Heterogeneous Learning in a Homogenized Space: Lessons from Pattern Recognition

Abstract

Given the fact that learning is a lifelong process, the lengthy childhood faces the biggest

hurdles during one‟s „schooling years‟ that provides societies a window of opportunity to

influence the growth of future generations through educators. A machine aided

methodology to align teaching-learning practices of early grade competencies in classrooms

is discussed in the context of India‟s mass-scale homogenized education system that leaves

a substantial proportion of children behind despite a high enrolment rate across primary

grades. An argument for a holistic educational mission utilizing a bouquet of heterogeneous

teaching-learning strategies is constructed in view of Education for All (EFA) goals –

emulating a scalable and inclusive „Gurukul‟ philosophy of ancient India. The methodology

presented here in supports a customizable teaching and learning environment that considers

the heterogeneous creative and learning needs of students.

[133 words]

KEYWORDS:

Learning Childhood Teaching- Learning Practices Non-linearity

Early-Grade Competencies Pattern Recognition

Introduction

Evolution has rendered the human species with a lengthy childhood, during which

individuals undergo rapid brain development. This prolonged phase of mental growth slows

down by the onset of the juvenile stage and practically comes to a stop by the time an

individual enters adulthood. Culturally, the completion of adolescence is marked by the end

of „nesting,‟ when a young adult is sufficiently equipped (skilled) to step into adulthood.

Although learning is a lifelong process, the individual is challenged with some of the

biggest hurdles during her „schooling years‟, such as learning new languages, causal

relations, and inductive reasoning. The prolonged sheltered period comprising of the

childhood, juvenile and adolescent phases provides societies a window of opportunity to

directly influence the growth of future generations through educators. As a result, despite

the non uniformity of learning processes and the rate of learning across the three phases,

school-based instruction is the common norm across many cultures.

Over the past two decades developmental psychologists, computer scientists and

educationist have come together to understand the intricacies of how children learn.

Theoreticians such as Kushnir and Gopnik (2007) have demonstrated the statistical

undertones of childhood learning and decision making. We begin by asking why children

choose to learn and why do they learn in the way they do. Using De Houwer et al‟s (2013)

definition of learning as an „ontogenetic adaptation‟ of an individual to the uniqueness of

her environment we propose „learning‟ to be a survival mechanism that supports a child‟s

urge to explore her immediate surroundings, which in turn creates opportunities for further

learning. In this discussion we are concerned with presenting a practical methodology to

best align teaching practices with the exploratory mode of childhood learning, with specific

reference to Pratham‟s (NGO) R&D early grade program.

A child‟s curiosity and exploratory behavior are two fundamental traits that have aided the

“ratchet effect, permitting cumulative modifications to occur that create increasingly

elaborate cultural practices” (Boesch & Tomasello, 1998). Her nascent mind, which lives in

a non-factual but empirical space, personalizes knowledge by drawing relationships across

multiple stimuli through the ecologically sound learning techniques of imitation and trial

and error. Active hypothesizing by a child introduces innovation into factual knowledge

and culturally established experiences; for example, while stacking similar soup cans on a

kitchen shelf (ordered packing), she discovers that when the number of rows of cans equal

the number of columns, the total count has a particular mathematical significance- it is a

squared number. The recent interest in establishing „efficient and effective‟ educational

practices in light of the universal primary education policy (Bruns, Mingat, &

Rakotomalala, 2003; Beteille, 2002) have culminated in the creation of highly stylized and

linear syllabi, which are antithetic to the non-linear learning mechanics at play during

childhood. It is necessary to re-evaluate our desire to dole out „schooling‟, which views a

child‟s natural tendency to play and grapple with disconnected knowledge as wasteful and

inefficient and question the philosophy of gauging education through efficiency parameters,

given a child‟s experimental and experiential modes of learning.

Since the school-system in India is heavily invested in „a means to an end‟ anachronistic

industrial educational philosophy, the curriculum is disconnected from a child‟s experience

and therefore lacking (Dewey, 1938). The educational system would best serve our children

by following a philosophy that is entrenched in the present, where she is given ample time

to exercise her curiosity in close parallel to the „Unschooling‟ philosophy (Holt, 1982).

The remainder of this article has to do with creating an encouraging learning environment

where children have the opportunity to learn through hypothesizing, and teachers are

responsible to guide children towards appropriate content.

This paper is divided into multiple parts–Section I is concerned with key facets of a child‟s

internal and external learning environments; grouping informed by the ability of children

(not necessary ability based grouping) to aid learning processes across rural schoolrooms in

India is presented in Section II; means of facilitating targeted teaching- learning

mechanisms aligned with a child‟s ability are explored in Section III. In Section IV,

outcome based program effectiveness is developed by comparing group-wise improvement

in competencies across the baseline and midline of an ongoing intervention operated by

Pratham. These are followed by a brief section on concluding remarks.

Section- I

The limited range of problems an individual chooses to engage with is influenced by her

local (or accessible) ecological, environmental, social and cultural environments. It is the

natural tendency of an individual to prioritize problems. Furthermore, the prioritization is

transient. Thus, the importance of a problem evolves over time. A case in point, a young

learner‟s sensory organs gathers environmental stimuli selectively. This discriminating

nature of information gathering and processing poses one of the key challenges to any well-

meaning and outcome oriented theory of learning considering the uniqueness of each

individual‟s sensory perception. Despite the improbable task of uniformly satisfying each

and every student‟s senses, it is still possible to create an environment that is conducive for

maximized learning, where a learner has the opportunity to hone her skills by acquiring

knowledge through means that suit her best, which we understand as a „child centric‟

classroom (Tzuo, 2007).

The psychological and emotional effects of the environment (education.edu) on a child‟s

behavioral and cognitive development need to be recognized, considering that all modes of

learning (in-school and out-of-school) are tangibly associated with her surroundings. It is

reasonable to assume that a hot, humid, and stuffy local environment would be a distraction

to a learning exercise. In this respect, the Government of India‟s Right to Education Act has

been instrumental in mobilizing the community and school system to adopt „child friendly‟

classrooms and schools. Although commendable, the predominant thrust on the external

environment is ultimately insufficient since it has covered only but a part of the entire

teaching- learning canvas.

The Government of India‟s flagship program for Universal Elementary Education (UEE),

Sarva Siksha Abhiyan (SSA), caters to 192 million children across 1.1 million habitats in

India. Between the financial years of 2007-2008 to 2011-2012, the SSA expenditure grew

by 1.6 times, indicating an urgency to improve the educational landscape in India.

