teachers say they cannot cope with needs of dyslexic children

(Cross-posted at D-Ed Reckoning)

As reported in the Independent:

The majority of state school teachers lack confidence in educating dyslexic pupils, a survey for Britain's biggest teaching union shows.

Fewer than one in 14 say they would be "very confident" in identifying a child with dyslexia while only 9 per cent say they would be "very confident" in teaching such a pupil. The survey, by the National Union of Teachers (NUT), reveals the vast majority believe they do not have enough training to deal with special needs children. (emphasis mine

My how quickly they give it. (And, by the way, that is a very unfortunate acronym.)

I'm not convinced that dyslexia is a legitimate disease or handicap or whatever the en vogue euphenism is today. I view dyslexia like the other bogus ailment "specific leearning disability"-- an educator created problem designed to excuse ineffective teaching ability.

I'll give you two good reasons:

1. The MRI evidence they're using to base the dyslexia theory on is bunk (pdf):

[T]he MRI scientists’ interpretation of brain-function data is what is logically referred to as a false dilemma or an argument from ignorance. The scientists observe a correlation between brain patterns and not learning to read.

The possibilities are:

1. The brain pattern caused the nonlearning.
2. The nonlearning caused the brain pattern.
3. The interaction of a third variable caused both the nonreading and the brain pattern.
   

These scientists apparently don’t consider possibilities 2 or 3, but proclaim that the brain pattern causes the nonlearning. There is no question that there are individual differences in reading performance; however, if the kid can find his way into the right classroom and follow simple directions, he can be taught to read in a timely manner.

2. When kids are taught effectively, the incidence of "dyslexia" drops dramatically:

If it’s true that students in places like the worst slums in Baltimore and rural Mississippi taught with DI have 100% of the children reading—not guessing or memorizing—by the end of kindergarten, something is seriously wrong with the portrait of dyslexia. After all, these students exhibit all of the “warning signs” referred to in the analysis. When they come into kindergarten, they can’t rhyme, they can’t alliterate, they can’t blend orally presented words, and they have lots of problems figuring out unique sound patterns (such as repeating something like 4, 4, 4, 4 and yet are able to repeat four or more random digits). So they should all be dyslexic, and indeed historical performance records show that virtually all of them had been greatly retarded in reading, with the average fifth grader stumbling about on a weak second-grade level. Some of the schools that currently have no nonreaders coming out of K historically had end-of-first-graders scoring at the 6–9th percentile on standardized achievement tests. Yet, the new science tells us that we can expect 1/5 of the population to have dyslexia. That’s a 20% failure rate to teach reading in a fat-cat suburb where parents care about and influence the schools, and where they are lavishly funded with aides, material, and whatever.

You might want to take a look at this article (pdf) as well.

While normal children look at a capital letter R and see R, dyslexic kids are purported to see (backwards R). Normal children see receive; dyslexic children see recieve. Very little of this screwed up perception would actually manifest itself very directly in reading. If a reader actually sees (backwards R)ed, for instance, that child is most likely to say /rred/. If the child “sees” (backwards R) and thinks it’s R that’s not going to cause a decoding problem. If a child sees (backwards R)eb, that could cause a decoding problem, but most letters, written backward, are just backward letters.

Similarly, if the only problem is that a reader looks at receive and “sees” recieve that alone isn’t going to cause any reading difficulty. Look at all the people who write recieve but who think they’ve spelled the word right, and can certainly read what they wrote.

the high cost of low teacher quality

Cross posted from Joanne Jacobs:

Education Sector's How Low Teacher Quality Sabotages Advanced High School Math is a must-read. Kevin Carey summarizes:

Students who take advanced math courses in schools that employ the fewest well-qualified teachers are far less likely to be adequately prepared for college, or to succeed in college, than students who take the same courses — or even less advanced courses — at schools with the most well-qualified teachers. Students who fail to take advanced courses do poorly across the board. But it turns out that simply enrolling students in more advanced classes isn't enough — you also need good teachers to teach them.

Illinois makes all 11th graders take the ACT. The llinois Education Research Council combined ACT scores and high school grades to rate each students' college readiness.

To create a Teacher Quality Index (TQI), researchers looked at factors correlated with effectiveness: graduation from a "more competitive" college, less than four years of teaching experience, emergency or provisional teaching credentials, one or more failures on the basic skills test for new teachers, composite ACT score and English ACT score.

Few students who took only algebra and geometry were ready for college regardless of their school's Teacher Quality Index. But TQI correlates with college readiness for students who completed advanced algebra, trigonometry and calculus.

Students who took Calculus in the lowest TQI schools were five times less likely to be well-prepared than students who took Calculus in the highest TQI schools. In fact, students who took Calculus in schools with a TQI below the 10th percentile had a lower preparedness rate (16 percent) than students who only took Algebra II in schools that were above the 25th percentile.

There is a confounding factor: Low-TQI schools tend to be high-poverty schools.

Low-income students, who face some of the greatest barriers to education, are much less likely to be taught by teachers with the best qualifications.

More than 90 percent of well-prepared students and 55 percent of least-prepared students enrolled in college. After three years, 10 percent of the top category and 41 percent of the lowest category had dropped out.

Take a look at the charts: At schools with a TQI in the lowest 11th-25th percentile, less than half of students motivated enough to tackle calculus are prepared to succeed in college. In the bottom 10 percent of TQI, fewer than 20 percent of calculus students are prepared.

weighted and relative GPAs: pros and cons

LynnG's article, Weighted GPA, confused me for a moment, until I realized that high schools were using the term, "weighted GPA" to mean something very different from the way universities use the term:

Our High School is proposing to change the way high school grade point average is calculated. We currently use a a weighted GPA scale that gives more "credit" to Honors and AP level courses. Honors and AP are graded on a 6.25 scale (an A+ gets a 6.25) and the non-Honors/AP courses use a 5.25 scale. Also, health and physical ed courses are not included in the GPA calculation.

The high school administration proposes to end this and grade all students on a single 4.0 scale that includes all graded courses (scooping in band, pe, health, maybe others). I'm on the fence on this because I really don't know what the pros and cons are and I am hoping maybe some of you out there might help clarify.

If I were an admissions officer (I am not), I would back the high school administration, if only because this sort of system, where schools can have different scales for different courses, would be a nightmare. However, making life easier for bureaucrats isn't necessarily the best reason for supporting a system (or not).

It seems that the biggest disadvantage of this sort of weighted system is that it is based solely on the designation of the course. Perhaps I'm being cynical (it's happened before), but I have seen enough "honors" courses at the university that were utter crap that the idea of giving a student a higher GPA solely because he was enrolled in an advanced course is pointless, at least without some objective way to judge the rigor of the course.

She brings up an excellent point here:

Here's what we've come up with so far -- the change would primarily affect the class "rank." By taking easier courses and getting an A, you'll get a better GPA and a better class rank than if you take AP and Honors courses and get a B. The kids graduating in that all important (is it?) top 10% might be those that avoid AP and Honors and take easier courses for a better grade. Would this new system penalize kids that stretch themselves in AP and Honors? Or do colleges really not care about GPA and class rank, caring much more about the courses on the transcript rather than the grades achieved?

The issue here, of course, is the existence of "easier" courses, but that's a series of books in itself, so I won't address it. Her point is valid, though: Will going to a flat 4.0 scale penalize students who take more difficult courses (assuming that they are, indeed, more difficult)?

Yes, this is a potential problem. One solution -- though not a perfect one, as I'll point out -- is to use what universities call a "weighted GPA" (I'll use the alternative "relative GPA" to avoid the confusion I originally experienced).

