What does the research really say? (Math Edition)

The American Educational Research Association (AERA) recently published a study, Which Instructional Practices Most Help First-Grade Students With and Without Mathematics Difficulties?, that caught the attention of several media sources. Many of these sources misrepresented the research with headlines like:

• Here's How Not to Teach First-Grade Math
• Drill, Baby, Drill? Study Finds Worksheets, Practice Improve Math Skills More than Fun Stuff

Other outlets were truer to the research:

• Explicit Instructions Works Best for Struggling Math Students
• Music, Manipulative Are Fun, But Basics Best for Struggling Math Students

However, these pieces still ignore some of the nuances of the research. To his credit, one of the author adds some perspective in this short video.

Still, achievement in mathematics needs to be defined. From the paper:

We used the ECLS- K’s Mathematics Test to estimate children’s mathematics achievement. ... The test was based on the National Assessment of Educational Progress (NAEP)’s specifications. (p. 6)

If your idea of mathematical achievement is simply scoring well on a standardized-test, then direct instruction probably is the most efficient way to prepare students to achieve. 

For example, when putting together a piece of furniture from IKEA, it makes sense to follow the directions provided explicitly. Why would I explore assembling our coffee table when the directions provide step-by-step instructions on how to achieve my desired outcome? How else can I be sure that my table will look exactly like the one I ordered?

Item Number: 801.762.84

And, therefore, like every other IKEA coffee table, 801.762.84.

But what if I want something unique? In this case, the directions might not apply (or even exist). My stepson made this coffee table for us out of a part of a tree that was from my childhood home. It is one of my most prized possessions.

Now, he is a talented woodworker who can (and has) put together a lot of furniture using directions. When he wants or needs to be creative, however, he can be. For me, that is true achievement.

We need to apply the same approach to teaching mathematics. Focusing solely on achievement based on content assessed through a standardized-test misses an important element of mathematical ability - thinking beyond what can be explicitly taught. Dr. Yong Zhao does a good job of addressing this disconnect in this post. So I leave you with this:

Source

What does the research say? It depends on what one is looking to achieve.

Update (7/4/14): And now an example related to teaching language arts has surfaced.