Fuzzy Math Must Cause Fuzzy Logic

Constructivist educators say the kookiest things sometimes. Here's a good example in today's NYT.

Many parents and teachers remain committed to the goals of reform math, having children understand what they are doing rather than simply memorizing and parroting answers. Traditional math instruction did not work for most students, say reform math proponents like Virginia Warfield, a professor at the University of Washington.

Have you ever read an article on education that didn't contain enough false dilemmas to fill an undergraduate logic text?

There's reform math on one hand that has "children understand what they are doing" though no one has ever been able to prove that this is in fact the case since students taught using typical constructivist math programs tend to score just as poorly as the more traditional math programs which simply require "memorizing and parroting answers." Oddly enough, if constructivist taught students were better at "parroting answers" we might not have a math war going on now would we. But, the sad fact is that they are not any better than the traditionally taught kids in this regard which tends to give one pause when constructivists parrot the "children understand what they are doing" meme. No doubt such sentiments were learned by rote.

There is some truth in the "[t]raditional math instruction did not work for most students" meme that traditional math proponents should take to heart. Same holds for proponents of traditional phonics instruction. Most traditional math and phonics programs weren't and aren't any good, though constructivist heavy math and balanced literacy programs offer no improvements other than rosy rhetoric.

One area where reform math programs do fall down is in computation skills. All those hide-the -ball problem solving lessons that chews up mucho class time come at the expense of the all important practice that all but the looniest constructivists recognize is still needed to learn math. Understanding math (whatever that means) may be beneficial, but if that understanding doesn't translate into computational fluency, then the hapless students are not going to have a fun time in algebra or anything else that comes later.

Moving right along.

"It produces people who hate math, who can't connect the math they are doing with anything in their lives," Dr. Warfield said. "That's why we have so many parents who see their children having trouble with math and say 'Honey, don't worry. I never could do math either.'"

Any program that does not result in students learning math is going to cause those students to hate math. Those who can't do math (and by do, I mean compute) won't be able "connect the math they are doing with anything in their lives."

If constructivist taught students hate math any less than traditionally taught students it is not because they understand or are any better in math. Such has never been shown in any legitimate study. Only possible explanation is the "ignorance is bliss" theory that might be causing all this unexplained happiness. Kids who are never asked to do long division or manipulate fractions aren't going to be too upset that they can't do those things.

In part, the math wars have grown out of a struggle between professional mathematicians, who say too many American students never master basic math skills, and math educators, who say children who construct their own problem-solving strategies retain their math skills better than those who just memorize the algorithm that produces the correct answer.

Talk is cheap. Educators can say whatever they want. But, no one has ever proven that "children who construct their own problem-solving strategies retain their math skills better."

Remember, these kids who've constructed their own problem-solving strategies aren't scoring any better in test of simple math skills. They might be retaining something better, like maybe all the bad strategies they discovered along the way, but it's not math skills.

Memorizing the algorithm isn't going to do squat either. Practicing the algorithm until it can be performed with automaticity is what's needed. And, if it can be taught in an efficient way so that it is learned with understanding, all the better. It is a conceit of constructivists that they believe they are the only ones teaching with understanding. That and the inability to distinguish between memorization and practice leads one to the conclusion that they really have no idea what they are talking about.

No Discernible Effects

The What Works Clearinghouse has released a report on the research base of the elementary math program Saxon Math. The conclusion:

No Discernible Effects

Only one of the seven studies met the WWC's criteria with reservations.

Resendez & Manley (2005) reported no significant effects of the Saxon Elementary School Math program on overall mathematics achievement at grades 1–5. Using school-level data provided by the authors, the WWC confirmed that Saxon Elementary School Math did not have a statistically significant or substantively important effect on math achievement at each grade level from first to fifth grade. Based on this study finding, the WWC categorized Saxon Elementary School Math as having no discernible effects on overall math achievement.

The average performance gain was +7 percentile points which is not educationally significant. Compare this to the average gain of +12 percentile points for Everyday Math.

For both math programs, most of the results were not statistically significant.

I'd say that a school district has little basis to switch from whatever it is they are currently using to either of these math programs based on the research reviewed by the WWC.

It's the Vocabulary, Stupid

As was noted in the comments of this post, teaching low-IQ kids is exceedingly difficult. The problem is that low-IQ kids learn more slowly than their smarter peers. Unless we accelerate the learning of these kids, they will fall further and further behind.

We know how to accelerate the learning of some, but not yet all, of the many important academic skills.

We know how to accelerate the learning of written word decoding (i.e., reading) by teaching forty sounds and by teaching how to blend those sounds rapidly together. Thus, a general case can be learned that will permit the reading of any regular-sound English word. And, in this way, a great efficiency in teaching is achieved when a relatively small set of building blocks can be recombined into a large set of applications. Almost all kids without a cognitive disability can be taught to decode in a timely manner.

Similarly, spelling can be efficiently taught by using a related process of spelling-by-sounds, which is an effective procedure for spelling words with regular letter-sound correspondences. The process also assists with the spelling of irregular words.

Elementary math can also be efficiently taught as several problem-solving skills that operate as general cases. These cases have more limited applications than decoding, however, and thus generate less net gain in accelerated learning.

Language skills, involving general cases of grammatical rules and word classifications, appear to have about the same level of potency as arithmetic. Thus, language skills are also teachable even to low IQ kids.

The performance of lower performers can be accelerated to national norms by the end of third grade in reading, math, spelling and grammar skills through careful instruction. And, it stands to reason, that the academic performance of higher performers can also be accelerated at least as dramatically.

What remains a problem, however, is the acquisition of vocabulary and underlying concepts, which is not nearly as amenable to general case learning. The learning of vocabulary is a "linear additive set" which is described as follows:

In a linear additive set, the learning of one element gives little advantage in learning a new element. To be sure, there are families of words that have common root meanings and common meanings of affixes, which permit some limited general cases to be generated. But, by and large, the learning of proper names, new concepts, and the learning of synonyms for concepts already known by another name, involve linear additive sets in which each new element must be taught. Knowledge of the English language, which is absolutely essential to oral and written comprehension, serves largely to define intelligent behavior (Miner, 1957). Teaching this language involves a task of the first magnitude.

Generally speaking, schools do not systematically build vocabulary-concept knowledge. Current programs are structured to teach middle-class children or children who, to a large extent, are taught oral-language comprehension at home. It is assumed that this form of language learning is then transferred to reading comprehension at school.

Most schools employ some sort of basal reading program until the third grade which utilize a controlled vocabulary for instruction. Typically, about 1,500 hundred words are covered at this time. And, the average student has a working oral vocabulary of two to three times this size.