A relative GPA is relative to the mean GPA for the class (universities also assign relative GPAs to courses calculated relative to the overall mean GPA for all the courses in the department or school, in order to determine difficulty). The advantage of this (over the weighted GPA above) is that the relative GPA is not calculated as a function of class label, but the performance of all the students in the class. A relative GPA is, therefore, a real statistic, whereas a weighted GPA is not -- that is, a relative GPA is meaningful to an admissions officer (or a parent), because he can see not only what grade the student received, but also how well the student did relative to the other students in the course, while a weighted GPA is meaningless to an admissions officer, because he has no way of knowing whether the course was, in fact, advanced or more difficult beyond the certification of the student's school.

When relative GPAs are calculated and reported, they are always (in my knowledge) reported with the student's raw GPA. A relative GPA is essentially a curve, in the traditional (and not "raise my grade") sense of the term.

One way to calculate a relative GPA is to divide the student's raw GPA by the class mean GPA. Let's say we have three students, Hyung-Sik, Mary, and Tomoyuki, who receive As in three different courses, Organic Chemistry I, Introduction to Philosophy, and Overview of Ethnic Studies, respectively. If only raw GPAs are calculated and reported to the university, Hyung-Sik, Mary, and Tomoyuki will all receive As. But if the university uses relative GPAs, the grades reported for the three students will be calculated by dividing the raw GPAs by the class mean GPAs. So if the class mean GPAs for Organic Chemistry I, Introduction to Philosophy, and Overview of Ethnic Studies are 1.0 (a D), 2.5 (mid-range C), and 4.0 (A), Hyung-Sik, Mary, and Tomoyuki will receive relative GPAs of 4.0, 1.6, and 1.0. Unlike the weighted GPA LynnG described, the difficulty of the course in the relative GPA system is determined wholly by the performance of the class as a whole, and not by a class description, label, or determination, all subjective criteria.

Here is an example table of nine students in nine classes (I have no idea why blogger is forcing the table so far down the page, but it's there -- just scroll):

Student	Raw GPA	Class Mean GPA	Relative GPA
Hyung-Sik	4.0	1.0	4.0
Mary	4.0	2.5	1.6
Tomoyuki	4.0	4.0	1.0
John	3.0	1.0	3.0
Sue	3.0	2.5	1.2
Gerald	3.0	4.0	0.8
Bill	2.0	1.0	2.0
Lisa	2.0	2.5	0.8
Cindy	2.0	4.0	0.5

In this system, a student whose raw GPA is identical to the mean GPA of the course will receive a 1.0, which becomes the mean standard score. Relative GPAs can also be calculated by reporting the student's raw GPA and percentile rank, or by reporting the student's standardized score, or z-score (the difference of the student's score and the class mean score divided by the class standard deviation).

Another advantage of using relative GPAs is that it counters the administrative bias toward college-track courses. Why, for example, should Jim, who loves working with wood and excels at it, and wants to be a carpenter or woodworker, not receive the same advantage with respect to his GPA in shop? With a weighted system, Jim will likely only take 4.0-0.0 courses; with a relative system, Jim's superior work will be accurately reflected in his GPA.

The relative GPA is not a perfect solution. Whereas the relative GPA does give an objective assessment of the student's performance relative to the other students in the class, its major disadvantage is in small classes. One very low score (at the university, it would be that inevitable student who fails to drop the class in time, and there's always at least one), will drastically alter the class mean, and therefore, the student's relative GPA.

This presents a possible problem for using the relative GPA in pre-university schools, where class sizes are as a rule significantly smaller than university classes. One might counteract the effects of small classes by calculating the relative GPA with a trimmed mean (the outliers are removed from the sample). Confidence intervals can also be calculated to counteract this effect.

Either way, the relative GPA is a far more accurate and useful assessment tool than the weighted GPA, whether the school is primary, secondary, or the university.

teaching problem solving to second graders

Jill ran 2/3 of a mile farther than Steve. If Steve ran 7/3 miles, how far did Jill run?

If the NAEP is any indication, this is a simple problem that many students can't reliably solve by the 11th grade. Which is a real shame because if a student can't solve a simple problem like this, he can't do basic algebra. The student's math education has effectively come to an end.

The biggest stumbling block is translating the word problem into a mathematical expression. (Calculators are no assistance here.) This kind of mathematical reasoning eludes many students. Fortunately, it can be systematically taught. For example, in Singapore Math this skill is taught using bar graphs starting in third grade. A fair amount of digital ink has been spilled on bar graphs on KTM, so I'm going to show you a diferent way of teaching problem solving.

I'm going to show you how the technique is taught in Connecting Math Concepts (CMC) beginning in the second grade. By the end of the second grade, students should be able to solve a problem, like the one above, correctly at a high rate. Problem solving is taught the entire 2nd grade year in CMC, so it's going to take quite a few posts to cover it all. So let's intoduce the technique in this post and I'll periodically write new posts until we've covered it all.

In CMC, simple problem solving is taught via the concept of number families. Here's a number family:



Beginning in this first grade, the student is taught that number families show three numbers that always go together in addition and subtraction facts. In the example, the three numbers in the family are 2, 3 and 5. You can derive four problems from each number family, two addition and one subtraction:

• 2 + 3 = 5
• 3 + 2 = 5
• 5 - 3=2
• 5 - 2 = 3
  

The students are taught that the "big number" always goes at the end of the arrow and the "small numbers" always go above the line. (In DI courses skills are taught using terminology that the students are familiar with. Proper math terminology like subtrahend, minuend, and addend aren't taught, if at all, until after the students are firm on the skill. This reduces the liklihood of student confusion.)

Next the student is taught how to derive the addition and subtraction problems from the number families. Here's an example of each:



An addition problem can be written for each family that has a missing big number, like the bottom family in the picture. Students are taught that if the big number is missing, they are to write an addition problem that ends with the "how many" box (4 + 19 = []). For subtraction problems, students are taught that if one of the small numbers is missing, they are to write the big number first and subtract the small number from it to find the missing number (57 - 12 = []).

Once the students are firm on this skill, they are given some math puzzles to solve. For example, the students are directed to complete the number family, write the addition or subtraction problem, and the answer to the following set of facts: The big number is a box, the first small number is 38, and the second small number is 39.

the student should be able to derive the problem: 38 + 39 = 77.

Now the student is ready to learn about the concept of variables.

The student is told that sometimes a "letter" is used instead of a box in a number family. The letter works just like a box. It's the missing number.

Here's a problem:

The first small number is 14. The second small number is 56. The big number is P.

The student should be able to construct the proper number family using the skills he's been taught so far.


The student should also know that in order to solve for P, he has to add. The student should also be able to write the correct addition problem 14 + 56 = P and determine that P = 70.

The student is then instructed to cross out the P in the number family and write 70 like this:



This seems like a good enough place to stop for this post. Don't want to overload your second grade heads. This sequence takes about five weeks to go through--the first five weeks of second grade, including practice. I'd estimate that this sequence represents about an hour or two of instruction time and another few hours of guided and independent practice.

In the next post we start to get out of the puzzles and into the good stuff -- real problem solving.

Many of you can probably see where we're going with this already.

Here's a teaser.

A student should be able to set up simple comparison like "A is less than B" or "G is more than H" just by using the number families and rules for placing the "big number" and the "small number." Once that skill is firm it's just a hop, skip, and a jump away from setting up a problem like: J is 5 less than K. Solve for K if J = 3.

