palisadesk on the math police - & parents teaching math facts

A propos of Kindergarten children being asked to write journals and stories without any instruction in spelling (or even in pencil grip or how to form the letters), and also children being taught -- or not -- number facts and algorithms, this discussion has come up on a couple of other boards I read. One important issue stands out: there is enormous variability in what is required and/or permitted to be taught in these areas.

I advise all parents to get a copy of your district's curriculum documents, if you can (many have them online) and see what teachers are being told to do. It may surprise you. In many places, expectations for teaching the mechanics of writing -- pencil grip, letter formation, manuscript or cursive writing styles, even spelling -- have been *completely* removed from the curriculum. Teachers can of course model them or give instructions en passant, but cannot actually focus on these things as objects of lessons.

Catherine has brought up the use of "instructional coaches." This is becoming more and more common, and one of their (unstated) roles is to act as "literacy police" or "numeracy police." If they see teachers doing spelling, or printing, or teaching math facts systematically, they are to discourage these things and also discuss it with school administration. My district no longer requires math facts to be taught, and teachers have actually been forbidden to practice them in class. They can assign math fact practice for "homework" which is another way of outsourcing to parents, as Catherine has pointed out in the past. This disproportionately penalizes low-SES kids whose parents don't have the time or sometimes the expertise to teach these things to their children.

It's very often not a matter of teachers not wanting to teach "the basics," but of their being prevented from doing so. Many of my colleagues grumble quietly about it, but because it is ordered from on high it can't be openly flouted. It's not clear to me who makes these curriculum decisions higher up the ladder, but sometimes it does seem (as an anonymous person said earlier) that the goal might just be to keep the proles in their place! In my darker moments I am tempted to think this is so.

Outsourcing math facts to parents handicaps all children. I know we've talked about this a lot over the years, but I don't have the patience to go hunting the posts. Easier to write a new post now---

At least two high-SES, highly-educated parents we know told us they were never able to remediate their sons' deficiencies in math facts or in long division. One of these parents went to Harvard. They tried, but they did not get the job done. Even Kumon didn't get the job done for one of the kids. (Not sure why -- possibly because the parents realized what the situation was too late -- ?)

I was lucky because the Saxon Math "Fast Fact" sheets worked for C. after 2 other approaches I tried failed outright: flash cards and flash card software. When I switched to the Saxon worksheets, he learned rapidly.

I had no idea what to make of it. Can't learn his math facts using flash cards? Can learn them practically overnight using worksheets?

Later on, I read a Rafe Esquith passage advising parents that students need to practice material in the format they'll use it on the test. That makes sense. It's consistent with everything I know about animal training and with Dan Willingham's explanation of flexible and inflexible knowledge.

But how many parents know this?

I sure didn't.

At a board meeting recently, our new part-time Interim Director of Curriculum and Instruction made one fantastic observation. She said she'd told teachers that "If we were serving a low-SES population, with parents working two jobs to make ends meet, we wouldn't expect parents to be skilling and drilling the math facts. Our parents have busy lives and many demands on their time, and we shouldn't expect them to do it, either."

Then she added, diplomatically, that in fact parents here, nearly all of whom are high-SES and well-educated, are not getting the job done.

Last year, the 6th grade accelerated math class had to stop dead in its tracks so the teacher could teach math facts & the standard algorithms. The kids were all high-SES and their parents are well-educated.

Teaching math facts isn't simple or obvious. Skilled teachers do it far better than most parents.

Why Memorize the Math Facts?

This is from Hoagies' Gifted Pages, and was written by Aimee Yermish, Educational Consultant

Why Memorize Math Facts?

I think there's a basic problem here that we as the parents of gifted children must come to terms with. Not all useful learning is intrinsically interesting. Our kids have a right not to be bored in that they should not be held down, but they do not have a right not to be bored such that they have a right to skip anything that isn't fun to learn. Math facts are boring. Absolutely. But that doesn't mean that our precious children who don't tolerate boredom well shouldn't have to learn them. We have to teach our kids the difference between being bored because you are being taught something you have already mastered and being bored because the work is intrinsically boring but still important. We can turn our fertile brains towards making the practice fun and interesting, if we don't tolerate boredom well, but we don't get to just declare ourselves to be so brilliant that no one should ever make us do anything we don't feel like doing.

From AutoSkill, a provider of software (not an endorsement -- haven't yet looked into the products)

Why Automaticity in Math Facts?

The notion is that the mental effort involved in figuring our facts tends to disrupt thinking about the problems in which the facts are being used. Some of the argument of this information-processing dilemma was developed by analogy to reading, where difficulty with the process of simply decoding the words has the effect of disrupting comprehension of the message. Gersten and Chard illuminated the analogy between reading and math rather explicitly:

"Researchers explored the devastating effects of the lack of automaticity in several ways. Essentially they argued that the human mind has a limited capacity to process information, and if too much energy goes into figuring out what 9 plus 8 equals, little is left over to understand the concepts underlying multi-digit subtraction, long division, or complex multiplication (1999, p.21)."...Practice is required to develop automaticity with math facts.

"The importance of drill on components [such as math facts] is that the drilled material may become sufficiently over-learned to free up cognitive resources and attention. These cognitive resources may then be allocated to other aspects of performance, such as more complex operations like carrying and borrowing, and to self-monitoring and control (Goldman & Pellegrino, 1986. 134)."

I have a new academic therapy client, a delightful 4th grade boy on the spectrum. For various reasons, he missed a lot of 1st and 2nd grade. Academically, arithmetic is his weakest link. As nearly as I can determine, the only math facts he has to automaticity are adding and subtracting 0, 1, and 2 for even numbers, and multiplying by 1 and 2 for even numbers. Everything else requires him to actually do the calculation in his head or worse yet, his fingers. Calculation--> frustration--> anxiety--> decreased cognitive ability--> frustration--> anxiety--> decreased cognitive ability ...

I have three challenges: convincing him that putting the work in to getting to automaticity is going to be worth it, finding the methods that work most efficiently for him (flash cards aren't it), and keeping his anxiety low enough that he can learn.

Any and all suggests for the three challenges gratefully accepted.

math facts at The Key School

Grade Four Timed Tests
Fluency with Basic Math Facts
September 11, 2006

The goal of timed tests is computational fluency: by this we mean quick and accurate knowledge of math facts. As has been said before to parents in earlier grade levels (and is worthy of repeating), automatic recall of basic math facts is desired because it frees up students’ minds for complex problem solving. To this end, fourth grade students will prepare for weekly timed tests. Below are the details.

What: Each timed tests consists of 50 problems to be completed in four minutes or less, although many students set personal goals of two minutes. Timed tests begin with subtraction facts (0-20) and, in the winter, move to multiplication facts (0-9).

When: Timed tests are given every Wednesday for the entire year. Students keep corrected timed tests in their math binders along with a chart of their progress.

How: We review study tips with students and provide work sheets for practice. Enclosed are strategies for subtraction and multiplication to help your child polish his or her math facts at home. Students can make flash cards of difficult math facts. Additionally, the Lower School’s math library has a variety of math aids available for home practice; materials may be borrowed for two weeks at a time.

The Key School is supposed to be one of the best private schools in the country. Based in what my friend who has two kids there tells me, it is.

math facts & letter facts

Susan J left this comment:

Maybe we need another term besides "math facts." They are much more fundamental than contingent facts like, say, dates when certain historical events occurred.

Do kids still learn "letter facts" like the names of the letters and alphabetical order?

That's a terrific point. The term "math facts" does lend itself to the view that "math facts" are on a par with historical dates.

I'm going to start using the terms fundamental versus contingent to talk about the math facts.

(I guess we could call them math fundamentals...on occasion.)


here's Barry:

Call them something exotic so the reformers at large will think it's higher order thinking skills. Call them theorems, because that's what they are. 3 + 2 = 5 is a theorem which can be proven using Peano's axioms. And like all theorems, once proven, it can be used without having to re-prove it, thus alleviating our kids from having to draw clusters and go back to first principles each and every time they add, subtract, multiply or divide lest anyone think they were doing things by rote.