After the third grade, vocabulary shifts to an increasingly uncontrolled adult vocabulary. It is estimated that, on the average, 5,000 words are learned after third grade. Since schools do not systematically build vocabulary knowledge, students with weak home training in English language skills are often in trouble by fourth grade, if not earlier. It is this vocabulary-concept knowledge deficit that plays a major role in reading comprehension problems.

It is the vocabulary deficit that remains the educational sticking point for lower performers, though some inroads have been made. Since low IQ kids do not learn as quickly as higher IQ kids, their vocabulary acquisition rate is significantly reduced. The problem is compounded because low IQ kids tend to have low IQ parents and the language used at home tends to be much lower than in higher IQ families:

In an important study, White et al. (1990) investigated reading vocabulary size and growth differences between students in grades 1 through 4 in two low socioeconomic status (SES) schools and one middle SES school. Reading vocabulary was defined as the number of printed words that were both decoded and understood. White et al. (1990) found that even in grade 1, there were important differences in the size of the reading vocabularies of students in the middle SES school (about 4,800 words out of 19,050) compared to students in the two low SES schools (about 3,500 and 2,500 words, respectively). Also, the differences between the number of words known by students at each grade level indicated that vocabulary increases may exceed the 3,000 words per year commonly referenced (e.g., Baumann & Kameenui, 1991; Beck & McKeown, 1991; Graves, 1986). A prevailing finding was that vocabulary growth appeared to differ on the basis of SES. The vocabulary size of the students in the middle SES school increased by about 5,200 words per year while that of the students in the two low SES schools increased by about 3,500 words per year.

Further compounding the problem is that schools are increasing downplaying the need to learn facts, i.e., vocabulary and underlying concepts, in favor of higher order thinking and other constructivist laden nonsense. The logical processes involved in reading comprehension are general case sets which can be taught with some efficiency. Research has shown that when "poor readers" understand and are familiar with the concepts presented in a written passage their reading comprehension is at least as good as "better readers" who are not familiar with the concepts.

For example, in one study (Recht and Leslie, 1988), the researchers tested junior high school students who were either good or poor readers (as measured by a standard reading test) and who were also knowledgeable or not about the game of baseball (as measured by a test created for the study by three semi-professional baseball players). The children read a passage written at an early 5th-grade reading level that described a half inning of a baseball game. The passage was divided into five parts, and after each part the student was asked to use a replica of a baseball field and players to reenact and describe what they read. The researchers found that baseball knowledge had a big impact on performance: Poor readers with a high knowledge of baseball displayed better comprehension than good readers with a low knowledge of baseball.

If you've been reading this blog for the past few weeks and caught my series on how the brain works, you might be able to adduce what's going on here.

[T]he students with a lot of knowledge of baseball were able to read a series of actions and chunk them. (For example, if some of the text described the shortstop throwing the ball to the second baseman and the second baseman throwing the ball to the first baseman resulting in two runners being out, the students with baseball knowledge would chunk those actions by recognizing them as a double play--but the students without baseball knowledge would have to try to remember the whole series of actions.) Second, because they were able to chunk, the students with baseball knowledge had free space in their working memory that they could devote to using the replica to reenact the play as well as providing a coherent verbal explanation. Without being able to chunk, the students with little baseball knowledge simply didn't have enough free space in their working memory to simultaneously remember all of the actions, keep track of their order, do the reenactment, and describe the reenactment.

It is possible that low IQ kids may lack the cognitive abilities required to perform higher order abstract thinking, such as theoretical mathematics and the like. But, it is unlikely that such skills are required at the K-12 level. So, such a shortcoming is likely not a limiting factor for learning at this level. The problem is much simpler than that. The problem is that these lower IQ kids are simply not learning oral comprehension as quickly as their smarter peers and such learning is not as amenable to acceleration of learning through optimized instruction.

Currently schools are mostly structured to teach middle-class children or children who, to a large extent, are taught oral-language comprehension at home. This is why IQ correlates so well with general language ability. Smarter kids learn faster, are exposed to more vocabulary at home, read more, and, as a result, learn more of what's taught at school. Slower kids learn slower, are exposed to less vocabulary at home, read less, and as a result learn less at school.

Becker recognized this problem 30 years ago in his analysis of the Project Follow Through data.

Children coming from home backgrounds that fail to provide adequate training for the continuous growth of vocabulary and concepts are likely to continue to fall behind in public schools. Even after four years of intensive effort, children taught in the Direct Instruction Model are far short of an average high-school senior's vocabulary--a vocabulary that is presumed by most fourth-grade tests.

The data on our fifth and sixth graders strongly imply that the schools fail to build skills toward this goal. One might conclude that this is simply more evidence of the failure of compensatory education. When viewed from a different perspective, however, the data point to a failure of school programs to accomplish their assigned roles.

Advocates of compensatory education assumed that all learning problems would be solved by finding the critical stage where some magic could be applied to fertilize cognition. The Follow Through data suggest that a magical solution is unlikely.

Massive restructuring of school systems is required. As schools are presently constituted, there is no way that low-performing children can be adequately prepared for the vocabulary they will encounter by the fourth grade. Clearly, the first step toward improving this situation is to recognize that language learning does not end by the third grade. Once this is understood, programs can then be engineered to teach vocabulary-concept knowledge in a systematic way throughout the school years.

Much has been learned in the intervening years and the teaching of vocabulary has improved so that lower performing students at least up to the fifth grade level can continue to perform at national norm levels in reading comprehension. But, in most schools it is still business as usual with vocabulary acquisition still being downplayed or ignored all too frequently.

Today's Education Strawman ...

... comes courtesy of Australia's The Age attacking the idea of a national curriculum. But once you start reading the article you quickly realize that the columnist has more a beef with the particular national curriculum chosen, rather than the concept of national curriculum generally.

The columnist humanizes the argument by finding a dupe pre-service teacher, Sarah, and using her as an unwitting mouthpiece.

Earlier this year, Sarah had a disquieting teaching experience. She taught the latest in "direct phonics" lessons to a group of secondary school students in Melbourne who were deemed to need remedial help.

The passive voice -- the lazy columnist's best friend.

So here we have high school students who apparently can't read well because they lack decoding skills. The school appears to have placed them in a "direct phonics" course to remediate these skills. I assume that direct phonics (in scare quotes naturally) means that the students will be taught synthetic phonics (i.e., sounds are taught how to be blended rapidly) in a direct systematic and intensive manner. The reason, no doubt,is because this is the only kind of phonics that is effective with struggling readers, like these high school kids.

One can assume that if these kids are in high school and are still read poorly however they were taught to read in the lower grades, probably not a direct phonics, didn't work.

The lesson was completely scripted for Sarah. In a foretaste of what is in store for students in the centralised curriculum model currently described by neoconservative politicians and media pundits, it was a one-size-fits-all lesson that could be taught anywhere across the nation, at any time.

