A fab paper from Lant Pritchett (of KSG) and Amanda Beatty (of IPA).

The paper looks at the puzzle of flat learning. Flat learning occurs when students do not learn much despite spending a lot of time at schools. This has been seen in recent findings on education in India. The enrollments have risen but quality has been dismal with class five students unable to figure Class I stuff.

The duo point to some evidence from India and other econs on flat learning. The usual q on this is “why students are behind the curriculum?” They reverse the problem and instead ask, “why the curriculum is so ahead of the students?”

What follows is an amazing discourse on how one can use tools of economics to understand a problem. They introduce a concept called potential pedagogical function (PPF):

*In order to build a simulation model of school instruction and learning, we first construct a potential pedagogical function (PPF). Think of any instructional experience, whether it is a tennis lesson, a piano lesson, a lecture on quantum physics, learning addition in second grade, or a film on Greek history. A student enters an instructional episode with a given skill set or **capability in a set of domains. How much does a student actually learn—that is, expand his capability set–from an instructional episode?*

*To minimally characterize a given student’s learning from an instructional episode we need four elements.*

*First, what is the maximum gain of any student, which is the height of the pedagogical function. The main difference between our simulation and most of the existing literature is that explicitly or implicitly most of the empirical assumes that this is the only relevant characteristic of a PPF.*

*The second feature of a PPF is the shape. Does learning fall off symmetrically and linearly from a unique maximum? The PPF would be triangular *

*Third is the range of the pedagogical function (determined by the height and shape) which is the extent of the student skill over which the student learns, or the spectrum of skills over which episodes are applicable or relevant and allow for learning. Below we also refer to this as the width.*

*Fourth, with a “height only” PPF (as in Figure 6a) location is irrelevant, but with a PPF with a shape the location matters. To what level of student ability or capability is the instruction pitched. Particularly for any symmetric representation we can refer to the level of student ability on which the PPF is centered.*

They assume a triangle PPF:

*In our subsequent simulations, we use symmetric triangular potential pedagogical functions because this makes the math of the simulations easy (learning declines linearly away from the maximum) and makes the graphs easier to interpret (because PPFs will be triangles and distributions of student learning will start out as a “normal” distribution). We are not asserting the pedagogical functions are in fact triangular and nothing about the main findings of our simulations hinges on using this particular shape of the PPF.*

This gives way to an array of student skills and curriculum.

*Figure 7a shows the interaction of normal distribution of student skills and a triangular PPF centered on the mean of student skills of 340. We have calibrated the PPF and initial distribution in PISA/TIMSS units of OECD mean 500 and student standard deviation 100, so that centered curriculum reproduces (roughly) the PISA/TIMSS means and standard deviations.*

*When the PPF(66,ST,330,340) is centered on a assumed student ability of N(340,20) then children across the range of abilities all learn, but somewhat different amounts. (340 is roughly the mean for grade 5 students, using the PISA/TIMSS calibration discussed above.) Students two standard deviations above or below the mean, student A at 300 or student E at 380, learn 50—so that after the year of instruction they are at 350 and 430. The student at the mean learns 66 and so will emerge at 406.*

The paper then goes onto show how faster paced curriculum than student skills lead little learning gradually and as students goto higher classed it becomes almost no learning. There are lots of simulations possible with the PPF setting…

What is the way out? Early remediation and tracking: narrowing the curricular gap..The idea is to bring the curriculum closer to the centre of the skill sets of students…

*If an educational system recognizes an existing large gap between curricular pace and actual learning, then the change from “business as usual” expansion of inputs is almost complete.*

*More focus on “inputs” is unlikely to have much impact—and may detract attention from the real problem for a very long time.**Efforts that “re-center” teaching on student actual skill/ability can have enormous pay-offs, whether through remediation (such as Pratham’s programs in India or Early Grade Reading Assessment Plus-like programs), private schools, community controlled**schools, tracking, multi-grade teaching, or the adoption of other pedagogical reforms that allow teachers to focus on student mastery of basic skills. Our point is that these may or may not work in different contexts, depending on the extent of the curricular gap, and how much flexibility systems allow teachers and lessons to respond to it.**Re-centering curricula and in turn teaching could offer a low-cost solution to improving learning, if systems are willing to re-focus learning goals on the average learner. (We know they are able of remedial teaching from the Banerjee, Duflo and**Walton 2011 India results.)**A focus on meeting early and achievable goals, rather than end of school high stakes for student examinations like university entrance exams, could re-orient teaching and learning away from what happens for a small elite towards the typical student,**who is also then more equipped to move ahead.*

An amazing read…One can identify with this fast paced curriculum in most parts of school and college life..

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