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CurricularGamePlaying 23 Jun 2006 - 21:22 CarolynJohnston

Does it matter what mathematics curriculum your kids are using at school, as long as they are getting good grades in math?

Catherine and I both started tutoring our kids, supplementing their math homework, and looking into mathematics education, because our kids weren't doing well in their regular math classes. Had they gotten good grades all along, we might just be rolling along without asking any questions.

But my son was doing poorly in Everyday Math, a new-new-math curriculum, after having been very successful in Saxon Math, a traditional curriculum which emphasizes the incremental acquisition of new skills, including mastery of all the classic computations. It was clear that it was the new curriculum that had derailed him. But was that just my son, whose special needs make him a special case?

Proponents of Everyday Math claim that it integrates a child's mathematics knowledge, and makes it more useful to him, if the kids spend time working with math in the context of discovering and solving real-world problems; gathering data, measuring things, and so forth, at the expense of computation (if necessary). If so, then after (perhaps) a few years of struggle, we ought to see improvement in kids' understanding of math at the level of applications.

In other words, kids raised on real-world data and applications ought to at least be better at word problems. That's what makes this chart so powerful.

The chart shows scores on a subtest of math problem solving of the Comprehensive Test of Basic Skills (CTBS), a nationally-normed standardized test. The scores measure the same group of kids from Anne Arundel County's 14 lowest-performing schools in 2nd grade, and again in 4th grade.

The second graders had been working with either Everyday Math or Mathland, a similar 'discovery-based' curriculum (see the blue bars in the chart). When they took the test in 4th grade, they had been working with the Saxon curriculum for a year (see the white bars).

The kicker is that this subtest measures performance on word problems. This is the supposed weakness in traditional math programs that Everyday Math's approach is intended to remedy.

Check out this link to see how the news went over in Anne Arundel.

Curricular Game Playing
Curricular Game Playing, part 2
number bonds vs. 4-fact families
Numicom Dominoes

TitlesOfConstructivistMathCurricula 19 Jul 2005 - 01:46 CatherineJohnson

Jo Anne Cobasko has taken the time to construct a complete list of NCTM standards based math programs.

update: Department of Corrections

This list is David Klein's handiwork, not Jo Anne's.

Thank you, David! (For everything you do.)

All of us should keep this handy, because none of these programs ever calls itself constructivist, and schools don't seem to advertise this piece of information, either.

When I first raised the issue of TRAILBLAZERS being a constructivist curriculum with a teacher on the textbook selection committee, she looked at me blankly. I got a number of those blank looks before I discovered that everyone in the school knows what the word constructivism means, and knows what a constructivist curriculum is.

The reason I know this is that I finally read the original committee report, which states explicitly that the new curricula must have a constructivist approach with modeling. I was a little behind the curve there.

Elementary school

Everyday Mathematics (K-6)
TERC's Investigations in Number, Data, and Space (K-5)
Math Trailblazers (TIMS) (K-5)

Middle school

Connected Mathematics (6-8)
Mathematics in Context (5-8)
MathScape: Seeing and Thinking Mathematically (6-8)
MATHThematics (STEM) (6-8)
Pathways to Algebra and Geometry (MMAP) (6-7, or 7-8)

High school

Contemporary Mathematics in Context (Core-Plus Mathematics Project) (9-12)
Interactive Mathematics Program (9-12)
MATH Connections: A Secondary Mathematics Core Curriculum (9-11)
Mathematics: Modeling Our World (ARISE) (9-12)
SIMMS Integrated Mathematics: A Modeling Approach Using Technology (9-12)

Programs explicitly denounced by over 220 Mathematicians and Scientists:

Cognitive Tutor Algebra
College Preparatory Mathematics (CPM)
Connected Mathematics Program (CMP)
Core-Plus Mathematics Project
Interactive Mathematics Program (IMP)
Everyday Mathematics
MathLand
Middle-school Mathematics through Applications Project (MMAP)
Number Power
The University of Chicago School Mathematics Project (UCSMP)

printable page

Thanks, Jo Anne, for taking the time to do this!

key words:
DavidKlein
listofconstructivisttextbooks
constructivist textbooktitles
NSFfundedcurricula

NctmReformsAgain 14 Sep 2006 - 16:52 CatherineJohnson

In today's Wall Street Journal ($):