(Go to Part 2)

voluntary national math and science standards: draft Dodd-Ehlers bill

I attended a panel discussion of the bill drafted by Sen. Dodd (D-CT) and Rep Ehlers (R-MI) bill yesterday. The event was sponsored jointly by Fordham and the New America Foundation, at the latter's offices in DC. Michael Dannenberg, former staffer for Ted Kennedy and now director of the Education Policy Program at the New America Foundation moderated the panel discussion. Sen. Dodd opened with a statement on why we need national standards. He cited the plethora of "great" state test scores in math and science, and poor scores on NAEP, the 50 different state standards for math and science, and the need for a method to assess fairly how schools are doing, with respect to the requirements of NCLB which is up for reauthorization this year. Rep Ehlers was supposed to be there, but was unable to attend; he is a co-sponsor of the bill.

Other speakers included former Gov John Engler of Michigan, former Gov Bob Wise of W. Virginia (now president of Alliance for Excellent Education, Michael Casserly (Exec Director of Council of Great City Schools) and Michael Petrilli of Fordham.

Bill would task NAGB (these are the people who write the NAEP exam) to draft national standards for math and science. (Anyone familiar with the non-rigorous nature of the NAEP exams should be plenty concerned about this bill). These would be voluntary standards, but if states adopt them, then they get a grant to implement the standards and other things. Standards must "ensure that the volumary American education content standards are internationally competeitive and comparable to the best standards in the world."

Among the questions was one from Jeff Mervis of Science magazine. He asked what happens if states are falling short even after adoption of national standards? Would there then be a "national curriculum"? The question was addressed to Sen. Dodd who said the last thing the govt will do is tell local govts how to sequence and/or design curricula. Mervis asked again: "Does the bill tell the states how to meet the standards?" Dodd dodged the question again, but this time alluded to weaknesses in the NCLB law itself that prevents qualified teachers from teaching. He referred to the teacher certification requirements that make it mandatory for teachers to have certification in a subject area in order to teach it; so a biology teacher who may be qualified to teach chemistry could not teach chemistry under the current law. Don't know that that answered Mervis' question, but that's all I could glean from that one, folks.

The bil would not establish a national test, though Sen. Dodd said that maybe that would emerge as a result of states adopting the national standards. Perhaps they would get together and decide they needed to design and use a common test.

One comment from the moderator, Michael Dannenberg, intrigued me. He is definitely for this bill and said that the "standards based reform movement" has had the greatest success with respect to math. Wha HUH? What's he talking about? NCTM's standards? State standards? Has he even read Fordham's State of the State Math Standards report? Oh, he musta been talking about California, yeah, yeah, that MUST be what he was referring to. Or maybe the Focal Points, yeah, yeah, that's the ticket.

(Description of the bill, plus a link to the draft and a link to a video of yesterday's event can be found at Preparing US Students for the Global Economy.)

Among the key private endorsers of the bill are NEA and (wait for it) NCTM. Any questions?

what's possible in high school?

There's a fascinating article titled "The Incredibles" in yesterday's NYTimes EducationLife section. This article focusses on students who are superachievers in high school and may even be bored in college. It was clear from the article that there definitely are such students.

For example, the former mathematics department chairman of George Mason University now teaches at the Thomas Jefferson High School for Science and Technology, which is a public magnet school in Virginia. Some students are taking "Complex Analysis" which has A.P. calculus plus a second year of advanced math as pre-requisite. [Yikes! That's my field and I'm not sure I understand it all even yet.]

However, of more relevance to our discussions was this interesting comment by the president of Pomona College. "High schools are trying to imitate college and teach college-type material instead of the high school material they used to teach ... They are now learning the advanced stuff, but not the basic stuff. We are finding students who have learned about s-, p- and d-orbitals -- a theoretical concept in chemistry -- but they don't know that chlorine is a gas."

Another educator concurred. "High school-age students are not mature enough to grasp the subtleties of some material...."

preparing for collegiate success

I just came across information from the U.S. Dept of Ed, called the Tool Box Revisited. This was issued about a year ago (February 2006). What caught my attention is this passage:

"The highest level of mathematics reached in high school continues to be a key marker in precollegiate momentum, with the tipping point of momentum toward a bachelor's degree now firmly above Algebra 2. But in order for that momentum to pay off, earning credits in truly college-level mathematics on the postsecondary side is de regeur."

"By the end of the second calendar year of enrollment, the gap in credit generation in college-level mathematics between those who eventually earned bachelor's degrees and those who didn't is 71 to 38 percent."

I think what this report is saying, someone correct me if I've miss interpreted, is that unless you take "truly" college level math in high school, not pseudo, higher-order thinking skills with real world applications, your chances of getting ANY bachelor's degree is about 38%. Yikes!

today's depressing factoid

Performing at grade level by the end of first grade is critically important for the at-risk child. A study by Juel (1988) showed that the probability that a child who was a poor reader in first grade would be a poor reader in thefourth grade was a depressingly high +0.88.

Ouch.

It's a quadruple whammy for at-risk kids:

There are many at-risk children who are not likely to succeed when placed in widely distributed core reading programs. The problems stem from the programs not being designed with the degree of explicitness needed by the at-risk child. The programs often have serious instructional design flaws. Among these problems are (a) teacher explanations that include words the child does not know and that use sentence structures that are confusing for students with limited knowledge of language, (b) the rate of introduction of new skills is too fast, and (c) sequences that can cause confusion. For example, one program introduced letter–sound correspondences in alphabetical order, resulting in the letters b and d, and m and n being introduced in near consecutive order, and (d) too little practice and review.

From Using Direct Instruction Programs as Intervention Programs in Grades K–3, Direct Instruction News Volume 5, Number 2 Summer 2005

The worst part of this is that all four of these deficiencies are emtirely instructional in nature. It's purely a matter of educators not doing their job properly.

Ricky update

Wednesday, I had a tutoring session with Ricky, the 8th grader. The topic was limits.

I've learned to look at all of his worksheets first, to see what they're really covering, since their idea of covering a topic is very different from mine. He had three worksheets, all of them with odd little exercises on them that went something like this: "Get a bowl of Hershey's Kisses and take half the Kisses out of the bowl. Keep taking half of the Kisses out of the bowl. When you get down to only one Kiss, cut it in half and take out half. Will you ever empty the bowl? Why or why not?"

Uhm, okay. I see where this is supposed to go, but couldn't they at least give a definition? Even if they wanted to use induction, how about a definition at the end of the third worksheet?

Keep in mind that they haven't done Cartesian geometry yet. No y = mx + b. It's kind of hard to talk about limits in terms of math -- particularly to an 8th grader -- without being able to use a graph as an exemplar. Try it.

This is the first time he has questioned the curriculum. Not directly, but he's been remarkably willing to led the course lead him down the garden path, without questioning where the class is headed, until Wednesday. He appropriately asked me what limits were for.

"Trigonometry. Calculus. Engineering."

"What are we doing to do with them?"

"You'll have to ask your teacher."

And indeed, the boy had a point: What is an 8th grade class going to do with limits?

"You don't know?"

"I have no idea."

"Then why are we doing this?"

Well, one may well wonder. And I understand his mystification. Limits, as they were covering them, don't generate numbers, or seem to an 8th grader to have much to do with mathematics.

It was the following week that Ricky told me what had happened in class -- and I had to laugh a little (silently, of course). To demonstrate limits, the teacher had had all of the students stand on one side of the room. She had then had half of them move to the other side of the room, over and over again.

