the nativity gap in a nutshell

[I]mmigrant students actually do better if they begin their American education in high school rather than in elementary or middle school.

Foreign-Born Students New to N.Y. Outshine Native Born
by Sarah Garland
New York Sun
February 11, 2008 Edition

the nativity gap

the nativity gap

from Bostonian:

Where is the evidence, adjusting for race, that American math curricula are worse than those used in Asia?

William Schmidt, director of the U.S. national Research Center for the Third International Mathematics and Science Study, is the person to read on this subject:

The Role of Curriculum
A Coherent Curriculum: The Case of Mathematics (pdf file)

and see:
The Sequence of Mathematics Topics in Top-Achieving Countries (pdf file)


nativity gap

This Stiefel, Schwartz, and Conger study, while not an analysis of curriculum, supports Schmidt's argument:

Do Immigrants Differ from Migrants? Disentangling the Impact of Mobility on High School Completion and Performance
Leanna Stiefel, Amy Ellen Schwartz, and Dylan Conger

from the New York Sun's story:

Foreign-born newcomers to New York City's public schools are performing better than native-born newcomers, a New York University study shows.

The working paper by NYU education researchers titled "Do Immigrants Differ From Migrants?" has also deflated any notions that immigrant students tend to do worse in American schools the older they are when they arrive. On the contrary, the findings demonstrated that immigrant students actually do better if they begin their American education in high school rather than in elementary or middle school.

[snip]

Ms. Schwartz, speaking at an NYU symposium last week, said she and her colleagues had hypothesized that immigrant students "who come late are the ones who are really disadvantaged," guessing that their lack of language skills, the stress of moving to a new country, and institutional differences between the schools they came from and the New York schools might hurt their graduation rate and performance on tests.

Instead, they found that the foreign born "just do remarkably better," Ms. Schwartz said.

Foreign-Born Students New to N.Y. Outshine Native Born
by Sarah Garland
New York Sun
February 11, 2008 Edition

Here is Andrew Wolf's take:

Immigrant children outperform some native-born children in New York schools, my colleague Sarah Garland reported the other day. Indeed, it seems the longer newly-arrived children attend our schools, the worse they do. These conclusions come from a new study, "Do Immigrants Differ From Migrants?"

"The foreign born are whizzing by the native born at every level," one of the researchers, Amy Ellen Schwartz, said.

[snip]

If one drives past the Bronx High School of Science any given school day morning, one will encounter a seemingly endless caravan of yellow school buses. Most of these buses come from Queens, the borough known for its immigrant population. Sixty percent of those recently offered a spot at Bronx Science as a result of their test scores come from Queens, as are 40% of the new freshmen at Stuyvesant. It [sic] it turns out that a good number of these commuter students are recent immigrants, why do the city's specialized high schools seem to have such a disproportionate number of newly arrived students?

Whizzing By
BY ANDREW WOLF
March 3, 2008

I miss the Sun.

more from Wu

from Allison:

Going forward from what Catherine posted, Wu argues that most of what teachers know about fractions, and teach to their students, is wrong in the sense that it is unsupported by what the students have previously been taught.

Wu makes clear that you must be ruthless with your self when teaching. You must not allow yourself to use any concept you've not explicitly given your students. And almost all textbooks violate this rule in almost every lesson on fractions.

Nearly all textbooks avoid defining a fraction. Since they aren't defined, they don't define how you operate on fractions in terms of any real definition. Beyond that, when they do introduce operations on fractions, the books don't define operations in terms of what students know either. They teach rules without ever teaching where the rules come from. Their "explanations" invoke properties no one taught the students, but are just asserted. That means logically, their explanations are wrong, as you can't prove a statement by assuming the statement true.

For example, how does one justify multiplication of fractions? (I'll answer how later, but for now, discuss amongst yourselves.)