Arithmetic Problem
New Report Urges Return to Basics In Teaching Math
Critics of 'Fuzzy' Methods Cheer Educators' Findings;
Drills Without Calculators Taking Cues From Singapore
By JOHN HECHINGER
September 12, 2006; Page A1

The nation's math teachers, on the front lines of a 17-year curriculum war, are getting some new marching orders: Make sure students learn the basics.
In a report to be released today, the National Council of Teachers of Mathematics, which represents 100,000 educators from prekindergarten through college, will give ammunition to traditionalists who believe schools should focus heavily and early on teaching such fundamentals as multiplication tables and long division.
The council's advice is striking because in 1989 it touched off the so-called math wars by promoting open-ended problem solving over drilling. Back then, it recommended that students as young as those in kindergarten use calculators in class.
Those recommendations horrified many educators, especially college math professors alarmed by a rising tide of freshmen needing remediation. The council's 1989 report influenced textbooks and led to what are commonly called "reform math" programs, which are used in school systems across the country.
The new approach puzzled many parents. For example, to solve a basic division problem, 120 divided by 40, students might cross off groups of circles to "discover" that the answer was three.
Infuriated parents dubbed it "fuzzy math" and launched a countermovement. The council says its earlier views had been widely misunderstood and were never intended to excuse students from learning multiplication tables and other fundamentals.
Nevertheless, the council's new guidelines constitute "a remarkable reversal, and it's about time," says Ralph Raimi, a University of Rochester math professor.
Francis Fennell, the council's president, says the latest guidelines move closer to the curriculum of Asian countries such as Singapore, whose students tend to perform better on international tests.

So maybe it wasn't such a great idea after all for IUFSD to ban my Singapore Math course.

new timeline

According to their report, "Curriculum Focal Points," which is subtitled "A Quest for Coherence," students, by second grade, should "develop quick recall of basic addition facts and related subtraction facts." By fourth grade, the report says, students should be fluent with "multiplication and division facts" and should start working with decimals and fractions. By fifth, they should know the "standard algorithm" for division -- in other words, long division -- and should start adding and subtracting decimals and fractions. By sixth grade, students should be moving on to multiplication and division of fractions and decimals. By seventh and eighth grades, they should use algebra to solve linear equations.

Here's the Singapore sequence.

Lutherans turning into Catholics

A recent study by the Thomas B. Fordham Foundation, a Washington nonprofit group, found that only two dozen states specified that students needed to know the multiplication tables. Many allowed calculators in early grades.
Chester E. Finn Jr., the foundation's president and a former top official at the U.S. Department of Education, blamed the earlier math-council guidelines for state standards that neglect the basics. He described the new advice as a "sea change," saying that "it's a little bit like Lutherans deciding to become Catholics after the Reformation."
Understanding math, rather than parroting answers to poorly understood equations, was the goal of the council's controversial 1989 standards. Those guidelines called on teachers to promote estimation, rather than precise answers. For example, an elementary-school student tackling the problem 4,783 divided by 13 should instead divide 4,800 by 12 to arrive at "about 400," the 1989 report said. The council said this approach would enable children using calculators to "decide whether the correct keys were pressed and whether the calculator result is reasonable."
"The calculator renders obsolete much of the complex pencil-and-paper proficiency traditionally emphasized in mathematics courses," the council said then. In 2000, in another report, the council backed away somewhat from that position.
Still, in response to the earlier recommendations, many school systems required children to describe in writing the reasoning behind their answers. Some parents complained that students ended up writing about math, rather than doing it.
As the debate heated up, concern grew about U.S. students' math competence. In 2003, Trends in International Mathematics and Science Study, a test that compares student achievement in many countries, ranked U.S. students just 15th in eighth-grade math skills, behind both Australia and the Slovak Republic. Singapore ranked No. 1, followed by South Korea and Hong Kong. Fueling concern about the quality of elementary and high-school instruction: one in five U.S. college freshmen now need a remedial math course, according to the National Science Board.

low-income students

This is very exciting. The AIR report (pdf file) led me to believe that Singapore Math had been a flop in low-income schools because the student mobility is so high (and see Hirsch on this subject, too):

