Professor Eugene Volokh posted a comment on a Family Court case involving a dispute between parents over homeschooling versus public schooling. I initiated an e-mail correspondence with one of the people who left comments. I reproduce some of that correspondence here.
I.A
From: Malcolm Kirkpatrick
To: Dilan Esper
Dear Sir,
I saw your comment on homeschooling at the Volokh Conspiracy. Please reconsider.
From: Hyman and Penroe, Journal of School Psychology.
"Several studies of maltreatment by teachers suggest that school children report traumatic symptoms that are similar whether the traumatic event was physical or verbal abuse (Hyman, et.al.,1988; Krugman & Krugman, 1984; Lambert, 1990). Extrapolation from these studies suggests that psychological maltreatment of school children, especially those who are poor, is fairly widespread in the United States...."
Roland Meighan, "Home-based Education Effectiveness Research and Some of its Implications", Educational Review, Vol. 47, No.3, 1995.
"The issue of social skills. One edition of Home School Researcher, Volume 8, Number 3, contains two research reports on the issue of social skills. The first finding of the study by Larry Shyers (1992) was that home-schooled students received significantly lower problem behavior scores than schooled children. His next finding was that home-schooled children are socially well adjusted, but schooled children are not so well adjusted. Shyers concludes that we are asking the wrong question when we ask about the social adjustment of home-schooled children. The real question is why is the social; adjustment of schooled children of such poor quality?"
"The second study, by Thomas Smedley (1992), used different test instruments but comes to the same conclusion, that home-educated children are more mature and better socialized than those attending school." ...p. 277
"12. So-called 'school phobia' is actually more likely to be a sign of mental health, whereas school dependancy is a largely unrecognized mental health problem"....p.281
Clive Harber, "Schooling as Violence", p. 10, Educatioinal Review, V. 54, #1.
"...It is almost certainly more damaging for children to be in school than to out of it. Children whose days are spent herding animals rather than sitting in a clasroom at least develop skills of problem solving and independence while the supposedly luckier ones in school are stunted in their mental, physical, and emotional development by being rendered pasive, and by having to spend hours each day in a crowded classroom under the control of an adult who punishes them for any normal level of activity such as moving or speaking."
"Autobiographical Notes," in Albert Einstein: Philosopher-Scientist, Paul Schilpp, ed. (1951), pp. 17-19
"It is, in fact, nothing short of a miracle that the modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry; for this delicate little plant, aside from stimulation, stands mainly in need of freedom; without this it goes to wreck and ruin without fail. It is a very grave mistake to think that the enjoyment of seeing and searching can be promoted by means of coercion and a sense of duty. To the contrary, I believe it would be possible to rob even a healthy beast of prey of its voraciousness, if it were possible, with the aid of a whip, to force the beast to devour continuously, even when not hungry, especially if the food, handed out under such coercion, were to be selected accordingly."
A statistician in the office of the Attorney General gave me the charts below. This is what advocates of compulsory attendance statutes must defend...
I was a teacher in the Hawaii DOE schools for ten years.
Malcolm Kirkpatrick
..................................................................................
I.B
From: Dilan Esper
To: Malcolm Kirkpatrick
Malcolm:
Thanks for your note. I didn't say why I wasn't a fan of homeschooling in my comment-- I just noted my opposition. But since you raise it, I will tell you that my concern is about insuring that there is a collective base of knowledge that is shared by all Americans. I.e., I want every educated American to understand Darwinian evolution, STD prevention, that there are other religions that claim millions of reasonable people as adherents besides the one that they were raised in, that there are valid criticisms of religious belief that have persuaded many people, the basic principles that are enshrined in our Constitution and why they are important, etc.
My concern about homeschooling is not so much about outcomes-- I assume that most homeschooled kids do fine, but I also suspect that some kids would have done better in the public school system (it all depends on the teaching skills of the parents). And I fully understand any parent who pulls his or her kid out of the schools because the parent thinks he or she can do a better job educating the child, especially if the local schools stink.
But I suspect that in actuality, many children are homeschooled in part or in the main because their parents don't want them exposed to ideas that are different than the ones the parents hold or kids who might express those different views. And the problem is that there is a societal consequence that is paid because of that-- we end up with kids who don't understand basic biology, don't understand how to use contraception or have safe sex, and never get exposed to conflicting ideas or have the opportunity develop critical thinking techniques. Since education determines future national competitiveness, this seems like not such a good thing to me.
As I said in the comments thread, though, homeschooling is clearly constitutionally protected under existing law, so I wouldn't worry if I were you about my view gaining much traction. The most one could possibly see is some effort to require testing and instruction in particular subject areas.
