Saturday, May 24, 2008
No real rocket science.
1) We are homeschooling and are using Singapore Math. My understanding is that SM gets kids to Algebra in 7th grade, so I'm figuring 11th grade can be Calculus.
2) Child in question is about 1½ years ahead in math [we just legally finished 1st grade this week and are plowing through SM 3a right now]. Blame mom for starting him early. We're pretty much going at one year per year now, so I figure he's on pace for Calculus 1½ years earlier than normal Singapore 11th grade.
3) Math is about 1 hour per day, broken into ½ hour in the early morning with me and ½ hour in the late morning or early afternoon with Mom.
No real magic here:
A) We are using a curriculum that runs about 2 years faster then a typical US curriculum,
B) Mom got a bit of jump even on that, and
C) We do math pretty much every school day (and because I'm mean and because he only spends about 2 - 2½ hours per day on schooling we don't take summers off. I don't see much of a need) and it tends to be a priority subject [it is the first subject we do in the morning almost every day].
(Not sure whether it's OK to use M.R.'s wants his full name on the front page - will ask.)
I'm interested in the curricula you're using for other subjects, too.
In fact, I'd like to hear from concerned parent on that --- (and from everyone else).
Friday, May 23, 2008
My take on this is that kids come in normal distributions, i.e. they come to your classroom with a range of capabilities. In low SES districts the spread, the standard deviation, is quite large. I've had classrooms with kids ranging from 1 year above grade to 5 years below grade.
If you are in a failing district, like mine, you are blanketed with consultants, coaches (of which I am one), tight curriculum maps, walk throughs, and on and on. The sum total of this is that you're asking teachers to teach to a really narrow portion of a theoretical distribution while, at the same time, you are 'delivered' children with a 5-6 year span in abilities.
This means that if you follow the rules, and it's perilous not to, you are by definition throwing 80% of your class under the bus. Teachers adjust the curriculum to try to push as many of the distribution as possible through the eye of the needle. They teach to their median. So by definition 40% of your class is bored and 40% don't get it.
My district retention policy is "We don't have one!" Even if they had one there is no remediation program so the miniscule portion of students who are retained are put back into the very same classroom that failed them with the expectation that the second time through will be magic.
"Just stand right there in the middle of center field, Stan, and I'll hit you a few balls," says Ollie, as he proceeds to spray 60 balls at poor Stan; all at once and all over the outfield!
I am a sample size of one, but this matches my experiences. I am one of those 'naturals' who got to college, and realized I had three choices:
1. Study twice as hard to become a median student in chemistry
2. Study twice as hard to become a top student in economics.
3. Keep my same work habits to stay a median student in economics.
Shamefully, I chose option number 3 (and am now paying for it by working four times as hard to become a top student in an MS program I probably wouldn't have entered if I'd wised up earlier).
The other point is all those pesky foreigners are now entering the easy subjects like economics and biology.
Our dept. chair (eng) used to tell us if you had to look up basic info, then realize the other guy was going to get and keep the job since he could communicate in real time.
I wonder if ed school professors consider holding onto a job a 21st century skill?
A 1991 Atlantic Monthly article on The Other Crisis in American Education.
the 16-year decline and the 1995 "recentering"
By way of background: SAT scores declined from 1964 to 1980. Math scores rose most of the way back up to where they'd been but verbal scores did not, and in 1995 the College Board recentered the scores.
My district's scores, which are significantly higher than those for other schools in our demographic, assuming I've read the charts correctly (chart correlating income and scores here; chart for determining significance here) are:
V-540 M-568 W-540 total: 1648
Prior to 1995 those scores would have been:
1108 today; 1020 before 1995. Big difference.
decline at the top
Over the years I've seen various rebuttals of the claim that the decline was due to an expansion of the pool of test takers. See here and here.
What I had not seen was the data showing that the decline was concentrated at the top:
[N]orm-referenced tests .... were able to tell us not just about the existence of the decline but something about its magnitude--half a standard deviation on the SAT--and something about its source--the decline on all norm-referenced tests was much greater among students at the top of the score distribution than among those at the bottom.