A truly impressive string of cliches.

I suspect that automobile manufacturers used to say the same sort of nonsense about Henry Ford when he standardized the manufacture of automobiles. Then they either adapted or went out of business, so we don't hear about such complaints much any more.

One reason to standardize the curriculum is to improve quality control, the sort of quality control that might have prevented kids from reaching the high school level not knowing how to read well. "A supervisor entering a classroom can quickly determine what is happening and compare this with what should be occurring. The supervisor, therefore, is better equipped
to provide direct, practical demonstrations or suggestions to the teacher or aide. By standardizing the teaching program in this way, it is also easier to monitor the progress of the
children with criterion-referenced tests that children should pass if they have completed lessons at a specified level."

Then we have the "scripted lesson" critique. We are lead to believe that novice teacher Sarah, fresh out of school will magically turn out to be a master teacher. Perhaps, she'll be mentored by the schools current crop of expert teachers-- you know, the ones that weren't able to teach our hapless high schoolers. Scripted lessons are a hot button topic for educators. So why do many successful curricula use them -- because they work:

The scripts permit the selection and testing of sequences of examples that produce efficient learning if followed. Most teachers simply do not have time to find appropriate words and examples or to sequence skill hierarchies in the most efficient possible manner. When teachers phrase their own questions, they may choose terms unknown to lower-performing children or may include unnecessary verbiage. In choosing examples, moreover, they may teach incorrect rules because the positive examples have some irrelevant feature in common. In sequencing, it is easy to omit those skills critical for later, more complex tasks.

It's all about quality control. Back to the column.

In one 35-minute period of "teaching", every word that Sarah spoke, the precise time at which she delivered these words, and even the hand signals to accompany the words, were all tightly scripted.

Now we have "teach" in scare quotes. I wonder if the columnist would put scare quotes around his description of the failed teaching that preceded this?

We also learn that signals are bad when used as a cue for students to respond together. When students respond in unison, the teacher can determine which ones understand what is being taught (the ones who responded) and the ones who don't (the ones that didn't respond or incorrectly responded). This permits the teacher to provide a remedy to the students who still need more instruction. Another way of saying this is that signals permit the teacher to differentiate the instruction by targeting students who need more instruction and determining when they have learned. So much for one size fits all.

According to educators, signals are apparently good for choir and band practice, but bad when teaching reading, even though the effective use of signals obviates the problem of having the slower kids imitate the faster kids when responding. Without signals, it becomes difficult to determine who has learned the material and who is merely parroting what the smarter kids are saying.

When Sarah talked with me (her English education lecturer) some time after this experience, she had mixed emotions. After an exhausting week of planning, teaching, marking, staff meetings, in-service activities and much more, this scripted curriculum seemed a welcome relief. "I didn't have to think," she said.

She laughed, although it was clear she was still ambivalent about the experience. Then she asked: "But what sort of teaching is it when I'm not required to think?"

Presumably better that the instruction the kids received previously which forced the state (the entity running the schools) to intervene against the wishes of the educators, who were failing to do perform their job adequately.

The only time teaching a scripted lesson requires little thinking is when all the students are responding correctly. Students who are responding correctly are learning the material. Then the script, really is like the lines delivered by an actress and all the teacher has to do is read the lines, making sure that the students are responding correctly. This is a job most people would kill for.

However, invariably, there will come a time when some students will not respond correctly when they are supposed to. This is where the teaching comes into play. At this point the teacher has to first recognize that the students have responded incorrectly and then to provide a remedy. This requires the teacher to deviate from the script and follow the specified correction procedure, fix the mistake in learning, and then resume with the lesson. In this case the script is more like a flow chart and the teacher is required to make all the difficult decisions to know when to provide remedies when students aren't learning in addition to presenting the scripted material inn a lively and brisk manner that keeps the students on task and engaged.

This remains an exceeding difficult job than requires much training and classroom ability for teachers to get right. The experience is that teachers need at least two years of training to know how to teach the scripts correctly with low performing children so that these children are actually learning instead of being passed through the system as they are currently. This job requires a lot of thinking, otherwise we'd hire monkeys to read the scripts to children-- they work for bananas.

Now you should be able to answer the columnist's rhetorical question.

Indeed. At a time when neo-conservative commentators and politicians are touting the benefits of an efficient, centrally controlled curriculum, where decision making at the local level is taken out of the hands of teachers and schools, Sarah's story should give us cause to reflect.

Parents might well ask: Is this the sort of curriculum we want for our children? Do we want our children taught by a teacher who is not required to think?

No, we want them to continue to fail to learn how to read, write, and do math as they currently are. Idiot.

Studies Show ...

American Institutes for Research (AIR) has updated their Comprehensive School Reform Quality Center Report on Elementary School Comprehensive School Reform Models (PDF) to include new research studies.

As in its previous study, the Direct Instruction Model and Success for All were found to be the most successful models. The report also points out that only a few of the models had a substantial research base to support their effectiveness.

For more than one third of the models, the CSRQ Center identified only 10 or fewer studies that seemed to be relevant for our review of the overall evidence of positive effects of the models on student achievement. In contrast, one model (Direct Instruction) had more than 50 and another (Success for All) had more than 100 studies that were originally considered for review in Category 1. After screening more than 800 studies for quality in Category 1, we found 95 studies that met CSRQ Center standards. Again, these were unevenly distributed, with nearly one fourth of the models having no studies that met CSRQ Center standards and with
five models (America’s Choice School Design, Direct Instruction, Literacy Collaborative, School Development Program, and Success for All) having five or more studies that met CSRQ Center standards.

I liked this gem from the Direct Instruction description.

Based on its experience, NIFDI feels that family and community involvement is peripheral to accomplishing its mission to accelerate student achievement. The NIFDI model assumes that since parental involvement cannot be controlled by school leaders, the Full Immersion Model of DI should not require parental involvement.

If you read the edusphere blogs, you'll know that parental involvement is frequently touted as the holy grail of education reform. Good work if you can get it.

It is not a coincidence that the two education reform models, DI and SfA, that achieve the best results, i.e., significant boost student achievement, dramatically alter the structure and nature of schooling. This is because schools, as they are currently configured, are not concerned with student achievement, especially the achievement of low-SES and low-IQ kids.

But don't get your hopes up just yet because another study by Rand finds that MOST SCHOOLS FAIL TO FULLY ADOPT REFORM MODELS DESIGNED TO BOOST STUDENT ACHIEVEMENT.

