Back when most schools used the Iowa and Stanford achievement tests, children could demonstrate skills that exceeded their current grade levels. The watered down, standards-based tests that more and more states are using under No Child Left Behind only rate children on whether they meet standards that, in fact, are low relative to grade level.

## Monday, March 31, 2008

### Why Left-Brainers Don't Get High Grades, Part II: Formative Assessment

## Saturday, March 29, 2008

### Why Left-Brainers Don't Get High Grades, Part I: "Grading to the Standard"

In an accidental bipartisan collaboration, the liberal brainchild known as the Standards of the National Council of Teachers of Mathematics and the conservative brainchild known as No Child Left Behind have drastically diluted and diminished the math standards against which our children are graded.

NCTM Standards tell educators that communicating problem-solving strategies is key to learning math. NCLB tells states to devise tests to hold schools accountable to student achievement. The resulting state tests, following the standards, only award full credit to explained answers, and, so that not too many schools will "fail," dumb down the actual content.

The risk of failure has also pressured school districts to make teachers both teach to the test and “grade to the standard.”

Accordingly, the guidelines for the standards-based report cards now used by the Montgomery County District in Maryland say that grades must reflect “what students know in relation to the standards.” Or, in the words of the Christina School District in Newark, Delaware, “their progress towards meeting the state standards.”

All this discourages teachers from assessing skills that extend above and beyond what are now the official benchmarks for particular grades. Indeed, the Montgomery guidelines explicitly rule out “extra credit.”

The upshot: children who once would have been assessed for, and rated with, above grade-level math skills--e.g., a 3rd grader who rates at a 6th grade level--now merely “meet expectations.”

## Thursday, March 27, 2008

### Right-brain biases against school boys

In an Op-Ed in today's Philadephia Inquirer, veteran education reporter Richard Whitmire calls on presidential candidates to take on the under-appreciated plight of today's school boys.

## Wednesday, March 26, 2008

### Math problems of the week: Reform Math vs. other math

One way to see how Reform Math stacks up with other math programs (whether traditional American math, or math as it's still taught in other countries) is to compare specific assignments. Once a week, OILF will do just that.

## Tuesday, March 25, 2008

### Math vs. language arts: an increasingly blurry line

## Monday, March 24, 2008

### Reform an even greater threat to high school math?

An anonymous poster sent me a link to this article in the Ledger-Enquirer, which reveals the latest front in the secondary school math wars: the state of Georgia.

## Sunday, March 23, 2008

### Front page accolades for right-brained classrooms

Breathless articles on right-brained classrooms are a staple of today's education reporting. Consider a front page article in today's Philadelphia Inquirer about the University Park Campus School in Worcester, Mass. This public high school receives student teachers, mentors, and training for school staff from nearby Clark University, and "international recognition and numerous accolades for its ability to take low-performing students and turn nearly all of them into first-generation college-bound teens."

## Friday, March 21, 2008

### New data on learning style differences: gender and ethnicity

In support of such right-brained Constructivist practices as hands-on, group-centered learning, American education experts are quick to enlist multiculturalism. Claiming that traditional instruction favors white, Western males, they happily hold forth on how much more relational, holistic, multi-modal, and/or social girls and nonwhites are.

## Thursday, March 20, 2008

### Chess in the classroom: left-brained, right-brained, or hare-brained?

“One of the things that we hear is that too much of what we do is based on rote memorization,” says Superintendent Luna. “The part I really like about this program is that kids are thinking ahead.”

## Wednesday, March 19, 2008

### Reform Math and nonverbal learning styles

The school community acknowledges and embraces all experiences, beliefs, and ways of knowing mathematics.

All students have access to and engage in challenging, rigorous, and meaningful mathematical experiences.

Such practices empower all students to build a relationship with mathematics that is positive and grounded in their own cultural roots and history.

If I'm remembering correctly, when we were discussing mathematically-gifted but language-impaired kids, you told me that the curriculum allows strategies to be demonstrated in words, numbers, OR, pictures. Is that right? I'm now wondering about problems that use the word "explain", as in "explain [how you got] your answer" rather than "show" ("show how you got your answer"). Is it still the case that the child could answer in numbers (e.g. a series of number sentences) or pictures (e.g. a geometric representation of fractions?)? I'd like to get a better handle on just how well the curriculum accommodates, in particular, the mathematically-gifted but language impaired children that comprise so many of the children on the autistic spectrum, who often literally see the answer, pictographically or numerically, with no accompanying words in their heads.

I don't have a simple answer to your question, as it depends somewhat on the problem, concept, grade level & teacher. Most problems do ask the students to show how they got an answer using pictures, numbers, and/or words. There is no set rule as to what is meant by "explain" but the idea would be that someone else should be able to look at the work and know exactly what the student did--often a combination of pictures, numbers and words is necessary to communicate clearly in mathematics. As far as the curriculum is concerned, a central goal is for students to learn to express mathematical thinking through drawing, writing and talking. A teacher would therefore work to develop students' skills in all three areas. Also keep in mind that instruction is also driven by state tests, and on the PSSA students need to explain their thinking in writing on some of the open-ended questions. Therefore teachers need to have students practice this skill throughout the year...

