Onward and upward

Nearly 80 percent of New York City high school graduates need to relearn basic skills before they can enter the City University’s community college system.

The number of kids behind the 8-ball is the highest in years, CBS2′s Marcia Kramer reported Thursday.

Officials: Most NYC High School Grads Need Remedial Help Before Entering CUNY Community Colleges | Basic Skills Like Reading, Writing And Math Need To Be Re-Learned | March 7, 2013 10:55 PM

palisadesk on students reading different words than the ones on the page

I write this post to another board a few years ago to explain a major cause of these errors as in Catherine's example:

In fact there has been some solid research on this phenomenon. I can't cite chapter and verse off the top of my head, but it was done by Engelmann or perhaps others in the DI community, and investigated just that pattern you mention: children who consistently misread when for then, of for from, where for there, and similar errors of words that are usually both syntactically and visually similar. [Catherine here, interrupting for a moment: the problem I was asking about mostly involved substituting one preposition for another.]

I may not be summarizing the research 100% correctly, but the gist of it is that what we are seeing is the result of the learner having been presented with two very similar things at the same time (or almost the same time), and not having been taught either one to mastery, so that the two became fused in memory in an indistinct way, and one would be randomly substituted for the other. In the case of most of these word substitution errors, the child is correct some of the time and incorrect some of the time -- so s/he doesn't ALWAYS read "when" for "then" or vice-versa. S/he randomly says one word or the other whenever s/he is presented with either of the duo. Over time, this habit becomes a neural circuit and a learned response that is very resistant to change. It rarely is self-corrected, the way some other decoding errors are, because the misreading usually makes sense even if it is incorrect (it may not make the CORRECT sense, but it is not unintelligible). "Julia talked to Edith when she went to the mall" means something different from "Julia talked to Edith then she went to the mall", but the inaccurate reader is unlikely to notice. It's not like the horse/house instance, where if a child reads "The rider mounted his house" s/he will usually recognize that can't be right.

The DI research indicated that children easily learn what they called misrules (usually due to poor or misleading initial presentation) , and these word substitution errors fall into that category. The more the error is practiced, the harder it is to supplant it and engrave a correct response. It may take hundreds of corrections of when/then errors before the reader reliably gets those words right (has a new neural pathway). Many examples of b/d confusion are the same thing - they are not visual discrimination errors in most cases, but are simply instances of children not having learned one of the pair thoroughly before the other was introduced. When words *are* visually similar, the likelihood of confusion is increased, but the visual similarity is not the cause of the confusion. Some children, for instance, repeatedly confuse other letter pairs, or words, that bear no resemblance to each other -- r and g, for instance, and further inquiry usually finds these were introduced about the same time, the child was not provided with adequate practice to mastery, DID remember that it was either one sound or the other, and would randomly say either /g/ or /r/ when presented with either stimulus (leading teachers to say "he knew it yesterday!" when they don't appreciate the randomness of the response -- but randomness within a very narrow range of options, usually only 2 or 3). One student I had consistently confused the words "and" and "said" which had no relation or resemblance to each other, but were introduced the same week on his classroom "word wall."

One effective remedial strategy -- not the only one -- is to teach these pairs explicitly, but first one word at a time. With when/then, for instance, practice writing the word, dictating "when" sentences, reading phrases and sentences with "when" and stories with "when" (reminding the student at the outset that /when/ is the word s/he will encounter, and no discrimination between when and then will be required); then do the same with the other in the pair, then mix them up -- but have the student slowly and carefully sound out each word if necessary. The solution to those misrule/misreading learned errors is careful and targeted practice to mastery.

One analogy I use (if someone thinks of a better one, please share) is to compare the student's experience confusing when/then to someone with a drawer full of socks -- let's say 30 pairs of socks, half of them grey and half of them black. If you pull two random socks out of the drawer, you will get a matched set half the time. It may not matter much that you get a mismatched pair the other half. Unless you have some reason to pay attention, you don't need to change anything. A grey sock and a black sock keep your feet warm, so what?