Schools that embrace comprehensive reform models designed to improve student achievement frequently do not fully adopt all practices recommended by the model developers, according to a RAND Corporation report issued today. The findings call into question whether the comprehensive school reform model approach that has been adopted by more than 8,000 schools nationally can become a key strategy to help improve student performance. A survey of 250 schools from Florida and Texas that embraced comprehensive school reform models found that none had adopted all of the changes the models called for to boost student achievement, according to the study by RAND Education. The reason most often cited for failing to adopt all aspects of the reform packages was a shortage of support for needed improvements and investments such as teacher training. "

At the current level of implementation, comprehensive school reform models are likely to have only modest or no effect on student achievement," said lead author of the report Georges Vernez, who is a senior social scientist at RAND, a nonprofit research organization. "Without substantially more support, it is not likely most schools will be able to faithfully adopt these models of school improvement." Comprehensive school reform is based on the idea that a school should have a coherent educational strategy that addresses every aspect of its operation.

More than $2 billion in federal funds have been used to implement the approach at schools nationally. Studies assessing the success of comprehensive school reform models have been mixed, with some showing a modest improvement in student achievement and others finding no impact. Most of those studies assumed schools had adopted all aspects of the reforms. RAND researchers surveyed principals and teachers at the schools in the study, and visited a number of campuses in order to more closely assess adoption of the chosen comprehensive school reform model. Researchers found some types of changes were embraced more often than others. Schools were most likely to adopt the curriculum prescribed by the model developer, but were less likely to adopt the recommended instructional practices.

Practices designed to increase parental involvement were the aspect least likely to be adopted. Most of the schools in the study did not have the level of support recommended by developers of the models. Teachers reported receiving about half of the recommended initial training and only one-quarter of the recommended ongoing professional development, according to RAND researchers. In general, teachers reported a lukewarm commitment to adopting their school's reform model and most felt the training they received was not adequate. However, in schools where the level of support increased, so did adoption of the developer-recommended practices, according to researchers.

You can lead a horse to water, but you can't make it drink.

New Look

Experimenting with Beta Blogger's new templates. Might be a little messy until I work out the kinks. You've been warned.

On Textbooks

Bob Dixon, on math textbooks:

And speaking of asking kids to do something they haven't been taught, "critical thinking" problems are a regular part of the text. Those problems are much like the ones we'd see in a book of brainteasers. Here's one:

Work with a partner. [Good idea, especially if your partner is an adult who knows how to do problems like this.] Arrange the digits 1, 2, 3, 4, 5, 6, 7, and 8 into two decimals so that their sum is as close to 1 as possible. Use each digit only once. The sum cannot be equal to or greater than 1.

They [also] have these "critical thinking" problems along the lines:

Jane is 7 years older than her brother, and the sum of their ages, plus 5, multiplied by 4, is the age of their house. How old is everyone and everything?

The people who author these books are the same ones who look back derisively at my mathematics education because we had to figure out when a couple of trains, leaving opposite coasts and going different speeds, would meet up. The problem wasn't all that authentic, but I think the algebra for solving it was. I have nothing against the "Jane is 7 years ..." problem per se. If you've taught the algebra for solving ... just about anything ... then no problem. But in my daughter's text, "critical thinking" means "something relatively difficult to do that we haven't taught anyone how to do, mostly because we don'’t know how to do that."

Bad Schools, Not Poverty, Cause Bad Student Performance

I've been playing around with the 2005/2006 released scores for Pennsylvania's PSSA exam while doing a little research on the KIPP school in Philadelphia and stumbled upon a few interesting results.

A few months back, the edusphere was atwitter with Richard Rothstein's Kozol-esque claim that poor kids would perform better if they were placed in more affluent schools.

Let's see if this claim has any bearing to reality (at least in Pennsylvania).

I looked at the the data for the 7th grade PSSA exam, a grade when most poor kids have not yet dropped out. There were 803 schools with disaggreagated data for low SES students.

I limited my analysis to schools to good schools, i.e., schools that were capable of successfully educating poor kids. My theory is that bad schools are the cause of education failure in of and themselves. This failuire hits poor kids especially hard.

I defined "good school" as being any school whose pass rate for poor kids was above 67.3, the state mean. I was left with 140 schools (17.4%), showing you what a rotten job our schools do with poor kids in general. I was under the impression that the reason we have this expensive public education system in the first place is to educate all these kids who otherwise couldn't afford to be educated on their own. As always, socializing the problem by getting big government involved has failed to solve the problem. But I digress.

Then I determined the performance of these good schools having high concentrations of poor kids (greater than 50%). Only 18 schools met the criteria. The average concentration of poor kids in these schools was 72%. The average pass rate for these schools turned out to be 76.6%.

As a point of comparison, there were 258 "bad" schools (93.5%) with highly concentrated (average concentration: 81.4%) poor students. The average pass rate for the poor kids in these bad schools was an abysmal 38.9%.

Next, I determined the performance of the good schools with low concentrations of poor students (less than 50%). 112 schools met the criteria and had an average concentration of 24.3% poor kids. The average pass rate for these schools turned out to be 74.7%.

The pass rate for the 410 low concentration (27.3%) "bad schools" was 52.9%.

The conclusion is that Rothstein and Kozol are wrong. Poor kids in predmoniantly poor schools will perform about the same as poor kids in more affluent schools as long as the school is a good school. The problem is that the vast majority of our schools aren't any good. In these schools there is over a half a standard deviation disparity in the performance of poor kids in predominantly poor schools.

The problem isn't poverty; the problem is bad schools.

Those Who Can't Teach, Inflate Grades

The headline to of this Pittsburgh Post-Gazette article intrigued me:

Tougher reading program means low city grades

Let's see what's going on.

Parents of some Pittsburgh elementary school students will find an unwelcome surprise -- unusually low marks in reading -- when their children bring home report cards Nov. 17.

Because the Pittsburgh Public Schools this fall introduced a standardized grading system and what it described as a more rigorous reading program, some students have seen their performance slip on classroom tests.

That will translate into lower grades on report cards than parents are accustomed to seeing, said Susan Sauer, curriculum supervisor for elementary reading, and Barbara Rudiak, executive director for 18 district elementary schools. Some parents already have noticed a drop in their children's test scores.

Ok, so it wasn't the more rigorous program that caused the drop in grades, it was the switch to a standardized grading system. But it gets better.

"This has created a certain amount of controversy with principals, parents and teachers," said Dr. Rudiak, who is project manager for the "Treasures" reading program, purchased from Macmillan/McGraw-Hill for about 13,250 students in kindergarten through grade five. The program is also used in elementary classrooms at the district's K-8 schools and accelerated learning academies.

Low grades cause controversy because they show schools aren't teaching. Most professions would respond to feedback indicating widespread practioner underperfformance by trying to self-regulate and improve before the government steps in. What do you think the educrats will do?

Go read RightWingProf's post on academic groupthink first and see if that influences your answer. We'll wait.