The decline at the top was so steep that the absolute number of students scoring over 650 on the verbal half of the SAT declined 45 percent between 1972 and 1982. That means the pool of top talent available for scholarship and research, for business and industry, and for the military has actually shrunk. We need to enlarge it again as quickly as we can by encouraging excellence in our schools, and we need tests that will let us gauge our progress at that vital task. The best-calibrated gauge for these purposes is a norm-referenced test. That is why a national census of educational quality should include not just a test of V and M, but a norm-referenced test of those essential, all-purpose abilities.
The importance of these periodic checks on test constancy is well illustrated by data on the SAT. They show that efforts to hold the difficulty level of the test constant over the years were quite successful from 1941 to 1963; less so from 1963 to 1973, when some downward drift occurred, making it a bit easier to get higher scores after 1963 than before. The SAT was also easier to read in the 1960s and the 1970s than it was in the 1940s and the 1950s; the difficulty level of reading passages on the test declined, as measured by the Dale-Chall formula, from a corrected grade level of 13 to 15 to only 11 to 12.24
All in all, SAT scores in recent decades probably underestimate the great American score decline by about 8 to 12 points, roughly one-tenth of a standard deviation.
A National Census of Educational Quality—What Is Needed by Barbara Lerner NASSP Bulletin / March 1987 p. 56
the one that got away
While the rest of the country was falling apart, SAT-wise, some schools sailed through those years unscathed. Daniel Singal's 1991 article summarizes a study of the ones that got away:
What has caused this great decline in our schools? The multitude of reports that now fill the library shelves tend to designate “social factors” as the prime culprit. Television usually heads the list, followed by rock music, the influence of adolescent peer groups, the increase in both single-parent families and households where both parents work, and even faulty nutrition.
Those who attribute the loss of academic performance to social factors don't take account of the small number of high schools around the country that have managed to escape the downturn. Some are posh private academies; a few are located in blue-collar neighborhoods. What they have in common is a pattern of stable or even rising test scores at a time when virtually all the schools around them experienced sharp declines. There is no indication that the children attending these exceptional schools watched significantly fewer hours of television, listened to less heavy-metal music, were less likely to have working mothers, or ate fewer Big Macs than other children. Rather, they appear to have had the good fortune to go to schools that were intent on steering a steady course in a time of rapid change, thus countering the potentially negative impact of various social factors.
It would seem obvious good sense to look closely at this select group of schools to determine what they have been doing right, but as far as I can determine this has been done in only two national studies. The better one was issued by the National Association of Secondary School Principals (NASSP) in 1978, under the somewhat pedestrian title Guidelines for Improving SAT Scores. Now out of print and hard to find, it contains one of the most perceptive diagnoses available of the underlying malady in our schools.
The report identifies one main characteristic that successful schools have shared—the belief that academics must invariably receive priority over every other activity. “The difference comes,” we are told, “from a singular commitment to academic achievement for the college-bound student.” These schools did not ignore the other dimensions of student life. By and large, the NASSP found, schools that maintained excellence in academics sought to be excellent in everything else they did, they “proved to be apt jugglers, keeping all important balls in the air.” But academic work came first.
Two other factors help account for the prowess of these schools in holding the line against deterioration. The first is a dogged reliance on a traditional liberal-arts curriculum. In an era of mini-courses and electives, the tiny group of high schools that kept test scores and achievement high continued to require year-long courses in literature and to encourage enrollment in rigorous math classes, including geometry and advanced algebra. Though the learning environment in those schools was often “broad and imaginative,” in the words of the NASSP, fundamentals such as English grammar and vocabulary received heavy stress. The other key factor in preserving academic quality was the practice of grouping students by ability in as many subjects as possible. The contrast was stark: schools that had “severely declining test scores” had “moved determinedly toward heterogeneous grouping” (that is, mixed students of differing ability levels in the same classes), while the “schools who have maintained good SAT scores” tended “to prefer homogeneous grouping.”