Steve H

I've never liked this either. I think it's a carfully-selected term used to degrade the importance of the knowledge. when I told my son's Kindergarten teacher (years ago) that I supported an educational approach that emphasized basic knowledge and skills, she said that I would like one of the second grade teachers who required each child to give her a "math fact" to enter the room.

They are just clueless.

From his first grade teacher I learned about "superficial knowledge". I wanted to tell her that it is fundamental knowledge.

Basic knowledge and skills are the foundation of education. You build from the bottom up rather than the top down. Somehow they think that education should be thematic or top down; that kids can learn basic knowledge and skills by osmosis.

Basic facts and skills require hard work.

Hard work is a filter.

The only point I would add here is that achieving expertise requires hard work and expert teaching.

I've been trying to make my way through the research on expertise, with limited success. It is vast.

However, I've managed to do some mighty skimming.

As far as I can tell, expertise is expertise; the mechanisms by which one acquires expertise are (largely) the same.

These days I think about athletics and athletes when I'm confused by an issue in K-12 education.

There's a reason you never, ever, see an Olympic athlete who is self-taught.

That reason is that expertise requires superb teaching.

I'm not sure whether the strong form of this statement is correct.* Certainly I've seen many people who are self-taught (I taught myself to write).

There must be a literature somewhere on self-teaching.

Nevertheless, the weak form of the statement is certainly true.

Our kids need expert teachers who themselves take the development of expertise seriously. Hard work isn't enough.

I would rewrite every school mission statement in this country to reflect this understanding.

I'd take out all the "lifelong learners" and "critical thinkers" and "all children can learn" foofaraw.

I'd insert the word expertise.

__________________

* One of the reasons why I'm not sure is that procedural learning and knowledge, which I believe is dominant in athletics, seems to follow a slightly different set of rules than declarative knowledge, which is dominant in academic disciplines.

Procedural knowledge seems to be much more vulnerable to error. Once you learn a procedure - a golf swing, say - the wrong way, you can't unlearn it.

As far as I can tell, declarative knowledge is less vulnerable. If you mislearn a fact, you can overwrite it in memory. I'm guessing it's possible to learn from error in declarative knowledge.

caveat: I don't "know" these things. This is what I surmise based in many years' surfing literature on memory.

Dan Willingham on overlearning

Practice Makes Perfect - But Only If You Practice Beyond the Point of Perfection

I've just found this link again for Samantha.

Question: Just how much should students practice what they learn? On the one hand, it seems obvious that practice is important. After all, "practice makes perfect." On the other hand, it seems just as obvious that practicing the same material again and again would be boring for students. How much practice is the right amount?

Answer: It is difficult to overstate the value of practice. For a new skill to become automatic or for new knowledge to become long-lasting, sustained practice, beyond the point of mastery, is necessary. This column summarizes why practice is so important and reviews the different effects of intense short-term practice versus sustained, long-term practice.

That students would benefit from practice might be deemed unsurprising. After all, doesn’t practice make perfect? The unexpected finding from cognitive science is that practice does not make perfect. Practice until you are perfect and you will be perfect only briefly. What’s necessary is sustained practice. By sustained practice I mean regular, ongoing review or use of the target material (e.g., regularly using new calculating skills to solve increasingly more complex math problems, reflecting on recently-learned historical material as one studies a subsequent history unit, taking regular quizzes or tests that draw on material learned earlier in the year). This kind of practice past the point of mastery is necessary to meet any of these three important goals of instruction: acquiring facts and knowledge, learning skills, or becoming an expert.

We've just come to this realization with Christopher: he is nowhere near "procedural fluency" with any kind of computation beyond his math facts.

Ed had been complaining that Christopher "doesn't know his math facts," which was ticking me off since I was there for many, many Saxon Fast Facts sheets; he certainly does know his math facts.

Turns out Ed doesn't know what the phrase "math facts" means; he was thinking "math facts" means "computation."

(question: Is this man living in the same house I'm living in?)

I had subliminally noticed that Christopher is too slow on computation, but of course I'm intensely focused on just getting him through the course in one piece. (I'm defining "one piece" as "grade goes back up to a B.") Also, I'm trying to write books.

So: blind spot.

Yesterday we got the ITBS results and - bingo. He's strong on everything in math except computation. (The computation test was hard. Lots of problems; very short time to work.)

math: 88th percentile
computation: 75th percentile

Eighty-eighth down to 75th: that seems like a huge difference to me.

Ed says when he works with Christopher he's still having to write out a division problem in order to divide a number by 2.

Obviously I let him drop out of KUMON way too soon.

I'm going to fix this problem with edhelper. (Susan & instructivist both like that site, iirc.) The KUMON sheets were too much, and were getting far too expensive since it's the same price every week no matter how many worksheets you do.


how to remember something forever

This is serendipity. I've found the passage I was searching for the other day:

Although practice takes on a different character for the longer-term, it is no less important. Studies show that if material is studied for one semester or one year, it will be retained adequately for perhaps a year after the last practice (Semb, Ellis, & Araujo, 1993), but most of it will be forgotten by the end of three or four years in the absence of further practice. If material is studied for three or four years, however, the learning may be retained for as long as 50 years after the last practice (Bahrick, 1984; Bahrick & Hall, 1991). There is some forgetting over the first five years, but after that, forgetting stops and the remainder will not be forgotten even if it is not practiced again. Researchers have examined a large number of variables that potentially could account for why research subjects forgot or failed to forget material, and they concluded that the key variable in very long-term memory was practice.*(see below *) Exactly what knowledge will be retained over the long-term has not been examined in detail, but it is reasonable to suppose that it is the material that overlaps multiple courses of study: Students who study American history for four years will retain the facts and themes that came up again and again in their history courses.

* It is likely relevant that there is not only more practice in this case, but that the practice is distributed across time rather than concentrated in a few months (see former column, "Allocating Student Study Time.")

math night

Trailblazers Math Night happened last night.

Apparently there were some walk-outs. Parents had been told they would be able to ask questions; instead they were treated to the standard "Math Night" dog and pony show that appears to be the main fuzzy math marketing tool. No questions were taken, though parents who wished to do so could write a question on a Post-It and attach it to board that had been set up outside the auditorium.


cross-posted at the Irvington Parents Forum:

Hi all---

Some background on “Math Nights” ---

Math Nights appear to be a constructivist innovation. Traditional math curricula don’t urge schools to host math nights for parents; nor do innovative curricula such as Primary Mathematics & Saxon Math.

The stated purpose of math nights is to head off parent complaints. Publishers know large numbers of parents will be unhappy with these programs, so they create marketing materials and events for districts to purchase along with the curricula itself.


The main Trailblazers document advising schools on how to manage parents can be found here, here (pdf file), and here.

My favorite passage:

Be pro-active with parents. Don’t wait until complaints hit. People have done a lot of things to involve parents, from math nights to big math carnivals, where the kids teach the activities to the parents. There are letters in the program that go home to parents. In one district, the coordinator ran a six-week course for parents and taught them mathematics, essentially. It depends on what will work with your audience. Teachers need to communicate with parents, making sure that the parents see the math facts practice and that the arithmetic they value is visible.

Don’t wait until complaints hit!

I love it!

I propose that the Board adopt as a matter of policy a rule barring the district from purchasing curricula whose supporting documents say things like “Don’t wait until complaints hit.”


Another favorite:

The math nights have helped [with parent complaints] a lot. I took one of my math nights and just addressed Trailblazers. I actually took them through the steps of how they teach addition and subtraction, using all the base-ten blocks and the manipulatives and how it flowed into the algorithm. After that, I did not have another negative letter. There are still a lot of parents who are worried that, at the end of 3rd grade, kids haven’t memorized all of their multiplication facts. The focus of the math night that I just had was on games that parents and children could play at home to work on math facts, just using decks of cards and things. These are things they can work on with their kids that are fun and easy to do. I don’t want to spend a half hour in class memorizing multiplication. We have far greater things, bigger things to think about.