Mukherjee and Sikdar (2012) show that in contrast to “enrollment increasing” schemes,

which have received approximately 98% of the finances, “quality improvement” schemes

have seen an increase from 0% in 2007-2008 to 0.31% in 2011-2012, demonstrating an

overwhelming negligence of the supply of quality educators, namely high performing and

emotionally sensitive teachers. The UEE charter has in effect encouraged the government

to fill schoolrooms with students without paying attention to their learning. As a result, the

dropout rate between classes 1 through 10 stands at 60%, and 20% of those who

discontinue their education do so because they are not interested in studies (Central

Statistics Office, 2011), implying that 12 out of 100 children enrolled in grade 1 will

dropout by grade 10 simply because school is not engaging enough. The currently prevalent

“banking model of education” (Freire, 1993; 1996), where students are discouraged from

questioning newfound information has curtailed the evolution of the “industrial” school

system in India; creating a disconnect between schooling and learning. It is not then a great

surprise that 50% of children with more than 4 years of formal schooling have not learned

to read and write the primary school language or master basic numeracy (ASER, 2014).

As is generally agreed, the purpose of mass education within a democracy is to create an

empowered society. Supporting the importance of education in governance, Aristotle had

once said, “All who have meditated on the art of governing mankind have been convinced

that the fate of empires depends on the education of youth” (Adjibolosoo, 2005). Education

affects an individual as well as the space in which she operates. Classically, education

benefits society through the betterment of individuals. The positive impact of quality

education on development (Payton, et al., 2008; UNICEF, 2000; Hanushek & Woessmann,

2007) at the societal and individual level reaffirms the importance of education. One of the

aims of this paper is to assist policy and decision makers improve education quality,

considering the wider social benefits of education and schooling. We take inspiration from

Plato‟s polemic on education (Cornford, 1945) and affinity for non-structured pedagogy

when he says, “Enforced exercise does no harm to the body, but enforced learning will not

stay in the mind. So avoid compulsion, and let your children‟s lessons take the form of

play,” while presenting our analysis geared towards a more intuitive and personalized

model of teaching and learning in stark contrast to India‟s standardized universal education.

Considering the direct impact of institutionalized education on society (Meyer, 1977),

wherein specific roles are allocated to people with select skill sets, the current primary

education setup works as a first step to sieve candidates. Given, that the educational

standards and funding are primarily regulated by the government, much of what a child

is formally taught in school is dependent on the politics of the existing government. In

effect the universality of her “lesson plan” is questionable. Furthermore it is possible for

citizens to have a free existence in a non- democratic setup, while those living in a

democracy may not have the opportunity to exercise the much promised freedom in lieu

of an education system that supports and maintains a hierarchical order.

Given the self-preserving nature of governments, universal education could for all practical

purposes teach children to tow the line with the philosophy of the ruling segment. Case in

point, consider the name, “Mahatma Gandhi,” literally “Gandhi, the Great Soul”- How

many educators in India are open to a critique of the Mahatma? Use of a specific adjective

has curtailed any curiosity about the flaws in “his” movement or personhood. Ironically,

Gandhi Ji‟s educational philosophy was woven around the concept of Swaraj to avoid

“dependence on the state”, and “aimed at educating the whole person, rather than

concentrating on one aspect” (Burke, 2009). Although Gandhian education was not

designed for a 67 year old democracy, it is aligned with the critical pedagogy of Freire,

which encourages education immersed in the local culture and identity of students,

providing learners an opportunity to exercise their natural mode of learning through

exploration, questioning, and active engagement, much like Tagore purposing education to

be a means of promoting „ānanda‟ (eternal bliss) in individuals and „shānti‟ (peace) in the

world. In comparison mass scale homogenized education risks hampering the discovery of

individual talents as suggested by Plato.

In 2013 primary school enrollment for children in the age-group 6-14 in India went up to

96.7 per cent, with an average attendance of 70.7 per cent and 71.8 per cent across

primary and upper primarily schools respectively. This heartening upward trend towards

universal access resulted from the government‟s aggressive elementary education policy

under the aegis of the 2009 Right to Education Act (RTE). The input based education

policies are disconnected from the outcomes of schooling - educational maturity,

confidence and learning. As a result approximately 50 per cent of children in the 2nd

grade failed to read simple everyday words and constructs in their regional language.

Also, 25 per cent children in grade 3 could identify individual letters but could not read

simple words as per the Annual Status of Education Report (ASER); a citizen led

nationwide educational survey (ASER, 2013). It is evident that that a large proportion of

school-aged children have not been able to pick up basic reading and numeracy despite

multiple years of schooling. Furthermore, despite a stark rise in expenditure in primary

education, education quality in terms of learning outcomes has not progressed

substantially between 2005 and 2015. The implementation and practice of the RTE Act

is haunted by teacher absenteeism, insufficient teacher motivation, non-availability of

related and relatable reading material, and an outdated pedagogy has helped create a

Cerberus of non-learning across schools in India.

Through the remainder of this article means of improving pedagogic practices will be

explored with the conviction that a progressive oriented education system should

substantially invest in the learning improvements of the children it caters to. Suggestions

of improving teaching and learning will build on the successful, „Teaching at the Right

Level‟ (TaRL) methodology practiced across Pratham Education Foundation‟s

(Pratham) education that have helped young learners across 21 Indian states. Evidence

from Pratham‟s early grade competency development program (R&D program) running

across two blocks in Uttar Pradesh will be presented in the following section.

Section- II

The R&D program targets to strengthen early-grade competencies of students across 30

schools in the Bhadarpur and Nagar Kshetra blocks of Uttar Pradesh, covering both urban

and rural habitations, with 20-25 children participating from each school. Activity based

teaching and learning sessions are held five days a week in 15 schools and once per week in

the remaining 15 locations. During each session two hours are reserved for both math and

language. Mothers of participants are given educational material and encouraged to engage

with their children after each session. The program is aimed at the holistic development of

children. The math and language competencies and sub-competencies are shown in Table 1.

(Insert)

Table 1: Math and Language Competencies and Sub-competencies

The intervention aims to strengthen the competencies of a cohort over a two year period

between grade 1 and grade 2. The children were tested on 86 questions during the baseline

and 79 questions through the midline (7 questions asked during the baseline were omitted.

A child‟s performance was scored into three buckets, 2, 1 and 0 depending on whether the

she gave the correct response, attempted the question but answered incorrectly, or did not

attempt the question at all. Some questions had a scoring range of 3, 2, 1 and 0

corresponding to a correct response, partially correct response, incorrect response, and no

attempt respectively. The responses were scaled to a 0 to 1 range for the purposes of this

analysis.

