders each using different methods to reach the same answer.

Then again, we have the resources and the inclination to do math quizzes at the dinner table (and this at the plea of our children — which is probably some sort of multiples-related competition, too, now that I think about it, and in that sense should be discouraged, but oh well). The crucial public-policy question should probably be, which curricula serve best the kids whose parents can’t or won’t teach math facts at home. From what I’ve seen, there’s evidence to support both approaches, and I’m not sure any amount of internet comment perusal will move my understanding of the issue any further forward.

I’m far MORE irritated right now to read that we’re adopting a new district-wide K-5 math curriculum when our state is considering cutting the school year from 180 to 175 days next year, eliminating teaching assistants for 3d graders, increasing class sizes by 2 students across the board, slashing teacher-development funding, etc ad nauseum. And that on top of the $1.5 million drop in local funding. What a pathetic waste of money.

LikeLike

“Lo and behold, our kids all came home with photocopied addition/subtraction flashcards THAT EVENING and the weekly class newsletters for the next month emphasized that kids wouldn’t be able to keep mastering concepts without being able to rattle off those addition/subtraction facts within a second or two.”

I wonder if they were in an NCLB panic and gearing up for standardized testing. The timing (just before spring break) is interesting. I’ve heard of schools doing this (going all traditional just before the testing). I suppose it’s the educational equivalent of foxhole religion.

By the way, I believe Catherine has stated in the past that flash cards aren’t particularly effective.

LikeLike

I also enjoy the education posts. And I don’t know how to get around the many ignorant stereotypes of mothers who care about education.

One thing I’ve noticed is that education is so different from school to school. (and state to state…and region to region.)

My kids go to a poor urban school (well, urban for Wisconsin!), but live in a neighborhood where most of the kids go to private schools.

My solution to the huge challenges at our school was to become the PTA President and slowly start to work closely with the Principal to address them.

Yes, this comes with its own stereotype – tell someone you are the PTA President and they immediately jump to “helicopter mom” or “overbearing SAHM with nothing better to do.” I deal with this constantly.

But – we’ve made significant changes and improvements over the last 4 years at our school. So, I’ll deal with the stereotype. I know I’ve made a difference. And yes, maybe sometimes I get shrill.

Frankly, I’ve been shocked at how much parental involvement it has taken to have a good public school experience. And I have a huge long list of problems yet to be addressed: Lack of Foreign Language Instruction, Atrocious School Lunch Meals, Disintegration of Gifted/Talented programs….

But at the end of the day, we are having a great experience at our local public school. Overall, I wouldn’t trade it for anything else.

LikeLike

Personally I think much of the American educational system has a staffing model that *requires* the “SAHM with nothing better to do” support system. Or shall I say, education’s traditional “hire overqualified women who are barred from other lines of work” staffing model no longer applies, yet the surrounding infrastructure has not been updated. But that’s another topic for another time!

LikeLike

“Personally I think much of the American educational system has a staffing model that *requires* the “SAHM with nothing better to do” support system.” Oh, yeah. That was the conversation with friends yesterday. I love when my real life conversations and my blog conversations dovetail.

The educational system with all the holidays and projects and parent-teacher conferences and afternoon shows does assume that there’s at least one parent home full time. It actually becomes a self-fulfilling prophesy. Women (usually its them) end up quitting their jobs or taking low paying flexible jobs, because no 9-5 job allows for all that time off. Then the women who are desperate for flexible jobs, which don’t exist, end up taking stupid, low paying jobs at the school just so they can keep up with all the demands from the school.

LikeLike

For those of you that don’t know if your kids are doing Everyday Math, check out the home work – are there “Study Links” (i.e., S.L. 10.2) or “Home Links”? Do your kids learn lattice multiplication (and partial products multiplication) in 3rd grade, as well as traditional methods?

The workbooks (Math Journals) are quite distinctive, too.

LikeLike

Here’s a very popular YouTube video on Everyday Math.

LikeLike

There’s no standardized testing in our district until the end of third grade. They ramped up the rapid-drill math facts in class at the end of third quarter, too. I suspect this had more to do with finishing the “concepts introduction” part of the year and getting ready for fourth-quarter review.

I trust our teachers to communicate honestly (next year, there will be a LOT of open discussion about test-prep) and I believe what they said: at the end of second grade, kids should be able to add and subtract quickly from 1-19 (and, by extension, do column addition). Flash cards might be a useful visual prompt to help your child memorize those facts.

LikeLike

re: Digital Divide

“1) Closing the Digital Divide is a precondition for reducing poverty.

Many antipoverty experts believe that closing the Digital Divide is not a top priority, arguing instead that the poor need clean water and jobs before they need computers.”

I would be among them.