I had an experience a couple of years ago that made me aware of how this process works. I had to go around and do an attendance-taking chore first thing in the morning and check off two or three students in several classrooms (long story why -- not interesting). Most of the students I knew, and I would just look in the door and see if they were there and mark the attendance sheet. One Grade 4 class, however, had 2 girls on this list, both of whom were new to me. They did not look anything alike, really -- different ethnicities, one much taller, but both wore hijab and had very unusual first names. When I was first introduced to them, I failed to ensure I knew which one was which by solidifying identifying details in my mind. Usually, both were present, and I'd look in and say to myself, There's N. and there's F -- good -- but I could have N and F mixed up, I just noted they were both there. They would straighten me out when I met them in the hall, if I addressed them by the wrong name, but I continued to mix them up for months. I realized partway through the year that this was a similar error to the mislearning children sometimes do:

--I was introduced to 2 new items to learn at the same time, and they shared some common features but I did not spend time to adequately solidify recognition of the special features of each

-- I was frequently required to rehearse my mislearning but not in a situation where it mattered if I was correct or not, and where I rarely received corrective feedback so that I could stop myself and say, Wait a minute, N is the shorter one, or some other identifying factor.

-- The more times I repeated my random error (it was random because half the time I got their names right), the more likely I was to repeat it in the future.

-- the problem was solved by one girl moving, so after that I knew the remaining girl's name. Even so, a year later, I sometimes addressed that girl by the other girl's name. The experience did provide me with an insight into how these misrules/ mislearnings happen.

The DI research into this was part of their development of the Corrective Reading Program. They did a lot of empirical testing to find out how many times students needed to get those confusions corrected before they would master them and be error-free. The number of correction required varied with the age of the student -- the longer s/he had been making the error, the more correction required. Secondary students needed many more corrections than primary students. They have published some of this data, but it is not (probably) of that great an interest to most people. The principle of mislearning and misrules and how to correct them is of general interest, however.

So is the preventative measure, one of which is to introduce the items separately (sometimes separated by long periods, days or weeks or months), ensuring each is learned to mastery (in the case of word reading, by sounding-out all through the word, and segmenting all-through-the-word for spelling). At the upper grade levels, the DI programs also have students spell the words aloud in addition to blending and segmenting them. I've been meaning to look up the research on this (I know they included it because it improved results in large-scale field trials) but don't remember the details. Oral spelling of the words is not a feature of the programs for beginning readers.

Other programs I have heard of (not the DI ones) take the bull by the horns and DO introduce commonly confused items together -- but emphasize practice to mastery right at the start, so that the confusion and "practicing mistakes" does not have a chance to occur.

No doubt there are many other reasons why individual students get particular words wrong, but many of these common substitution errors do seem to share the same features and have similar origins. Many beginning readers are not expected to master correspondences or be accurate in their word reading (if they "make meaning" it is enough) so the Engelmann hypothesis and experimental data explain the phenomena I usually see.

I'm going to look through my notes from Morningside re: "close-in non-examples." I remember them having a distinct procedure for teaching two mixed-up words.

Help Desk: algebra remediation

A friend of mine is a special ed teacher at a highly selective science-oriented magnet school. She has observed a number of incoming freshman who are unable to handle beginning (9th grade) algebra. I'm guessing that some (most? all?) of them have no inherent math disability, but have merely been poorly instructed (most come from elementary schools that use Everyday Math/Investigations and from middle schools that use Connected Math).

Anyway, when she asked me what I knew about math remediation programs that might help prepare these kids for algebra, I realized I had absolutely no ideas and should turn to ktm for help. Any suggestions?

slower math students in Singapore

from the Air report on math education in Singapore:

The topic structure in Singapore’s framework is efficient because topics are not taught and retaught as students move through the primary grades. Instead of repeating topics that students have already learned, teachers simply reintroduce them as a foundation on which to build new mathematical content. This practice, however, may not be suitable for students who have more difficulty with mathematics. The Singapore system recognizes that students who have trouble with mathematics may not attain mastery by following Singapore’s regular program of mathematics instruction and that these students may need special assistance to attain competence.

Beginning in grades 5 and 6, Singapore identifies its weaker students on the basis of a general examination of mathematics and language competency. These students receive special assistance and are taught according to a special fifth- and sixth-grade mathematics framework. This special framework mandates that students in the slower track

• receive approximately 30 percent more mathematics instruction than students in the regular track, and

• be exposed to the same mathematical content as students in the regular track, although at a slower pace.