As shown in Table 1, the skills range from phonological awareness to basic numeracy;

covering fundamental competencies required for successful primary level learning.

Pratham‟s TaRL methodology was developed for basic reading and numeracy

interventions. This research aims to adapt the TaRL methodology for the multi-competency

teaching and learning environment of the R&D program.

It was observed that some students are better math learners than language learners (or have

had more exposure to math prior to the camp) and vice versa, and a select group of students

find a particular topic easier to understand, thereby creating a need for an adaptation that

harnesses the performance patterns of students and student groups in its design.

The logic and methodology of grouping children within classrooms into „learner clusters‟ to

improve activity based learning are explored considering complexities such as classroom

size, time limitations on teacher and student interactions and competency specific learning

of children. Tracking learning trajectories of students and performance based groups in a

heterogeneous classroom provides insights for better informed program designs. Pattern

recognition techniques provide valuable tools to satisfy individualistic learning of students.

Performance grouping based on question-wise responses of students helps one chart

capacities across multiple competencies. The discovery of student clusters aids in

measuring their aggregate performance across the program and similar set of questions. For

example, clubbing two groups of students who have answered similar number of questions

does not take into consideration their differential performance across multiple questions.

Simplistic division of students is too naïve for such a complex set up. Prior knowledge of

student abilities can aid instructors in conducting targeted activities. The student clustering

presented here functions as a reference point for a more fluid grouping mechanism

dependent on a teacher‟s observations. The proposed clustering is equipped to track student

bodies with high variation of performance without creating differential tracks for the

students. Furthermore, the proposed grouping dynamic and transient much like Joplin

grouping. Essentially, grouping students into clusters could facilitate program managers to

align their teaching styles to the common learning patterns of children in her program or

participating in a multi- competency teaching- learning exercise. The advantages of group

learning are not discussed as they are beyond the scope of this paper.

Given, the goal of creating a humanistic setting within a model classroom beyond

mechanistic instructions and mechanical learning, the analysis presented in this paper

attempts to intimately harmonize teaching with every child‟s learning at a personal level.

The set of analysis tools aids an instructor to create paths for self-motivated learning, by

delivering activities and lessons that engage a child appropriately. We argue in favor of

enhancing learning across classrooms by appropriately motivating „learning clusters‟ based

on their learning patterns.

A priori insight of learning outcome based student clusters can help instructors in creating

effective lessons for students who may not be inclined to internalize a competency or

concept if taught in the traditional manner of „one shoe fits all‟. Observing group activities

of students could provide clues about how best to teach for maximized learning. It is

possible that these observations will feed into a teacher‟s insight of how to teach

competencies that don‟t excite particular sets of children- such as teaching math to a

language proficient child, in such a way that it catalyses her willingness to learn

mathematics. Automating student „tracking‟ by combing human and machine intelligence

to capture non-intuitive patterns would also bypass situations where teachers end up

tracking eager learners at the expense of children lagging behind.

A grouping mechanism that is cognizant of a child‟s disposition, ability and predilection for

a particular subject matter could potentially catalyze the alignment of schoolrooms with its

inhabitants and the demands of today‟s market, which stresses less on conformity but rather

on creativity and well cultivated innate talent of individuals. A school or teacher would

then be responsible for creating the natural conditions for the student to sprout and in doing

so encourage self learning. This knowledge driven teaching-learning would require

continuous assessments and evaluations to discover the knowledge gaps and learning

patterns of children, thereby empowering the school system to fill these fissures in a child

friendly manner. Paraphrasing Sir Ken Robinson (2010), transforming our industrialized

educational landscape into an agrarian one would serve as a necessary step to modernize

schooling through an emphasis on „empowered‟ learning.

The details of performance-based grouping of children and competency clustering are

presented in Section III. It is hoped that the said techniques encourage and enable

pedagogic modifications required to harness a child‟s scientific method of learning,

involving hypothesizing, hypothesis testing, theory modifications and retesting of concepts.

Section III

The R&D camps had two broad learning goals, namely advancing the learners‟ literacy and

numeracy. The strategy to improve literacy was undertaken by developing their

phonological and phonemic awareness, ability to read simple texts (stories found in class 2

texts) with comprehension and fluency, to articulate own thoughts confidently and their

ability to write grammatically correct sentences, either when dictated or when given a

context or textual premise. Special emphasis was given to encourage the natural curiosity of

a child in her learning processes. The program not only focused on developing basic math

skills, but encouraged students to process, communicate and interpret numerical

information in a variety of contexts as well. The lessons aimed at fostering an appreciation

and enjoyment of mathematics by working on problem solving skills, pattern recognition,

data interpretation, abstraction in addition to operations. Colloquial terminology and

language was used to communicate mathematical concepts. To ease children into the camp

setting, a warm up phase was initiated that familiarized participants about basic school,

class and learning preparedness. A total of 510 children enrolled in the five-days-a-week

camp across 15 schools, of whom 428 and 391 students were tested at the baseline and

midline respectively. The analysis that follows considers only those 383 children who were

assessed at the baseline as well as the midline. Each of the 15 schools had an average of

25.5 „common‟ children, with a standard deviation of 5.5; the 10 rural schools had

approximately 27 children, while there were 24 children in the 5 urban schools. The

children scored an average of 37.3 points (out of 86) with a standard deviation of 5.5

points; the average across rural schools was 39.6 points and 32.5 in urban schools.

69.5% of the students scored less than 43 points out of 86 on the baseline assessment

covering multiple competencies as shown in Table 1, and of the 383 children 107 (28%)

scored less than 30 out of 86 points, indicating a need to encourage greater participation

and improving learning. It was observed that some parents considered their children to be

too young to engage in meaningful „learning‟ oriented interactions. It would be prudent to

investigate what proportion of children who scored low on the baseline were not fully

engaged in their home surrounding. Community awareness to promote parent-child

engagement may be a solution to boost the confidence of children.