Yes, you can learn to use the rule properly without understanding where it is from, but you'll only go so far, and more, you will mistrust your teachers and mistrust math. Math will seem to be an endless series of magical statements with no relationship, and sooner or later, you'll run out of time/space/effort for keeping track of them. Properly understood, math is coherent, because every new step you take follows from the ones before.

a likely story

I'm sorry.

I have to say it.

I didn't buy the grew apart after 40 years of marriage business for one second.

question: Why exactly did we all have to read earnest accounts of 'gray divorce' & suchlike for a solid week?

Off-topic, I know.

we begin

Definition of a Fraction

Recall that a number is a point on the number line (§5 of Chapter 1). This chapter deals with a special collection of numbers called fractions, which are usually denoted by m/n, where m and n are whole numbers and n ≠ 0. We begin by defining what fractions are, i.e., specifying which of the points on the number line are fractions. The definition will be both clear and simple. If you find it strange that we are making a point of giving a definition of fractions, it is because this is something thousands (if not hundreds of thousands) of teachers have been trying to get at for a long time. Most school textbooks and professional development materials do not bother to give a definition at all. A few better ones at least try, and typically what you would find is the following:

Three distinct meanings of fractions — part-whole, quotient, and ratio — are found in most elementary mathematics programs.

[snip]

Such an explanation is unsatisfactory for several reasons. To say that something you try to get to know is three things simultaneously strains one’s credulity. For instance, if I tell you I have discovered a substance that is as hard as steel, as light as air, and as transparent as glass, would you believe it? Another reason for objection is that a fraction is being explained in terms of a “ratio”, but most people don’t know what a ratio is.2 In addition, while we are used to the idea of a division a ÷ b where a is a multiple of b (see §3.4 of Chapter 1), we are not sure yet of what 2 ÷ 3 means. So to use this to explain the meaning of 2/3 does not seem to make sense. Finally, we anticipate that fractions would be added, subtracted, multiplied and divided, and it is not clear how one goes about adding, subtracting, multiplying and dividing a part-whole, or a quotient, or a ratio.

This is why we opt for a definition that is both simple and clear.

Chapter 2: Fractions (Draft) (pdf file)
H. Wu
Department of Mathematics #3840
University of California, Berkeley
Berkeley, CA 94720-3840

"KIPP schools routinely outscore many that serve middle-class"

Report finds KIPP students outscore public school peers

Again.

I remember, 5 years ago, when I first started telling people KIPP kids were twice as likely to take algebra in the 8th grade and pass Regents as our kids.

Now here it is, 2010, and I'm still telling people KIPP kids are twice as likely to take algebra in the 8th grade and pass Regents as our kids.

Same deal with Scarsdale. Last winter our Interim Director of Curriculum reported that 80% of Scarsdale students take algebra in 8th grade.

Then she added: "We're not Scarsdale. We certainly don't have the resources of Scarsdale."

'We're not Scarsdale' explained why we can't have 80% of our kids taking algebra in 8th grade. If we were Scarsdale, we could, but we're not Scarsdale so we can't.

A parent in the audience logged onto the internet, pulled the data, and reported back to the board before the night was out that in fact Irvington has exactly the same per pupil dollar spending on instructional programming as Scarsdale, so: check.

But no matter.

Tonight the board will undoubtedly approve funding to enable our Interim Director of Curriculum and a generous contingent of teachers to devote a week or two this summer to rejiggering Trailblazers in consultation with a math person from up Bedford way. Bedford School District seems to be the last Trailblazers site in the county apart from Irvington (Scarsdale adopted Singapore Math 2 years ago), so obviously we Irvington taxpayers need to pay them, too.