While we wait, let me tell you about Pittsburgh's new reading program "Treasures" which is a new basal reading program that tries to mimic reading research in an attempt to qualify for Reading First funds. The important thing is that it has not been researched and it has no evidence of success. What it does have is lots of pretty pictures. Many school districts selected this program on this basis rather than the more rigorous "does it actually work" basis. Lets dub this the Pretty Picture Fallacy.

But even in education, you reap what you sow, pretty pirctures not withstanding, as we're about to find out.

Aligned to state learning standards and the federal No Child Left Behind Act, the program should boost student performance on the Pennsylvania System of School Assessment, said Richard Sternberg, principal of Grandview Elementary in Allentown and president of the Pittsburgh Administrators Association.

Ms. Sauer and Dr. Rudiak said changes in elementary reading complement the district's "Excellence for All" plan, which includes a 2009 deadline for academic improvement.

Should boost performance? Should boost performance?

Based on what, you may ask.

Based on the typical educrat standby -- a wild ass guess. This is how education works in this country.

Educators select new programs based on such tangibles as pretty pictures and other faddish nonsense, and then guess, without evidence, that it'll work. When it turns out five or six years later that the new program doesn't work, the next best thing will be out and they'll switch to that without remorse and without regard to all the children damaged by the current program.

And, just because this is a phonics based program containing the five essential elements of reading instruction doesn't mean that it's any more likely to succeed. Such reasoning is based on the following logical fallacy:

If a dog is a Dalmatian, it has spots.
Therefore, if a dog has spots, it is a Dalmatian.

The first statement is true. The second statement doesn't follow from the
first.

The probable response from most readers is that nobody could be naive enough not to recognize this flaw. English setters, some terriers, sheepdogs, and many mutts have spots. Unfortunately, there are many educational parallels to the argument that all dogs with spots are Dalmatians. Here's one:

If a beginning-reading program is highly effective, it has various features: phonics, phonemic awareness, and so on.
Therefore, if a program has these features, it will be highly effective.

Current reform practices revolve around this logic, but the logic is as flawed when it refers to effective programs as it is when it refers to Dalmatians.

It takes a lot more than phonics to make a good reading program. It takes a lot more than reading comprehension, vocabulary, fluency, and phonemic awareness for that matter.

There's only two ways to know whether a reading program has fit the puzzle together correctly--test it beforehand or inflict it on hapless students and let the chips lie where they may. Course two is the typical course of action taken by most publishers by the way.

If we want to find out how well the program works, the fail safe method is to look at the performance of the students, under, say, a fair grading system.

Before this school year, each teacher decided what constituted an "A" or other grade in elementary reading. Some teachers gave more weight to take-home work than colleagues did, and some teachers designed their own tests because they didn't like those provided with the previous program, Harcourt "Collections," Ms. Sauer and Dr. Rudiak said.

Such discretion has been eliminated as the district standardizes instruction within a school and among schools to promote equal treatment of students, they said. All teachers now use tests provided with the "Treasures" program.

The distinction the journalist was looking for, but failed to produce, was the objective vs. subjective distinction. The old grading scheme was subjective and permitted the schools, through the teachers, to juice up the grades by making easy tests, grading tests more easily, and/or giving more weight to non-test work (i.e., more subjective criteria).

The new grading scheme is more objective and takes power away from the schools to fudge grades by using their own subjective measures.

Educators don't like objectivity and empirical results. You'll find out why this is so soon enough if you don't know already.

Initially, the district decided that the weekly tests would make up 40 percent of a student's grade; unit tests, given about every five weeks, 50 percent; and assignments, 10 percent.

But that formula quickly yielded so precipitous and widespread a drop in grades that officials revised the system. In hindsight, Dr. Rudiak said, the initial formula gave too much weight to tests -- and did so when the format was brand new to students and teachers.

Imagine if you were a patient getting treated for a broken arm using a new experimental treatment. After the treatment the doctor makes you get an x-ray to see if the bone set properly. The x-ray shows the bone did not set right. The doctor, however, tells you that the x-ray machine has indicated too many mis-set bones using this new treatment, so the doctor tells you that they've adopted an additional criterion for determining if bones are really set properly. If the patient filled out his insurance forms correctly, then they've been a good patient and good patients heal properly. Therefore, your broken arm has set properly. You leave the doctors office relieved that the new treatment has successfully healed you, even though your bone has not set properly.

This is what's going on in Pittsburgh. The objective tests made by the curriculum publisher are indicating that kids aren't learning what the publisher intended.

There are three potential reasons for this: one, the curriculum isn't any good; two, the teaching isn't any good; or three, some combination of one and two.

I'm going with option three. The curriculum is untested and the authors of that curriculum have no track record of success and the schools in Pittsburgh have no track record of success teaching kids like the kids in the Pittsburgh school district.

Pittsburgh Federation of Teachers President John Tarka said his members advocated for a change in the grading system to keep students from being unfairly penalized. While cautioning that "we have more work to do," he said the revised formula is better for students and restores some of the flexibility teachers need to be effective.

"There's a fine line between there not being guidance and something being too rigid. Neither one is good," Mr. Tarka said.

Could someone explain these two paragraphs to me in a way that makes sense.

How does allowing students to pass when tests indicate that they've failed "unfairly penaliz[e]" the student? Is it that under NCLB, failing students indicate failing schools?

And, how does allowing schools to pass kids who don't deserve to pass enable teachers to be effective? Effective in what? Social promotion?

Assignments now make up 30 percent of the grade, while unit tests and weekly tests each account for 35 percent. Ms. Sauer and Dr. Rudiak said they still expect some students to have lower-than-typical report card grades, in part because of the rigorous "Treasures" program.

While the Harcourt program tested students on passages they had read before, "Treasures" requires students to apply comprehension and other skills to unfamiliar texts. It includes more nonfiction passages than the old program.

So now subjective assignments are worth three times as much, and even that won't mask the failure in the Pittsburgh school district.

Ms. Sauer and Dr. Rudiak said additional adjustments to the grading system may occur in the future. Mr. Sternberg said students are catching on.

"As a matter of fact, they're starting to do better now," he said.

Better than what?

Continued Light Blogging Today

Here's some recommended reading in my absence:

Elementary History Teacher has a good post on the educrats in her state mandating that social studies be taught thematically instead of chronologically.

Edspresso has a good post on the new Kipp Philadelphia school which has in three short years managed to get some amazing results out of its first cohort of students, now in seventh grade, who've been in the school since fifth grade. I'll have more on this tomorrow.

Kitchen Table Math has had a lot of good posts on mastery learning in the past week that are a good continuation of my "how we learn" posts.

Financial Woes in the Philly School District

Readership of the Philly Inquirer and Daily News is so low that these papers are being forced to lay-off staff. One reason is the high incidence of lame-brained agenda journalism, such as articles like this one on the "protests" which have arisen due to the budget cuts threatened by the Philly School District.