Since the subject of antipoverty experts has come up, William Easterly’s The White Man’s Burden is a fantastic book, with important implications for public schools.

LikeLike

As a teacher, all I can say is, “Amen!” These are the same things we complain about. We cram in as much as we can, but administration tells us not to teach things like handwriting. Computers may be the way of the future, but I need to be able to read their work right now. So some of us do it anyway because it’s the right thing to do. Same for math facts. In fifth grade we are still giving them time to learn their times tables that they were supposed to memorize in the third grade. We sneak time from 2.5 hours of reading to get in extra math practice. It’s disheartening to work for administrators who say they are all about the kids but don’t do what’s best for them.

LikeLike

“…administration tells us not to teach things like handwriting.”

So it’s not a fluke–it’s policy.

LikeLike

Yup, at least in my district! They also told us not to teach spelling (!!!) and grammar, even though 5th grade takes the Writing state test and half of it is grammar. (But the test doesn’t count toward AYP – yet – so they don’t care.) We (in 5th grade – but not 4th or 6th!) teach it anyway because that is just *wrong*.

LikeLike

Strangely enough, the workbooks I’ll use over the summer with my 1st grader arrived this week. We, too, have learned that our school has decided to cut out time spent on handwriting, in order to gain time for “21st century skills,” (whatever those may be.) As he’s the youngest of 3, I’ve learned that it’s best to supplement at home, as possible, and to get out when you can. Positive interaction with the school district? We’ve tried that, but the average tenure of a school system superintendent is something like 5 years. By the time they might understand your arguments, they’re looking for another job.

This is, of course, why upper-income districts appear to do well. Educated parents can and will supplement their children’s education, in order to provide their children with the basics. Spelling. Grammar. Legible handwriting. A basic grasp of math facts, and the traditional algorithms for addition, subtraction, multiplication, and division. An interest in reading which keeps them reading–even if it’s Captain Underpants.

If you criticize the schools, parents will thank you. Quietly. In passing, at community events. They won’t stick their necks out, though, as they’re afraid of retribution.

If you have a special needs child, they won’t elect you to the school board, even if you’re the most qualified person in the race.

Our district claims to use Everyday Math in grades K-5, but they don’t use it as a curriculum. Each teacher supplements, heavily, as he or she sees fit. If your child ends up with a teacher who understands math, it could be wonderful. If your child gets the teacher who doesn’t understand math, he’s in deep trouble, as that teacher could choose to spend very little time on math in the classroom. By the way, our school has admitted that they spend half the time on math which Everyday Math requires. Don’t get me wrong–it’s a bad curriculum. To be fair, though, I must admit that our district doesn’t use it in an organized fashion.

LikeLike

“To be fair, though, I must admit that our district doesn’t use it in an organized fashion.”

I haven’t handled the materials myself, but from what I’ve heard, ED math throws a mountain of stuff at the teacher and there’s very little chance of going through the whole pile in a single year. It’s really only natural that teachers or districts treat Everyday Math selectively. Unfortunately, the less savvy teachers and schools are going to wind up skipping the wrong stuff. Over the long term, this is going to create more inequity than there really needs to be.

I think fattextbookitis is a typically American affliction. When I was in high school (and I know this is the norm), we’d get these huge fat textbooks on glossy paper with lots of illustrations and cover only about half the material in the course of a year. In contrast, with Singapore Math, my daughter goes through two slender (200 page) math workbooks in the course of a school year, and they cover almost everything. Likewise, when I taught high school kids in Russia, all the textbooks I saw at my school were slender and there was a strong national curriculum.

LikeLike

You posted this a few hours before I left for DC for the weekend. Sorry for such a late and probably irrelevant by now comment.

Anyway, my kids’ school uses Investigations, which seems to be an Everyday-Math-like curriculum. Apparently it was revised a few years ago in response to concerns about little priority placed on math facts, etc. Our district only started using Investigations this year. Before, we used a curriculum that involved a lot of cutting out flashcards, which I hated. I hate anything that requires my involvement in homework. I have enough of my own to deal with. So far the kids seem to be doing well, though of course they may hit 10th grade and reveal themselves to be incapable of adding 2+2. We’ll see, I guess.

I am trying to remember how I learned math. I love the rules and shortcuts and quick ways of doing math. But the other thing to know about me is that I am very much a big-picture thinker and a visual learner, and while I was given “traditional” ways of learning math, I created my own conceptual understanding to go along with it. But I was a gifted kid with a particular way of learning; most kids are not like me. They need the support for learning the conceptual framework.

I wonder why it is that nowadays math curriculum is the rallying point for opponents of the current public education system. Back in the 90s, it was phonics vs. whole language. Maybe it’s my big picture thinking, but to be honest I have a hard time taking these curricular wars seriously as a result. We always think this micro-decisions are going to have huge effects, but I’m not sure they do.