The mathematics framework for students needing compensatory assistance adds review material to strengthen students’ understanding of previously taught content. For example, topics on numbers and geometry taught in grade 4 are repeated at a faster pace in grade 5. The introduction of some new concepts such as ratios, rates, and averages, which are normally introduced in grade 5, are delayed until grade 6 for the weaker students (Ministry of Education, 2001a). What is important, however, is that because slower students spend extra time studying mathematics, topics usually taught in grades 5 and 6 do not have to be completely sacrificed to make room for repetition.6

To support the framework for slower students, Singapore has developed a Learning Support Program to help educators identify these students and provide them with extra help (Ministry of Education 2003c). Mathematics Support Teachers (MST), who receive on-the-job supervision and specialized training to ensure that they are professionally competent, deliver compensatory assistance.

In the United States, we expect all students to meet the standards in state frameworks, but the standards do not help teachers address the needs of slower students. In fact, U.S. standards do not acknowledge that students learn at different rates. No Child Left Behind addresses the needs of failing schools, but it does not directly require that failing students receive help. Although some research evidence supports the belief that students benefit when the curriculum is adjusted to match their ability levels (Loveless, 1999), a distinct alternative curriculum would raise concerns in the United States about potential harm to students from ability grouping. Singapore’s approach differs from traditional ability grouping in that Singapore establishes a framework that requires students to master the same content as other students, not a watered-down curriculum as often happens in U.S. ability grouped classrooms. Singapore also provides extra assistance from an expert teacher.

What the United States Can Learn From Singapore’s World-Class Mathematics System: An Exploratory Study (and what Singapore can learn from the United States)

Apparently teachers in Singapore do not deliver 10-minute mini lessons followed by 40 minutes of one-on-one work with the students who are "struggling."

help desk - precalculus

This year's math course has been a disaster. Beyond disaster, actually. Where math is concerned, this year has been epically^* bad.

Some kind of emergency repair has to happen this summer - but what?

Any suggestions?

I could conceivably sign C. up for an algebra 2/precalculus course at the local community college - but are the teachers there going to be any better? At this point, we desperately need an actual math teacher: a person who can teach math to a student who doesn't teach math to himself.

We could do ALEKS, but ALEKS is super-slow and overwhelmingly procedural; the 1 1/2 courses I took on ALEKS taught me one disembodied procedure after another. At this point disembodied procedures might be better than nothing -- but then again to the extent C. learned anything this year he learned disembodied procedures.

I could insist that the two of us work through Foerster (I own the teacher's edition).

We could work our way through Saxon.

I could advertise for a math teacher or check out the various tutoring companies....

We also have to do serious SAT prep (though that's not going to be onerous & time-consuming).

I'm thinking this wasn't the summer to sign up for the precision teaching institute at Morningside.

^* My neighbor's son, who is a terrific writer, is constantly inventing words he says ought to exist, and having watched him do this a few times, I think he's right. Epic is an excellent word, and its non-existent cousin epically is the word I need today.

education, not remediation

With my tiny district's per pupil spending now somewhere north of $30K and rising, and a new law requiring Response to Intervention, I'm getting desperate.

So this morning I wrote this plea for adopting programs that work and unadopting programs that don't work:

Response to Intervention wouldn't break the bank if we used evidence-based decision making: if we rigorously evaluated curricula and teaching methods for evidence of effectiveness -- and had a Plan B in place for abandoning curricula and teaching methods that aren't working sooner rather than later.

Example: we use 'balanced literacy' to teach reading.

Scientists who study reading instruction, and the National Reading Panel of 2000, tell us that children should be taught to read using "systematic synthetic phonics instruction." Balanced literacy is far less effective than phonics.

Exactly as the science predicts, here in Irvington we have a very large number of struggling readers. I believe the number is currently 18 or 19%, but I will check my notes. We currently have 5.5 "literacy specialists" remediating all of our struggling readers K-8, and after Response to Intervention kicks in I assume we'll have to hire more.