A majority of the 86 questions were scored on a three point scale (0, 1, 2) corresponding to

not attempted, attempted but incorrect, and correct responses respectively. Some questions

used a four point scale (0, 1, 2, 3) corresponding to not attempted, attempted but incorrect,

partially correct, and correct responses respectively. The responses across all the questions

were scaled to [0,1] with the extremities corresponding to „not attempted‟ and a correct

response respectively. The transformation used to scale the responses is shown below:

Replace variable 𝑥𝑖𝑓 with rank 𝑟𝑖𝑓

𝑟𝑖𝑓 ∈ 1, … , 𝑀𝑓

Map the range of variable onto [0,1] by replacing the ith

value of the fth

variable by

𝑧𝑖𝑓 =𝑟𝑖𝑓 − 1

𝑀𝑓 − 1

The transformed performance values are treated like interval-scale data, permitting the use

of the “Euclidean” distance measure to calculate the distance matrix that serves as an input

to the hierarchical agglomerate clustering (bottom-up) algorithm, which begins by treating

every student as an individual cluster in the first iteration and merges these clusters based

on their performance across all 86 questions using “complete linkage” through successive

steps until a singleton cluster is obtained. The resultant cluster tree (dendrogram) was

cropped to obtain an appropriate number of student clusters, namely 5 student groups where

the students‟ performance was less dissimilar within a cluster than across groups. The

clustering algorithm was written and run using R, an open source statistical analysis

platform.

Using the children‟s performance across all 86 questions while clustering gives us

competency and question level insight into student group performances. In comparison,

utilizing „averaged‟ performance of students would have given a grouping outcome with no

way of distinguishing performance across competencies. The clustering methodology used

takes into account which set of questions the student group responded similarly to. For

example, using “averaged” properties it would not be possible to distinguish between two

groups, students who have answered 25 similar math questions correctly, and those who

correctly attempted 25 similar language questions, as both student groups would have an

average number of 25 correctly attempted questions. Our algorithm picks up such

differences while formulating the groups. Clustering results based on the students‟ abilities

across distinguishable competencies provides educators a rich source of information

teaching- learning grouping. The results of clustering are shown in Figure 1.

(Insert)

Figure 1: Question wise performance of students divided into 5 clusters

and ranked according to questions correct and attempted

(Insert)

Table 2: Student count in clusters (percentage calculated out of 383

students), averaged sum of response of students, and percentage of correct

responses (out of 86 questions)

The student populace attending the five-days-a-week camps was divided into 5 clusters.

The resultant groups were assigned ranks based on their averaged score out of a maximum

of 86 points during the baseline. As shown in Table 2, 17.5% of the students scoring an

average of 64.5% of maximum points constitute the highest ranked group of

„accomplished‟ students, namely group 5. Students in groups 4 (17.8% of students) and 3

(12.5% of students) achieved an average score of 48.4% and 46.7% respectively. Despite

the minimal differences in their average performance, group 4 students outperformed group

3 on math competencies. Group 2 students constitute the second largest student cluster with

25.3% of sample. Their performance mirrors those of in group 4, although on average they

achieved 40.7% on the baseline assessment. 26.9% of the student sample constituting

Group 1 scored an average of 27.9% on the assessment. These students consistently showed

lower exposure to the concept of print. Identifying such distinct groups based on their

competencies potentially serves not only as a tool to inform better grouping methodologies

for teaching- learning, but as a way to track the students through the intervention by

comparing their performance between the baseline, midline and endline as demonstrated in

Section IV.

(Insert)

Table 3a: Group-wise Math Competency scores [0,1]

Table 3b: Group- wise Language Competency scores [0,1]

Considering that early childhood learning as a period for focused concept development,

necessitates instruction aligned with differences in pre-camp knowledge and skill base of

students, modifying the delivery mechanism to meet the students‟ individual learning

trajectories, and providing instruction based on continuous formal (tests) and informal

(observation) assessment. In support of differential teaching-learning, data from a self-

paced, self learning platform such as Khan Academy (Khan, 2011) suggests that the

learning trajectories of children showed a high degree of homogeneity in terms of time

taken for course completion and total number of mastered concepts, despite evidence of

heterogeneity of time spent and time taken to master individual concepts, indicating that the

end points of the learning exercise for the participants in Khan Academy‟s math module

were similar but the students faced varying levels of difficulty across different conceptual

hurdles. In similar ilk, in-class teaching-learning may be modified to mimic self- learning,

by providing need based guiding to students facing similar hurdles using ability based

group information. In conjunction with Figure 1, Table 3a and 3b, provide an estimate of

group performances across multiple competencies, thereby providing an effective outcome-

oriented performance tracking multidimensional metric. Comparing baseline performance

with midline performance, it would be possible to learn for which set of students was the

program most effective, as measured by increase in competency of a particular group,

hence bringing out insight for program improvement. Furthermore, the program could be

more effective in delivering and managing activities pertaining to particular set of

competencies that the instructor is comfortable with, which group-wise competency

tracking would make explicit.

Siraj and Taggart‟s (2014) research into school effectiveness detail salient features and

activities undertaken by “good” teachers and prevalent in effective schools such as

organizational skill, positive classroom (respectful) environment, personalized and

interactive approach to teaching learning, use of dialogic teaching, and effective use of

plenary sessions to encourage participation, are all related to good communication practices

as outlined in Bühler (1934/1990) and Jakobson‟s communication model (Waugh, 1980),

through which information production, dissemination, acquisition, and processing is

absorbed effectively by the recipient. Therefore, the best teachers tend to get down to her

student‟s level and pass on knowledge that helps students understand a concept, or provide

a guide to facilitate self discovery of knowledge. Response based clustering of students

functions as a guide for such differentially sensitive dissemination, which is pertinent for

children considering the plasticity of their learning strategies in addition to their

„Phenotypical plasticity‟ (Bogin, 1997), which gives them the ability to adapt quickly to

changing conditions. While the child is learning to learn, it is imperative that those

responsible for her rearing take special care in providing an environment which encourages

and builds upon her natural modes of acquiring new information, namely exploration, play,

exercising curiosity and experimentation. In effect, the entire school environment is but an

extension of a stage, where a valuable subject matter and information is communicated

from actor/addressor to the addressee, except that the additional complexity of evolving

memory landscape of young children needs to be considered as well. An individual‟s

memory storage occurs through parallel means of gist and verbatim memories, where the

former are predominant inputs for intuitive decision making. Group- wise performance

across multiple competencies (Table 3a&b) show that children are more inclined towards

tasks requiring gist memory (global judgments), such as pre-math, pattern recognition (in

math) and picture naming, picture identification, and noun identification (in language), and

are especially poor performers in verbatim tasks (requiring exact memory) such as

symbolically adding or subtracting numbers, even though the children are able to perform

well on bundling and pre-math, thus providing us a guide to develop and deliver lessons

that build on their gist recall and gradually transform into verbatim exercises, which is

supported by common sense where it is most efficient to work on the „concept‟ and then

working towards „application‟ of the concepts.