Parents and students will rally outside school district headquarters this afternoon to protest cuts being considered to erase a $73 million budget shortfall.

"We're drawing a line in the sand," said Helen Gym, a parent activist. "We're calling for a protective order on our schools. There will not be another school cut."

The protest comes in the wake of last week's finger pointing among city and school officials over the budget deficit.

The article starts off with the big number fallacy--big numbers given out of context look impressive. The author might as well say 289.5 gazillion; that means about as much sense to the reader. Better yet, the author should have just written the first paragraph like this to achieve the same effect:

Parents and students will rally outside school district headquarters this afternoon to protest cuts being considered to erase a really super big budget shortfall.

Had the journalist lacked an agenda and wanted to accurately report the budget shortfall in an informative way it would have taken five minutes of work.

According to the district's own budget numbers, it had $1.9 billion dollars budgeted for FY 2005/2006 and there were 176,000 students attending schools in the district. Do the math.

A $73 million cut, represents a cut of $414 per student from operating expenditures of about $10,875 per student. (Actually, according to School Matters, the district's total expenditures were $12,761 per pupil in 2004 alone which is a better indicator of the district's profligate spending.)

That's a cut of about 4.0%. Are the tears welling-up yet?

How about if I told you this little nugget from p. 23 of the budget:

Enrollment in District-operated schools continues to decline from about 182,000 to about 176,000 in part due to the DistrictÂ’s continued support for charter school expansion.

Let's do the math: (182,000 -176,000)($10,875) = $65 million. So, if the district trimmed expenses to account for the drop of 6,000 students this year, the cut needed would be only $8 million at best.

And, if the district hadn't built the School of the Future (p. 13), cost $63 million, they'd be running a $55 million surplus.

Let's recap:

• The district spends somewhere between about $11k to $13k per student. Cutting $414 per student is like removing a pimple of the ass of this bloated budget.
• The district lost 6,000 students, so cuts should be inevitable and shouldn't affect the quality of education.
• The district wastes a lot of money, such as on boondoogles like the school of the future.
  

I also noticed that the journalist failed to mention that the mayor of Philadelphia, a majority of councilmen, and the governor of Pennsylvania are all Democrats. I'm sure, if they'd been all Republicans, party affiliation would have been mentioned somewhere in the article a week before elections.

This is one reason why I am down to only getting the Sunday newspaper and, even then, most of them go straight into the trashcan without being read.

Giggle

People here really take seriously the notion that our mission is about trying to figure out what works and not letting our personal political views affect that.

-- Dr. Gill said of the Rand think tank.

In their own words

It seems to me that one thing educational theory has been unable to address is the possibility of multiple theoretical perspectives, the possibility that there is no one taxonomy, set of standards, methodology, etc., that will define The Way to do education.

Certainly, any approach to learning theory that suggests that an experiment can be conducted in (say) a double-blind model in order to test hypotheses in terms of (say) achievement of learning outcomes in my view demonstrates a fundamental misunderstanding of the nature of the enquiry.

We need to move beyond consensus, beyond sameness.

Courtesy of Half and Hour.

This is the sort of rationalization you get from a non-professional in a pseudo-profession with no standards of accountability who wants to continue practicing proven, unsound methods no matter the results.

Imagine walking into a doctor's office with a migraine and doctor Killpatient wants to put you on a regimine of anal leeching. When you question his methodology and suggest that the medical research has shown that a triptan class of medications is the most effective course of treatment, the good doctor informs you that there are multiple theoretical medical perspectives and that there is no standard that defines how to do medical treatment. As he's pulling out the leeches, he informs you that any theory that suggests that double-blind experimentation that tests the achievement of medical outcomes is a fundamental misundestanding of the nature of the medical inquiry. It's time to move beyond consensus.

At this point, most sane people would be out the door already, leaving the little cloud of smoke like in the roadrunner cartoons.

Can't get there from here

Here is the heart of the problem: American public education -- because of the way it is structured, administered, funded and understood by parents, teachers, administrators and taxpayers -- is incapable of delivering on the promises of NCLB. The root of the problem isn't in the law; it's in the American education system. It can't get there from here.

Today's public education system essentially tells parents: "This is the school your child will attend. This is when we teach, what we teach and who will teach." In short, it puts the system ahead of the child.

Eugene Hickok, a Bradley fellow in education at The Heritage Foundation, in today's WaPo.

Ridiculing Pseudoscience

There is a legitimate place for ridicule, sarcasm, and satire when arguing a position, especially when the opposing position is inherently ridiculous. Such is the case when arguing with many educrats who hold positions based on pseudioscience bordering on religious fanaticism.

These people typically have an absolute attachment to a particular position and rational argument cannot dissuade them. In that case, ridicule is perfectly acceptable. Sometimes it's the only way to illustrate the absurdity of an opponent's position.

Ridiculing an opponent based on his irrational position is not the same as making an ad hominem argument which is merely a personal attack. Someone needs to explain the distinction to these guys. Not that'll do any good at this point; they've drunk the Kool aid.

I raise the issue because a little debate has broken out between Allen and Anon in the comments due to Professor Plum's ridiculing of educrats as imbeciles.

Here's Allen's position:

Plum's quite a guy but in this he's wrong and it should be self-evident.

His assertion, "they are imbeciles", is clearly not true. Ed school profs, school administrators, school board members and teachers are not imbeciles at least not in the classic, definitional sense. This is Plum's way of dismissing a point of view with which he disagrees and that results in practices which he can prove don't work. Yet they, the "imbeciles", are unimpressed by his proofs and continue espousing and using bad methods.

What possible explanation could there be for preferring unproductive practices over productive? Plum's response is dismissing the plyers of educational snake oil as imbeciles.

Since they aren't imbeciles - they drive cars, write checks, dress and feed themselves, write dissertations - there must be some other, rational explanation for preferring dull tools over sharp. A reason Plum, and all the other edu-pundits I read, either can't or can't be bothered to try to understand.

That's a lousy attitude to hold if you're trying to diagnose an institutional illness because without understanding these seemingly illogical actions you've reduced your own actions to dart-throwing. Whatever remedies you want to apply, without an understanding of the cause of the situation, they're made random due to that ignorance.

Anyone care to proffer a reason one batch of edu-crats might choose constructivism or whole language and another batch choose direct instruction and phonics? To make the task more difficult, and worthwhile, any answers that are inherently self-inflating, are forbidden. That means no psych evaluations of insanity which imply the sanity of the diagnostician and no intelligence estimates which imply the brilliance of the estimator.

And, here's Anon's position.

Allen, I hear what you are saying. You are arguing that if Prof. Plum can't pinpoint exactly why Constructivists do what they do, then he should not instead resort to a type of name calling, for this is an example of coming to a conclusion without valid premises. Such conclusions, I hear you saying, do not follow the principles of logic and are thus invalid. Is this your basic argument here?

