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NCEE: Only 5% need calculus

May 7, 2013 by 44 Comments

Only 5 percent of students will use calculus in college or the workplace, concludes a new report on college and career readiness by the National Center on Education and the Economy. Most community college students could succeed in college courses if they’ve mastered “middle school mathematics, especially arithmetic, ratio, proportion, expressions and simple equations.” Many have not.

The report calls for providing an alternative track — less algebra, more statistics — for high school students who aren’t aiming at university STEM degrees.

In a few years, high school diplomas in North Carolina will show whether a graduate is prepared for a four-year university, a community college and/or a career.

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Brookings: Ability grouping is back

March 18, 2013 by

Elementary teachers are using ability grouping once again, according to the 2013 Brown Center Report on American Education by Tom Loveless.

Ability grouping was very popular from the 1960′s through the 1980s, but came under attack as inequitable in the 1990′s. In 1961, 80 percent divided children into robins, bluebirds and sparrows, or the like. (I was a bluebird in 1958.) By 1998, only 28 percent of fourth graders were being placed in reading groups by ability. That shot up to 71 percent by 2009, Brookings finds.

Math ability grouping rose from 40 percent of fourth graders in 1996 and 42 percent in 2003 to 61 percent in 2011.

With more computers in elementary classrooms, teachers may be “more comfortable with students in the same classroom studying different materials and progressing at different rates through curriculum,” writes Loveless.

Although ability grouping is coming back, efforts to de-track middle school math are continuing. However, pushing more eighth graders into algebra isn’t raising achievement, the report finds.

States with rising percentages of eighth graders taking Algebra I, Geometry, and other advanced math classes were no more likely to raise their NAEP scores from 2005-2011 than states with declining percentages of eighth graders in those courses.

When more students take pre-algebra and algebra, the courses appear to be watered down, writes Loveless. However, there’s no watering-down effect for geometry.

The U.S. is often exhorted to emulate the high-scoring  “A+ countries” — Belgium (Flemish), Czech Republic, Hong Kong, Japan, Korea, and Singapore – in math instruction. However, “the average A+ country made no more progress in math achievement than any other country in TIMSS” since 1995, the report finds.

And the Finns may do well on PISA but they’re nothing special on TIMSS.

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Algebra 1 for all — but it’s not always algebra

March 13, 2013 by

Nearly all high graduates in the class of ’05 passed Algebra I — or a course labeled Algebra I, concludes a new federal study. But fewer than one in four studied the challenging algebra topics needed to prepare for college-level math, the National Assessment of Educational Progress study found. Most geometry and “integrated math” also were watered down. From Education Week.

Education watchers hoping to close persistent achievement gaps among students of different racial and ethnic groups long have pushed for all students to take “college-ready” class schedules, including at least four years of high school math, including Algebra I and II, Geometry, and Calculus. Here, at least, the transcript study shows this push has paid off: Graduates in 2005 earned on average 3.8 credits in math, significantly more than the average of 3.2 credits earned by graduates in 1990. Moreover, from 1990 to 2005, black graduates closed a six-percentage-point gap with white graduates in the percentages of students earning at least three math credits, including in algebra and geometry.

Two thirds of Algebra I and Geometry courses covered core content topics. However, the quality of courses varied widely. Only a third of algebra students spent 60 percent of their time on challenging topics such as functions and advanced number theory. Only a fifth of geometry students primarily studied rigorous material.

“We found that there is very little truth-in-labeling for high school Algebra I and Geometry courses,” said Sean P. “Jack” Buckley, the NCES commissioner, in a statement on the study.

“Honors” meant nothing in algebra:  ”Regular” Algebra I classes were more likely to be rigorous than “honors” classes. Geometry honors classes were more likely to be rigorous, but only a third of honors geometry classes contained challenging material, compared with 19 percent of regular geometry classes.

