Deep Practice and Its Promise for Math Education

By Robert Sun

It’s not often that an inner-city American school rises to the top of national rankings in academics, and yet Baldi Middle School in Philadelphia has beaten the odds— not just once, but multiple times. Its track record reveals some important insights for anyone concerned with improving the learning experience for children.

In a nationwide online maths competition involving 6,000 schools in 45 states, Baldi ended the latest school year ranked #1, as students solved almost 20 million maths problems correctly in just ten months. Baldi has consistently ranked among the top ten schools in the US in this competition for each of the past five years.

How was this productive culture established? Why do Baldi students embrace maths with such enthusiasm when the subject intimidates so many children?

To begin with, Baldi’s leadership, with support from the community and parents, has instilled a high-performing culture characterized by three traits: the school’s 1,200 children feel attached to their school and its mission; the environment supports productivity and performance; and students are energized to sustain accelerated effort over time.

But there’s something also at work in Baldi’s classrooms—a concept known as Deep Practice. The idea of Deep Practice is evident in many pursuits, but rare in primary and secondary academics. In sports, for example, when we swing a bat and miss the ball, we receive instant feedback through our senses. Players learn easily and naturally through a practice loop where proficiency is attained through immediate awareness of success or failure.

When solving maths problems, there usually is no similar form of encouragement. Create a Deep Practice system for maths that provides an immediate and non-judgemental feedback loop, however, and the subject is suddenly no longer intimidating. By allowing students to tackle a complex subject in manageable parts—stopping when an error occurs and practising that one skill until it is perfected—they march steadily toward mastery. This is the hallmark of Deep Practice.

Critical Thinking and “Chunking”

Using Deep Practice techniques, skills that might take months of conventional practice can be mastered in a matter of days. These techniques have released a tremendous amount of energy not just in maths, but in other subjects as well.

The benefits of Deep Practice go beyond curriculum attainment. They are vital to meeting the most ambitious requirements in modern education—including the problem-solving and critical-thinking objectives of the Common Core State Standards in Mathematics (CCSSM) currently being instituted in the majority of American schools nationwide.

Critical thinking is one of the hardest mental skills to acquire, mostly because we humans don’t like to think. We find thinking difficult and generally avoid it if possible. That’s because our brains were not designed to think. Our brains evolved to quickly process vast quantities of visual information.

Computers can now beat the best human players in chess, but we are just beginning to design computers that can steer robots over uneven terrain or even drive a truck, because processing the vast amount of changing visual information is so complex.

The portion of our brain allocated to thinking is the neo-cortex, commonly referred to as the “working memory.” It is by nature limited. That is why we have difficulty carrying on more than two conversations simultaneously; overtax our working memory and our ability to reason slows or may break down altogether.

There are two ways for information to enter into our working memory for processing. The first is from the environment—what we experience through our senses and problems that we encounter. The second is to draw from our “long-term memory,” which is our storehouse of accumulated factual knowledge.

In his book Why Don’t Students Like School, Daniel Willingham describes how we have developed two distinct ways around the limitations of our working memory capacity.

  1. Through repeated practice, humans turn tasks into habit loops that become automatic. These are held in our long-term memory as stored procedures that can be called upon and executed without taxing our working memory. When a child is first learning to tie his shoes, almost all of his working memory capacity is devoted to the task, but after building automaticity he is able to tie his shoes without thinking.
  2. Humans possess the ability to “chunk” data by grouping information.  Chunking reduces the number of variables that our working memory needs to retain. If I present 12 letters of the alphabet randomly and ask you to quickly memorize them, it will tax your working memory—but if I presented them as CNN, FBI, IBM, ABC, the task is easier because the letters are “chunked” in your long-term memory — as long as the acronyms CNN or FBI already have meaning to you.

If America is to succeed in implementing the primary objective of the CCSSM—to enable students to think critically and thereby approach maths with focus, coherence and rigour—it needs to encourage repeated practice to build automaticity (stored procedures) and insure that their long-term memory contains comprehensive knowledge related to mathematics.

Stocking the Pantry

Put another way, CCSSM is like asking our children to not merely be able to cook, but to become gourmet chefs. When a child’s pantry is sparse, he cannot fulfil those expectations. Stocking our children’s pantries with knowledge is essential if we want them to think critically.

From the moment they are born, children are exposed to thousands of impressions and varied sources of information. Researchers from the LENA Research Foundation have studied the impact that early parent/child interaction has on a child’s later academic achievement, using an unobtrusive device that records up to 16 hours of conversation. After five years of looking at many different families, the findings are sobering.

The number of words spoken by a parent to a child in a family receiving financial assistance is about 600 per hour. In a family where the parents were in a professional career, the number is 3,100 per hour. By the age of three, the deficit for a disadvantaged child is already 30 million words.

Another interesting finding of the research showed that TV talk, in many cases, was actually detrimental. The only way for information to become stored in long-term memory is when a child is engaged and thinking. Merely hearing words without active engagement will not stock the pantry.

This research points to the drawback of relying on a passive style of teaching that does not engage students. Imagine a teacher lecturing and relaying facts and figures—essentially laying important ingredients onto a table—and hoping they will be collected and put into the pantry. When a student is not actively engaged, those items never get into the pantry, but pile up and eventually fall off the table’s edge.

We have known for more than 100 years, thanks to studies conducted by Hermann Ebbinghaus in the 1800s and confirmed by modern research, that 90 per cent of what a child is taught in class is forgotten within 30 days. We sometimes forget that without students taking ownership through active engagement, we are basically on a treadmill.

Lessons from Deep Practice

We must remember the importance of stocking the pantry if we want our children to develop strong critical-thinking skills. We need to learn from the Deep Practice successes of Baldi Middle School and other Philadelphia schools.

Since 2002, the year it began employing Deep Practice techniques district-wide, the Philadelphia School District has seen its percentage of students scoring “advanced” or “proficient” in maths more than triple to nearly 60 per cent. Using Deep Practice to stock a child’s pantry may not be the most glamorous aspect of maths education. But when our students’ pantries are full, it’s evident there’s no limit to what they can accomplish—or to the future they will be inspired to invent.

ROBERT SUN is the CEO of Suntex International and inventor of First In Math, an online program designed for self-paced learning in mathematics.

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