There is a problem with using discrete objects to demonstrate limits (the same problem was in the Hershey Kiss exercise): You eventually get down to one. So when they got down to one student, Ricky said the teacher told them, "Never mind, let's do this example instead."

When you're teaching, you really need to think things out before you run them in the classroom. Been there, done that.

Next up that week was quadratic equations. To review, let's look at the preceding list of topics: Division, graphs (pie, bar, column, and area, not Cartesian), fractions, limits, quadratic equations. By the time I started this gig, they had already "done" linear equations -- except that they hadn't really, and we covered it.

For the first time, Ricky had an amnesia attack. I'm used to this. Teaching in a two-semester course sequence, you see lots of students the second semester you had the first who seem to have forgotten nearly everything you did the previous semester. But Ricky had a complete blackout. He couldn't solve 50 = 25 + x.

So I gently nudged him by doing it for him, step by step, then writing down another for him to do. Again, blackout.

I have a son, and I also have three younger brothers (well, had: my youngest brother died a couple of years ago). I know what a frustrated adolescent looks like, and he was getting frustrated. I backed off, and suggested I come back the next evening, and in the meantime, told him I'd email him some stuff he could do before I came back to refresh his memory of linear equations.

That worked pretty well, but he's still frustrated, and I can't blame him. Again, I got, "Why can't my teacher explain it like this?" and I have no (ethical) answer to that question, which doesn't help his frustration. He wants me to validate it, and it really wouldn't be appropriate for me to do so, though he's right. The problem is that he's turning his frustration not on the class or his teacher, but on math in general, and that's not good because he's very sharp, and he picks it up very quickly.

So who knows. Maybe I'll be turning into a therapist next. Sigh.

today's quote

Here's today's ironic education quote.

Alice Treuth said it's fun to work on laptops in her fourth-grade class at St. Francis de Sales Catholic School because she doesn't have to write.

Sigh.

An even more ironic update:

On the other side of the class, Michael Vogel raised his hand for help. A red squiggly line appeared under a word on his screen indication to Vogel that what he typed was incorrect.

"Why is it wrong?" Vogel asked [the teacher].

Everyday Math in Ann Arbor public schools

I'm always interested in what's happening in Ann Arbor, since I went to school at University of Michigan. I've been informed that the public schools there use Everyday Math and Connected Math Program. I'm familiar with both of them, moreso with EM since my daughter's school used that. Most of her teachers supplemented EM heavily--one teacher refused to use it at all. In the case of the one teacher that relied only on EM, I was tutoring with Singapore Math. I recall one student, a friend of my daughter's, quite bright, who at end of fourth grade claimed she was "bad at math" because she was unsure which of the four or so algorithms for each particular operation, she was supposed to use for which problem.

To see the kind of information parents are given about EM in Ann Arbor, check out the parents' guide for AAPS at Everyday Mathematics Parent Handbook.

helicopter parents pressuring their kids

Looks like another story that will bash "helicopter parents" who are too involved in their children’s education.

"One expert told me (for a story I’m working on for InTown: Westchester on Helicopter Parents) that the pressure to succeed begins in elementary school. Parents are using tutors for their elementary school kids not for remedial help, but for enrichment and to get them ahead, says Lisa Jacobson of Inspirica, a tutoring and test prep service based in Manhattan (inspirica.com). Ahead at age six! What’s happening to this world?"

So Little Time

Yeah, I’m looking to "enrich" my daughter so she knows her times tables in fourth grade!

a sorry state of affairs

Here's a nice little letter to the editor concerning the sorry state of math instruction:

I'd like to address the MCAS test and math education together. If what I suggest is happening (inflated evaluations in our schools) is true, we do need to have some measuring instrument which will accurately assess the comprehension of material beyond what the schools are reporting. In 1970, 6 percent of college freshmen reported having an "A" average in high school. In 2005, this figure was over 22 percent. In 1970, most of my 11-year-old sixth graders could pass a test on fractions, decimals and percents. In 2004, many of my above-average freshmen struggled if I included those concepts on an algebra test. Recently, a college-age clerk at a food store asked if 99 cents a pound was "close enough" to "a little over a half a pound." A junior college student thought that there were 12 yards in a mile. Understanding of this degree, or should I say misunderstanding, is just not acceptable.

That does seem to comport with today's math reality, rather than the rosy rhetoric. Math is supposedly now being taught with understanding, yet what we see is that many students have little real understanding of math and little facility solving simple math problems.

The traditional curriculum was far from perfect--too few kids learned higher math skills. But. today's math instruction seems to have gone from mediocre to worse.

I, for one, blame NCTM who are largely responsible for this current state of affairs. They claim to know how to teach math to kids. In reality, they don't. Their bromides have been failures. Sure, you can go through their standards and twist the words to come up with some sound math principles, but, overall, the framework they've laid down has resulted in actual instruction that is worse than what we had before.

It's time to give them the boot.

weighted GPA

Our High School is proposing to change the way high school grade point average is calculated. We currently use a a weighted GPA scale that gives more "credit" to Honors and AP level courses. Honors and AP are graded on a 6.25 scale (an A+ gets a 6.25) and the non-Honors/AP courses use a 5.25 scale. Also, health and physical ed courses are not included in the GPA calculation.

The high school administration proposes to end this and grade all students on a single 4.0 scale that includes all graded courses (scooping in band, pe, health, maybe others). I'm on the fence on this because I really don't know what the pros and cons are and I am hoping maybe some of you out there might help clarify.

Here's what we've come up with so far -- the change would primarily affect the class "rank." By taking easier courses and getting an A, you'll get a better GPA and a better class rank than if you take AP and Honors courses and get a B. The kids graduating in that all important (is it?) top 10% might be those that avoid AP and Honors and take easier courses for a better grade. Would this new system penalize kids that stretch themselves in AP and Honors? Or do colleges really not care about GPA and class rank, caring much more about the courses on the transcript rather than the grades achieved?

help desk

I worked an "overlapping triangle" problem in Saxon Algebra 2 today that threw me for a loop.

I finally got the correct answer, but I don't understand the solution in the solution manual.

(Image from Understanding sine at Homeschoolmath.net. I can't add labels to the illustration, unfortunately.)



Look at the bottom side of the left-most triangle, the one with two overlapping triangles.

Assume that the red segment measures 6 cm, the green segment 4 cm.

I've been taught that you would find the scale factor using this equation:

6 x SF = 10

However, the solution manual shows:

6 x SF = 4

I started checking various right triangle problems to see whether you can find a correct scale factor this way....and I'm stumped.

Just based in the triangles I've looked at, the 6 x SF = 4 formula for the bottom red & green segments also holds true for the corresponding 6 and H3 segments of the hypotenuse:

6 x SF = H3

Obviously it does not hold true for the ratio between the two vertical sides labeled 2.6 and 3.9.

What's going on?

++++++++

oh wow!

The homeschool.net page explains it!

hmmm . . .

I think Saxon blew it here. This was too big a leap for me inside a problem set.

Of course, Saxon isn't supposed to be a self-teaching book.

It may be time for me to take a class.

An actual class with an actual teacher.

Though I have to say, attempting to teach myself math I've never seen before is kind of cool.

My dad told me some relative of his taught himself calculus out of a book.

I like that idea.

+++++++

Someone needs to write a sci-fi novel about homeschoolers preserving knowledge for the future.

Which reminds me, I'm still worried about the solution manual for Moise and Downs.

Once it's gone, then what?