We have far greater things, bigger things to think about!

If you were wondering why it’s up to parents to discover how to help their children commit math facts to memory (not easy to do), this is it.


Last but not least, here’s a report from Barbara Martin, principal of the Holmes Elementary School in Chicago (“The Holmes school has 772 students in grades pre-K through 5; the student body is 100% African-American, and about 95% of the students live in poverty.”)

We invite parents to an orientation where we talk about all our programs early on in the year. Our math coordinator speaks to the group about math lessons. Math Trailblazers has parent letters that go home all the time telling about what’s going on in the math program. We do also have a math day, and on that math day, we invite parents to be in the room. The kids do math all day. In order to get the parents in the room, I offer them a little stipend.

I offer them a little stipend.


I looked up Ms. Martin’s test scores:

math
Third grade: 32.5% of the kids meet state standards
Fifth grade: 19.7% meet standards
Eighth grade: 15.7% meet standards

Look at their reading scores:
3rd grade: 18.5% meet standards
5th grade: 16% meet standards
8th grade: they're up to 43.5% meeting state standards


Reading scores are harder to raise than math scores, and yet this school is raising children’s reading comprehension while at the same time math scores fall.

Kendall Hunt doesn’t mention Holmes’ scores.

Instead, Ms. Martin is quoted:

Wherever students go into in the middle grades, if they’ve had a sound foundation in the primary grades, they will be prepared..... For some of my children, our feeder schools are saying, “Please, please send us more like these.”

Catherine J


letter from the superintendent

January 6, 2007

Dear K-5 Parents,

As you know, the mathematics Trailblazers program was adopted by the Board of Education in 2004 and is in its final phase of implementation this year in Grade 5. The District has provided strong support to teachers to ensure excellent initial training and ongoing professional development, and the results to date, are very positive. As with any new initiative, however, it is imperative that we continue to monitor children’s progress and to provide ongoing opportunities to keep parents informed as well as to continually evaluate the program’s effectiveness.

As part of our commitment, there will be a Math Information night for K-5 parents on January 22, 2007 at 7:00 PM in the Dows Lane Library hosted by staff from Dows Lane and Main Street Schools. Teachers will present information about the Trailblazers program, and parents will be able to ask questions to which they will receive responses that evening or soon after the session. As the date draws near, a separate flyer will be sent home by building principals requesting confirmation of your attendance.

In addition, since students in the current elementary program are not tracked and those in the current Middle School program are in leveled classes, the staff recognizes that the transition to 6th grade is a valid concern on the part of parents and one that will soon be addressed. Therefore, parents of current fifth graders will have an opportunity to attend a meeting in February 2007 to discuss this topic. Once again, information will be sent home later this month.

I hope that you will make every effort to attend these important parent meetings.

As always, we value the input of parents [ed.: no more input] and look forward to these opportunities to hear from you and to be able to respond and work collaboratively with you as we move forward.

Thank you for your ongoing support and cooperation and best wishes to you and your families for a healthy and Happy New Year.

Sincerely,

Superintendent of Schools

The polite term for that is chutzpah.^*

I wonder how much longer things can go on this way.

___________

^*Dictionary.com defines chutzpah a bit differently.

math night part 2
trailblazerspublicrelations
trailblazerssupportingdocuments

how to determine fluency for an individual child

An adult-to-child proportional formula can also be helpful in setting performance aims. Measures are first taken of the student’s tool skills rate and the rates at which a competent adult performs both the tool skill and the target math skill.^* The tool skill for answering math facts is writing random numbers without solving any problems. This fast-as-you-can number writing rate provides a ceiling for the fastest rate at which answers to math facts can be produced. The proportion obtained by dividing the adult’s performance rate on the target math skill by his or her tool skill rate is then multiplied by the student’s tool skill rate. The resulting figure is the fluency aim for the student. For example, if the adult solves math facts at a rate of 60 correct answers per minute and can write 120 random numbers per minute, his or her target skill to tool skill proportion is .5 (60 divided by 120). Based on the adult-child proportional formula, the fluency aim for a student whose tool skill rate is 80 would be set at 40 correct answers per minute (80 times 0.5). Providing direct and repeated practice on the relevant tool skills may be an effective way of improving the overall fluency of some children. Alternative modes of response, such as answering orally, should also be considered for children who exhibit very slow writing or poor fine motor control.

source:
Do Your Students Really Know Their Math Facts: Using Daily Time Trials to Build Fluency (pdf file)
by April D. Miller and William L. Heward
p 134
Intervention in School and Clinic, Volume 28, Number 2, November 1992

Effects of sequential 1-minute trials with and without inter-trial feedback and self-correction on general and special education students' fluency with math facts
(abstract)



^* tool skills; component skills; composite skills - see speed test

EM success story

from the Dallas comments thread:

I am a student whose school used Everyday Math textbooks, and I was more than prepared for higher level math courses. However, this is because my math teachers had us put the books under our desk, and passed out real math textbooks, like Saxon Math instead. Because of the strong basic math foundation imparted by the traditional method, I have already been able to take both AB and BC calculus, and passed both AP tests with a five. I did see many other students struggling with the class not because they didn’t understand the theory, but because they were unable to perform the basic math operations. Everyday Math had crippled their basic math skills, and those are critical foundations for higher-level math.

Mrs. Wilson, you say that parents should help their kids review math, and I agree with you there. But the sad truth is, many parents don't care. The majority of students receive instruction solely in the classroom, and never receive the benefits that your daughters received. You should not focus on problem solving skills and "higher level thinking" if it prevents the students from actually learning any math. Removing Everyday Math from everyday usage is one of the best things possible for DISD's math scores.

Mrs. Wilson's comment:

my daughters 3rd grade teacher who has taught for over 25 years likes this book because it encourages higher level, multiple step thinking. People complain their kids aren't memorizing multiplication tables. Heres an idea for you, practice them at home with your child.

This comment is revealing, and wrong on every count:

• It assumes that learning = memorizing & teaching = one-on-one flash card practice
  
• It assumes that some content is "beneath" teachers and should be farmed out to parents who are also, presumably, beneath teachers
• It assumes that teaching a child the multiplication tables is in all cases a simple and easily accomplished task
  

I wish to heck I could find the post quoting a Soviet teacher on the precision methodology and timing they followed for teaching the times tables.

Since I can't, I'll quote the National Math Advisory Panel, which says that "most" American children do not achieve "fast and efficient retrieval of facts." (January 11, 2007 meeting)

It is not a simple matter to teach many children their math facts, nor is it a simple matter to "practice" successfully at home. My own efforts with flash cards came to naught; I was lucky enough to stumble onto the fact that, at least for my own child, worksheets were what was needed. I have since heard the same story from other parents.

And, in the n of 2 category, I've spoken with two parents of math-disabled adult children who tried and failed to teach the math facts at home. Both were educated and intelligent women; their kids are intelligent, too. No learning problems, no behavior problems, no ADD. One of the two scored a 780 on his SAT-V.

Remediating a bad math program at home is an extremely difficult proposition.

A good teacher is far more effective than the most intelligent and dedicated parent.

place value makes the "short list"

cross-posted to Beyond TERC:

terrific post on place value:

Place value is one of those things non-mathematically trained grownups tend to take for granted (at least, I did).

The Singapore Math series teaches place value year after year. Singapore Math has a "true" spiral curriculum in that kids learn to mastery in year one, then study the same topic in more depth in year two and master that material, too, then study the same topic in still greater depth in year three and, again, master the material. Place value is one of the spiraled topics.

I didn't quite understand this, even though Christopher's brilliant 5th grade teacher (I don't use the term "brilliant" lightly) told me how important the topic was. She said she'd asked her friend, who had a Ph.D. in math education, what were the most essential & fundamental topics for K-5 kids to master.