Researchers analyzed the textbooks used; it’s possible teachers added more challenging supplemental material. However, “students who took classes that covered more rigorous topics in algebra and geometry scored significantly higher on the NAEP than those who studied beginner topics, regardless of the course’s title,” Ed Week reports.

It’s no wonder so many high school graduates are placed in remedial math in college, despite passing high school math courses, often with B’s and C’s.

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Double-dose algebra helps some students

November 3, 2012 by

When Chicago put below-average ninth graders in “double-dose” algebra classes with twice the instructional time, failure rates were high. But double-dose algebra has significant long-term benefits, conclude Kalena Cortes, Joshua Goodman and Takako Nomi in Education Next. Compared to similar students, Chicago’s double-dose algebra students were more likely to graduate from high school and enroll in college (almost always community college). They earned higher ACT scores in math and verbal skills. There’s some evidence they earned higher grades in advanced math and chemistry classes.

Starting with students entering high school in the fall of 1997, CPS eliminated lower-level and remedial courses so that all first-time freshmen would enroll in algebra in 9th grade, geometry in 10th grade, and algebra II or trigonometry in 11th grade. . . .  many students were unable to master the new curriculum, resulting in very low passing rates in 9th-grade algebra.

Instead of bringing back remedial math, CPS assigned below-average students to a regular algebra class and a second  class that included “writing sentences to show how they solved a math problem; explaining how they solved a problem to the class; writing math problems for other students to figure out; discussing possible solutions with other students; and applying math to situations in life outside of school.”

Perhaps because of all the writing, double dosing was especially effective for students with below-average reading skills and “moderately low” math skills.

Double-dosed students scored nearly 0.20 standard deviations higher on the verbal portion of the ACT, were substantially more likely to pass chemistry classes usually taken in 10th or 11th grade, and earned modestly higher GPAs across all of their non-math classes in the years after 9th grade. In other words, the skills gained in double-dose algebra seem to have helped students in other subjects and in subsequent years.

Nearly half of large urban districts use a double dose of algebra for low-skilled students. However, the Chicago study suggests that extra instruction helps students who are not too far behind, but does little for the truly low achievers. Should they get extra math instruction in middle school? Elementary school? Or a path to a high school diploma that doesn’t require algebra?

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Math needs a revolution too

October 27, 2012 by

Math Needs a Revolution, Too, writes Barry Garelick in response to The Atlantic story, The Writing Revolution. He first encountered reform math when his daughter was in second grade.

. . . understanding takes precedence over procedure and process trumps content. In this world, memorization is looked down upon as “rote learning” and thus addition and subtraction facts are not drilled in the classroom–it’s something for students to learn at home. Inefficient methods for adding, subtracting, multiplying, and dividing are taught in the belief that such methods expose the conceptual underpinning of what is happening during these operations. The standard (and efficient) methods for these operations are delayed sometimes until 4th and 5th grades, when students are deemed ready to learn procedural fluency.

Students are expected to “think like mathematicians” before acquiring the analytic tools necessary to do so, Garelick writes. Procedural skills are taught on a “just in time” basis.

Such a process may eliminate what the education establishment views as tedious “drill and kill” exercises, but it results in poor learning and lack of mastery. Students generally work in groups with teachers who “facilitate” rather than providing direct instruction.

As reform math has become the norm in K-6 classrooms, high school math teachers are trying to teach algebra to students who “do not know how to do simple mathematical procedures,” he writes.

In math, as in writing, learning the fundamentals may not be fun or engaging. It may require practice. But students who skip the basics rarely develop the ability to “think like mathematicians” or write like “authors.” They’re confused. And bored.

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America’s math problem

October 23, 2012 by

In America’s search for education equality, we’ve watered down math instruction, argues Jacob Vigdor in Education Next. That’s hurt high achievers without helping low achievers.

In the early 20th century, American high-school students were starkly divided, with rigorous math courses restricted to a college-bound elite. At midcentury, the “new math” movement sought, unsuccessfully, to bring rigor to the masses, and subsequent egalitarian impulses led to new reforms that promised to improve the skills of lower-performing students. While reformers assumed that higher-performing students would not be harmed in the process, evidence suggests that the dramatic watering down of curricular standards since that time has made our top performers worse-off.