Andrew persists

We got this email today from Clarice, Andrew's teacher:

Andrew has been pointing to a picture of the Arthur book Who is in Love with Arthur for a few days. Sometimes I think Andrew believes that we can make something appear just because he wants it. [ed: ditto]

Anyhow, yesterday he put the Arthur picture on his daily schedule and typed “dows lane Arthur bus yes.” We told him no, that we could not go on a bus to Dows Lane. So, while Annie was at lunch he came over to my desk with a pair of scissors and I asked him what he wanted. He pointed to my corkboard and I still did not know what he wanted. I told him to get what he wanted and he took my Irvington 2005-2006 directory off of the wall. On the front of it were tiny black and white pictures of each of the schools. He used the scissors to cut out the picture of Dows Lane, got a piece of Velcro off of the back of another item, and put it on the back of the Dows Lane picture. He then stuck the Dows Lane picture on his daily schedule next to the picture of the Arthur book. So, Annie went over to Dows Lane and got the book for him. He was happy for the rest of the afternoon and has been happy today until a 10 minute tantrum at noon. He typed “dows lane Arthur bus yes” again. I’d love to reinforce each effort to communicate, but the obsessive behavior that continually changes makes it very difficult.

This is a miracle.

Just a couple of years ago Andrew had no means of communication apart from grabbing our hands and pulling us to whatever it was that he wanted.

Now he's creating his own PECS cards.

He's still impossible; it's a wonder Clarice and Annie are still standing.

But they are.

Clarice and Annie persist, too.

so tell me, is this rote?

Educators love the false dilemma. One of their favored false dilemmas in math education is saying what they teach is "higher ordered thinking skills" and what was traditionally taught was "merely teaching by rote." Rote is not merely memorization, it is memorization without meaning or understanding. I contend that very little is taught by rote in any subject, even when memorization (or practice to automaticity) is required.

So let me give you an example of how one of the more difficult elementary math topics might be traditionally taught and you tell me if it's learning by rote.

Today's topic will be subtraction with regrouping (tens and ones). An example of such a problem is 66 - 37 = ?. Ordinarily, this topic gets taught after the student has learned how to do (and is firm on) subtraction without regroup (66 - 34 = ?). Let's further assume that the student knows how to do place value addition. This means the student knows how to decompose the number 66 into 60 + 6. In other words, the students knows that the number 66 comprises 6 tens and 6 ones.

Here's how the lesson might get taught traditionally:

Lesson One

I. Model Phase

When you work subtraction problems that use borrowing, you have to rewrite numerals so you have a new place-value addition. I'll show you how the new place value works.

[Write the number 36 on the board]

We're going to rewrite 36 for borrowing. We'll borrow 1 ten from the tens column and add that ten to the ones column.

How many tens do we start with? [point to the 3][students: 3]

I cross out the 3 and write the number that is 1 less than 3. What number is that? [students: 2]


Now I take the ten I borrowed and write it small in front of the 6.


The new place-value addition is 20 plus 16 equals 36.

We still have 36 because 20 plus 16 equals 36.

[repeat with a different number such as 57]


II. Lead Phase (if necessary)

Write the number 56 on the board.

Your turn. Cross out the 5 and write the number above it that is one less than 5. Then write the 1 ten you borrowed small in front of the 6. Raise your hand when finished.

(observe students and give feedback)

Check your work. Here's what you should have.


Everybody, say the new place-value addition for 56. [students: 40 plus 16 equals 56]

[repeat with another example if necessary]


III. Test Phase

[Write the numerals 84, 51, 45, and 72 on the board.]

Rewrite these numerals. Raise your hand when you're finished.

[Write on the board:]

Check your work. Here's what you should have.

Fix up any problems you got wrong.

End Lesson

[After the students are firm on the regrouping procedure, it's time to go on to using the procedure to solve subtraction problems]


Lesson Two

[Write on the board:]


You're going to do borrowing. For some column problems, you have to rewrite the top number so you can subtract. For other problems, you just subtract.

Here's how you figure out whether you need to borrow: You read the problem in the ones column. If the bottom number is bigger than the top number, you can't work the problem in that column, so you have to borrow.

Everybody, read the problem in the ones column. [students: 5 minus 5]

Can you work that problem? [students: yes]

So you don't have to borrow.

[Change the problem to:]


Can you work this problem? [students: No]

So you have to borrow.

[Repeat with a few more examples where borrowing is needed and not needed]

Give students a worksheet with the column subtraction problem: 53 -19 = ?

For this problem, you have to borrow because you can't work the problem in the ones column.

Rewrite the top number.

[Write on board:]


Check your work. Here's what you should have.

You'll make silly mistakes when you subtract unless you're careful about reading the new problem in the ones column.

I'll read the new problem in the ones column. 13 minus 9. That's a problem you can work.

You're going to work the problem now. Read the problem in the ones column. [students: 13 minus 9]. Read the problem in the tens column [students: 4 minus 1]

Write the answer to the problem. [check students work]

End Lesson

These lessons are taken from lessons 7 through 9 of Connecting Math Concepts, Level C which I've condensed a bit.

So tell me does anything in this lesson even remotely resemble rote learning?

The comments are open.

less math, more gambling

At least that's what they're recommending in Scotland:

Simple gambling games should be used as teaching tools in Scottish schools to make maths lessons more interesting, a leading academic said yesterday.

Professor Alastair Gillespie, chairman of the Scottish Mathematical Council, believes using dice and packs of cards in secondary school lessons would help pupils learn basic maths techniques such as probabilities. He also believes it would encourage more people to take up maths.

Too bad learning probability and statistics isn't the same as learning elementary math.

learning math is hard, part deux

(Part one of this post can be found here.)

In the first part of this post on the math program, Connecting Math Concepts, we were discussing about how the program is field tested and how error diagnosing and correction is built into the program. I needed to describe those two aspects of the program briefly to get to the aspect of the program that I intended to discuss -- practice.

Student practice is built right into CMC. That's one of the reasons why the program is field tested beforehand; to determine how much practice students need to retain the material taught. Unlike in most math programs, in CMC material is not just taught, tested and then permitted to lay fallow whereupon it is quickly forgotten by the student. Do you remember the threat of the dreaded end of year cumulative test back in K-12? You dreaded it because you knew that you had forgotten most of the material presented in the first half of the year. You don't have such a luxury in CMC, all tests are cumulative. The only time a skill isn't practiced or tested is because it's been incorporated into a more difficult skill. At the end of the year, students are expected to have retained all the material presented during the year. This is exactly what is needed when learning math.

Since CMC has been field tested with lower performing students and since CMC is designed to accelerate student learning as quickly as possible, you can get an idea for how much practice is needed for a lower performing student to retain the material. The program is designed to provide sufficient practice with a little bit extra to account for things like student absences, but not too much since that would hinder the acceleration. So, the practice provided in the program should turn out to be about what is necessary for a lower performing student to master the material at about the fastest rate he can handle. Cutting to the chase, the amount of practice that a lower performing student requires t o learn math is simply enormous if CMC is an accurate guide.

There is way too much practice for my son. I routinely cut out about every other practice lesson for each topic because I don't want him to get bored and our time for lessons is limited afterschool. Plus, I want to keep the ball rolling and stay far ahead of the wildly inappropriate nonsense that gets taught in his Everyday Math class.

So, you might be thinking that I'm only cutting out about half the material. Nope. I'm cutting out far more than that. I'm cutting out all the "extra practice" lessons that are scheduled for students after they fail a proficiency test. Since he's never failed any portion of any test so far, I haven't had to go back and reteach any lesson. At most he'll get a few problems wrong due to his desire not to being math work at night when he could be playing Lego Star Wars II on his PS2, but so far he's always stayed in the proficiency range no matter how fast I go.