Once again, I appreciate you taking the time to write.
2008/10/29
2008/10/17
Exactly Weasel
Weasel observes the difference between "well-educated" and "expensively schooled". Not much to add to this.
2008/10/15
The Line
Eric Kosslyn showed me this:...
Generating Pythagorean triplets:
Let N be the set of natural numbers.
Let a^1=a and let a^(n+1) = (a^n)(a). Exponentiation.
Identity: (x^2-y^2)^2 +(2xy)^2=(x^2+y^2)^2 (work it out if you do not see it).
For all x and y in N, x+y is in N and xy is in N, so
For all x and y in N
If a=x^2-y^2 and b=2xy and c=x^2+y^2 you have a,b,c, in N and...
a^2+b^2=c^2. Pythagorus.
We can use this to generate all pythagorean triplets, and then we can use pythagorean triplets to generate systems of simultaneous equations in two variables which come out "neat".
Example:
<3,4,5> and <5,12,13> are pythagorean triplets.
Let m(L1), the slope of line 1, be 4/3 and let m(L2), the slope of line 2, be -5/12.
Use <3,4> (from <3,4,5>).
Use <-12,5> (from 5,12,13>)
Take common multiples of the first and second elements: 48 is a multiple of both 3 and -12, 40 is a multiple of both 4 and 5.
Use p<48, 40> as the point of intersection. We let L1 and L2 intersect at the point p<48, 40>.
Then, from the vector form of the equation for the line we have...
for all p(x,y) in L1, there exists an r in R such that
(x,y) = <48,40> + r<3,4>
and
for all p(x,y) in L2, there exists r in R such that
(x,y)= <48,40> + r<-12,5>
Read "a => b" as "a implies b", or "a, so b".
Find two integer-valued points in L1:
r=6 => (x,y) = <48,40> + 6<3,4> => (x,y) = <48,40> + <18,24> => (x,y) = <66, 64>.
r=-8 => (x,y) = <48,40> + -8<3,4> => (x,y) = <48,40> + <-24,-32> => (x,y) = <24, 8>.
So {p<66,64>, q<24,8>} is a subset ot L1.
Find two integer points in L2:...
r=-9 => (x,y) = <48,40> + -9<-12,5> => (x,y) = <48,40> + <108,-45> => (x,y) = <156,-5>.
r=11 => (x,y) = <48,40> + 11<-12,5> => (x,y) = <48,40> + <-132,55> => (x,y) = <-84,95>.
So {s<156,-5>, t<-84, 95>} is a subset of L2.
I usually use p1, p2, p3, p4 with subscript 1,2,3,4, but I don't know how to do this in the Blogger fonts . It would be {p1(x1,y1), p2(x2,y2)} subset L1 ("subset" is a U on its side).
An n-dimensional cartesean coordinate system is a function from Euclidean n-space to R^n which is one-to-one, onto, and which preserves the relation "between". Make an analogy with a proper assignment of names to people in a group: each person gets a name, each person gets only one name, no name applies to more than one person.
Let m(pq) be the slope of the segment (pq) (this is not the proper notation, but I don't know how to make the superscript bar over "pq" in Blogger fonts). Slope is a function from intervals to real numbers.
Let d(p,q) be the distance from p to q. Distance is a function from pairs of points to real numbers.
Let u(pq) be the midpoint of the segment pq. Midpoint is a function frrom intervals to points.
Repetition of "function" in this presentation prepares students for later work, where functions become a topic of study in abstract. Students will find this much easier if they have encountered functions before. Writing a Math curriculum shares some features with writing a murder mystery. You cannot have the Great Detective tell the assembled suspects in the concluding chapter: "The butler did it" if the butler never appeared earlier. He has to walk on and serve cucumber sandwiches in chapter 3.
Exercise:...
...........................................................................................................................................................
Let T subset of E^2XR^2 be a cartesian coordinate system.
Let L1 and L2 be lines in E^2 such that
{p<66,64>, q<24,8>} is a subset ot L1
and
{s<156,-5>, t<-84, 95>} is a subset of L2.
Find:...
m(pq)=___
d(p,q)=___.
u(pq)=___
m(st)=___
d(s,t)=___
u(st)=___
point-slpoe form of L1:_______________________
slope-intercept form of L1: ____________________
intercept form of L1: _________________________
Standard form of L1: ________________________
vector form of L1: ___________________________
matrix (determinant) form of L1:__________________
point-slpoe form of L2:_______________________
slope-intercept form of L2: ____________________
intercept form of L2: _________________________
Standard form of L2: ________________________
vector form of L2: ___________________________
matrix (determinant) form of L2:__________________
L1 intersect L2 =___________________ ("intersect"" is a U upside down).
