Telecommunication H.S. and the “Bathtub of Mastery”

In New Visions’ newly released report, Design And Data In Balance: Using Design-Driven Decision Making To Enable Student Success, we take a closer look at one of New York City’s higher performing mid-sized high schools, the High School for Telecommunication Arts and Technology (Telly), through the lens of design. For those of us in the field of education and working in schools, design and design-driven decision making starts with a mental model of how students learn.  That is, effective schools must be organized (or designed) around this fundamental concept.  In this post, we present a basic model of student learning and highlight some of the strategies Telly has implemented to fill up and maintain students’ “bathtubs of mastery.”

The Bathtub of Mastery

In systems thinking mapping, we use a stock (rectangle) to represent the accumulation of skills and content mastery.  Think of this as a bathtub of mastery.  The bathtub is filled by an inflow of learning that occurs via curriculum delivered through courses (Figure 1). Every day a student attends school (attendance is an absolute precondition for learning and for many schools absenteeism is a serious problem), presumably she will learn some skills and content that fill up her bathtub of content and skill mastery. But if the student does not have opportunities to apply the skill within a certain period of time after learning it, the likelihood that she will eventually forget the content or skill is high.  The outflow in the image below represents the process of content and skill mastery “atrophying” (or being lost) over time (Figure 1).

Figure 1

Figure 1 helps visualize an important point: a student’s level of content and skill mastery is determined by the rate of learning and the rate of atrophying.  In other words, “mastery” is a dynamic, rather than a static state - filling and draining at the mercy of these two flows.   So how do we manage the rate of learning and the rate of atrophying to better stabilize and direct mastery?  

To increase the flow of learning  so that a student builds up content and skill mastery, the school must put resources into educating the student.  This can easily be summarized as the number of hours of instruction the school provides to each student.  Here we represent this as “hours of instruction per month” received by the student (Figure 2). And each hour will have a certain amount of effectiveness.  In other words, you could say that a student learns a specific amount of content/skills per hour of instruction.

Figure 2

Therefore, to increase the rate of learning the school has two and only two main levers: 1) Increase the amount of instruction time (exposure to content/skills) and 2) increase the effectiveness of each unit of time.

Once a student learns a concept, it is theoretically possible that she might remember it forever.  But in the absence of use, it is more likely that a student will forget what she has learned.  One way to express this idea is to say that the outflow (forgetting or atrophying) of mastery of content and skills is based on the “average time a skill sticks if not used” (Figure 3).  In other words, when a skill is used, the atrophying process is slowed.  It is as if the act of using the skill turns off the faucet of atrophy such that the stock of mastery does not drain as fast.

Figure 3

But, not all students enter school with equal levels of mastery to begin with.  If the stock of “content and skill mastery” is close to empty, then what little content or skills a student does have will not last for very long – especially if the atrophying outflow is not managed. If a student has higher levels of content and skill mastery, it is more likely that a student will remember the content and skills for a longer period of time (Figure 4).  This creates an important balancing loop that regulates the amount of content and skills mastery.

Figure 4

The implications of this very basic, simple model are profound.  Schools have three intervention points to increase and maintain a student’s mastery over time:  1) increase the hours of instruction, 2) increase the effectiveness of each hour, and 3) increase the length of time a student remembers a concept.  High performing schools know how to manage all three of these intervention points wisely.

How Telly Manages "Flow"

1. Increase The Hours Of Instruction (To Build Literacy, Writing, and Critical Thinking Skills)

At Telly, literacy, writing and critical thinking skills are prerequisite for success in subsequent courses.  To support a student’s mastery of these skills, Telly offers multiple courses in ninth and tenth grade that reinforce these skill sets.  In ninth grade, students will take a year of English, writing, global history, biochemistry, Spanish, math, physical education, and music.  Students are immersed in English, writing, global history, and bio-chemistry, all of which emphasize literacy and provide opportunities for students to develop stronger writing and critical thinking skills. In sophomore year, students’ core writing skills are deepened and expanded.  While students continue to build foundational skills (e.g. literacy and critical thinking), they now begin to develop research and presentation skills in their 10th grade global history class. 