LikeLike

I think I should get some sort of patience award for not bring-up teachers’ unions.

LikeLike

Gold star for you, MH.

Thanks for your comments, Wendy. This thread isn’t dead and this post is actually getting e-mailed around quite a bit. I’m done talking about it, but I’m enjoying the commentary.

I may do another post on the Paul Attewell article that came up in this discussion. I did some work with him in grad school and think he’s wonderful.

LikeLike

Our school has also added a great deal of drill on basic math facts, through computers. Yes, parents complained in earlier years that children weren’t learning to multiply or divide–and they were right. The going rate for tutors around here is reportedly $80 – $100 per hour. Mini-malls in surrounding towns host the likes of Sylvan, and Huntingdon, and Kumon. There are numerous other, non-franchised tutors in our small town.

The math wars have heated up in part because the state tests allow parents to gauge their kids’ preparedness. Spiraling is hard to defend when you’re the parent of a bright 5th grader who can neither divide nor multiply. Good book on the subject: _Math Wars_, by Carmen Latterell.

Our district has added phonics to the reading curriculum, when the whole-language based curriculum wasn’t teaching kids to read.

Our family loves Tom Lehrer. If you listen to his song, “New Math,” the lines which got the biggest laughs in the ’60s (“It’s not getting the right answer, but to understand what you’re doing,” ) are now truisms in elementary classrooms.

LikeLike

Does anyone else’s school use differentiated instruction? I thought my daughter’s 3rd grade teacher used it very well.

LikeLike

At my school, we didn’t differentiate until our senior year and that was elective.

LikeLike

I don’t think the educational system requires a SAHM parent. I’ve been part of a working couple for my kids’ entire school career (one now in HS, one in MS), and we did ok, with the help of afterschool care. Sure, it’s complicated to get to the shows and PT conferences, but not impossible. And we haven’t helped with homework since about 4th grade. (we do sometimes read over and comment on their essays when allowed)

That said, I agree with the general thread that the math curriculum in the US is not systematic and does not provide a good mathematical foundation.

LikeLike

LOL, so I printed out a few pages from the Singapore Math and Everyday Math practice tests. I gave them to the kids after dinner, and right now my 9 yo is teaching the 6 yo how to do some of the problems. It’s adorable.

LikeLike

I’ve so enjoyed this post and the ensuing commentary. All I can say is: Criticize your kids’ public school on your blog at your own risk. Even if your criticism of Everyday Math and standardized testing is couched in humor,it can come back to bite you.

MH – right on about the unions. And I say that as the daughter of a guy who taught high school English for 30 years and became teachers’ union president. He still gives me an earful about how teacher compensation should be based on merit and ability, rather than these lockstep salary schedules. I can’t begin to describe how it killed him to be a masters from USC, teaching AP English, and earning the same pay as the P.E. teacher with the 2.0 from Chico State. You know — the guy with no papers to correct, whose class time consists of yelling “run around the field!”.

LikeLike

I don’t know, Paula. For 30 years, my dad was a public school teacher with a masters in science, teaching AP Chem and Physics, and he earned the same pay as the other teachers, including PE, and he never complained about it. (And he’s not exactly a stoic non-complaining kind of guy.)

LikeLike

Wendy,

English would be especially galling, given how much more labor-intensive it is as a subject. But you know that. 🙂

LikeLike

To look at it differently, if an English teacher works 60 hours a week and a PE teacher works 40 a week for the same salary, it would be equally true to say that the English teacher is being paid significantly less on an hourly basis. Worse, the PE teacher is free to take on a second job during those extra 20 hours while the English teacher is still correcting papers.

LikeLike

“To look at it differently, if an English teacher works 60 hours a week and a PE teacher works 40 a week for the same salary,”

Well, that would be unfair, if it were true. But, don’t PE teachers usually coach as a part of their job functions? and otherwise coordinate the athletics programs? Ours does.

I’d guess the English teacher has a lot less market demand than the Chem/Physics teacher, producing a different kind of gall regarding, and one that actually matters for eduation, since it’s hard to find qualified science professors.

LikeLike

Amy, no, I get that. I’m just saying it doesn’t matter to some people.

Then again, if I’m in the faculty lounge and someone’s using the Scantron, I sigh noisily and on occasion bitch about how nice it must be to be able to give multiple choice tests. 😉

LikeLike

“But, don’t PE teachers usually coach as a part of their job functions?”

I know that non-PE teachers in the public system who coach get paid extra, so I expect that PE teachers who coach probably get the same deal. Coaching is a standard way for a classroom teacher to increase pay.

LikeLike