By substitution.
By matrix elimination.
By Cramer's rule.
............................................................................................................................................
That last answer should look like this..."L1 intersect L2 = {p<48,40>}".
Because we used pythagorean triplets for the slope and integers for the multipliers in generating points, the distance comes out integer. Because we used BOTH odd or BOTH even integers for the multipliers in generating points, the midpoint comes out integer. Because we built this exercise from the point of intersection p<48,40> to start, this comes out integer.
Once people know how to add and subtract rational numbers, (by third grade if their parents are doing their job), they are ready to start basic Analytic Geometry of intervals in one-space and lines in 2-space (which schools commonly call "Pre-Algebra" and "Algebra I").
I teach in the following sequence:
1) Linear equations in one variable
2) Linear inequalities in one variable (Let T subset of E^1XR^1 be a one-dimensional cartesian coordinate system).
3) Intervals in 1-space (inequalities with absolute value).
4) Slope of intervals in 2-spae.
5) Linear equations in 2-space.
US textbooks usually save graphing linear inequalities of one variable involving absolute value to the course we call Algebra II. This misses the opportunity to derive the equation of the line in 2-space from the definitions of "interval" and "slope".
Since the line between the points a and b is the set of all points p such that m(ap) = m(ab), the point-slope form of the equation of the line falls out of the defintition of the line.
Generating Pythagorean triplets:
Let N be the set of natural numbers.
Let a^1=a and let a^(n+1) = (a^n)(a). Exponentiation.
Identity: (x^2-y^2)^2 +(2xy)^2=(x^2+y^2)^2 (work it out if you do not see it).
For all x and y in N, x+y is in N and xy is in N, so
For all x and y in N
If a=x^2-y^2 and b=2xy and c=x^2+y^2 you have a,b,c, in N and...
a^2+b^2=c^2. Pythagorus.
We can use this to generate all pythagorean triplets, and then we can use pythagorean triplets to generate systems of simultaneous equations in two variables which come out "neat".
Example:
<3,4,5> and <5,12,13> are pythagorean triplets.
Let m(L1), the slope of line 1, be 4/3 and let m(L2), the slope of line 2, be -5/12.
Use <3,4> (from <3,4,5>).
Use <-12,5> (from 5,12,13>)
Take common multiples of the first and second elements: 48 is a multiple of both 3 and -12, 40 is a multiple of both 4 and 5.
Use p<48, 40> as the point of intersection. We let L1 and L2 intersect at the point p<48, 40>.
Then, from the vector form of the equation for the line we have...
for all p(x,y) in L1, there exists an r in R such that
(x,y) = <48,40> + r<3,4>
and
for all p(x,y) in L2, there exists r in R such that
(x,y)= <48,40> + r<-12,5>
Read "a => b" as "a implies b", or "a, so b".
Find two integer-valued points in L1:
r=6 => (x,y) = <48,40> + 6<3,4> => (x,y) = <48,40> + <18,24> => (x,y) = <66, 64>.
r=-8 => (x,y) = <48,40> + -8<3,4> => (x,y) = <48,40> + <-24,-32> => (x,y) = <24, 8>.
So {p<66,64>, q<24,8>} is a subset ot L1.
Find two integer points in L2:...
r=-9 => (x,y) = <48,40> + -9<-12,5> => (x,y) = <48,40> + <108,-45> => (x,y) = <156,-5>.
r=11 => (x,y) = <48,40> + 11<-12,5> => (x,y) = <48,40> + <-132,55> => (x,y) = <-84,95>.
So {s<156,-5>, t<-84, 95>} is a subset of L2.
I usually use p1, p2, p3, p4 with subscript 1,2,3,4, but I don't know how to do this in the Blogger fonts . It would be {p1(x1,y1), p2(x2,y2)} subset L1 ("subset" is a U on its side).
An n-dimensional cartesean coordinate system is a function from Euclidean n-space to R^n which is one-to-one, onto, and which preserves the relation "between". Make an analogy with a proper assignment of names to people in a group: each person gets a name, each person gets only one name, no name applies to more than one person.
Let m(pq) be the slope of the segment (pq) (this is not the proper notation, but I don't know how to make the superscript bar over "pq" in Blogger fonts). Slope is a function from intervals to real numbers.
Let d(p,q) be the distance from p to q. Distance is a function from pairs of points to real numbers.
Let u(pq) be the midpoint of the segment pq. Midpoint is a function frrom intervals to points.
