Inventing the new, new math symbols


Math with Bad Drawings suggests urgently needed math symbols.


75% of seniors aren’t ready for college math

Only 25 percent of 12th graders are prepared for college math and 37 for college reading, according to the latest Nation’s Report Card from the National Assessment of Education Progress (NAEP). Math scores fell over the last two years, while reading scores have been flat since 2009.

Remember that the weakest students have dropped out by 12th grade.

Low performers are doing worse while high achievers are improving, notes Liana Heitin on Ed Week. The percentage of students scoring at the “below basic” level was higher in both reading and math, compared to 2013.

That may be a side-effect of the rising graduation rate, which hit 82 percent in 2014.

Racial/ethnic gaps are huge: 64 percent of blacks and 53 percent of Hispanics score as below basic in math; only 7 percent of blacks and 11 percent of Hispanics score as proficient or better. By contrast, a third of whites and nearly half of Asian-Americans are proficient or better.

Here’s more on the knowledge and skills required to score “basic” or “proficient” on NAEP’s 12th-grade math exam.

In reading, 49 percent of Asians, 46 percent of whites, 25 percent of blacks and 17 percent of black 12th graders are proficient or better.

“College for all” remains the mantra. Nearly two-thirds of high school graduates will enroll in college immediately: 55 percent will complete a degree within six years.

Parents try Common Core math

Posted by BuzzFeed Video.

Tracking is linked to higher AP scores

Tracking in eighth grade — usually in math — correlates with higher scores on AP tests at the end of high school, concludes the 2016 Brown Center Report on American Education.

In eighth grade, the tracking question currently boils down to whether high achieving students who are ready for a formal algebra course will get one—or whether all students will take the same general math course.

States with larger percentages of tracked eighth graders produce larger percentages of high-scoring AP test takers, the study found. “The heightened AP performance held across racial subgroups—white, black, and Hispanic.”

There was no relationship between tracking and and the number of students taking AP tests — just to the number who earned a 3, 4 or 5.

Another section looks at how Common Core State Standards (CCSS) are changing instruction in math and reading.

Teachers are teaching more nonfiction in fourth and eighth grade, NAEP data show.

In addition, “data and geometry are receding in importance in fourth grade math, and course enrollments in eighth grade math are shifting away from advanced courses toward a single, general math course,” the report notes.

Eighth graders study algebra at San Francisco's Presidio Middle School in 2011. Photo: Lenny Gonzalez, MindShift

Eighth graders study algebra at San Francisco’s Presidio Middle School in 2011. Photo: Lenny Gonzalez, MindShift

That suggests fewer achievers will start on the path to passing AP Calculus.

San Francisco Unified middle schools no longer teach algebra, as part of the shift to Common Core standards, reported Ana Tintocalis for KQED last year.

For years, all eighth graders took algebra and many failed, said Lizzy Hull Barnes.  Now no one will take algebra till ninth grade.

This “is a social justice issue for SFUSD,” writes Tintocalis. “District officials say the controversial practice of tracking students — or separating them based on talent and ability — is simply wrong.”

Why the math curriculum makes no sense

“What would you do, if you could design high school math from scratch?” asks teacher Ben Orlin on Math with Bad Drawings. “Well . . . not what we do now,” he concludes. “The math curriculum makes no sense.”

We see math as an apartment building that’s been designed to stack one floor on another, writes Orlin. It’s more of a mountain.

Read the whole thing.

U.S. teens learn advanced math — after school

BEAM recruits low-income middle schoolers in New York City and prepares them for high-level math in high school and college. Photo: Erin Patrice O’Brien, Atlantic

“Online and in the country’s rich coastal cities and tech meccas . . . accelerated students are learning” more complex math than ever before, writes Peg Tyre in The Atlantic. A “new pedagogical ecosystem” — math enrichment camps, after-school and weekend classes, “math circles” and online sites — is growing rapidly.

“More than 10,000 middle- and high-school students haunt chat rooms, buy textbooks, and take classes on the advanced-math learners’ Web site the Art of Problem Solving,” she writes.  Richard Rusczyk, a former Math Olympian who founded the site, is opening two brick-and-mortar centers to teach advanced math and plans an online program for elementary students.

The Proof School, a small independent secondary school in San Francisco, also teaches “amped-up math” — often to the children of high-tech parents.