If attaining educational excellence is this simple, why have these high-quality schools become so rare? The answer lies in the cultural ferment of the 1960s.
So there you have it.
The hardy little band of schools where student achievement did not decline shared three characteristics:
- academics first and foremost, with a commitment to excellence in all endeavors
- “dogged reliance on a traditional liberal-arts curriculum”
- homogeneous grouping; schools with heterogeneous grouping had “severely declining scores”
My own district is doggedly moving in exactly the opposite direction. Character education and the whole child over academics, the fragmenting and blurring of the curriculum via "Exploratory" courses and interdisciplinary teaming thanks to the middle school model, and an "identified need" for "balanced classes." Balanced classes being the new term of art for heterogeneous grouping in these parts.
Oh, and more more technology.
Most school districts are headed in this direction, and the kids at the top will be hurt.
I think kids at all levels will be hurt, but if I had to guess I'd say the kids at the top and at the bottom will be worst off. More on them anon.
Nobody cares. The kids at the top are assumed to be bulletproof; as our middle school principal told a well-attended school board meeting, "I'm not concerned about the kids at the top."
The kids at the bottom can flounder and sink until they qualify for special ed. Then they'll get some "pull-out."
stagnation at the top - Fordham report
Tracking: Can It Benefit Low Achieving Children?
Linda Valli on tracking in 5 Catholic high schools, 1
Linda Valli on tracking in 5 Catholic high schools, 2
"school commitment" in Valli's study of tracking in Catholic high schools
7th grade depression starts in 1st grade
ability grouping in Singapore
characteristics of schools where SAT scores did not decline
The Other Crisis in American Education by Daniel Singal
Hiding in Plain Sight: grouping & the achievement gap
tracking: first random-assignment study
SAT equivalence tables
SAT I Individual Score Equivalents
SAT I Mean Score Equivalents
chickens have come home to roost
the deathless meme of the high performing school
Allison on the naturals
Do Electronic Technologies Increase or Narrow Differences in Higher Education Quality Between Low- and High-Income Countries?
by Norman Clark Capshaw
In developing the list, U.S. News also compiles statistics on the computer and Internet availability to students at the universities chronicled in its annual list. One of the data listed is the number of library volumes available at each institution. In addition, the list includes the number of computers available to students at the schools. It might be expected that, as the number of library volumes and the number of computers available to students increases, the ranking of the school would also climb. One would therefore expect a negative correlation1 between these variables and the institution’s rank.
This is indeed the case with the number of library volumes and volumes per student. The strong negative correlations indicate that there is some relationship between the number of library holdings and an institution’s place on the list. An even stronger correlation with volumes per student indicates that small-enrollment institutions with large library holdings are even more likely to be listed among the top schools (see Table 1). However, a counterintuitive result is obtained when analyzing the correlation of the number of computers available to students and an institution’s ranking (see Table 2). Alhough the correlation is small, its direction is counterintuitive and puzzling. It suggests that an institution suffers a penalty in its ranking when the number of computers it provides to students is large.
PEABODY JOURNAL OF EDUCATION, 83: 117–132, 2008
That is puzzling.
I wonder what they found out about SMART Boards.
Over the last 8 years, I've realized that there are two things happening in math education: talk and reality. The talk is about concepts like discovery and deep understanding. The reality is about basic competence and just getting the job done. In fifth grade, my son's Everyday Math teacher didn't get to 35 percent of the material. This wasn't carefully selected. She just stopped when the school year ended. To her credit, she did work hard to fix the basic mastery problems the kids came with. She had after-school help sessions. When I talked with her, she told me that she was not happy about how the kids got to her class in the first place, but she felt that she couldn't raise the issue. I did. It didn't seem to matter.
