kitchen table math, the sequel: 3/20/11 - 3/27/11

Saturday, March 26, 2011

lsquared on area conversions

lsquared writes:
I'm really wishing for a national curriculum right now--or at least a series of textbooks that goes K-10 instead of K-6 and another for 6-8.

I'm doing math with a friend's daughter. She's homeschooling, so I get to pick the book, and we're using a Singapore text. Our most recent section is converting units of area: cm2 to m2 and that sort of thing. So, I thought to myself, this is the US, we should also do problems with in2 and ft2--I'll go look through the elementary and middle school texts in my library (I have 2-3 full series of each sitting outside my office door at work). Guess what? None of the books teach the topic at all. Aargh! Everyone is assuming someone else is teaching it, and no one is.

The first time I saw anything about area conversions was in the Saxon Math books I used to teach myself math a few years ago.

I learned inch-to-centimeter and inch-to-foot-to-yard conversions in school, but I learned nothing about area or volume conversions, and I continue to find volume conversions slightly confusing.

Speaking of Saxon Math, I've been thinking I need to get back to my books. I had almost finished the second book in the high school series when I was diverted to whatever I was diverted to. At the time, I was finding logs difficult to deal with in the "shuffled" organization of Saxon Math, especially since I wasn't studying every day.

Speaking of logs, I was emailing with Barry G. earlier today and I compiled a list of all the topics I was never, ever exposed to in high school math or college statistics.

I'll post tomorrow when I'm at my other computer.

The list is too long to remember off the top of my head.

in Portugal

In the Wall Street Journal:
Just 28% of the Portuguese population between 25 and 64 has completed high school. The figure is 85% in Germany, 91% in the Czech Republic and 89% in the U.S.

There is substantial evidence from elsewhere that education confers broad economic benefits. Ireland was one of the EU's poorest countries a generation ago. But it threw EU subsidy money into technical education and remade itself as a destination for high-tech labor, made doubly attractive by low corporate taxes. Ireland is now, even after a brutal banking crisis, among the richest nations in Europe.

"They had an educated-enough work force that they could move into a technology industry, and they rose out of nowhere," says Eric Hanushek, a Stanford University professor.

Prof. Hanushek and a professor from the University of Munich have linked GDP growth with population-wide performance on standardized tests. They calculate that Portugal's long-term rate of economic growth would be 1.5 percentage points higher if the country had the same test scores as super-educated Finland.

Education long was an afterthought here. "The southern countries like Portugal and Spain and the south of France and Italy, we have always had some problems related with education," says António Nóvoa, a historian who is rector of the University of Lisbon. "That's been like that since the 16th century."

The repressive dictatorship that ruled Portugal from 1926 to 1974 had the idea "that people should not have ambition to be something different than what they were," Mr. Nóvoa says. The result was widespread illiteracy and little formal schooling; just three years were compulsory. Huge leaps have been made since the 1970s, he says, but "it is not easy to change a history of five centuries."

Portugal has just begun phasing in 12 years of required schooling; now, Portuguese can leave school after ninth grade. Many do.


A push to evaluate teachers triggered searing strikes and demonstrations in 2008, souring relations between powerful teachers' unions and the government. The political life of education ministers is measured in months: since the dictatorship ended in 1974, there have been 27.

parents protest cuts to quasi-private schools
To the system's critics, a fight that has developed over quasi-private schools is emblematic of what's wrong. With budgets tight, the government has imposed deep cuts on schools that are at the margin of the state's control—no matter that some are among the best.


In one town, A Dos Cunhados, the local school isn't run or owned by the government. It is managed by the Catholic Church, in an arrangement that dates to the end of the dictatorship, when the new Portuguese state found it didn't have enough facilities.

At the school, Externato de Penafirme, as at 90 others with what are called "association contracts," the state pays a management fee to a private entity, which broadly follows the state curriculum but hires its own teachers.

The deputy principal, Carlos Silva, once taught chemistry in the public school system. He was shuffled through four schools in four years. Frustrated, he quit and enrolled in a seminary. Afterward, as a priest, he asked his bishop about returning to the classroom, and was assigned to Externato de Penafirme.


Faced with the cuts, students and parents organized. In December, 4,000 people held hands in a big ring around the Penafirme campus. The pictures hit television. A Facebook group sprang up. In January, students walked out of dozens of the privately run schools for three days. To dramatize a claim the cuts would mean the death of their schools, students and parents from 55 schools ferried mock coffins to Lisbon and put them on the median strip outside Ms. Alçada's ministry.

Last month, the education ministry eased somewhat, agreeing to restore part of the lost funding for this semester.

A Nation of Dropouts Shakes Europe
March 25, 2011

personal history

How the Irvington Parents Forum came to be.