Check back in 2015.

nice work if you can get it

$60 - $80K

$83 million

from Saxon Math Warrior:

It was one thing for John Saxon to take on the mathematics education establishment. It was another for him to take on a special interest group whose followers were bankrolled by the federal government. With $83 million in federal tax dollars being pumped into the math education reformists’ camps during the 1990’s, any entrepreneur not in the chosen circle, who opposed reform math methods, and who was publishing his own math textbooks would have to battle more than their high-dollar funding. He would have to challenge the political ideology that guided all their decisions regarding America’s math program.

msmi 2010 Followup

msmi 2010: Institute on Fractions is now history. YAY!

I'll leave Catherine and any others to talk about their take on it. I'll have some future posts on what I think are the biggest lessons parents and teachers need to help their students understand fractions, but this is just a roundup.

In the course of 5 days, we covered: definition of a fraction, equivalent fractions, decimals, addition, subtraction, multiplication, division, decimals again, and percent. We had more to do, but we couldn't get to it.

Based on the reaction of the teachers, it was a success. I have NEVER had a class of students where so many students worked so hard. No matter what their background, everyone tried to do the problems. Their effort meant that as the week went on, the students were more engaged and more knowledgeable. The teachers also built up their camaraderie with each other.

Based on their personal comments to me and the anonymous survey I gave at the end, their overall impression was quite high. Several teachers told me that this course was the first time anyone had ever explained how to think about fractions. One told me it was "a revelation" to them, another told me this was the first time they'd see a way to visualize multiplication of fractions. Most responded to our survey saying that this material had changed how they would teach permanently. Several teachers had a different kind of revelation, too: that other people in other schools/cities/states knew and felt as they did. They were connecting the dots not only on fractions, but on the state of math education.

Not that everything was perfect. I was terribly out of practice for being a teacher--bad board technique, bad handwriting, bad short hand in my own thoughts and words, instead of being clear, specific and slow.

I made several errors in sizing up my audience too. I assumed that since I had told the principals what to expect, that they had told their teachers. I assumed that teachers, given a pointer to a web site that had, e.g. Wu's CV on it, would have read such.

The biggest complaint was that it was too much material/days too long, and not enough worked out examples. One solution to the latter is to strongly encourage the teachers to read the textbook a day ahead of time. But part of that is the nature of the beast: there is an enormous deficit of knowledge to overcome. Elementary math teachers didn't go into that field because of their stength in fractions. The breadth of math inexperience-experience even for teachers of the same grade was very large, yet being math experienced didn't quite help, because while those teachers probably followed Wu's proofs more easily, applying his ideas to actual math problems was still a new universe to them, and their skill was sometimes a hindrance, because he was asking them to think an entirely different way than they were used to.

Lastly, I'm thrilled to have met all the people involved. Wu is a delight to work with/for, and I'd do this again with him wherever we can. He was personable and charming as well as brilliant. His wife was just as delightful. CassyT, KTMer, is an exemplary woman. She's a brilliant teacher and student of human nature, and her insights into teachers saved me countless mistakes. She shared her expertise with me in countless ways, and the whole thing would have fallen apart if not for her.

So, where to go from here? First, more Wu institutes! Let's bring MSMI to your locale! Second, the really big thing is to help teachers turn what they learned here into changes in their school. That's no small undertaking. I'll talk about that more in the next post. Last, more documents for everyone: condensing of Wu for parents and teachers. I'm sure you'll see work product of that around here shortly...

more than one way to solve it

paraphrasing Wu at msmi2010:

The idea that there is always more than one way to solve it is propaganda. Sometimes you're lucky to have one way.

question: what is the opposite of fuzzy?

answer: SAT math

54 questions, 70 minutes, many working parts

no time to 'think'

no time for 'many ways to solve it'

to score well on the SAT, you need to use the fastest method, and you need to know what the fastest method is about 5 seconds after you start reading the problem

if not sooner

talk and chalk

from Have Technology and Multitasking Rewired How Students Learn? by Dan Willingham

