Core math doesn’t add up in California

California’s Common Core math standards are less rigorous than the state’s old standards, writes Wayne Bishop, a Cal State LA math professor, in the San Gabriel Valley Tribune.

The old standards, released in 1997, were written by Stanford math professors who wanted eighth graders — not just the private school kids — to learn algebra, he writes. The new standards stress verbal skills.

. . . the new test requires students to answer follow-up questions and perform a task that shows their research and problem-solving skills. . . . Any student with weak reading and writing skills is unfairly assessed. That is especially problematic for English learners.

Common Core reflects the belief that “mathematics is best learned through students’ exploration of lengthy ‘real world’ problems rather than the artificial setting of a competent teacher teaching a concept followed by straightforward applications thereof,” writes Bishop. In reality, “traditional (albeit contrived) word problems lead to better retention and use of the mathematics involved.”

In addition, Common Core “expects students to use nonstandard arithmetic algorithms . . .  in place of the familiar ones; e.g., borrow/carry in subtraction/addition and vertical multiplication with its place-value shift with successive digits,” writes Bishop.

He recommends Stephen Colbert’s “delightful derision” of Core confusion.

Pure math > ‘real-world’ math

Teaching kids to solve “real-world” problems is supposed to motivate students to learn math. It’s all the rage.

However, students taught abstract math — solving equations with x’s and y’s — do better in math, concludes a new report from the Organization for Economic Cooperation and Development (OECD). They’re even better at solving real-world problems, reports Hechinger’s Jill Barshay in the Washington Monthly.

Furthermore, higher-income students are more likely to learn pure math, while teachers focus on applied math in teaching low-income students, according to Equations and Inequalities:  Making Mathematics Accessible to All.

In 64 countries and regions around the world, “the difference between the math scores of 15-year-old students who were the most exposed to pure math tasks and those who were least exposed was the equivalent of almost two years of education,” researchers found.

When students have a strong foundation in math, “they can apply that knowledge in another context,” said Andreas Schleicher, OECD’s director of education and skills development.

Many teachers who stress applied math, “teach students tips and tricks, how to solve small everyday problems,” he said. Students “know how to solve those problems, but they’re not good at transferring that knowledge to another context.”

Common Core rap

Common Core Essential Standards change how we teach, rap a group of STEM teachers in Charlotte, North Carolina.

The teachers don’t seem all that happy to be “reassigned to the pep squad,” notes Missouri Education Watchdog, which speculates it’s a professional development must-do.

Here’s the lyrics:

Chorus: Focus on student engagement
Practices communication
Relevant data, yes
Common Core Essential Standards change how we teach

No longer can a teacher be the sage on the stage
Common Core Essential Standards change how we teach
Become the guide on the side the students to engage
Common Core Essential Standards change how we teach
The other verses contain these points:

No list of algorithms to memorize
Graphing calculators and real world ties

A variety of problems, problem solving strategies
Complex texts and technologies

Hands-on inquiry with questions to promote
Analysis of data, not answers by rote

Clear and concise, rubrics (whole)* guide
students will improve the quality of work with pride

* hard to understand in the video

So, up until now, teachers haven’t tried to engage students, pose real-world problems or use relevant data? But once the new standards go into effect, they will.

In the comments, Barry Garelick notes that the new Common Core math standards, which the teachers see as cutting edge, have been criticized for being too traditional.

Real math

Students learn by solving real math problems, argues Dan Meyer on a wildly popular TED video, Math Class Needs a Makeover.  An algebra teacher and dy/dan blogger, Meyer is now working on a doctorate in curriculum design.

Rejected as a film student, Meyer tells Ed Week about the “narrative arc” of a real-world math problem. Intead of “shark terrorizes seaside town,” it might be “how long will it take me to get to Los Angeles?”

During what he calls the “second act” of a film, the characters encounter obstacles and find out what they need to do. In a math problem, the second act involves measuring, determining a formula, or finding out what information is missing.

The third act brings the exciting conclusion — with potential for a sequel.

Textbooks label the variables, present the measurements  and ask leading questions in an attempt to help students, Meyer says.  That can overwhelm students.

He starts with the hook: The final question.

For example, when teaching high schoolers, Meyer uses the digital projector to display a photo of himself shooting a basketball. Meyer has doctored the photo so that it shows the ball at several different points along the trajectory, stopping at the apex. “When I put that up on the board, the premise of that problem is obvious to every student. I don’t even have to say it. ‘Will the ball go in?’ That’s what we’re all wondering,” he says.

Then Meyer asks the students to figure out what information they need to determine whether his shot will go in. The students discover they have to measure the arc and need a protractor to do so—in a way writing their own second act. A textbook would have provided this information, Meyer says. But in the real world, “When on earth do you get all the information you need before you know you need it?”

The students can then solve the problem on their own.

Then they watch the video to see if they’re right.

Meyer believes in “delegating the sense-making of math to students.”

In my day, people were always rowing against the current, which seemed like a waste of energy. Or they were trying to calculate when trains going opposite directions would pass, instead of reading the train schedule.

 Get the Math, an educational reality TV show produced by WNET in New York, shows the real-world applicatons of algebra, reports Ed Week.

The single-episode program, as well as the companion website, features three short video segments designed to provide an introduction to teen-favored industries—music recording, fashion design, and video game development. . . . the professionals featured in each video offer examples of how they use mathematical knowledge as part of their creative processes.

Then comes the “challenge.” At the end of each segment, the pro gives a pair of two-student teams a specific industry-related algebraic problem to solve. The videos show the teams working through the problems and then presenting their solutions. The idea, of course, is that other students can play along in their classrooms.

The program, lesson plans and classroom activites are available at no charge at