If we were using the program "Jolly Phonics," a field-tested British (pdf file) synthetic phonics curriculum, we would have only 5% of our students struggling to read. That 5% would include kids like my two children with autism.

We can easily afford to teach the 'bottom' 5% of our students in a 1:5 or 1:3 ratio. We're pretty much doing it now.

Moreover, because fluent reading is the core skill underlying all future academic achievement, we would likely have fewer special education students. That is the goal of Response to Intervention law: to reduce the number of students needing special education.

For me, the most important path out of our financial crisis is to ardently embrace evidence-based decision making: do what works, stop doing what doesn't.

In the run-up to the first fields vote, when people were putting up hand-lettered signs overnight, someone put up a sign that said:

EDUCATION
NOT
REMEDIATION

That should be our principle. Remediation is fantastically expensive: it costs the taxpayer who must fund remedial teachers, and, more importantly, it costs the child who is struggling to learn.

Our district-wide goal should be to reduce to the absolute minimum the number of children needing remediation. We should adopt curricula and teaching methods that give our kids success.


update

I can no longer locate the Johnston & Watson PowerPoint that gave the 5% figure (I can email a copy if you'd like to see it). Palisadesk cites 10%.

you are here

from Paul B:

Kids can't do 6 times 7 because they are 'taught' multiple ways to multiply. Then they discover the one they like best (usually involves fingers) and stick to it until somewhere along the way they are given a calculator to expedite things.

They are assessed subjectively. They are promoted without regard to those assessments. And finally, they're never given targeted remediation or practice that is up to the task of keeping them on track.

Other than that there's not much wrong.

I have already confessed my own problems with 6 times 7.

Sadly, Job Security for Me: Everyday Math Marches On

Job security as in academic remedation in the Palo Alto/Portola Valley/Woodside area -- all school districts having adopted Everyday Math.

Here's a snippet from Old Math, New Math : Everyday Math, aka Chicago Math by Roxane Dover at Silicon Valley Moms' Blog (who also blogs at Rox and Roll)

I had seen firsthand the effects of a problematic math curriculum on otherwise motivated kids. My daughter is a keen student who is interested in math and science to a surprising level. We want to encourage our daughter to stay her course – and hopefully, one day, she will be among those solving the energy crisis, curing cancer or healing the environment. Mastery of math is key to success in science. What I saw when my daughter experienced Everyday Math for three years in K-2 was a rejection of math out of frustration and a related inability to master basic mathematical concepts because of the Everyday Math approach of teaching every concept in too many different ways. This approach gives students a cursory understanding of several ways of addressing concepts at the expense of mastery.

Specifically, mastery falls victim to a concept called “spiraling.” Spiraling means that concepts are introduced but not necessarily mastered before new concepts are introduced, then the previously introduced concepts are revisited and built upon before something else new comes along, repeat. Mathematics learning, which should be progressive and built on a solid foundation, is replaced in this curriculum by a method of throwing a multitude of ideas at the kids without giving the kids time to properly internalize them to create that solid groundwork. It’s like cooking spaghetti and testing it by throwing a handful of noodles at the wall to see what sticks. Everyday Math doesn’t want it all to stick; it’s just concerned that some of it does. And that’s not good enough to build the solid mathematical groundwork that our children require.

From the San Jose Mercury News:

Critics, however, say the curriculum and its nontraditional algorithms are confusing. "Everyday Math" follows a "spiraling" method, where students move quickly through new concepts and may not necessarily learn them the first time around, but they revisit them over and over again in different formats or applications. They also say it encourages students to use calculators too often.

They never develop mastery, said R. James Milgram, a Stanford University math professor who sat on a state curriculum review committee in 2000 when the state rejected "Everyday Math."

"The mathematics these kids are seeing is hardly mathematics at all," Milgram said. "They learn a mush of things, most of which are just wrong."

Milgram said that while the program at its core makes sense, there are only 500 or 600 elementary teachers in the state with the expertise to teach it properly. He said he has seen enrollment in "Everyday Math" districts contract as parents pull out their students and send them to private schools, and said that could happen in Palo Alto.

One local preK-5 private school saw a 28% jump in admissions applications. This when local unemployment is at 11%.