He said "place value."

I wish I could remember what Ed said about it the other day. We were talking about some "guess and check" problem-solving situation that was supposed to be a model of higher order thinking.

Ed said, "The way these kids are solving the problem shows they don't understand place value, and if they don't understand place value they don't have conceptual understanding."

One of the things that would be SOOOO helpful to parents like me (to most parents, that is) would be to have a list of the CORE topics you MUST make sure your child knows.

For instance, the other day Vicky said that decimals aren't as important as fractions.

I sort-of knew that already, but only because I've spent 2 1/2 years of my life immersed in K-12 math & math education. But, otoh, I didn't know it with conviction.

Most parents can't teach math on the side; even parents who have the capability to teach math on the side are going to find that their kids won't cooperate past the age of 10. (You can still teach a middle school child on the side - I've done it - but the amount of time you have to spend wrangling with them to get their attention steeply reduces the amount of time on task.)

What we need is a short list of THE essential skills our kids MUST have.

My list, so far, is:

• fractions

• place value

• long division
  

• measurement
  

from Lynn:

• automatic recall of basic facts

from independent george:

• order of operations
  

• properties of arithmetic

from instructivist:

• In addition to total mastery of math facts, I would put equivalent fractions on top of the list. Equivalent fractions directly leads to an understanding of proportions, percentages and all the other good stuff (scaling, unit rates...)

from Mr. Person:

I've had a list for a long time of core concepts/skills that are emphasized at each grade level.

1: Place Value
2: Addition/Subtraction Facts
3: Multiplication/Division Facts
4: All operations with whole numbers
5: All operations with fractions
6: Ratios and proportions

from Susan J:

Estimation.

Common sense. (Such as if you subtract a positive number the result should be smaller.)

[question: do the reform math programs do a decent job with estimation and common sense? do we know?]


update: it strikes me that the list already exists. It's the TOC for the Primary Mathematics series.

I'll pull it & post.

Fifth Grade Everyday Math Roundup

The school year is over (private school) and my son brought back the remains of his Study Links and Student Math Journal, Vol 2. Here are my comments.


1. There are a lot pages left undone. In the Math Journal, from page 260 to the end of the book (page 445), they did about ten pages. In the Study Links workbook, 40 percent of the pages aren't done. They ran out of time. The teacher said so, but also told parents that she thought the kids were all developing well with their critical thinking abilities. There is always the problem (with any curriculum) that the schools don't do what they are supposed to do. In my son's class, the teacher had to deal with students who didn't know their basic math facts. However, a good deal of blame can be placed on the lack of practice in Everyday Math. The school likes to put the blame on the kids, especially when they see some kids doing well.

Unfortunately, I can see them screwing up Singapore Math.


2. Singapore 5A and 5B workbooks add up to 208 pages. Everyday Math Study Links is 273 pages which are one-sided so that they can be torn out. This is really 137 pages. Singapore Textbooks total 192 pages. Everyday Math Student Math Journal is 445 pages! How can so much more seem like so much less? Easy. Too much superficial coverage and too little mastery of important skills. To be successful, a curriculum has to be carefully planned out for the 180 day school year. It seems to me that the developers of Everyday Math knew that few schools could ever get through the entire workbooks, but they knew it would look good in the curriculum review process.


In the Math Journal:

Page 265 has 11 questions on multiplying fractions. Not done.
Page 266 and 267 has 8 questions on multiplying fractions. Not done.
Page 269 has 8 questions on multiplying fractions. Not done.
Page 270 has 8 questions on multiplying fractions. Not done.
Page 271 has 10 questions on multiplying fractions. Not done.
Page 275 has 10 questions on multiplying fractions. Not done.
Page 278 has 7 questions on multiplying fractions and mixed numbers. Not done.

You get the idea.

Is this the fault of the school or the curriculum? Both? Plausible denial on both sides? Blame the kids?

It seems to me that it's easier to screw up Everyday Math. They are telling teachers that coverage is more important than mastery. The curriculum advisor talked about a new version of Everyday Math that emphasizes more practice. How do they do this? Do they cut down on the number of topics? Will they tell teachers which sections to skip if they run out of time?
Unfortunately, you can't just do what I suggest and compare workbooks side-by-side. Everyday Math will always look better in theory than in practice. I think they know that.


3. In spite of the many more pages in Everyday Math, they are behind in the important math skills that lead to algebra. Even if you take out all of the less important pages of EM, they are still behind. Perhaps one could take a big red edit pen to Everyday Math and trim it down to something that looks more like Singapore Math, but it would still be less.


4. I see absolutely nothing in Everyday Math that provides more understanding or critical thinking development than Singapore Math. There is nothing special about their explanations. There is little discovery. EM might have kids look for patterns, but this can be a hindrance as much as it can be a help. One could always trade off speed and amount of coverage for more understanding, but that's not possible unless you skip a lot of important material. That's a separate issue.

Singapore is Working--last chance to buy your CWPs

We switched to Singapore math in January.  I've seen a big improvement in my daughter's mathematical thinking since the switch.

We hadn't even gotten to multiplication yet, when a few months ago I asked her on a whim, how much is four 4's?  She came back with 16 very quickly.  

I asked her how she knew, and she said I'd taught her.  I said, "I did, how?"

She replied, "You taught me that 4 + 4 = 8 and 8+ 8 = 16."

We have since done a bit of multiplication, but I'm still impressed.  Seeing the program being used makes me realize even more how different it is, and how well designed it is.  It doesn't look that different until you really scrutinize it, and its full worth doesn't come out until you have used it.  It is even more apparent how well it works if you used a regular math program first. 

I just bought all 6 years worth of Challenging Word Problems, as CassyT posted, they are being discontinued soon.  I also bought next year's 2nd grade math.

After last summer's exodus of math facts from the brain, this summer we're  doing Right Start math games a few times a week to keep the math facts from jumping out of the brain and running off somewhere.  It is a fun way to review math facts, we're enjoying it so far!

Allison on Math Nights

MSMI has done several parent math nights.

When we are asked to give a math talk by a school and it is well attended, it is because the parents are upset. If it is very well attended, it is because the parents are in an uproar about the math program.

Since we generally are going in to fix the math program, or to support a math change to it, our goal is first to name the problem. We explain the issue (nationally, not just locally, not just here, wherever we are, but nationally) is that US curricula are not preparing kids for algebra. We tell parents what they know intuivitely but can't name. We tell them what they've watched their older kids suffered through. Then we explain we need to change what we teach, when we teach it, and what the teachers know about the maththey teach to fix it. When we are done, generally, parents calm down and give us the benefit of the doubt.

Usually, the second math night (a followup) has 1/4 of the turnout the first one had.

If a math night has no attendees, it is because math is doing just fine--the parents are concerned about some other problem.

Parents don't have time to go to meetings if things are fine. They go to indicate their disapproval or their concern.

We also found if the *children* put on the math night, as one of the grade night programs, it is well received--so if we want parents to learn about the math program, learn the games to practice math facts, etc. then it needs to be a child-centered event. Parents come when kids put on a math carnival. They even enjoy it. It does not need to be fuzzy math--kids LOVE stumping their parents at mental math calculations and bar modeling.

We tell parents what they know intuivitely but can't name.

Knowing intuitively that something is amiss: this is the chronic problem parents face. You know something--your cognitive unconscious knows something, rather--but you can't name it.

I remember, when I first became politically engaged here, living in a state of chronic anxiety that a) I didn't know what I was talking about and b) I was about to be publicly called out on not knowing what I was talking about. I spent hours Googling and reading, and reading and Googling, to make sure everything I said and wrote in my district had already been said and written by someone who did know what they were talking about.

Kitchen Table Math was incredibly important to that effort. I wrote posts to put into words what my cognitive unconscious already knew (or suspected), and I said nothing, in district, without ktm commenters vetting it first.

Funny thing: at some point I stopped feeling anxious, and I stopped obsessively fact-checking myself.