But allow me to present you with the following:

What would you conclude if you were trying to understand why an educated person say, wouldn't agree that 2+2=4. First you tried using manipulatives, showing this person that if you first gave him 2 M&Ms, and then you gave him 2 more M&Ms, that he now had 4 M&Ms. But the person said no, that what was in his hand did not prove that 2+2=4. So, you continued to make you explanation more detailed, going further and further into a discussion of mathematics, and what the concept of numbers represent, etc. Yet, the more you talked to this person, the more you found out that the person did not believe there was a such thing as integers, despite epochs of legitimate mathematical discovery on the subject.

But this individual just keeps insisting that 2+2 does not equal 4, and that no math is real, it is all a theory. No matter what, this person will not admit anything.

Would you proffer a reason this educated person might say such nonsense? Would you defend him by coming up with euphemisms to describe his point of view, or coming up with a term to describe his philosophy? Would coming up with a term to describe his philosophy then validate his philosophy, by virtue of the fact that you either came up with a term for it, or that the philosophy was well known, and already had a term? Or would you still insist that this guy is wrong, that everybody knows 2+2=4, and that no amount of his rationalizing and theorizing was going to change that fact?

Is there any chance you might resort to characterizing him as stubborn, nutty or just plain contrary for the sake of being a pain in the ass? Or would you instead, label him, and refuse to try and characterize him because his belief system has a name?

Would you never conclude this person was imbecile, or stubborn or ignorant?

What if you discovered that this person had fiduciary links to the philosophy via a say, a TV-based religion, or a line of self-improvement books and tapes, and the guy was making a lot of money spreading this philosophy? Would that change your tact on any of the way you'd handle his arguments?

Just curious as to what you think...

I think I side with Anon on this one (as does SteveH). Allen raises some good points, but I think you go down the rabbit hole when you try to determine the motives behind some of these positions. Motives likely vary, but the nuttery is a constant.

Update: Mr. Person of Text Savvy has his taken on this imbecile business and threatens more to come.

Stalinist Airbrushing in the Edusphere

Looks like constructivist nutter, Doug Loon, has engaged in a little digital airbrushing over at his blog Borderland. (I'd link, but the intellectual midget has set up a childish redirect, so just use google.)

Here's the backstory.

Loon didn't like having his precious opinions (as opposed to legitimate theories) challenged and not being able to respond without engaging in postmodern nonsense, thereby opening himself up to even more ridicule, he did the next best thing--he erased the entire incident from the history books.

We have the blog equivalent of a black hole over there now. You can't see the original argument directly, but you can tell it once existed by looking at Loon's other posts (and comments) and the links to Loon's original post.

They're back at their echo chamber blogs now gathered 'round the campfire singing kumbaya and bemoaning the fact that not everyone has drunk the constructivist Kool-aid. Now that their views being challenged, they find themselves between a rock and a hard place--they have to either defend the indefensible, thereby prolonging the pain and looking silly, or refuse to respond to the challenge, thereby looking cowardly and silly.

Looks like they're opting for plan B at this time.

You're a hero, Doug, a true hero.

Update: Trotsky lives! The comments are either back up or never were missing in the first place. So my allegations of Doug being a Stalinist airbrusher may have been premature. Narrow-minded censor-yes. Stalinist air-bruasher--no.

Wet Streets Cause Rain

This blurb comes from a Michael Crichton speech given to the International Leadership Forum on April 26, 2002. Crichton was criticising the media for failing to provide any factual support for their endless speculation or "theories," but his citicisms apply equally to educators.

Media carries with it a credibility that is totally undeserved. You have all experienced this, in what I call the Murray Gell-Mann Amnesia effect. (I refer to it by this name because I once discussed it with Murray Gell-Mann, and by dropping a famous name I imply greater importance to myself, and to the effect, than it would otherwise have.)

Briefly stated, the Gell-Mann Amnesia effect is as follows. You open the newspaper to an article on some subject you know well. In Murray's case, physics. In mine, show business. You read the article and see the journalist has absolutely no understanding of either the facts or the issues. Often, the article is so wrong it actually presents the story backward—reversing cause and effect. I call these the "wet streets cause rain" stories. Paper's full of them.

In any case, you read with exasperation or amusement the multiple errors in a story, and then turn the page to national or international affairs, and read as if the rest of the newspaper was somehow more accurate about Palestine than the baloney you just read. You turn the page, and forget what you know.

That is the Gell-Mann Amnesia effect. I'd point out it does not operate in other arenas of life. In ordinary life, if somebody consistently exaggerates or lies to you, you soon discount everything they say. In court, there is the legal doctrine of falsus in uno, falsus in omnibus, which means untruthful in one part, untruthful in all. But when it comes to the media, we believe against evidence that it is probably worth our time to read other parts of the paper. When, in fact, it almost certainly isn't. The only possible explanation for our behavior is amnesia.

The question is why do we still listen to anything educators say. Hasn't a century of failed "reforms" taught us anything? Taught us that they know almost nothing about their own profession -- education?

Professor Plum said it best a few days back:

The truth is, they are imbeciles.
...

You'll be shocked (or maybe not) at how boneheaded, smug, and just plain stupid these persons are.

They can't define knowledge.

"Knowledge is uh uh uh...what you know." [Oh, good.]

They can't give a coherent definition of learning.

"Learning is uh er oh mmm uh what happens when you learn." [Get the ropes.]

They can't list the phases of mastery---acquisition, fluency, generalization, retention.

"Phases of what?

They can't define a concept, rule, or cognitive routine.

"A concept is an idea. A rule is an idea, too, sort of, but uh uh uh er er."

They can't tell you the criteria for logically adequate curriculum design.

"A good curriculum is a seamless web [insane] of holistic experiences experienced in the context of naturalistic and learner-centered activities in a democratic and nurturing community. Howz that?" [Stick your head in the toaster and jump in the bathtub.]

In other words, they don't know anything about their business.

The Educrat Stranglehold

This article on Project Follow Through (PFT) dovetails nicely with this post at Rightwingprof on how we need to break the ed school stranglehold on education before we can solve our education crisis.

The PFT article explains how our educrats ignored the results of PFT because they did not comport with their favorable, though ineffective, teaching methods. The results were an embarrassment to educrats:

Nobody was more surprised than the constructivist curriculum authors when PFT demonstrated two things.

First, the basic-skills-oriented DI far outperformed both the control groups and the other models.

Second, the five constructivist-style curricula actually reduced school performance in districts that were already among the lowest performers nationwide.

DI even outperformed the constructivist models in areas in which they were supposed to excel.

Three tests of success were employed: academic (students' ability to answer questions correctly), cognitive (students' ability to reason for themselves), and affective (students' feelings about themselves).