The Russian School of Mathematics offers classes in 31 locations nationwide.

The Russian School of Mathematics offers classes in 31 locations nationwide.

STEM parents hope to “supplement or replace what they see as the shallow and often confused math instruction offered by public schools, especially during the late-elementary and middle-school years,” writes Tyre.

U.S. elementary teachers often are uncomfortable with math says, Inessa Rifkin, a co-founder of the Russian School of Mathematics, which enrolls 17,500 students in after-school and weekend math academies in 31 U.S.
locations. She thinks kids start to go astray in second or third grade.

Teachers at the Russian School help students achieve fluency in arithmetic, the fundamentals of algebra and geometry, and later, higher-order math. At every level, and with increasing intensity as they get older, students are required to think their way through logic problems that can be resolved only with creative use of the math they’ve learned.

“Students quickly learn their math facts and formulas,” then use that to explore the world, writes Tyre.

From the math-and-science site

Imagine a rope that runs completely around the Earth’s equator, flat against the ground (assume the Earth is a perfect sphere, without any mountains or valleys). You cut the rope and tie in another piece of rope that is 710 inches long, or just under 60 feet. That increases the total length of the rope by a bit more than the length of a bus, or the height of a 5-story building. Now imagine that the rope is lifted at all points simultaneously, so that it floats above the Earth at the same height all along its length. What is the largest thing that could fit underneath the rope?

The options given are bacteria, a ladybug, a dog, Einstein, a giraffe, or a space shuttle. The instructor then coaches all the students as they reason their way through.

Einstein is the right answer. But the point is get students to “execute the cognitive bench press: investigating, conjecturing, predicting, analyzing, and finally verifying their own mathematical strategy,” writes Tyre.

Bridge to Enter Advanced Mathematics (BEAM), a New York City nonprofit, looks for joyful problem solvers in low-income middle schools. They’re offered “a three-week residential math camp the summer before eighth grade, enhanced instruction after school, help with applying to math circles, and coaching for math competitions, as well as basic advice on high-school selection and college applications.”

Singing an aria from Tosca requires years of training in music. Credit: Metropolitan Opera

Singing an aria from Tosca requires years of training in music. Credit: Metropolitan Opera

Tyre implies that conceptual understanding and “problem solving” can be learned without foundational skills, responds Barry Garelick, author of Confessions of a 21st Century Math Teacher.

She compares a regular ninth-grade algebra class to a lecture “on the basics of musical notation” versus a middle-school problem-solving students singing “an aria from Tosca.”


Singing an aria from Tosca requires “years and years of training in basic vocal skills,” writes Garelick. “Musicality is built up from mastery of the basics.”  Similarly, students learn to solve complex math problems by learning how to solve basic problems, then harder problems and so on.

Here’s a profile of the Los Angeles math teacher whose student earned a perfect score in AP Calculus — and whose students all pass the AP exam.

Teachers “should always think of the next level,” said Anthony Yom, who was born in Korea. “Where are they going in the next level, what are they learning in the next class? Then, you can do some backward planning, and that will help you do a good job at explaining things.”

A perfect score

Cedrick Argueta, right, is congratulated by his calculus teacher, Anthony Yom, left. Photo: Al Seib, Los Angeles Times

Of 302,531 students who took the Advanced Placement Calculus exam last year, only twelve earned a perfect score, reports the Los Angeles Times. Cedrick Argueta, the son of a Salvadoran maintenance worker and a Filipina vocational nurse, was one of them.

At Lincoln High in a heavily Latino neighborhood of Los Angeles, students shouted, “Ced-rick! Ced-rick!” when Principal Jose Torres announced his score, reports the Times.

Math has always just made sense to him, he said. He appreciates the creativity of it, the different methods you can take to solve a problem.

“There’s also some beauty in it being absolute,” Cedrick said. “There’s always a right answer.”

He credits “everybody else that helped me along the way.”

Both parents are immigrants. His father, Marcos, never attended high school. His mother, Lilian, said that she told Cedrick and his younger sister to finish their homework and to “read, read, read.”

His math teacher, Anthony Yom, says all of his AP Calculus students have passed the exam for three years running. Last year, 17 of 21 earned a 5, the highest score.