Friday, March 25, 2011

Religion and the Public Schools and Teacher Evaluations

Two new posts from the temporarily dormant Throwing Curves on religion in the schools and the ongoing legislative efforts to revamp teacher evaluation procedures.

Teacher Evaluations and LIFO

Religion and the Public Schools

Thursday, March 24, 2011

SAT math question

I have two questions, actually, but I'll post just one for the time being.

Here it is.

For me, SAT math questions are non-routine. They are problems, as opposed to exercises.

Here's my question.

Is that true for kids scoring 700 and 800 on the SAT?

Or is it true for me because my math knowledge is still pretty tenuous?

When I watch Salman Khan work SAT problems, I don't feel like I'm watching a person solve problems.

I feel like I'm watching a person do exercises.

Am I wrong?


The National PTA partnered with experts on the Common Core State Standards to create grade by grade guides that reflect the Common Core State Standards. The site also has a brief powerpoint of additional materials for mathematics describing focus and coherence. Slide #5 caught my attention:

'nuff said.

help desk - why square root of 5?

The correct answer is E.

When I do this problem, I get .618, which is the same thing as (square root of 5 minus 1) divided by 2.

But how do you come up with E specifically?

Off hand, I don't see how.


Evaluating Teachers - a teen's perspective

Having one son in a charter school and sports means plenty of driving. Yesterday, I was taking three boys from the high school to the baseball fields a couple of miles away and was lucky to hear this nugget of wisdom:
C: The principal was observing Mr. X (the Latin teacher) today. Class was so much better than usual, we didn't just sit there and read like we usually do.
T: Totally.
J: Yeah, teachers really seem to have better lessons when Principal Y or Mr. Z (Headmaster) is watching them. It's like they think it though better and try to make it more fun to show-off or something.

MSMI 2011: Fractions and Rational Numbers

This year, Middle School Mathematics Institute (MSMI) is offering two professional development institutes this summer for elementary and middle school math teachers that are specifically geared to the math content they teach: MSMI 2011: Fractions and MSMI 2011: Rational Numbers.

MSMI 2011: Fractions is a 5 day (plus 5 day followup) institute, June 20-24, 2011 in downtown Saint Paul, MN. MSMI 2011: Rational Numbers is a 4 day (plus 5 day followup) institute, June 27-June 30, 2011. Both institutes will be held at the CoCo Coworking and Collaborative Space. Local arrangements are available at the Crowne Plaza in St. Paul, a short walk from CoCo.

These institutes are designed to develop fractions and rational numbers in a coherent, sequential, and precise manner that builds both conceptual understanding and procedural fluency. Teachers will learn how to help their students increase the depth of knowledge by providing the scaffolding needed for abstract mathematical reasoning. Teachers will develop a better understanding of how they math they teach relates to the math taught prior to and beyond their classroom. By teaching this material in a coherent, precise fashion, teacher will be able to lead students to understand and master this mathematics, enabling their students to achieve a solid foundation for Algebra 1.

Why fractions and rational numbers? MSMI concentrates on fractions and rational numbers following the National Mathematics Advisory Panel's recommendations on "Critical Foundations for Algebra". Fractions are the first abstractions in school mathematics. Fractions prepare students because they depend on precise definitions in order to be well defined. Fractions are handled best by thinking symbolically, not by analogies (no more pie pieces, pizza slices, etc.) Negative numbers have no grounding the way counting numbers do. They are best handled by thinking symbolically and working with definitions. Learning to work with fractions and negative numbers helps students because if they can handle these elements for fractions and negative numbers, they can handle them in algebra.

Institutes are not geared toward any specific textbook or pedagogy, but provide deeper content knowledge immediately applicable to any classroom. The textbook for these institutes is Hung-Hsi Wu's Understanding Numbers in Elementary School Mathematics . This material is aligned with both Minnesota state standards and Common Core standards.

Allison Coates will teach the Fractions institute. UC Berkeley Professor Emeritus Hung-Hsi Wu will teach the Rational Numbers institute.

Topics covered in Fractions Institute include:
Formal definitions of Fractions and Decimals

— Equivalent Fractions and the Fundamental Fact of Fraction-Pairs

— Addition and Subtraction of Fractions and Decimals

— Multiplication of Fractions and Decimals

— Division of Fractions

— Complex Fractions

— Percent

— Ratio and Rate

Topics for Rational Numbers institute include:

The Two Sided Number Line

— A Different View of Rational Numbers

— Addition and Subtraction of Rational Numbers

— Multiplication of Rational Numbers

— Division of Rational Numbers

While the summer session of 4 or 5 full days provides the bulk of the mathematics content, 5 follow-up Saturday sessions are provided throughout the school year. Saturday sessions review material from the institute and provide time for teachers to discuss implementation of institute material in their classes. In these sessions, teachers work together to determine what works best for their students in their classrooms, and provide feedback to each other.