In addition, I've never given him any worksheets from the extra practice workbooks or the blackline master worksheets. And, i skip all the games that sneak in more extra practice since there's no one to play against since he's the only student. Occasionaly, I'll play against him to give him an idea how fast I can work the problems so he has any idea how fast he's going to be expected to work the problems. He's not as fast as I am yet, but he routinely does his problems in half the time allotted in the timed exercises. So, he's starting to approach automaticity on some of the stuff he's learned so far.

Lastly, I've been known to skip the last 30 or lessons at the end of the year since most of this material will be quickly reviewed at the beginning at the next level.

I'd estimate that I cut out about 2/3 to 3/4 of the total practice provided in CMC which accords pretty closely with Engelmann's estimation that higher performers can be accelerated at about 3-4 times the rate of lower performers. And, it doesn't surprise me at all that lower performers need every last bit of all that practice I'm cutting out. Math is all about learning abstract concepts and our brains are not wired to learn abstract concepts easily. It also doesn't surprise me that in most math program, with the exception of Saxon, lower performing kids aren't getting close to the amount of practice they need to retain the math they've been taught.

Hence the widespread failure we see in math education.

And, this assessment doesn't even get into the messy area of the initial presentation of the material enabling the student to understand the concepts in the first place. I'll cover that aspect of CMC in future posts since we're now just starting to get into the interesting areas of math instruction. I'll leave you with this. CMC presents the material so clearly and concisely that I only have to "teach" for about five minutes each lesson. The rest of the time he's working problems using the skills I just taught or practicing previously taught skills. Ironically, that's probably far less teaching that goes on in your typical discovery learning/constructivist heavy math class. I'll show you who's the real guide on the side.

college prep

eduwonk links to The College Puzzle, a blog on college preparation that I suspect will become a regular read for me:

My blog discusses the important and complex subjects of college completion, college success, student risk factors (for failing), college readiness, academic preparation. I will explore the pieces of the puzzle that heavily influence, if not determine, college outcomes and success rates of college students. Furthermore, I've spent a great deal of time analyzing the messages that students receive about college preparation. I'll explore those messages and their roles in college outcomes.

Here are two of the factoids I've been looking for:

Only 22 percent of entering community-college students who want a four-year degree actually get one, nationwide. At minimally selective four-year colleges, fewer than half finish their degree. Too many students are not staying in college.

Ed said the other day that what we need to know about Irvington kids isn't how many go to college (practically everyone), but how many graduate from college in 4 to 6 years. I keep hearing about Irvington High School graduates who've dropped out of college after a year. I now know of at least 5 kids myself.

The plan is for the kids to go back, and I'm sure they will go back.

But it worries me that any "unplanned leaves" are happening at all.

In any case, affluent suburban schools should certainly be keeping track of their college graduation rate.

Author bio:

Michael W. Kirst is Professor Emeritus of Education and Business Administration at Stanford University since 1969.

Dr. Kirst received his Ph.D. in political economy and government from Harvard. Before joining the Stanford University faculty, Dr. Kirst held several positions with the federal government, including Staff Director of the U.S. Senate Subcommittee on Manpower, Employment and Poverty. He was a former president of the California State Board of Education.. His book From High School to College with Andrea Venezia was published by Jossey Bass in 2004.

Answers in the Toolbox

Answers in the Toolbox Revisited:

The report does show that of all eighth graders in 1988:

• 78% graduated on time in 1992 with a standard diploma;
• 53% entered postsecondary education directly from high school;
• 48% persisted from their first to their second year of postsecondary study;
  
• 35% earned a bachelor’s or associate degree by December 2000.

Ricky, my tutee

Like I said, I'm fairly new to pre-university education, though I see the results, and all my colleagues agree that we've been getting students with poorer and poorer math skills over the years. Having said that, we don't want to get into how I ended up tutoring (it's a long story). My tutee -- I'll call him Ricky -- is an 8th grader. His parents both have PhDs (before you ask why they aren't helping him, I do not know, and there really is no tactful way to ask). I'm being intentionally vague about details because, well, for personal and political reasons.

Ricky is extremely sharp, by the way. He immediately understands what I'm saying. I never have to explain anything more than once (he has the attention span of a gnat, though he is only in the 8th grade). Ricky enjoys learning, and is naturally curious. He's like a knowledge sponge. When I started working with him, he couldn't tell me what 16-9 was without reaching for his calculator. He had no mastery of basic operations, so that's what we did. He resisted at first (why do I have to do this when I can use my calculator?) but now that he has that information mastered, he can do things like basic algebra much more quickly and effortlessly, and he understand now.

Back to the course.

Okay, I may not have an ed PhD (thank God for that!) and I may not have pre-university classroom experience, but I've been teaching, writing exams, producing materials, and creating (and fiddling with) curricula for a long time. So even though I may not have any primary or secondary school teaching experience, the basic principles are the same.

They use worksheets (in-class worksheets -- the really frightening ones, with substance-free discussion and "food for thought" questions and "try this!" exercises -- as well as the take-home worksheets -- traditional math problems -- she gives them so they'll get decent scores on the state exams.

We have a problem right there. This is an admission that what they're doing in class -- the discussion and "food for thought" questions, and the "try this! Create three ways to calculate the area of a circle!" exercises -- are not teaching students the skills they need to get decent scores on the state math exams. If I were teaching the class and my students weren't learning the material, I'd change what I was doing. But this has not occurred to the teacher.

What strikes me, however, is how disorganized the course is.

They hop from topic to topic weekly, with no logical progression from topic to topic (for example, going from simple linear equations to probability -- and why they're doing probability in the 8th grade, I do not understand). They don't spend enough time on one topic to actually learn it, nor do they cover any topic to any depth, which makes no sense to me. The first thing on the list when they go back after break is limits -- why would 8th graders be doing limits when they don't understand basic fractions? Why would 8th graders be doing limits even if they did understand basic fractions?

The teacher also gives them "review" sheets (the sneer quotes are there because "review" implies a topic that's already been covered, and they don't cover a topic in any sense of the word). One was on long division. Ricky couldn't do it. He'd never seen anybody do long division, nor did he understand factoring. I asked him if his teacher had shown them how to do this, and he said no -- which normally I would take with a grain of salt, had I not seen so much disorganized nonsense already. He said she sent it home with this -- and he dug out another worksheet, a "how to" sheet on long division. He's in the 8th grade.

Forget the silly in-class worksheets, and forget the fact that the teacher sends them home with worksheets (traditional problems) so they'll get decent grades on the state exams. Here's my question: How can you send work home with your students and ask them to do something they've never been shown how to do? How can you justify that? If I tried to get away with that, I'd be in the Dean's office -- and it wouldn't be pretty.

The biggest battle has been teaching him to approach a problem, take it apart, and figure out how to solve it. It's been as much tutoring logic as math. (Does that mean I've been teaching "higher-order thinking" skills?) I had to be sort of ruthless at first because he didn't understand why he had to learn all this, but I've got him not only solving the problem, but checking it by finding a second way to do it and using that to work backwards. Like when we were doing probability (I still think that's weird). There was a basic problem on the worksheet, one of those standard balls problems (there are 30 red balls in the basket and the rest are blue. The probability of choosing a red ball is 0.75. How many balls are there total?) So I showed him how to calculate the total number of balls with the equation 0.75x=30. Then we calculated the number of blue balls, and checked it by first calculating the probability of choosing a blue ball, then subtracting that from one to find the probability of choosing a red ball. Once he started to catch onto the logic, he started picking it up fast. What's sad is that a kid that bright shouldn't need a tutor.