Yom, 35, said he treats his students like a sports team. They’d stay after school, practicing problem solving for three or four extra hours, and they’d come on weekends. On test day, they wore matching blue T-shirts sporting their names, “like they’re wearing jerseys to the game,” Yom said.

Cedrick also earned perfect scores on the science and math sections of the ACT, he said. He’s taking four more AP exams this year, including Calculus BC.

He hopes to earn a scholarship to Cal Tech to study engineering.

New math, old math: Who needs math?

Common Core math isn’t really new math, writes A.K. Whitney in The Atlantic. One hundred years ago, reformers argued for teaching all students — not just the smartest — to understand and apply math. In The Reorganization of Mathematics in Secondary Education, they backed algebra for all to teach “habits of thought and of action.”

However, progressive educators, followers of Dewey, pushed back, arguing that most Americans don’t need to understand math.

William Heard Kilpatrick, a very influential professor at Columbia University Teachers College, “set his sights on reforming math education, making it less about building the intellect and more about whether it was needed for everyday living,” writes Whitney.

Advanced math should be offered only to students with interest, talent and plans for engineering or science careers, Kilpatrick’s committee argued in a 1920 report, The Problem of Mathematics in Secondary EducationMost students could make do with arithmetic.

In 1922, 40 percent of U.S. students took algebra; that dropped to 30 percent by 1934. Twenty-three percent took geometry in 1922, but only 17 percent in 1934.

When progressive ideas about math fell out of favor, “deeper understanding didn’t quite catch on either,” writes Whitney.

Math was taught for understanding before the Common Core, responds Barry Garelick in a comment. Parents who object to how Common Core is being implemented have valid concerns, he writes.

I was in kindergarten when Sputnik went up and U.S. complacency crashed. We heard a lot about what “Ivan” could do that we kids couldn’t. That led to “new math” in the ’60s, which was all about understanding. It confused people too.

Math teachers group-think about what’s best

Traditional teaching is “outmoded and ineffective,” according to the new guard’s group-thinking, writes math teacher Barry Garelick after a day at “education camp.” Teachers no  longer debate “best practices,” he writes as the only traditionalist.

Scaffolding — starting with what students know and teaching more in small steps — is out, he learned at ed camp. Instead, teachers are supposed to provide “feedback and guidance” that helps students solve completely new problems, a moderator said.

“Think-Pair-Share” — students discuss a problem or question with a partner, then share their ideas with the class — is obsolete, Garelick learned.

. . . students didn’t know what to say to each other about whatever it was they were to discuss. And that was likely because they had little or no knowledge of the subject that they were supposed to talk about, and which was supposed to give them the insights and knowledge that they previously lacked.

However, student-centered and inquiry-based approaches are still alive and well,” he writes. Feedback and guidance are the new think, pair, share of math teaching.

‘They knew I had a future … ‘

Education Secretary Arne Duncan mentored Lawanda Crayton 25 years ago.

Twenty-five years ago, Arne Duncan was an “I Have a Dream” Foundation mentor at a Chicago elementary school. The outgoing education secretary reunited with Lawanda Crayton, when she was interviewed for NPR’s StoryCorps interview project.

The foundation helps low-income children with “tutoring in early elementary school all the way through help with college tuition,”  reports NPR.

Crayton’s  mother was “an abusive alcoholic,” she told Duncan in the intrerview. “I remember being put in the hospital, I had a broken bone in my leg, had cuts on my face — all from my mother.”

I was a very angry young woman . . . But you and I had a very dynamic relationship, because I spent a number of days being tutored by you in math, and it became one of my favorite subjects.

Crayton was motivated by the program’s rewards. “And for us it was like, hey, if we do well on this test we can go on a trip … anything that was going to get us out of the war zone that we were in. I wanted as much homework as I could get in order not to go home.”

Every year I embraced everybody a little bit more and I accepted that they wanted to be a part of my life. They knew I had a future, I had a life, and I had a purpose, because I never thought that I had that, and it took these blessings to put that in my life. If I didn’t have that support, I wouldn’t be here.

The foundation paid for Crayton to attend a Catholic school, then go on to college.

She had no family at her college graduation. But she’d called Duncan. “You were there. You came. You were just as proud of me as I was of myself.”

Crayton now works in information technology as a project manager and mentors children.