Online registration is available here. Additional information is available on the web site.

Monday, March 21, 2011

FedUpMom on multiplying by 10

I have just this moment figured out that FedUpMom has a blog!

This has been a difficult year.

A difficult couple of years, actually.

Nowhere to go but up-----

Molly on junior high vs middle school

Looking back at my own junior high experience and comparing it to my kids' middle school experience, I think momof4 has hit the nail on the head. Junior high was about academics, and the adults trusted that the adolescents were cable enough to work through their personal growth issues on their personal time. Middle school seems to be about everything but academics.

In junior high, I had really solid instruction in writing,including extensive grammar instruction. We did science labs that required the exact same sort of write-up that my high school labs later required. We studied actual history and civics (as opposed to the nebulous social studies).

In middle school, my daughters don't write, they produce power point presentations. The few writing assignments are given as group projects - my oldest was recently assigned a group poem to write. While they do science experiments, these seem to be purely for demonstration value as the students are never required to record observations in any standardized form.

My middle school daughters frequently miss class in order to attend assemblies during which some nominally well-known person tells them how important it is to stay in school and get an education. The irony of cancelling class to have an athlete extol the virtue going to class seems lost on middle school administrators.

chemprof on docent science

Steve H on the STEM sessions at the Celebration of Teaching and Learning:
They are mostly about engagement (it's the student's fault and/or responsibility) or about selling something.
and "docent science," which is what my colleagues and I call it. Science appreciation is another good term. I guess I can see that they figure that most students won't actually go on and do STEM in college, but they are really limiting their students' options. Plus, I can't tell you how many students come to college thinking that there are careers in science appreciation. 
I've always had a simmering interest in math, and for years I bought 'math appreciation'-type books, which I always found somewhat unsatisfying and never finished reading.

Finally, after writing ktm for awhile and teaching myself math so I could re-teach math to C., I realized I didn't want to appreciate math. I wanted to learn math.

"Understanding math" - which I think of as a kind of feeling I have at times - is tremendously fun, but it's not fun when I can't actually do the math I'm "understanding." Hard to explain.

I've also learned the importance of "getting used to" math as opposed to understanding it. Or, at least, I've had the experience of learning to do something I can't understand and then, after awhile, coming to feel that it's "natural" and "logical" to do whatever it is I've been doing.

This process is starting to happen a bit with counting, which I have found utterly mystifying. Recently I discovered that a great deal of what I've been doing in counting problems involves the commutative property and the definition of multiplication.

Who knew?

I can't tell if all this self-teaching I've been trying to do is a good thing or a bad thing.

question about value-added measurement

My copy of the Harvard Education Letter arrived with an excerpt from a new book on value-added measurement. I have a question about this passage:
Misconception 2: Value-added scores are inaccurate because they are based on poorly designed tests. Most standardized tests are indeed flawed, but this is not a problem created or worsened by value-added.
Seven Misconceptions About Value-Added Measures
by Douglas N. Harris
Harvard Education Letter - March|April 2011
p. 8
Is that correct?

As I understand it, New York's state tests can't be used for value-added purposes. The tests are shorter in some years, longer in others, and somehow don't correspond to a one-year measurement of learning. Or so we were told. Certainly they don't provide any sense of where a child might be within a year's worth of content. New York tests are scored 1 to 4, so if your child scores a middling 3, what does that mean on a scale of 10 months? Nobody knows.

I had been assuming that in order to use a standardized test as a value-added measurement, the tests had to be normed month-by-month as the Iowa Test of Basic Skills is normed:
Grade Equivalent (GE)
The grade equivalent is a number that describes a student's location on an achievement continuum. The continuum is a number line that describes the lowest level of knowledge or skill on one end (lowest numbers) and the highest level of development on the other end (highest numbers). The GE is a decimal number that describes performance in terms of grade level and months. For example, if a sixth-grade student obtains a GE of 8.4 on the Vocabulary test, his score is like the one a typical student finishing the fourth month of eighth grade would likely get on the Vocabulary test. The GE of a given raw score on any test indicates the grade level at which the typical student makes this raw score. The digits to the left of the decimal point represent the grade and those to the right represent the month within that grade.
When your child takes the ITBS from one year to the next, it's simple to see whether he's made a year's progress in a year's time. If, at the end of grade 3, he scored a 3.10 on computation (grade 3, month 10), he should score a 4.10 on computation at the end of 4th grade.

But how would you make that determination using the New York tests?

Or is there some other comparison you make from year to year?