If school systems adopt the math council's new approach, their classes might resemble those at Garfield Elementary School in Revere, Mass., just north of Boston. Three-quarters of Garfield's students receive free and reduced lunches, and many are the children of recent immigrants from such countries as Brazil, Cambodia and El Salvador.
Three years ago, Garfield started using Singapore Math, a curriculum modeled on that country's official program and now used in about 300 school systems in the U.S. Many school systems and parents regard Singapore Math as an antidote for "reform math" programs that arose from the math council's earlier recommendations.
According to preliminary results, the percentage of Garfield students failing the math portion of the fourth-grade state achievement test last year fell to 7% from 23% in 2005. Those rated advanced or proficient rose to 43% from 40%.
Last week, a fourth-grade class at Garfield opened its lesson with Singapore's "mental math," a 10-minute warm-up requiring students to recall facts and solve computation questions without pencil and paper. "In your heads, take the denominator of the fraction three-quarters, take the next odd number that follows that number. Add to that number, the number of ounces in a cup. What is nine less than that number?" asked teacher Janis Halloran. A sea of hands shot up. (The answer: four.)
Ms. Halloran then moved on to simple pencil-and-paper algebra problems. "The sum of two numbers is 63," one problem reads. "The smaller number is half the bigger number. What is the smaller number? What is the bigger number?" (The answers: 21 and 42.)
In this class, the students didn't use the lettered variables that are so prevalent in standard algebraic equations. Instead, they arrived at answers using Cuisenaire rods, sticks of varying colors and lengths that they manipulate into patterns on the tops of their desks. The children use the rods to learn about the relationship between multiplication and geometry. The goal: a visceral and deep understanding of math concepts.
"It just makes everything easier for you," says fifth-grader Jailene Paz, 10 years old.

Cuisinaire rods for bar models!

That's so cool!

TERC time

The Singapore Math curriculum differs sharply from reform math programs, which often ask students to "discover" on their own the way to perform multiplication and division and other operations, and have come to be known as "constructivist" math.
One reform math program, "Investigations in Number, Data and Space," is used in 800 school systems and has become a lightning rod for critics. TERC, a Cambridge, Mass., nonprofit organization, developed that program, and Pearson Scott Foresman, a unit of Pearson PLC, London, distributes it to schools.

parents don't get it part 1

Ken Mayer, a spokesman for TERC, says many parents have a "misconception" that Investigations doesn't value computation. He says many school systems, such as Boston's, have seen gains in test scores using the program. "Fluency with number facts is critical," he says.

parents don't get it part 2

Polle Zellweger and her husband, Jock Mackinlay, both computer scientists, moved to Bellevue, Wash., from Palo Alto, Calif., two years ago so their two children could attend its highly regarded public schools. She and her husband grew suspicious of the school's Investigations program. This summer, they had both children take a California grade-level achievement test, and both answered only about 70% of the questions correctly. Ms. Zellweger and her husband started tutoring their children an hour a day to catch up.
"It was a really weird feeling," says their daughter, Molly Mackinlay, 15. "I do really well in school. I am getting A-pluses in math classes. Then, I take a math test from a different state, and I'm not able to finish half the questions."
Eric McDowell, who oversees Bellevue's math curriculum, says parents misunderstand Investigations.

If it weren't for the parents, teaching would be a great job.

math wars and war wars

In the Alpine School District in Utah, parent Oak Norton, an accountant, has gathered petitions from 1,000 families to protest the use of Investigations. His complaints began more than two years ago, when he discovered at a parent conference that his oldest child, then in third grade, wasn't being taught the multiplication tables.
Barry Graff, a top Alpine school administrator, says the system has added more traditional computation exercises. Over the next year, Alpine plans to give each school a choice between Investigations or a more conventional approach. Mr. Graff, who says Alpine test scores tend to be at or above state averages, expects critics to keep up the attacks and welcomes the national math council's efforts to provide grade-by-grade guidance on what children should learn.
"Other than the war in Iraq, I don't think there's anything more controversial to bring up than math," he says. "The debate will drive us eventually to be in the right place."

wow

I bet things are hopping over at math-teach & math-learn.

[pause]

hmm

No action thus far.

Once Wayne Bishop posts this baby, we'll be in a shooting war.

update: Bishop's got it!

let the fun begin

what Singapore students can do at the end of 7th grade

-- CatherineJohnson - 12 Sep 2006