Math Learn Direct Save Mathlearndirect Math Id Administrator Components Com Clickheat Includes Heatmap Main Php Math Learn Direct If D =- R X T, American Education REALLY Suffers By Comparison « The Marquette Educator

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You probably confronted the formula in math or science classes when working on word problems.  Basically you were asked to solve either for the D, the R, or the T when the other two were known.  It always came down to “how far, how fast, or how long it took.”  

I’d like to suggest that this formula can serve as a useful way to conceptualize learning in general, and school learning in particular.  It’s not perfectly accurate by any stretch, but for our purposes the formula represents a somewhat fresh way to frame schooling, and the results it produces rank as startling.

How Does It Work? 

Think of D as the total distance learners have traveled, namely all of their achievement to date.  Now think of R as the rate of learning as influenced by the factors that promote or inhibit it.  Then finally think of T as the total amount of learning time.   If someone has engaged in high quality learning experiences (R) for extended amounts of time (T), they’re likely to be high achievers (D).   

For school learning, how far a student has come depends on how much the school context has accelerated learning in the instructional time available.   Viewed this way, the interplay between Rate and Time becomes vital to school success.    

The bottom line is as follows:  if we know the learner’s achievement (D) and how much time was spent in instruction (T), then we can estimate the effectiveness or quality of that learner’s school experience (R).   

The formula gets even more interesting because, using averages, the same calculations can be done with groups — classrooms, schools, districts, states, and even countries.   Well, I did some of that number crunching for America compared to other nations, and found the results shocking.  

Surprise, Surprise, Surprise

In a post last week I shared with readers an article from Time Magazine that focused on the dreaded summer slide in students’ learning.  The article suggested that two-thirds of the achievement gap between disadvantaged and advantaged American school children could be attributed to summer slippage.  Suffice it to say, those findings have monumental implications for education. 

However,  it was a table in the article that had nothing to do with the summer months that ended up surprising me even more.  The table compared 14 industrialized nations in terms of the number of school days, the number of instructional hours, and their students’ mathematics achievement.

Although we hear constant cries for more school weeks and days and longer school days, it turns out that the 180 days of schooling in the United States results in more instructional hours (1080) than any of the countries being compared.   That’s because our average daily instructional time is 6.0 hours.***  The only countries really close to us are Mexico (1047 hours or 5.24 hours over 200 days) and New Zealand (968 hours over 194 days). 

What’s key here is that despite having the most instructional hours, America ranked 12th in achievement!  Even that sad conclusion, though, is not what surprised me most.  

In sharp contrast to the U. S., South Korea’s math scores topped the charts.  At first glance, the number one ranking might seem attributable to this nation maintaining the most  schools days at 204.  But here’s the thing – South Korea’s number of instructional hours measured only 545 — the lowest of any country and only about half as many as the U.S.   What this means is that we are being notably outperformed by a country that provides only half as much instructional time!

This same pattern of higher test scores and fewer instructional hours plays out for Japan (ranked second in achievement; only 3.0 hours per day for 200 days) and Denmark (ranked fifth; only 3.24 instructional hours over 200 days).  In other high performing nations — New Zealand (ranked third), Australia (ranked fourth), and Germany (ranked sixth) — the number of instructional hours were 5.0, 4.1, and 3.9, respectively.  And Norway, Luxembourg, and Spain also outperform us despite instructional hours per day averaging only 3.44, 3.65, and 4.05 

Another way to treat the data would be by correlating it, so I did that, too.  The resulting coefficient measured -.39.  This finding suggests that math achievement did not increase with an increase in the number of instructional hours.  On the contrary, high math achievement tended to be associated with lower numbers of instructional hours.   How could that be?   

What the Unexpected Findings Mean  

The big takeaway here is that increasing the number of school weeks and days and lengthening the school day will not by itself result in greater math achievement.   There are several plausible explanations for what’s going on here, but my strong hunch is that it’s the quality of the learning environment that matters most to achievement. 

It’s not the quantity of time; it’s how the time is used.   Although this conclusion seems like common sense and falls well short of rocket science, the analyses here represent an important reminder.   

Apparently class time is probably better spent in those countries with higher achievement and fewer instructional hours.  I say “apparently” because other factors could be contributing  to these counterintuitive results.   Below I share a mix of factors associated with better use of instructional time and other guesses at what might be going on:

• The various shareholders in those countries (teachers, students, parents, school leaders, society at large) place a higher value on education generally than we do in America.
• Those nations place a greater value on math education, and as a result, devote proportionally more instructional energy to it .
• Students in those countries are more school ready, better supported at home, and rate as superior learners overall.
• The demographics, especially economic factors in urban areas, are more favorable. 
• Inattention, misbehavior, or a lack of effort by students are not tolerated.
• The stakes for students are more intense and higher, moving them into career tracks or out of the educational system altogether.
• Their instructional methods are simply superior.
• Teachers there are better prepared and more effective.
• Instructional materials facilitate learning to a greater extent.  
• Sophisticated assessment systems make teaching more targeted and learning more likely.
• At some point instructional time per day yields diminishing returns.  

The bottom line is that it could be any combination of these and other factors that cause American schooling to lag behind.  If you have additional  explanations, please share them, because I’m sure that my list falls well short of complete.   

RATE Drives the Equation

It’s important to keep in mind that this analysis was done on only one data set with a single standardized test in mathematics only.  These patterns might not hold true for other academic areas like literacy, science, and social studies.  But strictly for the sake of argument, let’s say that they do.  

In that case, then American educators need to make significantly better use of our instructional time whether it gets expanded or not.  We should do everything possible to make our school environments more vibrant accelerants of learning.  So as far as our D = R  X  T equation goes then, our K-12 educational system must aspire to provide a better R(ATE) of learning through quality education.    

Simply put, getting our classroom dynamics right will be the ultimate formula for success.

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***Since this post went live, I’ve learned that the United States counts the full school day in its calculation of instructional hours whereas other nations may not.  Even so, there remains a strong likelihood that we’re not making the best use of actual instructional time in our country.