Drill and skill

“Drill and kill” — practicing math skills taught by the teacher — works best for struggling first graders, concludes a new study. Yet teachers with the most math-challenged students are the most likely to use ineffective “student-centered” strategies, researcher George Farkas, a UC Irvine education professor, found.

. . . “routine practice or drill, math worksheets, problems from textbooks and math on the chalkboard appear to be most effective, probably because they increase the automaticity of arithmetic. It may be like finger exercises on the piano or ‘sounding out’ words in reading. Foundational skills need to be routinized so that the mind is free to think.”

Hands-on activities that use manipulations, calculators, movement and music may be fun, but they don’t improve first graders’ achievement, according to Farkas. It takes a teacher explicitly teaching facts, skills and concepts with plenty of time for practice.

“Teacher-directed instruction also is linked to gains in children without a history of math trouble,” writes  Maureen Downey. “But unlike their math-challenged counterparts, they can benefit from some types of student-centered instruction as well – such as working on problems with several solutions, peer tutoring, and activities involving real-life math.”

A friend who teaches in a Title 1 school lamented that her students didn’t do as well in the math CRCT as the classroom next door where the teacher used worksheets all the time. My friend’s classroom was a beehive of fun activities around math, but the worksheet class continually outperformed hers.

The study was published online in Educational Evaluation and Policy Analysis, a peer-reviewed journal of the American Educational Research Association.

Do timed tests cause math anxiety?

One third of students end up in remedial math in college and “the level of interest in the subject is at an all-time low,” writes Jo Boaler, a Stanford math education professor, in Ed Week.  She blames timed math tests — solve 50 multiplication problems in three minutes — for causing math anxiety that cripples learning

Math has become a performance subject. Children of all ages are more likely to tell you that the reason for learning math is to show whether they “get it” instead of whether they appreciate the beauty of the subject or the way it piques their interest. The damage starts early in this country, with school districts requiring young children to take timed math tests from the age of 5.

Common Core State Standards, which call for math “fluency,” may encourage timed testing, Boaler worries.

Stress caused by timed testing can lead to changes in the brain, permanently hurting children’s ability to learn math, she writes.

There are many good teaching strategies for encouraging fluency in math, but the ones that are effective are those that simultaneously develop number sense—the flexible use and understanding of numbers and quantities—without instilling fear and anxiety. Strategies that involve reasoning about numbers and operations, such as the pedagogical approach called “number talks,” are ideal for developing fluency with understanding.

Beyond the fear and anxiety, timed tests also convey strong and negative messages about math, suggesting that math ability is measured by working quickly, rather than thinking deeply and carefully—the hallmark of high-level mathematical thinking.

Children can learn math skills and concepts in tandem, writes Barry Garelick on Education News.

Reformers criticize traditional math instruction as “skills-based,” implying “students who may have mastered their math courses in K-12 were missing the conceptual basis of mathematics and were taught the subject as a means to do computation, rather than explore the wonders of mathematics for its own sake.”

Students have struggled with math for a long time: If one dinosaur eats two cavemen per hour, how many cavemen can four dinosaurs eat in 30 minutes?  When I was in elementary school in the ’50s, before calculators or timed tests of math facts, many kids were anxious about math because there were right and wrong answers. We didn’t tackle the lowest common denominator to appreciate math’s beauty or explore its wonders. We though the point was to “get it.”

“New math” came in a few years later, when my brother was in first grade. In trying to teach concepts, it made kids even more anxious.

My daughter did timed tests of addition and subtraction problems in first grade — 25 years ago! They probably did multiplication in second grade.  She thought the tests were fun. Of course, she was good at it. But Boaler says math anxiety is worst for high-ability students.

Why math tutors prosper

Many elementary students never learn basic math facts,  writes Lynne Diligent on Dilemmas of an ExPat Tutor.  They end up in remedial math classes in college. She advocates drill on math facts, more homework and no calculators till 11th grade.

I no longer teach Grade 3; I am now a private tutor. Unfortunately, I am now running across a number of 14-year-olds who are using calculators to add 5 + 3, or 7 + 6, or 9 + 2.

 Diligent also calls for requiring students to learn concepts before moving on, instead of  “spiraling” through the same things year after year.   

And she believes teachers should “instruct and explain, and then follow up with practice to master the skills,” rather than putting students in groups and telling them to figure out problems on their own. But group work is great for math tutors, she writes.