I hadn't become an expert on math or math instruction or public schools in general, but somehow I knew enough to feel confident that anything I said -- even something I said off the top of my head -- would be in the realm. Which it generally was.

I also, and I hesitate putting this in print, developed a sense of how thin my adversaries' knowledge was. That's not a criticism. Administrators can't possibly know everything about every subject (that's the problem with central administrators choosing math curricula), and an administrator who went to ed school before constructivism was in full bloom may not actually know that much about the doctrine and its history, however committed s/he may be to "rolling out" one constructivist initiative after another.

In short, at some point it dawned on me that I could pretty much say whatever I wanted and get away with it. I could get sloppy and no one would know but me.

That came as a bit of a shock.

I see politicians and pundits differently now.

Politicians and pundits are churning out an awful lot of content.

How often do they actually know that what they're saying is true?

How much fact checking happens in politics?

I'm guessing not too much.

Taming the Math Perfectionist

(I was going to make this a comment on another post but it got so lengthy and unwieldy that here I am making it a full-on independent post. Pardons.)

Speaking of perfection/distraction/panic/etc, we've finally made a bit of headway with a problem we've been having at our house for some time: my daughter is a pretty bright girl, enough that, well, I really haven't had to teach her anything yet. (My son, I teach; my daughter, I expose and she just does it.)

The dark side to this behavior is that if she comes across something she doesn't just "get" immediately, she shuts down and panics.

[[Small digression for background:

We cruised through Singapore 1 with no hiccups, and I put the brakes on Singapore 2 when it was clear (starting multi-digit addition/subtraction) that she didn't have her single digit facts down cold enough yet. That didn't seem to bother her because while she didn't have immediate recall of the facts, she certainly "got" simple addition, it wasn't a conceptual issue for her. We spent a couple of months working through just Math-U-See Alpha which is nothing but hammering well-grouped math facts until she made significant progress. We're starting back to Singapore 2 tomorrow morning, in fact.

OK, enough digression.]]

A. happens to greatly enjoy computer games, so while we were hitting the math facts hard, I spent some time looking at various math practice sites for her. I ended up giving Math Whizz (based in the UK) a try and we had a bit of a break-through with it.

It started with an evaluation, in which I told her that it was (by definition!) going to ask her questions that she could not answer, because it had to know at what point she could no longer answer questions. She freaked out a little when it got to multiplication and asked me for help, I told her I couldn't help her because that would goof things up -- if it thought she knew multiplication well, then it would be giving her even harder multiplication that she definitely couldn't do. We talked about the fact that she was required to fail in order for it to work. She eventually got used to this idea.

Then, later when the assessment was all over, she was doing one of the lessons which was something she was "sure" she couldn't do and she panicked, asking me how she could get out of it. I came over and said:

"Well, let's take a look at this. You know if you get the wrong answer, it'll just give you slightly easier stuff next time, so no big deal."

"OK, let's just put in all zeroes!"

"Well, sure, we could do that, but let's see if we can get as far as we can with this, and then maybe it can see *how* we got it wrong and use that information to figure out what you need practice with."

So, I left her alone to Fail With Style ... and wouldn't you know she got most of the questions right. When freed to "get them all wrong" because the system needs her to fail if she doesn't understand it, the stress and panic went away, and she went on to figure 8 of 10 of them out. And she was excited by that, instead of freaking out that it wasn't 10 out of 10. (It was 3 digit subtraction with regrouping, which we sure haven't covered officially yet. And, now that I think about it, I'm a little mind boggled that she placed high enough for them to try that in the first place. Hmm.)

I've been worried about what was going to happen once we started hitting things that she just didn't "get" immediately because it was bound to happen at any point and, before, it would have been a disaster for her. I am currently ... cautiously optimistic.

Effective Mathematics Instruction The Importance of Curriculum

I found a nice little study comparing a fourth grade Direct Instruction math program with a well regarded fourth grade constructivist program. The results were surprising, to say the least. (Cross posted at D-Ed Reckoning.)

The study Effective Mathematics Instruction The Importance of Curriculum (2000), Crawford and Snider, Education & Treatment of Children compared the Direct Instruction 3rd grade math curriculum Connecting Math Concepts (CMC, level D) to the constructivist fourth grade math curriculum Invitation to Mathematics (SF) published by Scott Foresman.

Invitation to Mathematics (SF)

SF has a spiral design (but of course). and relies on discovery learning and problem solving strategies to "teach" concepts. The SF text included chapters on addition and subtraction facts, numbers and place value, addition and subtraction, measurement, multiplication facts, multiplication, geometry, division facts, division, decimals, fractions, and graphing. Each chapter in the SF text interspersed a few activities on using problem solving strategies. Teacher B taught the 4th grade control class. He was an experienced 4th grade math teacher and had taught using the SF text for 11 years.

Teacher B's math period was divided into three 15-minute parts. First, students checked their homework as B gave the answers. Then students told B their scores, which he recorded. Second, B lectured or demonstrated a concept, and some students volunteered to answer questions from time-to-time. The teacher presentation was extemporaneous and included explanations, demonstrations, and references to text objectives. Third, students were assigned textbook problems and given time for independent work.

The SF group completed 10 out of 12 chapters during the experiment.

Connecting Math Concepts (CMC)

CMC is a typical Direct Instruction program having a stranded design in which multiple skills/concepts are taught in each lesson, each skill/concepts is taught for about 5-10 minutes each lesson and are revisited day after day until the skill/concept has been mastered. Explicit instruction is used to teach each skill/concept. CMC included strands on multiplication and division facts, calculator skills, whole number operations, mental arithmetic, column multiplication, column subtraction, division, equations and relationships , place value, fractions, ratios and proportions, number families, word problems, geometry, functions, and probability. Teacher A had 14 years of experience teaching math. She had no previous experience with CMC or any other Direct Instruction programs. She received 4 hours of training at a workshop in August and about three hours of additional training from the experimenters.

Teacher A used the scripted presentation in the CMC teacher presentation book for her 45 minute class. She frequently asked questions to which the whole class responded, but she did not use a signal to elicit unison responding. If she got a weak response she would ask the question again to part of the class (e.g., to one row or to all the girls) or ask individuals to raise their hands if they knew the answer. There were high levels of teacher-pupil interaction, but not every student was academically engaged. Generally, one lesson was covered per day and the first 10 minutes were set aside to correct the previous day's homework. Then a structured, teacher-guided presentation followed, during which the students responded orally or by writing answers to the teacher's questions. Student answers received immediate feedback and errors were corrected immediately. If there was time, students began their homework during the remaining minutes.

The CMC group completed 90 out of 120 lessons during the experiment.

The Experiment

Despite the differences in content and organization, both programs covered math concepts generally considered to be important in 4th grade--addition and subtraction of multi-digit numbers, multiplication and division facts and procedures, fractions, and problem solving with whole numbers.

Students were randomly assigned to each 4th grade classroom. The classes were heterogeneous and included the full range of abilities including learning disabled and gifted students. There were no significant pretest differences between students in the two curriculum groups on the computation, concepts and problem solving subtests of the NAT nor on the total test scores. Nor did any significant pretest differences show up on any of the curriculum-based measures.

The Results

Students did not use calculators on any of the tests.

The CMC Curriculum Test

For the CMC measure the experimenters designed a test that consisted of 55 production items for which students computed answers to problems, including both computational and word problems. The CMC test was comprehensive as well as cumulative; problems were examples of the entire range of problems found in the last quarter of the CMC program. Problems were chosen from the last quarter of the program because the various preskills taught in the early part of the program are integrated in problem types seen in the last quarter of the program.

The results here were not surprising, although the magnitude of the difference between the two groups may be.

The SF class averaged 15 out 55 (27%) correct answers on the posttest up from 7 out of 15 correct on the pre-test. The CMC class averaged 41 (75%) correct on the posttest up from 6 out of 15 correct on the pretest. I calculated the effect size to be 3.25 standard deviations which is enormous, though biased in favor of the CMC students.