Another few months, and I'll turn Ricky into a card-carrying math geek.

on motivation

If you don't subscribe to the Direct Instruction listserv, you should.

Besides learning a lot of good stuff about good teaching techniques and other education issues, you get to witness an epic battle betwixt good and evil. In this case, evil is personified by Gerald Bracey who fancies himself as the gadfly of the board after joining a few months back. Problem is that Jerry is out of his league on the DI board as was demonstrated by this recent exchange on motivation.

Bracey:

Of course, no one mentions anything as soft and squishy as intrinsic motivation.

...

My comment on intrinsic motivation had to do with learning. Skinner could not account for his own behavior without it, although he tried.

Martin Kozloff (aka Professor Plum):

Intrinsic motivation is semantic nonsense.

Motivation. Motive force. Alleged to be "behind" or prior to action.

How do you know if a person "is" motivated?

They DO something.

WHY did they do something?

They were motivated.

Uh huh. Not too circular.

Extrinsic motivation. That is, the event towards which one is moving is external. Like what? A meal. She is cooking so that she can eat. He is training so that he will finish a race.

Yes, the event is outside, but why would anyone prepare a meal unless eating it felt good? Why would anyone run a race unless they anticipated a pleasing outcome.

In other words, the external event is NOT what motivates. It is merely the means to an end---which is feeling. Which is INTERNAL.

Therefore, so-called extrinsic motivation is really intrinsic. {Score one for me.]

If you say that intrinsic motivation might be wanting to do well, I'd like to know where you got the definition of "well." Was that intrinsic? Or was it gotten from the social environment?

And why would anyone want to do well? Because that is considered important in the culture. And where is this culture? It is OUTSIDE the person. So, intrinsic motivation is really extrinsic. [Score two for me.]

In summary, the words are kakos.


Finally, you don't need the concept of motivation to account for behavior---if by account you mean answering the question Why is she doing that.

The answer (if you include the concept of motivation) is that she is motivated to do so, which means nothing more than she wants to. Which is as helpful as explaining avoidance behavior by saying a person is afraid.

How do you know they are afraid?

They avoid the situation.

How come?

They are afraid.

How do you know?

They avoid the situation.

How come?

Afraid.

World without end, Amen.

[Score three for me. A hat trick.]

James MacDonald:

I, and possibly other members of the list, would like you to write complete
thoughts, including the evidence or rationale behind your comments. You
made a comment about Ohio State football, but did not say what the problems
were. You mention that Skinner could not account for his own behavior, but
do not give examples of this. Essentially, I am requesting a scholarly
discourse - not the out of the blue, non sequiturs you write.

Bracey:

I don't do pablum.

Kozloff:

Mais non, mon ami, I must disagree.

Pablum is what you do best!

[Come on, young Bracey. That was funny, and you know it.]

To Be Continued?

weapons of math destruction

I learned of Weapons of Math Destruction from Linda Moran. (You can join Linda's listserv here.)

It's a hoot.

This is a good one.

learning math is hard

Update: For more one error detection and correction, take a look at this video (quicktime) starting at about 5:30. He's talks about error correction with reference to reading instruction. It continues on into this clip up until about 7:00 and math gets discussed for the last 3 minutes or so.

That's my current position based on teaching my six year old son math for the past year and a half.

Actually, that observation isn't based on my son having difficulty learning math. So far he hasn't. It's based on the the material we've skipped. It is that differential that separates the higher preforming math students from the lower performing math students. That differential represents an enormous amount of practice.

Unlike most parents who use Saxon to teach math, I'm using Connecting Math Concepts. Both programs are scripted, both use a mastery learning "basic skills" approach, and both have lots of practice built into the program. Both are complete programs which don't require parents to know how to teach math; knowing elementary math is sufficient. For most kids there is not much difference between the two. Contrast this with Singapore Math which does require some teaching skill to present and requires practice to be supplemented. That's not meant to be a knock against Singapore Math, each program has its strengths and weaknesses. I actually think that the ideal K-6 elementary math curriculum would be some combination of all three programs, capitalizing on the strengths of each.

For the purposes of this post, however, I want to focus on the practice aspect of learning math. To master elementary math a student needs to practice what's been learned until it is automatic. Unfortunately, most math programs do not provide sufficient practice to safeguard against the ravages of forgetfulness.

Most parents do not take control of the educational process until there the need to remediate becomes evident. At this point, there is a tension between the need to devote time for practice and the need to reteach the child to get him back on track as quickly as possible. Practice tends to get the short end of the stick at this point. It shouldn't.

One aspect I like about CMC is that it's been field tested so you can be certain that if the student has the math skills to enter a level of the program, the program will teach clearly enough and provide enough practice for the student to reliably master all the material presented in this level within one school year, about 120 lessons.

The most important aspect of CMC, however, is that error diagnosing and correcting are built right into the program, unlike almost every other math program. Let's face it, if students didn't make any errors while learning math, a trained monkey could teach math using almost any commercially available math program. It is in the diagnosing and correcting of student errors where most math programs fail. When students derail, many teachers are unable to get them back on the track. Math, being brutally cumulative is not forgiving at all when students derail.

This is CMC's greatest strength.

CMC is designed to minimize students errors in the first place by providing clear instruction in small instructional steps. Students are then tested frequently (workbooks are checked after every lesson and tests are given every two weeks) to check student errors. based on the ten unit tests, student errors are evaluated and a built-in remedy is provided to the student based on the errors the student made. The student is then retested to see if the remedy worked before the student is permitted to advance. If the student were permitted to advance without mastering the material, then the diagnosing and correction of errors would be become much more difficult come the next ten unit test because now the teacher doesn't know where the student went astray. Was it one of the new skills taught in the past ten lessons of was it one of the previously taught skills? Now extrapolate out 80 more lessons and try to figure out where the problem is for a newly taught skill that the student can't do. Forget about it.

Contrary to popular belief, the greatest shortcoming of the "constructivist" math programs is not the less than clear presentation of new skills, though this is certainly a problem; it is that error detection becomes virtually impossible. This is not so much a problem in a class full of higher performers, but it is deadly in a class where students make errors.

I see this post is getting a bit longish and I still haven't touched on the main point -- practice. So, I'm going to break it up into two posts since there's already much to chew on in this post. More to come.

Part two here.

Andrew on the couch

math jokes

Via NYC Educator, I discovered Miss Cellania's math jokes.

Basic unit of laryngitis: 1 hoarsepower

365.25 days of drinking low-calorie beer: 1 lite year

1 million microphones: 1 megaphone

1 million aches: 1 megahurtz

1 millionth of a fish: 1 microfiche

It's subtle humor, of course.

SAT and sentence combining

I had the strongest feeling while taking the multiple choice sections of the SAT writing test that we need to commence sentence combining exercises around these parts.

Richard Hudson on Grammar teaching and writing skills: the research evidence

Grammar teaching could be surreptitious, as it were, with a clear underlying theory of grammar but minimal use of grammatical terminology. This is in fact how a lot of grammar teaching has been done; and in particular there is a well-recognised activity called 'sentence combining' which seems to be widely used in the USA. There is some evidence, apparently good, that this kind of activity benefits children's writing (Abrahamson 1977; Barton 1997; Hillocks 1986; Mellon 1969; O'Hare 1973), and in some studies it turned out that this kind of grammar teaching produced better results than more traditional teaching of grammatical analysis. For example, " Hillocks surveys the many studies of the effects of sentence combining, and finds them overwhelmingly POSITIVE at all levels (grade 2 to adult). 60% show significant gains in syntactic maturity; 30% non-significant gains; 10% no gains." (Weaver 1996, reporting Hillocks (1986)).