With names like Cognitive Curriculum and Self-Esteem, the constructivist curricula were supposed to boost higher-order thinking and self-opinion.

According to PFT, they actually reduced both.

At first, the response to PFT was to attack the research project and DI:

The purpose of these attacks was to prevent a mutiny among the constructivist academics running most university education departments, and to retain control of the purse strings at foundations and in the federal government.

Of course, subsequent research has confirmed the PFT results. SO the educrats changed their tactic to ignoring the elephant in the room.

After the initial barrage of attacks, the constructivists adopted a new strategy regarding PFT: silence. The best news about failure is no news and, unlike their curricula, the constructivists' political strategy works.

You can gauge the success of the campaign of silence for yourself: Ask any teacher or administrator you know about Project Follow Through, the world's largest education research project, and you'll most likely get a blank stare.

Since school districts are generally free to pick whatever curriculum they want, here is how the system works:

This is convenient for constructivist curriculum authors, who are generally also professors at influential teachers' colleges. Constructivist orthodoxy is so dominant today it is almost impossible to get a teaching degree at most schools without openly subscribing to it.

Each year, teachers' colleges crank out thousands of teachers and administrators determined to stamp out successful non-constructivist programs, such as DI, in an effort to ensure the continued flow of billions of dollars of grant money and curriculum sales into programs that are proven failures.

PFT's enduring lesson is that the American people, even acting through the federal government, are powerless against the entrenched interests of the education monopoly. Despite our intent to wage a "war on poverty," we have for decades unwittingly financed the engineers of our own defeat.

The author, like Ryan from Edspresso, is more optimistic than rightwingprof, but I don't think anyone disagrees that the vested interests of the edublob, unions, ed schools, politicians and their minions make for a formidable barrier standing in the way of decent publicly susidized education.

Grading the Tests

There's been a lot of back and forth in the comments about the difficulty level of the tests that states have created in response to NCLB. Educators seems to uniformly agree that they are unable to get most kids to the proficiency level by 2014. Parents don't seem to have any idea what's even on the tests. So why don't we take a look at the testing regime of a state to see what's going on.

I'm going to pick Pennsylvania because a) that's the state I'm most familiar with and b) they make a lot of information available on their website, a poorly laid out website for sure, but you can usually find what you're looking for if you poke around long enough.

The Tests

Pennsylvania does not release actual test questions from its PSSA test; however, they offer the next best thing -- lots of sample questions from each test. Good enough for our purposes. Here are representative problems (pdf) for the upcoming 2006-2007 tests for 5th and 8th grades and from the 2005-2006 exams for 11th grade. (all in pdf form.). The tests are given at the end of March.

Math	Reading
5th Grade	5th Grade
8th Grade	8th Grade
11th Grade	11th Grade

Before you look at the tests, let me tell you what it means to be proficient. To be "proficient" on the tests here's the percentage of questions that the students would have to answer correctly.

	Math	Reading
5th Grade	65%	67%
8th Grade	62%	75%
11th Grade	62%	73%

These proficiency percentages were calculated from the cut scaled scores given on p. 117 and the raw score to scaled score conversion tables given in appendix II-9 of this monster 2005 technical report (pdf).

So in math, a student could get 1 out of every three problems wrong and still be proficient. In reading, the student could get one out of every four problems wrong and still be proficient.

Here's a few more notes before you jump into the sample questions. In the math portion, students are permitted to use calculators on all but a tiny fraction of calculation questions on the fifth and eighth grade exams. In addition, a formula sheet and ruler are provided, as indicated in the scoring sampler.

Now go ahead and take a look at the sample problems.

In math, you'll see that many of the problems at each grade level are simplistic. Many of the problems can be solved easily by plugging the multiple choice answers into the calculator. Few, if any problems, require multiple steps to answer. Few of the problems contained in each test are at grade level; many questions test skills that should have been taught years before. Manipulation of fractions, a critical skill needed for success in algebra, is barely tested at all.

In reading, the passages are about at grade level (using the lexile calculator); however, the comprehension questions are simplistic, frequently requiring that the student find the requested fact in the text.

Here are the disaggreagated scores from the 2005-2006 PSSA exams. The table shows the percentage of students who scored at or above the proficient level. Math scores are given first followed by reading scores (math/reading).

	All	Asian	White	Hispanic	Black	Low SES	IEP
5th	67/61	83/73	74/68	47/36	40/34	49/40	33/24
8th	62/71	82/81	70/78	39/45	33/44	42/50	20/27
11th	52/65	72/70	58/71	25/35	22/35	29/41	11/19

The scores break down almost exactly along IQ distribution lines. There is an achievement gap of roughly a standard deviation between whites and blacks/hispanics in both math and reading. And, there is an achievement gap of 0.4 between asians and whites. This indicates that about 4/10 of asians in PA are from northeast asia and 6/10 are from southest asia which seems about right to me based on my observations from the Philadelphia area.

Here's another basis of comparison.

Here's the placement test given for the middle of fouth grade for Singapore Math. Compare the questions to the 5th grade math PSSA questions.

Here's the placement test given for the middle of sixth grade for Singapore Math. Compare the questions to the 8th grade math PSSA questions.

Here's the placement test given for the second year of algebra (8th grade) for Singapore Math. Compare the questions to the 11th grade math PSSA questions.

Singapore is tops in the world for math achievement. One reason for that achievement is the rigorous Singapore Math curriculum the country uses. Another reason is that Singapore is full of brainy northeast asians. That's why I selected the placement tests that were one to three years behind the PSSA tests, giving less brainy U.S. students an extra one to three years to catch-up.

Here's the post test for Connecting Math Concepts (CMC) level F, a fifth grade math program. The curriculum has been extensively field tested so that almost every student, including the ones with IEP, who has completed the six years in the probram will be able to answer at least 80% of the post test questions correctly. Compare the questions on the post test to the PSSA questions. Now look at the high percentages of black,hispanic, low SES, and IEP students who are not proficient in Pennsylvania (the 11th grade IEP students are performing at the chance level, i.e., randomly filling in the bubbkles will yield the same score). Now ask yourself why less than 2% of schools use CMC or a math program like it.

The comments section is open.

John Dewey on Constructivism

Ed school mole John Dewey has posted another letter at Edspresso. This time he clarifies the definitional problems with constructivism. Mr. Person (of Text Savvy) and I discussed this very issue here.

My view is that it's not constructivism when you've given the student all the information to solve the problem. And, almost every teacher provides some kind of guidance and scaffolding during instruction because unguided discovery learning doesn't work.

It really doesn't matter what you call it anyway. The only thing that matters is what the students have learned or haven't learned at the end of the day and what they've retained by the end of the course. In math, it's easy to determine what works and what doesn't: how well the student solves math problems he's been taught.