The SF Curriculum Test

The SF test was published by Scott, Foresman to go along with the Invitation to Mathematics text and was the complete Cumulative Test for Chapters 1-12. It was intended to be comprehensive as well as cumulative. The SF test consisted of 22 multiple-choice items (four choices) which assessed the range of concepts presented in the 4th grade SF textbook.

The SF class averaged 16 out 22 (72%) correct answers on the posttest up from 4 out of 22 correct on the pre-test. However, surprisingly the CMC class averaged 19 (86%) correct on the posttest up from 3 out of 15 correct on the pretest. I calculated the effect size to be 0.75 standard deviations which is large, even though the test was biased in favor of the SF students.

You read that right, the CMC students out performed to SF students on the SF posttest.

The NAT exam and math facts test

The CMC group also scored significantly higher on rapid recall of multiplication facts. Of 72 items, the mean correctly answered in 3 minutes for the CMC group was 66 compared to 48 for the SF group for the multiplication facts posttest. I calculated the effect size to be 1.5 sd.

Posttest comparisons on the computation subtest of the NAT indicated a significant difference in favor of the CMC group. Effect size = 0.86. On the other hand, neither the scores for the concepts and problem-solving portion of the NAT nor the total NAT showed any significant group differences. The total NAT scores put the CMC group at the 51st percentile and the SF group at the 46th percentile, but this difference was not statistically significant.

Discussion

The CMC implementation was less than optimal, yet it still achieved significantly better performance gains compared to the constructivist curriculum. The experimenters noted:

We believe this implementation of CMC was less than optimal because (a) students began the program in fourth grade rather than in first grade and (b) students could not be placed in homogeneous instructional groups. A unique feature of the CMC program is that it's designed around integrated strands rather than in a spiraling fashion. Each concept is introduced, developed, extended, and systematically reviewed beginning in Level A and culminating in Level F (6th grade). This design sequence means that students who enter the program at the later levels may lack the necessary preskills developed in previous levels of CMC. This study with fourth graders indicated that even when students enter Level D, without the benefit of instruction at previous levels, they could reach higher levels of achievement in certain domains. However, more students could have reached mastery if instruction were begun in the primary grades.

Another drawback in this implementation had to do with heterogeneous ability levels of the groups. Heterogeneity was an issue for both curricula. However, the emphasis on mastery in CMC created a special challenge for teachers using CMC. To monitor progress CMC tests are given every ten lessons and mastery criteria for each skill tested are provided. Because of the integrated nature of the strands, students who do not master an early skill will have trouble later on. Unlike traditional basals, concepts do not "go away," forcing teachers to continue to reteach until all students master the skills. This emphasis on mastery created a challenge for teachers that was exacerbated in this case by the fact that students had not gone through the previous three levels of CMC.

Why didn't the CMC gains show up on the NAT problem solving subtest and total math measure? The experimenters opine:

Our guess is that a more optimal implementation of CMC would have increased achievement in the CMC group, which may have shown up on the NAT. In general, the tighter focus of curriculum-based measures such as those used in this study makes them more sensitive to the effects of instruction than any published, norm-referenced test. Standardized tests have limited usefulness for program evaluation when the sample is small, as it was in this study (Carver, 1974; Marston, Fuchs, & Deno, 1985). Nevertheless, we included the NAT as a dependent measure because it is curriculum-neutral. The differences all favored the CMC program.

That no significant differences occurred either between teachers or across years on the NAT should be interpreted in the light of several other factors. One, the results do not indicate that the SF curriculum outperformed CMC, only that the NAT did not detect a difference between the groups, despite the differences found in the curriculum-based measures. Two, performance on published norm-referenced tests such as the NAT are more highly correlated to reading comprehension scores than with computation scores (Carver, 1974; Tindal & Marston, 1990). Three, the NAT concepts and problem solving items were not well-aligned with either curriculum. The types of problems on the NAT were complex, unique, non-algorithmic problems for which neither program could provide instruction. Performance on such problems has less to do with instruction than with raw ability. Four, significant differences on the calculation subtest of the NAT favored the CMC program during year 1 (see Snider and Crawford, 1996 for a detailed discussion of those results). Because less instructional time is devoted to computation skills after 4th grade, the strong calculation skills displayed by the CMC group would seem to be a worthy outcome. Five, although the NAT showed no differences in problem solving skills between curriculum groups or between program years, another source of data suggests otherwise. During year 1, on the eight word problems on the curriculum-based test, the CMC group outscored the SF group with an overall mean of 56% correct compared to 32%. An analysis of variance found this difference to be significant...

And, here's the kicker. The high-performing kids liked the highly-structured Direct Instruction program better than the loosey goosey constructivist curriculum:

Both teachers reported anecdotally that the high-performing students seemed to respond most positively to the CMC curricula. One of Teacher A's highest performing students, when asked about the program, wrote, "I wish we'd have math books like this every year.... it's easier to learn in this book because they have that part of a page that explains and that's easier than just having to pick up on whatever."

It may be somewhat counter-intuitive that an explicit, structured program would be well received by more able students. We often assume that more capable students benefit most from a less structured approach that gives them the freedom to discover and explore, whereas more didactic approaches ought to be reserved for low-performing students. It could be that high-performing students do well and respond well to highly-structured approaches when they are sufficiently challenging. These reports are interesting enough to bear further investigation after collection of objective data.

Allison and Palisadesk on high-SES versus low-SES kids and schools

ALLISON:

Here in the Twin Cities, we are experiencing multiple and opposing forces at the same time.

Hainish, I see some low-SES kids in private schools here that are worse off than if they were in high performing low SES schools. The rest of the school is barreling along doing discovery math, and these kids have no chance to learn. High SES kids are eventually tutored privately, but low SES kids aren't. It is more noticeable in reading, where these kids get no phonics instruction, but the high SES kids eventually get IEPs and massive services to support terrible reading comprehension.

But, they are better off than being in Minneapolis public schools, where they would get no phonics and TERC investigations.

Plenty of low SES charters here are a total disaster. they may not be quite "guide on the side" but the teachers largely have no idea content matters. So there are no drills in math, no sense of what must be known year to year. No urgency.

Another big factor I see here is the "school expects home to teach math facts, but forgets to tell home that." A typical example for me is parents are shocked to find out their 4th grader is not competent at multiplication, and teacher is recommending summer school. They come to me to ask what is going wrong, and how do they help their child. Among other things, I suggest they ask teacher "how many minutes a day is spent on math facts in class?" They do, and receive the response "none".

Meanwhile, I see other schools where the parents are involved but to negative effect. In another typical example, the parents provide a steady steam of complaints if their child is not getting an A. This encourages group work and discovery learning, rather than tests that can be graded.

PALISADESK:

HAINISH: "Palisadek, if you are correct, then low-SES students in high-SES-area schools should be worse off than those in low-SES schools."

I think this may well be true, for several reasons. As Allison explained, the low-SES kids don't have the outside tutoring/afterschooling etc. that higher-income families routinely provide, and they tend (this is a generalization) to respond poorly to unstructured learning situations, which much "group work" and "exploratory learning" seems to be. They haven't got the resources at home or school to do artsy projects, may not have access to a computer or the Internet (or even a telephone!) at home, may have other responsibilities after school, not be able to afford field trips and school clubs/sports etc.

A previous school I worked at was in a neighborhood separated by a large city park from a very wealthy area of manicured million-dollar homes. The school for that neighborhood served these very affluent families, who comprised most of the enrollment, but on the edge of the neighborhood, bordering a freeway, there was a smallish public housing project. The children there also attended this school. So you had the very poor and the extremely rich. The school got allocated some extra special education staff for the "project" kids, but both socially and academically those children were isolated and tended to be academically unsuccessful. A top teacher from my school transferred there a few years ago and tells me that the great divide is still present, and the school does not have the kind of supports low-SES kids need.