Recognizing the communicational nature of the teaching- learning environment and

processes and applying it to the cycle of „teaching > dissemination > acquisition > learning

> assessment > modified dissemination > reacquisition > relearning > reassessment‟ puts a

sequencing constraint on the pedagogic process, especially assessment (interpreted as a

functional feedback mechanism to gauge teaching-learning) by requiring test structuring

leading to monotonic performance, where the test gets harder as the test progresses, thereby

building on what the learner knows best and moving towards the gaps in her learning. The

required monotonic nature of the test is also in line with the idea of creating a child friendly

learning ecosystem where having „easy‟ questions first opens up the communication

channel throughout the assessment as shown in Figure 2.

(Insert)

Figure 2: Monotonically decreasing performance across a test with

multiple questions

A child friendly test especially for children who have had limited exposure to quality

teaching- learning and appear to come off as non-expressive in the initial stages of

interaction, should have hurdles only later in the assessment. Figure 3a & b show the

group- wise performance of children on math and language competencies, clearly

indicating that non-advanced learners have to psychologically cope with non-performance

in the very beginning of the assessment while they are being tested on Concept of Print

even though many may have never handled a book before. It is possible that the number of

high „no attempt‟ responses could decrease if the test began from Picture Naming, a task

that the groups of students are „good‟ at and then move on to more difficult questions

(based on response of students) such as Concept of Print. Such a design would also

preserve a child-friendly philosophy by beginning with competencies that a majority of

students (especially less advanced) are able to perform well in, and then move on to

competencies that are progressively more difficult.

The analysis presented herein also provides an opportunity to track student groups across

multiple competencies. At the end of the program we would want to see which competency

improved the most, and how did it differ across groups, which would then give us an

indication about the program‟s effectiveness in teaching certain competencies to specific

groups of children. In Section IV, we‟ll look at means of tracking the learning and

performance of children across the baseline and midline by using the analyses apparatus

discussed throughout this section.

(Insert)

Figure 3(a): Group- wise Language Competency scores [0,1]

(Insert)

Figure 3(b): Group- wise Math Competency scores [0,1]

Section IV

The average student performance between the baseline and midline assessment showed an

improvement of 20.2 percentage points; the average score of students at the baseline was

43.5%, which increased to 63.7% at the end of the first year of the intervention. The group-

wise (baseline clusters) progress of performance is given in Table 4 shows that the program

was most effective for students who belonged to group 3 at the baseline, with an increase of

26 percentage points. The most „accomplished‟ baseline group, namely group 5 showed

least amount of improvement through the intervention with an increase of 13 percentage

points.

(Insert)

Table 4: Group- wise progress of performance between Baseline and Midline

Considering the competency based holistic development goal of the R&D program, it is

crucial we map out the group- wise progress of math and language competencies. The

result of this mapping is shown in Table 5 (a) and Table 5 (b). No directional definition of

„progress‟ was used, instead, the difference between the competency wise performance

between the midline and baseline was used, therefore both negative and positive progresses

show up. A drop in performance indicates that the program did not consolidate on the

existing capacity of the student group in a particular competency.

(Insert)

Table 5 (a): Group- wise progress of math competencies through the intervention

Table 5 (b): Group- wise progress of language competencies through the intervention

The maximum improvement in mathematics was witnessed for Pre-Math, Pattern, Ending

Numbers and Number Recognition competencies. Students from groups 5 and 4 regressed

on their Word Problem Solving scores. But the most salient point while mapping group-

wise competencies comes to light when we look at Subtraction; a majority of students were

competent in subtraction in the beginning of the program, which probably led to a lessened

focus on this math ability, leading to a general decline of subtraction prowess through the

course of the intervention.

In contrast, maximum language related improvement was seen Noun Identification, Oral

Comprehension and Phonological awareness for starting sounds, although Phonological

awareness for ending sounds showed consistently negative progress for students belonging

to Groups 4, 2 and 1. Although Group 3 students showed marked improvement of their

written comprehension skills (increase of 0.44 points), the performance of all other groups

declined. Contrary to this pattern, group 3 students showed least amount of improvement in

scribbling.

The program had heterogeneous effect for different student groups; indicating the need for

level-wise group based teaching-learning methodology for the various competencies, for

which the information provided on the group-wise competency levels throughout this

analysis is particularly useful. The analysis in Section 4 so far has tracked group level

performance of students clustered based on their ability at the baseline. Considering the

varied effects of the program on individual students, it is perhaps non-trivial to note that the

grouping at the end of the first phase of the intervention is different from the clustering at

the baseline. Figure 4 shows the performance based grouping of students at the midline.

(Insert)

Figure 4: Performance based grouping at the midline

As shown in Table 6, 86.9 % of the students scored more than 45% points at the midline,

which includes 65% students constituting Group 5 who on average secured 75% on the

assessment. A majority of students in this group attempted Word Problems in the

mathematics section, indicating an increased confidence in their personal estimation of their

ability. In comparison Group 4 students uniformly attempted and correctly answered

language related questions, while choosing to skip a big portion of the math assessment.

Group 3 students displayed mixed results; a majority did not attempt number recognition,

addition and subtraction questions in the math section, and written comprehension

questions, reading, dictation, and phonological awareness questions in the language section,

indicating a gap in reading-writing and numeracy. Students in Group 2, like their peers

from Group 4 consistently performed poorly across the entire math section. In addition they

comparatively underperformed in oral and written comprehension questions, in addition to

reading and dictation tasks. Students in Group 1 performed well on picture identification,

noun identification and pattern recognition questions. Constituting approximately, 7.6% of

the student sample, on an average they made no attempts on 69.6% of the questions. 76%

of this group belonged to the „lowest achieving‟ Group 1 at the baseline.

(Insert)

Table 6: Student count in clusters (percentage calculated out of 383 students),

averaged sum of response of students, and percentage of correct responses (out

of 79 questions) at the midline

Through the course of the intervention the average score across multiple competencies and

groups was 0.33 and 0.58 for mathematics and language respectively, which when

compared to the performance at the baseline, shows that the program had a greater degree

of impact on improving the language competencies of learners on average. Tables 7a and

7b show the competency wise performance of the groups at the midline. The performance

of students in Group 4 across language competencies is much higher than the students in

other groups. The average performance of non-Group 4 students is particularly low writing

and reading based skills such as written comprehension, reading and dictation. High

performance on skills that were pictorially assessed such as noun identification and picture

identification, suggests that students were most receptive to teaching- learning activities

with a visual component. The consistently low performance of Group 4 and Group 2

students on mathematics competencies is concerning, indicating that the program design

was probably not aligned to the learning patterns of linguistically aligned children.