When you encounter a new technology, try to think in abstract terms about what the technology permits that was not possible in the past. It’s also worth considering what, if anything, the technology prevents or makes inconvenient. For example, compared with a chalkboard, an overhead projector allows a teacher to (1) prepare materials in advance, (2) present a lot of information simultaneously, and (3) present photocopied diagrams or figures. These are clear advantages. However, there are also disadvantages. For instance, James Stigler and James Hiebert noted that American teachers mostly use overhead projectors when teaching mathematics, but Japanese teachers use chalkboards.³³ Why? Because Japanese teachers prefer to maintain a running history of the lesson. They don’t erase a problem or an explanation after putting it on the board. It remains, and the teacher will likely refer to it later in the lesson, to refresh students’ memories or contrast it with a new concept. That’s inconvenient at best with an overhead projector.

³³ James W. Stigler and James Hiebert, The Teaching Gap (New York: Free Press, 1999).

Having managed to follow most of Wu's lectures, I am a huge fan of this method - and a huge non-fan of the PowerPoint now-you-see-it, now-you-don't approach to teaching.

limits of working memory
working memory posts

Saxon Math Warrior

from Education News:

John Saxon was hated by the math education establishment from the time he published his first algebra book in 1981. He still is, 14 years after his death in 1996. A West Point graduate with three engineering degrees, he declared war on those he blamed for creating the “disaster in American math education.” He insisted that math leaders had overseen this debacle and there was no personal accountability being demanded for the results of their radical ideology.

In John Saxon’s Story, a genius of common sense in math education, readers learn about his battles, his strong and colorful personality, and how his historically-based traditional math program made him, much to his surprise, a multimillionaire. This was in spite of high-powered and politically-connected math leaders’ efforts to destroy him.

The author, Nakonia (Niki) Hayes, is a retired math teacher and principal who used the Saxon program. She says she wrote the biography because John Saxon made a valuable and positive impact on thousands of American children. Go to Saxon Math Warrior for more information about how to order this original biography.

wow!

MSMI2010 was amazing.

Amazing!

Still collecting my thoughts - will post - but in the meantime, Niki Hayes' John Saxon bio is out!
My copy arrived in the mail last week.

The brain hurts most when being expanded...

Professor Wu at the beginning of MSMI2010 ...

...and at the end of MSMI2010.


That's the result of 40 hours of extreme fraction action.

Notice how giddy and hard working the attendees are after 5 days!

Better sign up now for next year's institute on Geometry.

NJ adopts Common Core Standards

From an email I received from The NJ Coalition for World-Class Math:

Dear Group:

 

Well, it's over.

 

Yesterday, the NJ State Board of Education adopted the Common Core Standards in Math and English-Language Arts yesterday.  They never offered the public a chance to provide testimony on the final standards prior to adoption.

More info here:

NJ adopts new federal standards for math, language arts | dailyrecord.com | Daily Record

 

Critics: NJ rushing to adopt new math, language arts standards | dailyrecord.com | Daily Record

Where Have All The Portfolios Gone

Now that my son is finishing 8th grade and heading to high school, I'm still waiting to get back all of his work hidden away in portfolios. They are educational black holes. Is some student work (good and bad) kept as examples without telling students? Do some teachers use the work in reports or their own class work without telling the kids? I know it won't do us much good now, but it would be nice to get the work back. I wrote to our school long ago about how hiding work in portfolios does not help parents and kids, but I never heard a word back.

gone fishing

Well, not fishing, exactly.

I'll be attending the Middle School Mathematics Institute in Minneapolis!

Allison on SAT prep

I would teach anyone taking the SAT that they should *know the strategy* to answer the question by the time they've finished reading it, or they should move on and go back to it later.

The goal of SAT prep and math courses, generally, should be to study enough math that nearly all of the problems are that immediately clear to you--you know by the time you've finished reading them how you're going to solve them.

21st century

SMART Boards & SMART Tables, too




Senior Bertrand Ngampa gives a presentation on an interactive whiteboard at W.T. Woodson High. (Dayna Smith/Post)