Why should these exercises be so much more successful than traditional analysis? It seems reasonable to assume that it is at least in part because they are exercises in the production of language, and specifically in the production of written language, so they feed much more directly into the child's growing repertoire of productive skills than exercises in grammatical analysis do. In short, they are more closely integrated into the teaching of writing, so the skills acquired in isolation are more likely to transfer directly into a usable skill. However this conclusion does not necessarily rule out the possibility of transfer from grammatical analysis under the right conditions.

This sentence combining quiz is pretty good. Here's a simple page for kids.

I think a couple of you may have rounded up sentence combining exercises the last time this come up. If so, I'd love to get the links.

(quick note: I didn't have good luck with Killgallon's books on sentence composing and neither did Susan S as I recall. I may go back to them in another year. We'll see.)

the trouble with fractions

Just found this at joannejacobs; Joanne found it at Chalkboard.

fractiongate ($)

no-knead bread

I made this today.

It tastes as good as it looks.

Costs approximately 20 cents per loaf.

There is nothing to it.

everything you need to know

As far as I can tell there is only one way to sc*** up this bread: forget to put the lid on the pan.

It's possible you can sc*** it up by adding 5x as much yeast as the recipe calls for. I don't know. I added 5x as much yeast as the recipe calls for to the same loaf I baked without a lid. (Must have the lid. Lid is key.)

You can not sc*** this up by mixing up a batch of dough, setting it out to rise, and then forgetting the whole thing until you happen to glance at your bake stand and think, Holy cow, how long has that been sitting there?

This may not sound like the definition of freedom, but it is. The fact that you can't sc*** this bread up by letting it rise too long means you don't have to get bogged down doing & re-doing mental math to figure out things like Where will I be in 18 hours when the dough finishes its first rise and Will I be asleep when the dough finishes its second rise?

None of that matters.

If you're some place else, it's not a problem.

If you're asleep, it's not a problem.

The dough can wait.

It's probably better if it does wait.

hello

I'm relatively new to thinking about pre-university education -- my son has been out of school since before education went completely off the deep end, and had a relatively normal education. Not, mind, that I'm unfamiliar with ed schools and their faculty -- much the opposite, I fear.

I live in what is supposed to be one of the best school districts in the state, and have been tutoring an 8th grader in math. I may blog about it in the future, but right now, I'm too horrified.

That's enough. I have work to do. More later.

And thanks for inviting me!

toga! toga! toga!

Carolyn wrote,

"A group blog... this is going to be great!"

which I believe is a sly reference to an Animal House quote by Flounder who I'm thinking should be KTM's new mascot.

He was a legacy afterall.

Is math all that different than a toga party?

American Educator Magazine

My renewal form for American Educator just arrived, so I thought I'd tell everyone how to subscribe.

1 year $10
2 years $20
3 years $30

make check payable to:
American Federation of Teacheres
Order Department
555 New Jersey Avenue, NY
Washington, D.C. 2001

Money well spent.

SAT test

So I took the practice multiple choice test on writing.

I got 100% correct.

Thank God.

more later


sample SAT test
SAT test
get your recentered SAT scores right here

50 words or less

Barry asked us to come up with 50 words or less, then did it himself!

The NCTM has embodied the principles of constructivism, embedded them in their standards, and the textbooks that grew out of them (thanks to NSF funding) force classrooms to adhere to the constructivist non-think ethic whether they like it or not.

This reminds me of the description of UK writing instruction I keep coming back to:

[Judith] Koren describes how two British women she knows became effective essayists and speakers. “Each week, they’d had homework exercises like this: While preserving every essential point, reduce a 100-word essay to 50 words, then to 20, then to 10. Reduce 500 words to 50, 1,000 words to 100. Week after week, year after year....
(appeared in American Enterprise Magazine)

I love this from Woodrow Wilson, too:

If I am to speak for ten minutes, I need a week for preparation. If fifteen minutes, three days; if half an hour, two days; if an hour, I am ready now.

math is like a bowl of popcorn

From the Baltimore Sun:

But others disagree. John Haven, whose children attended Montgomery County public schools, believes far too much time in classrooms is spent on nonessential math work. He made an unscientific study of math teaching in Montgomery and concluded that, by his standards, 20 to 40 percent of what is taught is a waste of time. "It is a huge impact on math instruction. It is like having popcorn parties every Tuesday and Friday," he said.

I think that might have been John Hoven who gave us that quote. Anyway, read the whole thing.

back to the future

Thanks to Catherine for inviting me! A group blog... this is going to be great!

I would like to gather some thoughts from you all on what should happen to the original KTM website. I can leave it there indefinitely as long as we continue to pay the webhost, but should we really do that? There's a lot of great information there about mathematics and language arts resources and education -- think about the indexes and the threads and just plain great posts like Ken's response to the guy who flunked out of engineering -- but it can be very hard to dig through and find it. Should we parse through it and offer a condensed, informative website for people looking for information?

Or should we write an aggregate book -- with a title something like "Our math educations, ourselves"?

Or should we leave it alone?

constructivism -- just a hoax?

In an email from a noted education writer for a major metropolitan newspaper, this writer said the following with regard to constructivism:

Life is too short for me to try to distinguish for readers the difference between true constructivism and guided discovery. It really is not an interesting issue, because readers only care if their kids are learning, and I dont think I have ever seen anything in a public school that could qualify as true constructivism, and there is almost nobody out there with any influence pushing for t. c. It doesnt exist except in a very few private schools, if there.

This is from a writer who no matter what arguments you proffer in opposition, will respond, "oh, but what I meant was..." From what I've seen, the theory of constructivism has manifested itself in textbooks such as TERC's Investigations, or Connected Math Program, or Everyday Math, or IMP, or Core-Plus. One can make arguments that EM is not really constructivist. Well go ahead and make them. It sure isn't guided discovery. And it isn't mastery learning either. So you tell me what it is?

Adherents of constructivism will of say "Well of course we don't use constructivist techniques every day; it would be impractical." But they use them often enough. Giving students problems for which they do not have enough information or skills to solve them is but one example.

But enough of me talking. How would you respond to this darling of the edu-journalism community in 50 words or less?

January 1

Happy New Year!

calling Mark Roulo

I've gotten a bunch of invitations out, but am sure I'm still missing people.

One person I know I'm missing is Mark Roulo.

I need an email address!

labeling failure

From the Times:

To move forward, the country must also find new ways to support and transform failing schools, beyond labeling them failures and presuming that the stigma will inspire better performance.

I don't understand all the hub-bub over labeling schools that are failures as failures. There's nothing wrong with a little truth in advertising. Plus, there's the the what's good for the goose is good for the gander aspect. Schools have been labeling perfectly normal kids who've they failed to teach as "learning disabled" for quite some time now and I don't see the NYT bemoaning that state of affairs.

So what's wrong with calling these failing schools "teaching disabled"? No one ever complains when we call other failed businesses "bankrupt," "underperforming," or "struggling." Why should schools be immune from accurate labeling. At least when we label a school as failing it places the stigma back where it belongs--on the failed education professionals.

If we want the market to work like it's supposed to, accurate labeling is a necessity. When a new family is looking to move into the school district, we want the realtor to be able tell them that the school is "teaching disabled," so unless little Johnny and Susie are super students there's going to be lots or academic failure or the expense of tutors in the family's future.