(Insert)

Table 7 (a): Group-wise Math Competency scores [0,1] at Midline

Table 7 (b): Group-wise Language Competency scores [0,1] at Midline

Charting the progress of student performance across multiple competencies between groups

at the baseline and midline (Table 8) provides a map to understand the program

effectiveness heterogeneous student clusters with differing learning patterns for the

multitude of language and mathematics competencies. In the language section, maximum

improvement is seen for noun identification and oral comprehension. The disparity between

the considerable improvement in scribbling and writing comprehension, begs the question

whether, the program was simply effective in encouraging students to participate in writing

exercises, which is a first step to learning writing with comprehension. A most surprising

insight is the inverse relation between phonologically break ending sounds with other

phonological awareness competencies. A reasonable hypothesis to understand this

particular phenomenon is related to traditional classroom practices employed for language

teaching where teachers, despite careful training, often pay very little time and attention on

the latter segment of a multisyllabic/mono word which she repeats in the class. And rather

she lengthens the first vowel of the construct, leading to the poor performance for the latter

segment of the phonics.

(Insert)

Table 8: Competency-wise Progress between Baseline and Midline Groups

The non-obvious negative progress in subtraction skills seen for all student groups is

counterintuitive considering that it was one mathematics skill in which a majority of

students showed a greater degree of competence. It is possible to explain this fall in

performance if we assume that the camp instructor probably spent less time on repeating

and working through subtraction exercises while delivering the flat curriculum to all her

students, resulting in insufficient subtraction-learning time through the intervention.

Students who moved from lower groups at the baseline to higher groups at the midline

showed substantial improvement in pre-math skills. Students showed increased

performance in pattern recognition skills as well. Number recognition and addition

improved most for students who transitioned to Group 5 at the midline.

As demonstrated in this section and Section 3, there is immense potential in analyzing

student performance and assessment data through machine-aided pattern recognition

techniques so as to gain insight into the learning progress of children involved in an early

grade competency learning camp. The heterogeneity of student abilities at the baselines,

and their various learning trajectories through the course of the intervention are concerns

that could be tackled effectively by adopting grouping and differential teaching at the early

grade levels. In addition to the counter productiveness of an overambitious curriculum as

demonstrated in (Pritchett & Beatty, 2012) a flat teaching- learning exercise is the antithetic

to heterogeneous learning patterns of children. Aligning a variable instruction model is

possibly the way forward to improve the R&D learning camp so as to aid students accrue

larger learning gains.

Conclusion

Mass-scale homogenized education across India leaves a substantial proportion of

children behind. Despite a high enrolment rate across primary grades, several rigorous

exercises (Educational Initiatives, 2010; ASER, 2014) have demonstrated the gaps of an

input oriented education policy and practice that does not consider ground realities and

learning levels of children. Looking forward, perhaps it is necessary to adopt a holistic

educational mission that utilizes a bouquet of heterogeneous teaching- learning

strategies for Education for All (EFA) goals – emulating a scalable and inclusive

„gurukul‟ philosophy. There is no replacement for customized teaching- learning

delivered through teachers paying individualized attention to attend to the creative and

learning needs of students. The question of how to apply educational customization at

scale is a core concern of strategizing and implementing an effective education policy.

The privatization of education is perhaps a means to break through the inertia embedded

in schooling, which is largely managed by the public sector. A parallel but equally

important query is to think about how such creative interventions can be imbibed into

elementary education, especially during the early years of learning when children

undergo rapid development. This essay provides a stepping stone to begin addressing

this issue by demonstrating the possibilities of aligning teaching with learning patterns

of children through the amalgamation of a humanistic learning environment and

machine- aided pattern recognition of student abilities and learning propensities. The

fixities of curriculum design, while reasonably effective for higher education, is

unsuitable for younger children. We ought to seriously relook at eclecticism of education

and syllabus design for effective learning across the early grade and elementary levels in

the nation. Adopting machine learning insights serves as a means to introduce „design

intelligence‟ into education programs. The experimental R&D program at Pratham could

benefit from testing the practicality and quality of the „design intelligence,‟ namely

adaptive programming of interventions for maximized child- friendly learning.

Revelations from machine enabled pattern recognition of student clusters, and the ability to

track their performance across competencies provides instructors an opportunity to

smoothen the path to learning new things by facilitating dynamic grouping within a

classroom where children are encouraged to hone their theories and perceptions of subject

matters while engaging in collaborative hypothesis testing. Thus, minimizing the chances

of emotional roadblocks that arise when a child feels „left behind‟ for not knowing what the

instructor is teaching. Grouping and differential task dissemination that build on the various

components of a competency also provides ample opportunity for a child to practice and

master a concept before moving onto the next challenge.

A third question that needs exploring pertains to the practice of limiting programs to a

limited set of activities and competencies; why is learning in schools not extended to

music, dance, drawing, sport etcetera which would have attracted those learners whose

primary inclination is performance , kinesthetic and creative intelligence. For example,

enabling learning through music, which relies on rote, repetition, and creativity, while

also exploiting patterns and sonority of lyrical notes could possibly help long term

imprinting of knowledge and skills and enhancing memory and recall in children.

In conclusion, universal primary education is aimed at enabling freedom and opportunity

in every citizen from a young age. It is meant to foster love for knowledge, curiosity,

and knowledge acquisition amongst children. The quintessential substance of education

is development of a young individual by enabling an environment promoting the joy of

learning. And because socio-cultural cognition is triggered by one‟s localized

environment, fostering a locally influenced, personalized curriculum and customized

education design is a reasonable means of harnessing the individuality of every child.

Policies promoting the uniqueness of a child have the capacity to create a more efficient

and useful child development platform. Instead of aligning education with business or

industrial opportunities, it is appropriate to alter business perspectives based on

development of children, and availability of varied talents. Furthermore, a homogenized

state is not and cannot be a reality for a multi-lingual and pluri-cultural nation such as

India. Hypothetically, even if everybody had one common learning (through an enforced

education policy) it would still not lead to “one people” as persons would form

heterogeneous groups based on other social and cultural parameters that define their

identity such as their state of origin, caste and creed among other things. There is

therefore no reason why we cannot promote educational heterogeneity without

sacrificing the spirit of unity. Implementing a multi- pronged educational initiative is

bound to be carefully drafted, and fraught with implementation issues, but that is a

matter for decision makers, implementers and educationists to sort out. The development

of children should not be held back because the government finds it “hard” to implement

a plan, for that is the spirit of democracy, where the country sweats for her children

today so they may serve their nation to their best capacity in the future.