For example, at my school the library has been kept open after school for parents and children to come in and use the computers for research, skill practice, homework and so on. Even though math facts are taught, many children need much more practice than can be given in class; we recommend some online sites for practice and pay for some sites where children can practice reading skills online (about 40% of our students have internet at home). Teachers also provide tutoring and support over the lunch hour and run academic clubs like math clubs and spelling clubs to reinforce basics in an engaging way.

Upper-income schools don't, in my experience, provide this kind of thing. Their students are leaving after school for Little League, swimming, horseback riding and gymnastics. Our students are leaving to care for younger siblings or help mom and dad at the bakery.

Adding to the difficulty is the fact that the lower-SES parents feel uncomfortable in a milieu of affluence (less so if it is a mix of working poor and working class), so parents aren't as involved in the school as they would be in one that was more reflective of their own social station.

One benefit, we do get away with a lot of direct teaching (phonics included) even though it is less than optimal. I compared my school's test results with those of one near my home, which has a median family income of 250K (I live on the poor side of the highway, LOL). My school roundly trounced this school, despite being 60% ESL and 95% nonwhite. Test results are only one indicator, but it does show that our kids are learning and we hope they will have a chance to make their way in the world.

John Saxon on the need for speed

Rapid and accurate recall of basic facts and skills dramatically increases students' mathematical sbilities. To that end we have provided the Facts Practice Tests. Begin each lesson with the Facts Practice Test suggested in the WarmUp, limiting the time to five minutes or less. Your student should work independently and rapidly during the Facts Practice Tests, trying to improve on previous performances in both speed and accuracy.

Each Facts Practice Test contains a line for your student to record his or her time. Timing the student is motivating. Striving to improve speed helps students automate skills and offers the additional benefit of an up-tempo atmosphere to start the lesson. Time invested in practicing basic facts is repaid in your student's ability to work faster.

After each Facts Practice Test, quickly read aloud the answers from the Saxon Math 8/7 Homeschool Solutions Manual as your student checks his or her work. If your student made any errors or was unable to finish within the allotted time, he or she should correct the errors or complete the problems as part of the day's assignment. You might wish to have your student track Facts Practice scores and times on Recording Form A, which is found in this workbook.

source:
Facts Practice Tests and Activity Sheets
Saxon Math Homeschool 8/7 Tests and Worksheets
Saxon Math Homeschool 8/7 ($18.50 at Rainbow Resource)

Yes!

I do wish!

Until I figure out celeration charts, Recording Form A will do nicely.


Facts Practice Tests - Saxon 8/7:

A multiplication
B equations
C 30 improper fractions and mixed numbers
D 40 fractions to reduce
E circles
F lines, angles, polygons
G fractions
H measurement facts
I proportions
J decimals
K powers and roots
L fraction-decimal-percent equivalents
M metric conversions
N mixed numbers
O geometry
P integers
Q percent-decimal-fraction equivalents
R area
S scientific notation
T order of operations
U two-step equations
V algebraic terms
W multiplying and dividing in scientific notation

Is Your Student Being Taught "Fuzzy" Math

Parents may wonder if their student's math curriculum is "fuzzy" math. Here are some general identifying marks of "fuzzy" math:

1. Very little practice (You might have someone tell you that new studies show that too much drill kills interest in math. That is not true -- it makes students efficient and confident.) Lack of pencil and paper work -- in the "fuzzies' minds it's bad to do a lot of pencil and paper work.
2. Individual problems on the homework are not actually graded. Students are given credit if they show that they "tried" to do it. It doesn't even matter if they successfully solved the problem.
3. Calculators are used to do what children should be learning to do mentally. Some people may even be so bold as to claim that there are students who will never learn all of these math facts anyway. Calculators are said to be sufficient.
4. (Almost exclusively) student-centered activities. Students work in groups to figure out something, and the teacher may not even be involved at all.
5. There will be little or no instructions, certainly no explicit instructions. Activities are student directed and teacher input is lacking. Students are sent home to figure it out by themselves and the next day the class is asked by the teacher if there were any questions.
6. "Real world math" is what it's all about. It's one of the buzz words. After all, who doesn't want students prepared for the "real world".
7. Students are told to write paragraphs explaining all of the steps that are used to solve the problem. Or students are expected to write about how they feel about math. Or as Walter Willaims referenced, students write on such topics as "If Math were a color, what what that be?" In other words, students are writing their math. So much for the benefit of symbols and digits to help solve a problem efficiently, in the least amount of time.
7. Math books are huge, thick books, and pages are filled with visual "clutter" which distracts students' thoughts. (For some "adhd" or "add" students, these pages can be a disaster. It is no wonder it takes them 50 minutes to do a 15 minute assignment.) There is a lot of "non-math" content such as photographs in color and motivational stories which are meant to "inspire" kids to greatness, I suppose, but which have no place in the middle of a math assignment.
8. Patterns, patterns, patterns. Looking for patterns, drawing patterns. Probability will be prevalent by 4th or 5th grade. And much time spent on data analysis projects (finding the mode, the mean, the median) starting in elementary school. What is appropriate for a high school course is inappropriate for elementary children. The time spent on one "projects" may be days and will indeed use lots of pencil and paper. Notice here: It's OK for them to do pencil and paper work. It's just not OK for me or you to do pencil and paper work on traditional math practice.
9. And here's one dead give-away that the curriculum takes a "fuzzy" math approach:
Students are given problems in one lesson, for which they are not at all prepared. Students spend much, much time on these problems, only to discover that the concept is taught a lesson or two later So if your student has no idea what is being asked, look ahead and you'll probably find that the concept is coming up. This is called "discovery learning" because students have a wonderful opportunity to "discover" the concept on their own. Imagine your 4th grader being forced to "discover" how to do long division with no input from anyone else!!

I'm sure there are more I've overlooked. One more that is obvious. Your student is (perhaps suddenlyl) discouraged, thinks he/she is not smart, gives up trying. I know one student who had been in my 5th grade class and was an excellent and a very diligent student. What didn't come naturally, she learned by shear determination and perseverance. How sad I was to hear that she was threatening to kill herself because her high school math was so hard for her and she didn't think she was ever going to get it. Her teacher's approach was to assign the algebra/geometry lesson, forcing the students to teach themselves, and then ask if any of the stusdents had any questions or problems. If there were no questions, they proceeded on to the next lesson.)

So, do any of these ring a bell to you? Well, if so, you must rescue your student as fast as possible. Go to Kitchen Table Math for insights into two parents who faced similar situations and successfully helped their students.

a theoretical mathematician evaluates constructivist math

This statement, from a theoretical mathematician, was first posted to the Bridgewater-Raritan Parents Math Forum.

I am a theoretical mathematician (Ph.D. UCLA 1996), who taught as an Adjunct Assistant Professor at UCLA for 2 years ('96-'98), and then as an Assistant Professor at Illinois State University (ISU) for 4 more years ('98-'02). In addition to my experience teaching college math and computer science, through interaction with many of my colleagues at ISU I became well-versed in issues of Mathematics Education. (ISU has one of the largest Math Ed. programs in the country.) In fact, many of my fellow faculty were involved in drafting the NCTM standards, both past and present.

Both my daughter (eighth grade) and my son (fourth grade) have used EDM exclusively for their in-school math instruction. As a mathematician I find the program abysmal, and I know that I am not alone (amongst mathematicians and others) in this assessment.

Let me share with you a portion of an email that I sent to our local (Hollis, NH) school board. This should serve to encapsulate (at least in part) my position on EDM.

As you could tell, I am passionately opposed to the use of Everyday Math (EDM). My experience with it, both personal and professional, has been uniformly negative. I also have large amounts of anecdotal evidence that confirms that the only way our kids learn any math while using EDM in school is when parents become frustrated and just teach them math the "old fashioned" way.

What I object to is the "Emperor's New Clothes" syndrome: everybody telling me how great this program is, but there being absolutely no evidence that it provides any benefit at all. What is particularly telling are the words and phrases that its advocates use: "It makes math more enjoyable," or "The kids really like the games." Of course they do!