. . . America’s lagging mathematics performance reflects a basic failure to understand the benefits of adapting the curriculum to meet the varying instructional needs of students.

When Charlotte-Mecklenberg schools placed below-average-performing eighth graders into algebra, they proved more likely to pass algebra by 10th grade, but less likely to pass geometry or advanced algebra ever, Vigdor notes. By contrast, Chicago improved success rates for below-average students by giving them a “double dose” of  algebra tailored to their needs.

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Fluent on facts, weak on abstraction

October 19, 2012 by

Fluency in addition and multiplication isn’t everything, writes Education Realist.

. . . plenty of solid math students don’t have fluency and—here is the important part—many exceptionally weak math students have strong fact fluency.

Ed Realist’s “math support” students, who are trying to pass the exit exam and graduate from high school, tend to be very literal and easily thrown by symbols. Ed Realist  asked students to read a simple equation as a sentence. When a student turned x + 6 = 14 into “what number do I add to six to get 14?” the answer was clear to most of the class.

One student, Gerry, still didn’t get it.  He said he could only do math if it doesn’t have letters.

 “You need to look at these problems from a different part of your brain.”

. . . “X + 6 = 14. This is when you have to do stuff to both sides, right? I can’t do that.”

“Read it again. But instead of saying x, say ‘what’.”

“What plus 6 = 14? 8.”

Gerry said he couldn’t do fractions. But when he turned x/5 = 9 into “what divided by 5 is 9?” he got 45 right away.  “I feel like a math genius,” he said.

“You know a lot more math than you think you do,” the teacher said. ” You just have to figure out how to ask the question in a way your brain understands.”

Not everyone is capable of understanding abstractions to the same degree, Education Realist concludes.

Some people do better learning the names of capitals and Presidents and the planets in the solar system. They’d learn confidence and competence through interesting, concrete math word problems and situations, and enjoy reading and writing about specific historic events, news, or scientific inventions that helped society. Instead, we shovel them into algebra, chemistry and literature analysis and make them feel stupid.

She quotes psychologist James Flynn on why IQ’s have risen steadily and significantly since the start of the 20th century (the “Flynn effect”).

Modern people . . .  are the first of our species to live in a world dominated by categories, hypotheticals, nonverbal symbols and visual images that paint alternative realities.

. . . A century ago, people mostly used their minds to manipulate the concrete world for advantage. They wore what I call “utilitarian spectacles.” Our minds now tend toward logical analysis of abstract symbols—what I call “scientific spectacles.” Today we tend to classify things rather than to be obsessed with their differences. We take the hypothetical seriously and easily discern symbolic relationships.

Well, some of us do. Flynn has a new book out, Are We Getting Smarter?

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‘Personalizing’ helps kids solve math problems

October 1, 2012 by

“Personalizing” algebra questions — using a sports or music context, let’s say, instead of farming — helps students, according to Southern Methodist University researchers whose latest study is slated for publication in Journal of Educational Psychology.

Struggling students are easily discouraged by new problems and distracted by unfamiliar words, said Professor Candace Walkington.

She asked ninth graders who were using Cognitive Tutor software about their interests in areas such as sports, music, and movies. Then she randomly assigned them to take the linear-equation unit with standard word problems or one of four variations tailored to their interests.

The students who received personalized word problems solved them faster and more accurately than students who received the standard questions, particularly when it came to translating the story scenarios into symbolic equations.

Moreover, the strongest effects occurred for students who were struggling the most before personalization.

“Problems that required a relatively high reading level and more-challenging knowledge components, those were the steps of the problem that were particularly affected by the personalization,” (Carnegie Learning founder Steven) Ritter noted during the Sept. 12 discussion at Carnegie Mellon.