Bibliography

Adjibolosoo, S. (2005). The Human Factor in Leadership Effectiveness. Oklahoma City:

Tate Publishing.

ASER. (2013). Annual Status of Education Report. New Delhi.

Retrieved from

http://img.asercentre.org/docs/Publications/ASER%20Reports/ASER_2013/ASER2013_re

port%20sections/aser2013fullreportenglish.pdf: ASER.

ASER. (2014). Annual Status of Education Report. New Delhi.

Retrieved from

http://img.asercentre.org/docs/Publications/ASER%20Reports/ASER_2013/ASER2013_re

port%20sections/aser2013fullreportenglish.pdf.

Beteille, T. (2002). Elementary Education in India. Social Initiatives Group, ICICI.

Boesch, C., & Tomasello, M. (1998). Chimpanzee and Human Cultures. Current

Anthropology , 39 (5), 591-694.

Bogin, B. (1997). Evolutionary hypotheses for human childhood. American Journal of

Physical Anthropology , 104 ((Suppl 25)), 63-89.

Bruns, B., Mingat, A., & Rakotomalala, R. (2003). Achieving Universal Primary Education

by 2015 A Chance for Every Child. Washington: The World Bank.

Bühler, K. (1934/1990). The Theory of Language: The Representational Function of

Language (Sprachtheorie). (D. F. Goodwin, Trans.) Amsterdam: John Benjamin's

Publishing Company.

Burke, B. (2009, November 9). Mahatma Gandhi on Education: Excellent Collection of

Quotes from the National Council for Teacher Education.

Retrieved from http://infed.org/mobi/mahatma-gandhi-on-education/#education

Central Statistics Office. (2011). 18th Conference of Central and State Statistical

Organizations; Agenda-4: Education Statistics-- Issues. Government of India, Ministry of

Statistics & Programme Implementation, Bhubaneswa, Orissar.

Cornford, F. M. (1945). The Republic of Plato, Translated with Introduction and Notes.

London: Oxford University Press.

De Houwer, J., Barnes-Holmes, D., & Moors, A. (2013). What is learning? On the nature

and merits of a functional definition of learning. Psychonomic bulletin & review , 20, 631-

642.

Dewey, J. (1938). Experience and Education. New York: Kappa Delta Pi (Lecture Series).

education.edu. (n.d.). Retrieved from http://www.educause.edu/research-and-

publications/books/learning-spaces/chapter-6-psychology-learning-environments

Educational Initiatives. (2010). Quality Education Study.

Retrieved from http://www.ei-india.com/wp-content/uploads/Main_Report.pdf.

Freire, P. (1993). Pedagogy of the City. New York: Continuum.

Freire, P. (1996). Pedagogy of the Oppressed. New York: Continuum.

Hanushek, E. A., & Woessmann, L. (2007). The Role of Education Quality for Economic

Growth. Policy Research Working Paper No. 4122, The World Bank.

Holt, J. C. (1982). How Children Fail (Classics in Child Development, reprint of (1964)

ed.). New York: Dell Publishing.

Khan, S. (2011). Let‟s use video to reinvent education. TED.

Retrieved from

www.ted.com/talks/salman_khan_let_s_use_video_to_reinvent_education?language=en.

Kushnir, T., & Gopnik, A. (2007). Conditional Probability Versus Spatial Contiguity in

Causal Learning: Preschoolers Use New Contingency Evidence to Overcome Prior Spatial

Assumptions. Developmental Psychology , 43 (1), 186- 196.

Meyer, J. W. (1977). The Effects of Education as an Institution. American Journal of

Sociology , 83 (1), 55-77.

Mukherjee, A. N., & Sikdar, S. (2012). Public Expenditure on Education in India by the

Union Government and Roadmap for the Future. India Infrastructure Report.

Retrieved from www.idfc.com/pdf/report/2013-14/IIR-2013-14.pdf.

Payton, J., Weissberg, R., Durlak, J., Dymnicki, A., Taylor, R., Schellinger, K. B., et al.

(2008). The positive impact of social and emotional learning for kindergarten to eighth-

grade students: Findings from three scientific reviews. Chicago, IL: Collaborative for

Academic, Social, and Emotional Learning.

Pritchett, L., & Beatty, A. (2012). The Negative Consequences of Overambitious Curricula

in Developing Countries. CGD Working Paper 293, Center for Global Development,

Washington, D.C.

Retrieved from www.cgdev.org/content/publications/detail/1426129.

Robinson, S. K. (2010). Bring on the learning revolution. TED. Retrieved from

http://www.ted.com/talks/sir_ken_robinson_bring_on_the_revolution/transcript?language=

en.

Siraj, I., Taggart, B., Melhuish, E., Sammons, P., & Sylva, K. (2014). Exploring Effective

Pedagogy in Primary Schools: Evidence from Research. London: Pearson.

Tzuo, P. W. (2007). The tension between teacher control and children‟s freedom in a child-

centered classroom: Resolving the practical dilemma through a closer look at the related

theories. Early Childhood Education Journal , 35 (1), 33-39.

UNICEF. (2000). Poverty Reduction Begins with Children. Policy review document of the

Division of Evaluation, Policy and Planning. New York: United Nations Children's Fund.

Waugh, L. R. (1980). The Poetic Function in the Theory of Roman Jakobson. Poetics

Today , 2 (1a, Roman Jakobson: Language and Poetry (Autumn number)), 57-82.