L:

MC:

Well no, the idea is not just for the teacher to know exactly what the student did, but rather for the student to learn to communicate his or her thinking in a clear way. So "mental math" would not be an adequate explanation. I would certainly think the child would be marked off on the PSSA for that response, given the guidelines that are put out (unless there is some special accommodation in place.) Communication has been a goal of reform mathematics programs since the publication of the standards in 1989.

L:

So if a child doesn't know what his/her thinking was in solving the problem (because it was all subconscious and/or nonverbal thinking), how could this child possibly explain his/her thinking in words? Except to say "I solved it pictographically with the following pictures in my head..." or "it just came to me."

The only alternative I can think of is that such a child would have to imagine how a more verbal person would have solved the problem, and then explain how this hypothetical person would have solved it.

I can certainly appreciate the fact that it would be much more of a challenge for a mathematically gifted but language impaired child, but your question is beyond the realm of my expertise. Perhaps your research will shed some light in this area? I hope I have answered your question about the goals of the curriculum.

L:

Yes, you have.

Unfortunately, these goals, with their narrow notion of what math is about, shortchange the mathematically gifted (ALL those who see the answers nonverbally, including many mathematicians I know). This is, as you know, one big problem I have with the curriculum.

It is too bad that those who have chosen these goals and this curriculum don't seem to know much (or care much?) about how nonverbal children and mathematically inclined curriculum solve math problems.

## Monday, March 17, 2008

### Presidential platforms on math, science, and schools

OILF studiously avoids war, environmental regulation, healthcare, and economic policy. Its focus on left-brainers and right-brain biases should give you no inkling of my opinions on these other issues--however important they are in general, and in the presidential election.

## Sunday, March 16, 2008

### Social norms vs. the alternatives

"Indeed, it has been said that democracy is the worst form of government except all those other forms that have been tried from time to time," observed Winston Churchill in a speech to the House of Commons back in 1947.

## Friday, March 14, 2008

### False dichotomies in math and social skills

## Thursday, March 13, 2008

### Earning high grades in Reform Math

A's in math is one of our family's left-brain traditions. Many of us are mathematicians, scientists, economists, and programmers, and even those with learning disabilities or non-quantitative careers have maintained the streak of top grades in grade school math--at least through trigonometry. Then, a year and a half ago, my daughter entered grade school.

## Wednesday, March 12, 2008

### Rethinking traditional academics

One good thing about the Constructivist revolution is that it provokes fresh thought about the grade school traditions we all take for granted. Why, for example, should we bother teaching English grammar to native English speakers?

## Tuesday, March 11, 2008

### The assault on reason is bipartisan

## Monday, March 10, 2008

### Social pressure, self-esteem, and cooperative learning

## Sunday, March 9, 2008

### Science and science prodigies

Science now turns off so many people that Philadelphia's nearly 200-year-old Franklin Institute Science Museum has shortened its name to The Franklin--treating science like the grease that, accordingly to urban legend, KFC has tried to hide behind its own recent name abbreviation.

## Friday, March 7, 2008

### Teacher pay and teacher quality

An article in today's New York Times profiles a new NYC charter school, The Equity Project, that plans to pay its teachers salaries of $125 k plus bonuses. TEP will fund these salaries with large class sizes (30 students), reduced support staff (only 2 social workers), and extended teacher responsibilities and work hours. To qualify, applicants need scores in the 90th percentile on the GRE, LSAT or GMAT, and in their subject area tests, and "excellent" grades in their subject area courses.

## Thursday, March 6, 2008

### Politics and the Math Wars

## Wednesday, March 5, 2008

### Why teach fractions?

So asks Dennis DeTurck, an award winning math professor and dean of the college of arts and sciences at the University of Pennsylvania. Children don't understand fractions; fractions are as obsolete as slide rules. Calculators and decimals let us breeze where once we slogged, baffled by expressions like 1/2, by finding common denominators, and by inverting and multiplying.

## Monday, March 3, 2008

### Girls as justification for social classrooms

In the cover story of yesterday's New York Times Magazine, which asks whether we should teach girls and boys separately, we see yet another education professional repeating one of the most commonly cited justifications for social classrooms: the purported needs of girls. David Chadwell, the coordinator of Single Gender Initiatives at the South Carolina Department of Education, says that girl-only classrooms should focus on "the connections girls have (a) with the content, (b) with each other and (c) with the teacher." He recommends "a lot of meeting in circles, where every girl can share something from her own life that relates to the content in class."

## Sunday, March 2, 2008

### Good writing requires both right- and left-brain thinking

But in today's published fiction, right-brain inspiration too often trumps left-brain precision. B.R. Myers observed this seven years ago in his provocative Atlantic Monthly piece, "A Reader's Manifesto," in which he critiques the sloppy, pretentious prose of many of our most esteemed contemporary novelists. More recently, Ian MacKenzie's letter in today's New York Times Book Review takes reviewer Liesl Schillinger to task for praising a sentence in Charles Bock's Beautiful Children that depicts the tattooing of a character named Ponyboy: