Crazy about math

THUMBNAIL_IMAGE“Hell hath no fury like a mathematician whose child has been scorned by an education system that refuses to know better,” writes Barry Garelick in Math Education in the U.S.: Still Crazy After All These Years.

After a career in environmental protection, Garelick earned a teaching credential and began teaching and writing. He criticizes “the well-intentioned but highly injurious nonsense that passes for math education.”

“I often feel that I am explaining in detail why jumping out of an airplane without a parachute will result in death,” he writes.

50 years after algebra, teaching 21st-century math

Teaching Math in the 21st CenturyIt’s been 50 years since Barry Garelick took his first algebra course. Now launched on his second career as a math teacher, he writes about his struggles with the prevailing education philosophy in Teaching Math in the 21st Century.

As a long-term substitute in California middle and high schools, Garelick is witnessing the transition to the Common Core standards.

It’s all about teaching “habits of mind,” say the experts. Skills, schmills. Quadratic equations are so 1965.

Math needs a revolution too

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.

8 minutes, wrong answer

In this video, a very determined third-grade girl attempts to add large numbers using an Investigations Math strategy. It takes eight minutes to get the wrong answer. In one minute, she finds the right answer by using the traditional “stacking” method she learned at home. (It’s not allowed in school.)  Investigations is supposed to teach conceptual understanding. The girl says it’s “confusing.”

Also on Out in Left Field, Barry Garelick wonders how teachers can be evaluated if they’re forced to use ineffective curricula. Check out the lively debate in the comments.

Life’s a carnival

The first 2011 Education Buzz Carnival is up at Bellringers.

Why do Shanghai students outperform U.S. students (and the rest of the world) in math? It Isn’t the Culture Stupid, argues Barry Garelick.

In defense of Everyday Mathematics

The Case for Everyday Mathematics is made by Andy Isaacs of the University of Chicago Mathematics Project in response to Barry Garelick’s critique.

Isaacs writes:

The highly efficient paper-and-pencil algorithms that have been traditional in the U.S. may no longer be the best algorithms for children in today’s technologically demanding world. Today’s elementary school children will be in the workforce well into the second half of the 21st century and the school mathematics curriculum should reflect the technological age in which they will live, work, and compete.

I’m not sure what that means. That kids should use calculators all the time? Or something quite different?

Isaacs defends spiraling:

Research shows that students learn best when new topics are presented at a brisk pace, with multiple exposures over time, and with frequent opportunities for review and practice.

The program offers more supports for teachers and parents, he writes.

Lots of comments, including a response from Garelick on whether research supports EM’s effectiveness.

Confused, bothered and befuddled

Everyday Math left Barry Garelick’s daughter confused, he writes on Education News. New ideas came from nowhere and there was no textbook and no way for parents to figure out what had been taught in class.  “Spiraling” meant students half-learned concepts again and again without reaching mastery. Garelick set out to tutor his daughter and her friend, using Singapore Math. They were sixth graders but had to start at Singapore’s fourth-grade level to learn what they’d never mastered. He thought it was going well till the friend asked:

“How do you get from a number on top and number on the bottom of a line into a number that has a point on it?

… she was asking how you convert a fraction to a decimal. Now, Laura was bright and she knew what a numerator and denominator were, and what a fraction was, but apparently the EM lesson they were working on sprung this on them without warning.

Singapore Math teaches decimals in the context of fractions, he writes. Everyday Math introduced decimals without context.  

Garelick plans a second career as a math teacher.

Hong Kong fourth graders outperform  Massachusetts students in math on international tests, concludes an AIR study. The Hong Kong students, who were far more likely to display advanced skills, are expected to learn more complex number  and measurement skills. Hong Kong’s internal tests require high-level computation and deeper mathematical understanding. Tests in Massachusetts, considered the highest performing U.S. state, require much less.

Learning to love skills-free math

On Kitchen Table Math, Barry Garelick quotes from a 2006 report on federally funded training in “standards-based” math teaching, which Garelick defines as “how to teach the crap programs that NSF’s Education and Human Resource Division funded (like Everyday Math, Investigations, IMP, CMP, Core Plus, etc).”

The report lauds “changes in teachers’ beliefs” about the need for ability grouping.

“Before IMP, I felt that there were mathematically unreachable students. I felt that students could not go on to more challenging ideas like algebra, statistics, probability, or trig without basic skills. Fortunately, with my IMP training, I have a different feeling about students. I strongly believe in access to mathematics for all. (Teacher, 6–12 mathematics)”

Garelick writes:

Before this teacher started using IMP, he/she felt that basic skills were necessary in order to proceed in mathematics. After IMP, which essentially avoids content whenever possible, he/she saw the light. Yes, wonderful things happen when you pretend that content doesn’t matter, and that higher order thinking skills occur just by giving students “authentic” problems without the bother of all those and boring drills and instruction. They are able to reach for the stars. Unfortunately they do so by standing on a two legged stool.

After many years working in science, Garelick is preparing for a second career as a math teacher.

Learn math step by step

Barry Garelick writes about discovery learning in math at the Nonpartisan Education Review.

Students given well-defined problems that draw upon prior knowledge . . . are doing much more than simply memorizing algorithmic procedures. They are developing the procedural fluency and understanding that are so essential to mathematics; and they are developing the habits of mind that will continue to serve them well in more advanced, college level mathematics courses. Poorly-posed problems with multiple “right” answers turn mathematics into a frustrating guessing game. Similarly, problems for which students are expected to discover what they need to know in the process of solving it do little more than confuse.

Lefty stands accused of “widening the achievement gap” by running an extracurricular Continental Math League club for students who enjoy math. The principal wants a club for kids who aren’t doing well in math. Sounds like fun! Lefty suggests a better math curriculum so fewer kids are confused and struggling.