Table 1: Math and Language Competencies and Sub-competencies

Cluster No. Count (%) Points Points (%)

1 26.9 24 28

2 25.3 35 41

3 12.5 40 47

4 17.8 42 48

5 17.5 56 65

Table 2: Student count in clusters (percentage calculated out of 383 students),

averaged sum of response of students, and percentage of correct responses (out

of 86 questions)

Group Coun

t Sum

%

Pre-

Math

Bundling Ending

Number

Understanding

Problem

Solving Problem

Pattern Number

Recognition Add Subtract

5 67 64 0.81 0.79 0.73 0.5 0.8 0.34 0.1 0.1 0.97

4 68 48 0.79 0.68 0.51 0.38 0.76 0.23 0.04 0.02 0.97

3 48 46 0 0 0 0 0 0 0 0 0.99

2 97 40 0.29 0.31 0.3 0.2 0.47 0.05 0 0 0.93

1 103 28 0.14 0.23 0.17 0.14 0.3 0.03 0 0 0.74

Table 3a: Group-wise Math Competency scores [0,1] at Baseline

Group

Concept

of Prin

t

Phonological- Breaking units

Phonological- Combining units

Phonological- Startin

g sound

Phonological- Ending sound

Picture Identification

Picture Namin

g

Noun Identification

Scribbling

Dictation

Reading

Comprehension-

Oral

Comprehension- Written

5 0.81 0.85 0.92 0.82 0.94 0.85 0.76 0.04 0.58 0.17 0.33 0.17 0.49

4 0.68 0.54 0.18 0.17 0.96 0.72 0.65 0 0.28 0.09 0.24 0.17 0.48

3 0.67 0.83 0.83 0.71 0.96 0.75 0.72 0.06 0.62 0.13 0.44 0.02 0

2 0.49 0.59 0.41 0.21 0.92 0.67 0.59 0 0.1 0.08 0.24 0.12 0.31

1 0.18 0.12 0.1 0.08 0.88 0.59 0.5 0 0.04 0.03 0.19 0.09 0.24

Table 3b: Group- wise Language Competency scores [0,1] at Baseline

Cluster No.

(Baseline) Count (%)

Points (%)

@ Baseline

Points (%)

@ Midline (%)

1 26.9 28 47 19

2 25.3 41 63 22

3 12.5 47 73 26

4 17.8 48 69 21

5 17.5 65 78 13

Table 4: Group- wise progress of performance between Baseline and Midline

Rank Pre-Math Bundling Ending

Number

Understanding Word

Problems

Solving Word

Problems Patterns

Number Recognition

Addition Subtraction

5 0.14 0.16 0.21 0.21 -0.16 0.35 0.49 0.49 -0.46

4 0.2 0.25 0.45 0.3 -0.15 0.48 0.47 0.44 -0.71

3 0.77 0.72 0.7 0.59 0.47 0.57 0.5 0.48 -0.63

2 0.69 0.54 0.55 0.44 0.02 0.63 0.45 0.36 -0.68

1 0.76 0.31 0.41 0.34 -0.02 0.5 0.26 0.19 -0.61

Table 5 (a): Group- wise progress of math competencies through the intervention

Rank

Concept

of Prin

t

Phonological- Breaking units

Phonological-

Combining

units

Phonological- Startin

g sound

Phonological- Ending sound

Picture Identification

Picture Namin

g

Noun Identification

Scribbling

Dictation

Reading

Comprehension-

Oral

Comprehension- Written

5 0.06 0.09 0.03 0.14 -0.01 0.11 0.08 0.95 0.19 0.39 0.29 0.64 -0.11

4 0.12 0.31 0.51 0.65 -0.29 0.2 0.16 0.99 0.53 0.21 0.14 0.54 -0.37

3 0.15 0.11 0.09 0.24 -0.01 0.2 0.1 0.94 0.01 0.53 0.23 0.86 0.44

2 0.19 0.24 0.32 0.56 -0.31 0.2 0.14 0.99 0.55 0.16 0.06 0.53 -0.21

1 0.34 0.34 0.27 0.36 -0.56 0.22 0.15 0.92 0.41 0.09 -.01 0.41 -0.2

Table 5 (b): Group- wise progress of language competencies through the intervention

Cluster No.

(Midline)

Count (%) Points Points (%)

1 7.6 24 30

2 5.5 34 43

3 18.5 36 45

4 3.4 50 64

5 65.0 59 75

Table 6: Student count in clusters (percentage calculated out of 383 students),

averaged sum of response of students, and percentage of correct responses (out

of 79 questions) at the midline

Group Count RowSum

% Pre-Math Bundling

Ending Number

Understanding Problems

Solving Problems

Patterns Number

Recognition Addition Subtraction

5 249 75 1 0.98 0.95 0.75 0.65 0.73 0.59 0.57 0.42

4 13 64 0.38 0.04 0.23 0.13 0.06 0.23 0.1 0 0

3 71 45 1 0.63 0.73 0.51 0.23 0.59 0.24 0.07 0.03

2 21 43 0.24 0.05 0.12 0.02 0 0.11 0.03 0 0

1 29 30 0.87 0.29 0.36 0.34 0.11 0.43 0.11 0.04 0.02

Table 7a: Group-wise Math Competency scores [0,1] at Midline

Group

Concept of

Print

Phonological-

Breaking units

Phonological-

Combining units

Phonological-

Starting sound

Phonological-

Ending sound

Picture Identific

ation

Picture

Naming

Noun Identific

ation

Scribbling

Dictation

Reading

Comprehension- Oral

Comprehension-

Written

5 0.82 0.91 0.88 0.93 0.83 0.93 0.81 0.99 0.71 0.42 0.48 0.78 0.23

4 1 0.98 1 1 0.97 0.93 0.83 1 0.81 0.95 0.9 0.94 0.77

3 0.5 0.51 0.27 0.32 0.14 0.79 0.68 0.96 0.54 0.05 0.11 0.44 0

2 0.52 0.73 0.54 0.78 0.62 0.88 0.74 1 0.48 0.17 0.32 0.7 0.01

1 0.28 0.03 0.09 0.06 0.05 0.77 0.47 0.79 0.36 0.02 0.03 0.21 0.02

Table 7b: Group-wise Language Competency scores [0,1] at Midline

Table 8: Competency-wise Progress between Baseline and Midline Groups

Figure 1: Question wise performance of students divided into 5 clusters and ranked

according to score out of 86 points at the baseline

5

2

1

4

3

Figure 2: Monotonically decreasing performance across a test with multiple questions

Figure 3(a): Group- wise Language Competency scores [0,1] at Baseline

Figure 3(b): Group- wise Math Competency scores [0,1] at Baseline

0

0.2

0.4

0.6

0.8

1

1 6 11 16 21Co

mp

ete

ncy

sco

re [

0,1

]

Questions

Ideal monotonically decreasing test

0

0.2

0.4

0.6

0.8

1

Sco

re [

0,1

]

Language Competencies

Group-wise Language Competency PerformanceGroup 5Group 4Group 3Group 2Group 1Average

0

0.2

0.4

0.6

0.8

1

Sco

re [

0,1

]

Math Competencies

Group-wise Math Competency PerformanceGroup 5Group 4Group 3Group 2Group 1

Figure 4: Performance based grouping at the midline

5

2

1

4

3