What I believe has happened is that the teachers have been sold a bill of goods: most elementary and middle school teachers, while being dedicated and tireless in their devotion to wanting to teach our children, have not received adequate training in mathematics. (This I can attest to from first-hand experience; I once taught Calc I to a group of students destined to be "math teachers." I failed half of them (many couldn't do high school algebra). What was particularly disturbing was the fact that failing my class did not dissuade them from wanting to be teachers, it merely "redirected" them: without passing Calculus they simply could no longer be Secondary (i.e., High School) math teachers; Calculus, it seems, wasn't required for Elementary or Middle School (math) teachers.)

Hence, when a program (endorsed by "experts") comes along and tells them that they can do a better job teaching math by having the kids participate in group activities, making it "relevant" to their "everyday" lives, the teachers rush to adopt it: who wouldn't? However, the hard yet honest fact is that math is difficult, and requires work, dedication and perseverance to master. As Euclid said, "There is no royal road to mathematics."

But beyond all this, what troubles me most is the fundamental philosophical flaw in EDM: It ignores the core beauty and power of mathematics, viz., that it is an edifice constructed out of pure reason, all of whose inferences and deductions flow logically and unarguably from more basic facts. EDM asks the students to flit willy-nilly from room to room or even floor to floor in this structure, without ever exposing them to the skeleton, the underlying architecture.

The basic premise of EDM, so much so that its part of its name, that math should be valued or appreciated only insofar as it can be applied to "everyday things," is worse than misguided, it is a lie promulgated by people who, quite frankly, don't understand the first thing about mathematics. (Example: Do we study "Everyday English Literature?" Why do we still read Shakespeare? Are people really worried about being encountered by three old women stirring a big pot, and wanting to know how to deal with them?)

Let me recount for you what I used to tell all my students the first day of class: Being in a (math) class is like buying a membership to Gold's Gym. If you come to class, sit passively by, and then complain that you didn't learn anything, that you just don't "get it," that is akin to walking into the gym a month after you bought your membership and complaining that you haven't gotten any stronger, even though you come to the gym everyday and watch people work out. Being in a class, or in school, provides only the opportunity to learn, the teacher is there to facilitate the learning process, but the effort must emanate from the student.

In short, the "guided instruction" methodology, however well-intentioned, is in fact, "misguided": Imagine paying a tennis or golf pro to help improve your game, only to have her tell you to "try and discover the right method to strike the ball on your own." You would be justifiably outraged; you pay someone who is a better tennis player / golfer than you to teach you the right way to do it. Human minds are not designed to do math (unlike, say, to learn language); they need to be taught the right way to do it."

I hope that it comes through in what I have written that I am not blaming the teachers. In my (admittedly limited) experience, many of them are similarly frustrated by having to adhere to an administration-mandated (math) curriculum that they neither support nor believe in. I have rarely met a teacher who is not extraordinarily dedicated to her students, and I absolutely do not want anything I say to be construed as being critical of the job that they do. My point here was merely to demonstrate that some teachers (as well as administrators, school board members, etc.) are insufficiently trained to evaluate properly the merit of their math curriculum, and so rely upon others (like the NCTM) to do so for them.

Tony Falcone, Ph.D

This passage is beautiful:

The basic premise of EDM, so much so that its part of its name, that math should be valued or appreciated only insofar as it can be applied to "everyday things," is worse than misguided, it is a lie promulgated by people who, quite frankly, don't understand the first thing about mathematics. (Example: Do we study "Everyday English Literature?" Why do we still read Shakespeare? Are people really worried about being encountered by three old women stirring a big pot, and wanting to know how to deal with them?)

The night before Tony's statement appeared on the B-R Mathforum I had been trying to explain to Ed why constructivist math, from the perspective of a real mathematician, isn't even math.

Of course, I can't really explain it, not off the cuff at any rate.

Then Tony's statement landed in my email queue.

We are all lucky to have it.

teaching math facts is brain surgery

Fast and efficient retrieval of facts: Declarative Memory

• Cognitive and learning mechanisms are understood

• Most children in the U.S. do not achieve this

• Interfere with problem solving in which facts are embedded

repeat:

most children in the U.S. do not achieve fast and efficient retrieval of math facts


I'm starting to think parents are underpaid.

source:
Learning Processes Group
January 11, 2007
New Orleans, LA
Whole Number Arithmetic
Math Panel Update

Contributing Members
Dave Geary, Task Group Chair
Dan Berch
Wade Boykin
Valerie Reyna
Bob Siegler
Jennifer Graban, staff

see also:
somewhere on another planet not my own

Notice for parents new to KTM

I thought a post might be good for parents new to KTM and this problem.

Kitchen Table Math exists because many K-8 schools don't ensure mastery of basic skills. Parents have to do the work at home. And, as one can see by other posts, it's not just a problem in math. Everyday Math, a common math curriculum, spirals through the same material each year in the hope that students at all levels will master the skills when they are ready. They assume that this works by definition. They tell teachers to keep moving and to "trust the spiral". It doesn't work.

One night long ago, I told my son to stop fooling around and do his EM math homework (from a workbook, not a textbook). Ten minutes later, I saw him doing other things and told him to do his math. He said it was already done. I looked at the workbook and saw only 4 easy problems. When I asked the teacher about this, she said that they will get a chance for more practice when they spiral back to the same material. They talk about how spiraling builds on previous knowledge and skills, but I saw only repeated partial learning. One parent complained that three of her kids were covering the exact same material and they were in three different grades. Either they knew the material already and were bored, or they were still confused.

Parents learn the hard way that it doesn't work. Many schools know that it doesn't work too because they send home blanket notes to parents asking them to work on "math facts". They must know that that some parents can't or won't. Unfortunately, this problem doesn't just stop at basic arithmetic. It continues with things like fractions, percentages, and solving equations. Parents are left reteaching their kids at home or with tutors. Some parents don't see this problem until 7th grade when their bright child gets placed into the "slow" math track. It's unlikely that the student will recover after that point. It could be an ability issue, but too many students respond well to curricula like Singapore Math (as with my son) at home or with tutors. KTM is loaded with examples of how parents had to help their kids.

When my son was in fifth grade, his teacher found bright students who still didn't know the times table. Some were still adding 7+8 on their fingers. She had to stop trusting the spiral to get students back up to speed. This caused her to skip 35% of the material that year, but the focus on mastery did work. However, she did not try to get the lower grade teachers to improve mastery of the basics.

This is not difficult material if mastery of basic skills is ensured starting in the earliest grades. However, the "trust the spiral" attitude pumps problems along until many gaps have built up and teachers can't possibly diagnose and address each one. That’s why Everyday Math includes things called "Math Boxes" to try to get students to fix themselves. This makes math seem much more complicated than it really is. Schools talk about critical thinking and problem solving, but they don't define them exactly and many students can't show them on state tests designed to match these teaching ideas. Those vague skills don't make up for a lack of mastery of the basics. The best students are the ones with the best mastery of skills.

Unfortunately, the new Common Core Standards won't force K-6 schools to fix the problems of mastery. The use of the word "fluent" in the standard is sparse and the word is undefined. The new tests, like PARCC, are unlikely to put much pressure on schools to achieve a level of mastery that will keep all career doors open in K-8. Kids will still be pumped along, and the onus for keeping kids on track will still rest with parents. My advice to parents is to not trust the spiral. You have to ensure that your kids master the material the first time starting in the earliest grades. You have to ask the school when and how they track in math. You have to ensure that learning gets done to meet this tracking decision. You have to realize that "proficient" is not nearly good enough. Even "exceeding expectations" might not be good enough. Schools will talk about how wonderful it is that they get so many kids over a low cutoff proficiency level, but this is not very meaningful for individual students. Many parents quickly figure out that their standards have to be much higher that the state standards. Schools care about statistics, but parents care about individuals. What’s good for schools is not necessarily what’s good for your child.