[I never did get a good answer to this. The best I can figure is that the school thinks the onus is on the kids and that with EM, mastery will eventually be achieved. If not, it's the student's fault. That's basically what the curriculum head told me. "If a student struggles with math for several years in a row, then you can't blame the curriculum." She also said that she liked Singapore Math, but EM was a better choice for their "mix" of kids. (private school)]
One of the problems is that Everyday Math allows this to happen on purpose. But it's more than that. Teachers and schools know that you can't put off mastery that long, but they don't all get together to fix it. I'm not talking about doing hundreds of long division problems. I'm talking about the real basics. At that school, we had a parent-teacher meeting specifically about Everyday Math. The discussion was at the "talk" level. Most focused on the need for balance and there was a lot of agreement. Almost. I wanted to talk about details, but that wasn't appropriate for the meeting. So what changed? Almost nothing. They ended up dumping EM in sixth grade and went to something that aligned more with the algebra series they used. They still didn't fix the mastery problem. I've mentioned before that even if I could get our schools to use Singapore Math, they would still allow kids to get to fifth grade not knowing their times table.
The following comments are from a recent tri-state meeting of state officials and educators to discuss bad math scores:
" ... the system and not students are to blame for low math scores ..."
"Only 22 percent of high school students achieved proficient math scores ..."
"The teachers put the test together and they're all satisfied that it's a good test..."
"Have we not got our curriculums aligned properly?" [governor]
"Educators are now trying to make sure students are actually being taught what they're being tested on."
"Another goal is to make sure all kids are given a chance to learn higher levels of math."
This has nothing do do with balance, discovery, or deep understanding. It's competence. The best they can do is to blame alignment. It's much more than that, and I'm not optimistic.
Thursday, May 22, 2008
Saxson math lost out because it scored poorly on the rubric they used to evaluate the different programs.
Here is the "Student Lens" part of the rubric:
Is it just me, or does anyone else get the feeling the evaluation was rigged?
I. Student Lens
The materials provides the following for the needs/rights
a. The purpose of learning, including objectives, standards,
goals, criteria and evaluation rubrics are clear for students
b. Students can choose from a variety of strategies to
explore, solve, and communicate math concepts
c. Students are engaged through a variety of activities
which may include independent projects, cooperative
learning, manipulatives, technology, collaborative work, etc.
d. Students have opportunities for self-monitoring and
e. Materials make connections to real life applications
f. There is support for individual learning levels
I am so glad my kids are going to get "opportunities for ... self-reflection" in math class. I was afraid I was going to have to sign them up for yoga class.
Should I be worried?
p.s. Anchorage and Alaska are awesome. I am taking the summer off of school so I will be blogging again.
(crossposted at parentalcation)
Wednesday, May 21, 2008
Knowles' theory of andragogy is an attempt to develop a theory specifically for adult learning. Knowles emphasizes that adults are self-directed and expect to take responsibility for decisions. Adult learning programs must accommodate this fundamental aspect.
Andragogy makes the following assumptions about the design of learning: (1) Adults need to know why they need to learn something (2) Adults need to learn experientially, (3) Adults approach learning as problem-solving, and (4) Adults learn best when the topic is of immediate value.
In practical terms, andragogy means that instruction for adults needs to focus more on the process and less on the content being taught. Strategies such as case studies, role playing, simulations, and self-evaluation are most useful. Instructors adopt a role of facilitator or resource rather than lecturer or grader.
Good heavenly days.
How is this different from a middle school?
An exemplary middle school, I mean.
Andragogy applies to any form of adult learning and has been used extensively in the design of organizational training programs (especially for "soft skill" domains such as management development).
That, I believe.
The one realm of life as goofy and fad-driven as the education world is the business world.
Speaking of exemplary, you can get a copy of Paul S. George's The Exemplary Middle School, 3rd edition for 36 cents at Amazon.
Constructivism views learning as a process in which the learner actively constructs or builds new ideas or concepts based upon current and past knowledge. In other words, "learning involves constructing one's own knowledge from one's own experiences." Constructivist learning, therefore, is a very personal endeavor, whereby internalized concepts, rules, and general principles may consequently be applied in a practical real-world context. The teacher acts as a facilitator who encourages students to discover principles for themselves and to construct knowledge by working to solve realistic problems. This is also known as knowledge construction as a social process (see social constructivism). We can work to clarify and organize their ideas so we can voice them to others. It gives us opportunities to elaborate on what they learned. We are exposed to the views of others. It enables us to discover flaws and inconsistencies by learning we can get good results.