“It kind of makes sense if you think [about it], if you’re a big sports fan … you are probably better able to read things about sports because you understand the vocabulary, you understand the situations, and for you, the readability is better,” he said.

Core Knowledge’s E.D. Hirsch would predict this: Students need background knowledge to understand what they read. If students are struggling to read a story problem, they won’t have much mental energy left to tackle the math.

Here are five variations of the set-up to a math problem:

One method for estimating the cost of new home construction is based on the proposed square footage of the home. Locally, the average cost per square foot is estimated to be $46.50.

You are working at the ticket office for a college football team. Each ticket to the first home football game costs $46.50.

You are helping to organize a concert where some local R&B artists will be performing. Each ticket to the concert costs $46.50.

You have been working for the school yearbook, taking pictures and designing pages, and now it’s time for the school to sell the yearbooks for $46.50 each.

You work for a Best Buy store that is selling the newest Rock Band game for $46.50.

SOURCE: Candace A. Walkington, Southern Methodist University

Surprisingly, students who’d received “personalized” questions did better two months later on a new unit without personalized questions.

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Two paths to algebra in California

September 21, 2012 by

California will not block eighth-graders from taking algebra if the governor signs SB 1200, writes Deputy Superintendent Lupita Cortez Alcalá in a letter to Bill Lucia of EdVoice. School districts will not be forced “into a misguided one-size-fits-all approach to math education,” she writes.

What it does do is provide for clear and viable pathways: one for students who are ready for higher mathematics (algebra 1 in a traditional sequence and course 1 in an integrated sequence) and another for students who would progress through the grade level standards as called for in the Common Core standards.

Placement of students in mathematics courses, based on their readiness, remains a local decision – as it should be.

. . . adoption of the Common Core State Standards with California’s additions presented some unique challenges. California adopted two sets of eighth grade mathematics standards: the Common Core set and a set that combined elements of the Common Core eighth-grade and high school mathematics standards with California’s own algebra standards. Unfortunately, the “Algebra 1 at Grade 8” standards have created confusion in our school districts as it is a unique amalgamation, different from Algebra I, and not supported by instructional materials or curricula.

In focus groups, teachers and curriculum said “they want high expectations and high standards for their students – but also flexibility to decide when a student is ready for higher mathematics, based upon each student’s classroom performance – not impersonal directives from the Capitol,” concludes Alcalá.

I think this means algebra-ready students will take Algebra I without any Common Core additions. I think . . . (A reform of years gone by, integrated math teaches bits of algebra, geometry, trig and stats each year till students have mastered the concepts. It’s lost popularity.)

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Out of the equation

September 17, 2012 by

To conform with Common Core Standards, California has dropped eighth-grade algebra as a goal for all students. A bill sitting on Gov. Jerry Brown’s desk requires schools to teach pre-algebra to all eighth graders, regardless of ability, write Ze’ev Wurman and Bill Evers, who helped write state standards 15 years ago, in City Journal.

SB 1200 . . . would prohibit schools from offering any options in mathematics, even to high school students. The bill insists that only “one set of standards” be offered at “each grade level” across the entire K–12 span.

Since the late 1990s, California has worked hard to raise math achievement to international levels, they write.

. . . the state boasts the highest percentage of students taking algebra by eighth grade in the United States—68 percent, a fourfold increase over 15 years. Fifty-three percent of California eighth-grade algebra takers tested “proficient” or “advanced” on the California Standards Test this past academic year, up from just under 40 percent in 2002.

California changed math curriculum to introduce pre-algebra concepts as early as third grade, approved new math textbooks and trained teachers, Wurman and Evers write. If SB 1200 becomes law, that effort will be abandoned.

Algebra-ready eighth graders could take algebra under the Common Core regime, writes John Fensterwald on EdSource. There will be an accelerated path to algebra, according to Bill Honig, who chairs the state education board’s commission on implementation of Common Core. California and other states will have to design new Algebra I (or integrated math) standards based on Common Core to fit the new tests.

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