Part Five of a continuing series

Dear Jeff, Are students learning less under the Common Core?

Recently Louisiana posted sample 7th grade questions based on the new Common Core curriculum.  A lot of people noted that this was the type of problem they solved in the 2nd or 3rd grade, raising questions over whether students are learning less under the Common Core.

To answer this question, we must answer another: What does it mean to learn mathematics?

In Knowing and Teaching Elementary Mathematics (1999), one of more influential studies on elementary mathematics education, Liping Ma considers the question: Why do students in China routinely outperform American students on international math exams?

She found that while elementary mathematics teachers in China had considerably less formal schooling, they possessed “a profound understanding of fundamental mathematics,” and conveyed this understanding to their students.

For example, consider the question: “What is 4×18?”

For decades, mathematics instruction in the United States focused on computational competency, whereby student learning in mathematics was measured by whether they could apply a standard algorithm for multiplication:

18

×4

72

However, this is just one of many possible methods to finding the same answer.

A student or teacher with a profound understanding of fundamental mathematics could move readily and easily between different answers, like:

4×18 = 18+18+18+18 (because by definition 4×18 is the sum of four 18s).

4×18 = 4×2×9 = 8×9 (because multiplication is associative and we can regroup the factors).

4×18 = (4×10)+(4×8) (since four 18s is the same as four 10s and four 8s).

4×18 = (4×5)+(4×5)+(4×5)+(4×3) (since four 18s is the same as four 5s, four 5s, four 5s, and four 3s).

All of the above methods and more are emphasized in the Common Core. But gaining this fluency takes time, so students don't complete their times tables until the end of 3rd grade, and don't learn the standard algorithm for multiplication until 4th or 5th grade. 

It’s worth noting that even without the standard algorithm, 3rd grade students can still answer 4×18, through any of the approaches outlined above (or any of a number of others); in fact, this question is from a 3rd grade exercise.

More significantly, elementary arithmetic is not important because it allows you to calculate without a calculator, but because it prepares you for algebra. The previous curriculum did so poorly at this preparation that every year, of the 700,000 students who took a college algebra course, more than half of them failed it. 

Is this because algebra can only be learned by the most advanced students? Not at all. Research shows that students with a deep understanding of mathematics — such as that developed by the Common Core — can learn algebra as early as 2nd grade. By the 3rd grade, students can solve simple algebra problems like 36÷k = 9, and word problems (the bane of most algebra students) pose no special difficulty:

Leanne needs 120 tiles for an art project. She has 56 tiles. If tiles are sold in boxes of 8, how many more boxes of tiles does Leanne need to buy?

(from Grade 3, Module 7), which leads to solving the equation 8x+56 = 120.

So perhaps students are learning less.  But they will be able to do more.

Jeff Suzuki teaches mathematics at Brooklyn College, and is one of the founders of the Mid-Hudson Valley Math Teachers Circle, a group of teachers, professors, and mathematics aficionados working to promote mathematics education in the Hudson Valley. Email your Common Core questions to editor@excitingread.com.

You can read more about the early introduction to algebra at http://ase.tufts.edu/education/earlyalgebra