2. Increase The Effectiveness Of Instruction

But Telly doesn’t just offer more instruction, they have developed structures that are designed to increase the effectiveness of that instruction.  The first structure is small learning communities that provide deeper support for students.  Developing mastery in freshman year is supported by smaller class sizes, so teachers can better personalize instruction to fit students’ needs.

In addition to smaller classes, all freshman and sophomore students at Telly are programmed into groups of roughly 100 students who are assigned into one of three “small learning communities” with three core subject area teachers in English, global history, and science. The communities are designed to foster a small school atmosphere and a more personalized learning environment for students, particularly younger students who might struggle with the transition to high school.

The communities are a core strategy at Telly that are primarily driven by grade-level teams of teachers.  Teachers within them are afforded the space to focus on academic work and consider how each student’s work contributes to success within and across different classrooms and subject areas.  The small communities allow teachers to compare notes about a shared group of students. The students know that their teachers are watching them and talking about them and they know that the teachers meet every day.  Taken together, these practices also increase the amount of content and skills learned per hour.

The second structure that supports more effective instruction are teacher teams. Educators at Telly are organized in ways that make full use of their expertise.  In turn, their expertise is widely made available to other teachers throughout the school via collaborative teacher teams. Telly’s educators are part of a multilayered system of social structures: the leadership team (made up of the principal and assistant principals), department teams, grade teams, SLC grade advisors, guidance counselors, the programming team, the dean’s office, the testing coordination team, and college advisement teams. Each has a specific function and therefore sees the school from a distinctive vantage. By design, these multiple perspectives on the progress of students and the overall functioning of the school, which educators frequently discuss and share, fill gaps and compensate for one another.

The teams fall along two broad dimensions, operational supports and instructional supports, with the leadership team straddling both. The operational supports create stability by minimizing turbulence that might otherwise disrupt the school and classroom environments. The instructional supports allow teachers to hone their craft and develop their teaching expertise which increases their effectiveness.

3. Structures That Minimize The Atrophying Flow

Telly also has structures to manage the atrophying outflow. The programming strategy at Telly 1) considers where a student is on his or her current trajectory, 2) schedules a course (whether Regents-bearing or remedial) that has the potential to move that student to the next level, 3) ensures that course and material are aligned to the related Regents exam, and 4) maximizes proximal Regents exam testing dates (which, in New York City, occur three times a year). 

Exploiting opportunities means that the school administration must consider multiple scenarios and anticipate long term outcomes well before they happen.  Consider the different possibilities for a student who enters  ninth grade and who is high performing in math (Figure 4).  Over time, there are multiple scenarios that can play out - the student might pass the geometry course, but fail the Geometry Regents exam.  The student might pass the Algebra II / Trigonometry Regents exam but fail the course.  The possibilities can look like a complicated subway map!

The goal of effective student scheduling and programming is to meet students where they are.  As soon as a student steps out of one course, the next appropriate course or scheduled exam has to be right there for the student to step into.  In this way, an effective scheduling and programming system is like an invisible train that keeps the students moving forward, building on the content and skill mastery rather than allowing that mastery to atrophy.

In our next few posts,  we’ll build upon this basic model of learning and introduce a simulation program that examines these three intervention points more deeply.  By manipulating each of the three levers within a systems thinking lab, it becomes easier to understand the dynamic complexity of mastery over time. We will also map out attendance as an important precondition to mastery and show how smart programming and scheduling can minimize atrophy.

Susan Fairchild is director of program analysis and applied research at New Visions. Follow her on Twitter at @SKFchild.

Chris Soderquist is the founder of Pontifex Consulting, helping clients apply systems thinking to their adaptive challenges.  Follow Pontifex Consulting on Facebook.

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