Repetition of "function" in this presentation prepares students for later work, where functions become a topic of study in abstract. Students will find this much easier if they have encountered functions before. Writing a Math curriculum shares some features with writing a murder mystery. You cannot have the Great Detective tell the assembled suspects in the concluding chapter: "The butler did it" if the butler never appeared earlier. He has to walk on and serve cucumber sandwiches in chapter 3.
Exercise:...
...........................................................................................................................................................
Let T subset of E^2XR^2 be a cartesian coordinate system.
Let L1 and L2 be lines in E^2 such that
{p<66,64>, q<24,8>} is a subset ot L1
and
{s<156,-5>, t<-84, 95>} is a subset of L2.
Find:...
m(pq)=___
d(p,q)=___.
u(pq)=___
m(st)=___
d(s,t)=___
u(st)=___
point-slpoe form of L1:_______________________
slope-intercept form of L1: ____________________
intercept form of L1: _________________________
Standard form of L1: ________________________
vector form of L1: ___________________________
matrix (determinant) form of L1:__________________
point-slpoe form of L2:_______________________
slope-intercept form of L2: ____________________
intercept form of L2: _________________________
Standard form of L2: ________________________
vector form of L2: ___________________________
matrix (determinant) form of L2:__________________
L1 intersect L2 =___________________ ("intersect"" is a U upside down).
By substitution.
By matrix elimination.
By Cramer's rule.
............................................................................................................................................
That last answer should look like this..."L1 intersect L2 = {p<48,40>}".
Because we used pythagorean triplets for the slope and integers for the multipliers in generating points, the distance comes out integer. Because we used BOTH odd or BOTH even integers for the multipliers in generating points, the midpoint comes out integer. Because we built this exercise from the point of intersection p<48,40> to start, this comes out integer.
Once people know how to add and subtract rational numbers, (by third grade if their parents are doing their job), they are ready to start basic Analytic Geometry of intervals in one-space and lines in 2-space (which schools commonly call "Pre-Algebra" and "Algebra I").
I teach in the following sequence:
1) Linear equations in one variable
2) Linear inequalities in one variable (Let T subset of E^1XR^1 be a one-dimensional cartesian coordinate system).
3) Intervals in 1-space (inequalities with absolute value).
4) Slope of intervals in 2-spae.
5) Linear equations in 2-space.
US textbooks usually save graphing linear inequalities of one variable involving absolute value to the course we call Algebra II. This misses the opportunity to derive the equation of the line in 2-space from the definitions of "interval" and "slope".
Since the line between the points a and b is the set of all points p such that m(ap) = m(ab), the point-slope form of the equation of the line falls out of the defintition of the line.
2008/10/14
Palin in '12
Whitney Tilson, normally sensible, supports Barack Obama. Maybe she's right. Were it not for Governor Palin in the Republican VP slot, I would burn my ballot and vote for the Libertarian, Bob Barr. The major parties have never in my adult life (that is, since 1968) offered voters such unqualified candidates for President. Neither candidate demonstrates any appreciation for federalism or the market economy. Senator Obama has no accomplishments worth a mention. His record on Education issues consists of shoveling Annenberg Foundation money to State-worshipful indoctrination programs. He advocates compulsory community service (i.e., slavery) as a HS graduation requirement and high-paid ($4000 for 100 hours), do-nothing community service in exchange for college tuition. Senator McCain's signal accomplishment, the McCain-Feingold Incumbent Protection and Kiss Your First Amendment Rights Goodbye Act, should disqualify him from all elective office were the Democrats' alternative not ever worse. Senator Biden exhibits a detachment from reality (did you watch the debate?) that must cause one to question the sanity of the Delaware electorate. I mean:...Article I describes the powers of the Executive branch and gives the Vice President no legislative authority? Really? Did this man ever read the document he has repeatedly sworn to uphold and defend?
Governor Palin got my vote with her convention speech, accepting the nomination for Vice President. She did much better than Senator Biden in the debate (others disagree, here). She takes too conventional a line on on education issues, but McCain's advisor (Lisa Kegan) trumps that consideration.
Bill Gates bought me a beer, so I bloged about the Ed in '08 Education bloggers' summit. The goal of the summit was to raise Education issues to prominence. That has not happened. It seems the media avoid all topics which might incline voters toward Republican candidates this year.
Governor Palin got my vote with her convention speech, accepting the nomination for Vice President. She did much better than Senator Biden in the debate (others disagree, here). She takes too conventional a line on on education issues, but McCain's advisor (Lisa Kegan) trumps that consideration.
Bill Gates bought me a beer, so I bloged about the Ed in '08 Education bloggers' summit. The goal of the summit was to raise Education issues to prominence. That has not happened. It seems the media avoid all topics which might incline voters toward Republican candidates this year.
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