Kinda falls apart there at the end.
Tuesday, May 20, 2008
Sunday, May 18, 2008
I discovered today that the Public Agenda survey of professors in education schools is available online. From the press release:
In the first comprehensive survey of the views of education professors, Public Agenda found nearly eight in ten teachers of teachers (79%) believe the public's approach toward learning is "outmoded and mistaken," and suggest a different path for American education. In sharp contrast to the concerns expressed by typical Americans in earlier Public Agenda studies, small percentages of education professors feel maintaining discipline and order in the classroom (37%), stressing grammar as well as correct spelling and punctuation (19%), and expecting students to be on time and polite (12%) are "absolutely essential" qualities to impart to prospective teachers.
Professors of education offer an alternative set of priorities which translate into highly evolved expectations for K-12 teachers. Education professors overwhelmingly consider it "absolutely essential" to convey to prospective teachers the importance of lifelong learning (84%), teaching students to be active learners (82%), and having high expectations of all their students (72%). Their emphasis on a love of learning leads them to downplay more traditional educational practices. Fifty-nine percent, for example, think academic sanctions such as the threat of flunking or being held back are not important in motivating kids to learn. Six in ten (61%) believe when a public school teacher faces a disruptive class it probably means the teacher has failed to make lessons engaging enough.
"Professors of education have a particular vision of what teaching should be -- one that has some appealing features," said Deborah Wadsworth, Executive Director of Public Agenda. "But the disconnect between what the professors want and what most parents, teachers, business leaders and students say they need is often staggering. Their prescriptions for the public schools may appear to many Americans to be a type of rarified blindness given the public's concerns about school safety and discipline, and whether high school graduates have even basic skills," added Wadsworth.
Process Over Content
The process of learning is more important to education professors than whether or not students absorb specific knowledge. Nearly 9 in 10 (86%) say when K-12 teachers assign math or history questions, it is more important for kids to struggle with the process of finding the right answers than knowing the right answer. "We have for so many years said to kids 'What's 7+5?' as if that was the important thing. The question we should be asking is 'Give me as many questions whose answer is 12...,'" said a Chicago professor who was interviewed for this study.
Their focus on how to learn prompts a greater reliance on tools and less on teaching specific facts. For example, 57% think the use of calculators from the start will improve children's problem-solving skills. Only 10% of the general public, however, and 23% of public school teachers, agree. And only one-third of the professors (33%) would require students to know the names and geographic locations of the 50 states before getting a diploma. "Why should they know that?" a Los Angeles professor asked. "They need to know how to find out where they are. When I need to know that, I can go look it up. That's the important piece, and here is what's hard to get parents to understand."
It's damned hard to get parents to understand that.
It's damned hard to get parents to understand that because it is cracked.
I say that as a person from Illinois who once contemplated purchasing a t-shirt bearing the legend "University of Iowa, Idaho City, Ohio."
Full text of the report here (pdf file)
portrait of a heterogeneous classroom
From the university perspective, it is not particularly helpful for them to know a little engineering at the expense of the math/physics/chemistry they might otherwise take. I feel quite certain that engineering schools are good at taking students with a solid foundation of math and basic physics and getting them to where they need to be in engineering. They are not set up to take students who think they know engineering and remediating the math, physics, etc. that they should have as prerequisites.
I don't teach engineering, but I do teach calculus, and I have a similar problem. I would rather have students who have never heard of a limit or derivative, but can do algebra and trigonometry. The 40% of the class that come in with the backward set of skills (a little calculus, but not enough algebra) really struggle.
This is extremely good to know. I believe it. I'm pretty sure rudbeckia hirta has said the same thing over the years.
oh gosh. Speaking of rudbeckia, I found this terrific post from 2006 while Googling her blog. I should probably print that one out and scotch tape it to my collection of as-yet unused calculus textbooks.