Educational Equality Demands Rethinking Early Grade Schooling

October 11, 2022

It’s been over a decade since Malcolm Gladwell forever altered the way I think about privilege and achievement.  After reading Outliers - The story of Success, I joined his cult-like following & have since consumed every book & podcast episode that he’s written & recorded.

In Season 7, episode 7 of Revisionist History, he draws a connection between birth month & academic success.  This episode entitled Outlier’s Revisited explores - among other things - the consequences of parents’ tendency to begin their child’s schooling late if they’re young for their grade level.

Listening to Outlier’s Revisited triggered memories of some of the most hair-splitting work that I’ve engaged in over the past 14 years and got me thinking about a potential solution to the problem.

Since 2008, I’ve helped schools around the country implement Singapore Math curricula.  These institutions range from public to private to charter & urban to suburban to rural.  Although the student & teacher demographic differences are expansive, the challenges to implementing Singapore curricula are not.  Of the nearly 1,000 lessons in each K-5 textbook series, two stand out as exponentially more difficult for the targeted age group than any others - Adding crossing over 10 & Subtracting Crossing over 10, both of which can be found in the Numbers to 20 unit of each edition’s 1A textbook.

I’ve never given more thought & labor into helping make lessons work than I have with these two.  I’ve re-worked pacing plans, written & rewritten lesson scripts, and developed dozens of graphic organizers & practice sets to break the concepts into manageable chunks, hoping that I could ease the difficulty for mathematically vulnerable first graders.  These efforts have - at best - led to marginal gains.

The Adding & Subtracting Crossing ten lessons are a culmination of every foundational numeracy topic & skill that students have learned and practiced during the first year and a half of their schooling, & they ruthlessly penalize children who haven’t mastered each of them.  Proficiency with the following are needed for students to have any hope of feeling successful:

• Pivoting on the number line

• Part-whole relationships

• Number bond models

• Addition & subtraction strategies

• Place value to 20 models

Let’s examine what first grade students are expected to conceptually understand and fluently solve approximately halfway through their school year.

First grade students using Singapore Math curricula are tasked with applying their place value within 20 understanding to add single-digit numbers with two-digit sums, not by counting all or on, but instead decomposing the first or second addend.  To solve 8 + 6 for example, students are discouraged from counting up six times from 8 to arrive at 14.  Instead, they are expected to decompose the 6 into 2 and 4, creating the three-addend equation, 8 + 2 + 4 which is simplified as 10 and 4 or 14.

The complexity increases when they subtract single-digit numbers from teen numbers to arrive at single-digit differences.  Students are not expected to solve a problem like 13 - 8 by counting backwards eight times from 13 to arrive at 5.  Instead, they are expected to perform a chunking strategy.  One method is to break apart 13 into 10 and 3, subtract 8 from 10 and solve the equation by adding the difference to 3, in the end computing 2 + 3 = 5.  A second method utilizes a two-subtrahend equation.  To solve 13 - 8, students would first subtract 3 and then take 5 from 10 to compute the final answer.  To fluently solve this, students need to look at the equation 13 - 8, see it as equivalent to 13 - 3 - 5, and then comfortably perform the calculation.

Children are of course encouraged to use concrete models and pictorial representations before ever trying to apply these methods into mental strategies.  However, every numeracy topic for the remainder of first grade builds upon the foundational understanding that’s developed in the 1A Numbers to 20 unit.  Children who fail to master this heavy-hitter of the Singapore Math curriculum often find themselves playing catch up for the remainder of the school year & beyond.  Those who struggle to understand & calculate 8 + 6 or 13 - 8 feel overwhelmed later in the school year when they’re tasked with solving equations such as 78 + 6 or 43 - 8.

The cumulative effects of this dynamic grows exponentially in second and third grades when students are required to perform three-digit by three-digit addition & subtraction algorithms, & skip count by single-digit multiples to develop strategies for learning their times tables.  Children who master each foundation along the way build their mathematical tower higher, gaining easier access to more complex topics.  Those who don’t lose confidence, intervention efforts to help them often prove futile, and the root cause of their challenges normally goes unidentified.

By late elementary school many of these students are turned off to the subject and struggle with it for the duration of their academic lives.

At the onset of my training career, I often assigned blame for first graders’ struggles with the two daunting lessons I’ve mentioned.  Disinterested students coming from undisciplined households and/or incompetent teaching were easy targets for my own frustrations as I searched for the magic bullet that would finally make the concept click.  In all my studies, I knew that first graders in Singapore enjoyed far more success when engaging with these lessons.  Measuring American educational achievement against Singapore’s was an unfair comparison, but I still thought that the success gap shouldn’t have been as wide as it was.

In time, I learned that Singapore’s school year begins in January.  This made me realize that every child in Singapore is nearly a half-year older when they first encounter the nemesis’ that are Adding & subtracting crossing over ten within 20.  With advanced social, emotional, & cerebral development, they’re more prepared for academic rigor.

In the U.S., nothing is preventing a child in any grade from sharing a learning space with classmates 364 days older or younger than them.  These 52 weeks might seem insignificant in high school or college, but the kindergartener who was born on the last day of a school year’s cut off is potentially 20% younger than their oldest classmate.  It’s unreasonable to think that the oldest & youngest students in this hypothetical scenario should be studying the same content, much less be assessed, categorized, & judged by the same metrics.

This problem is exacerbated by parents who attempt to level the playing field for their children by holding them back an extra year before entering kindergarten.  In Outliers Revisited, Gladwell touches on this dynamic, stating that although it’s regrettable, no parent can be blamed for gaming a system that is inherently flawed.  Entering kindergarten late can help an individual student succeed, but it creates a much larger problem, because the age and developmental gaps within the same classroom expand.  The youngest kindergarteners suffer the most, but older students are also negatively affected.  The greater the age discrepancy in the same classroom, the more challenging it is for lower grade teachers to optimize any of their students’ learning.

Between the time that Outliers was written & Outliers Revisited was released, I concluded that educational leaders should begin rethinking our traditional grade level system.  Instead of grouping children by grade level, school’s might achieve better results by clustering students in age groups ranging from three to six months.  In this system, children would have different entry points during the year for starting school. For example, in a six-month cluster system, all children would be required to start kindergarten when they were between 5 ½ & 6 years old.  If a child didn’t meet the age requirement in September then they would begin a half-year later.

Executing such a plan would require year-round schooling, flexible groupings for different subjects, & research-backed planning as to when different age groups are ready to learn select topics.

I think it would make a great charter school mission.