Raising a 1960s Sunken Living Room Floor is an easy way to raise a sunken floor.

The equity and inequality dimensions of the learning crisis are examined in this note.

The vast majority of children in developing countries don’t meet the expectations of national curricula or the more basic levels of competence tested in citizen-led assessments.The 5th percentile of the distribution in OECD countries is the median level of achievement in many developing countries.The scale of this learning crisis has been documented, but the nature of the systemic failures that explain the prevalence of poor learning outcomes remains a key area of study.

The exclusion of most children from minimum acceptable learning competencies is a major failure of education systems in many developing countries.Poor learning among most children, especially where it is a result of poor quality education, is inequitable not only because it contributes to massive global (North-South) inequality, but also because the failure to develop and realise the talents of all pupils is unjust.The latter form of inequity is linked to notions of right or entitlement, and may be related to rights to opportunities to develop valuable human ‘capabilities’ and ‘functioning’.The right to education in the UN Universal Declaration of Human Rights is founded on the development of such capabilities.The goal of theSDGs is to focus on learning and its distribution.The new goals are more focused on learning than the MDGs were and are concerned with a minimum-proficiency approach.

South Africa and India are examples of countries where educational inequalities are higher than income inequalities, but average performance levels are low.An important empirical question is whether higher average learning levels are most readily reached by reducing inequalities or if they are the result of more general efforts to raise learning outcomes.We consider the potential benefits of a path through the middle, whereby attention to the left hand of the learning distribution, namely the poor-performing students and schools, may serve to both improve outcomes as a whole and to reduce inequality.

A large bulge of poorly performing students and schools at the left of the distribution may be an efficient strategy for raising learning outcomes as a whole.It would be an equitable thing to do if this was feasible or what successful countries do.

Equity issues include but are not limited to issues of inequality.While understanding inequalities in learning outcomes, such as the nature and size ofachievement gaps, is largely an empirical endeavor, assessments of equity are inherently require value-judgments about what constitutes fairness.Libertarians may favour more individual liberty at the expense of equality, focusing on equal access to basic services for example.Adler argues that balancing liberty and equality is a matter of justice.A theory of justice is the best known modern theoretical approach to such judgments.

The principle of equal basic liberties and fair equality of opportunity is the second of which requires more than equal access to basic services for individuals of similar natural endowments.A thought experiment in which decisions concerning the organisation of society are made from an ‘original position’ behind a’veil of ignorance’ regarding individuals’ own starting points in terms of advantage such as creed, wealth, gender, ethnicity, and so on.The worst-off would be worse if there were inequalities.There are examples of inequalities of access to higher education based on merit, wages for occupations with different levels of education, and discrimination in favour of disadvantaged minorities in education.Incentives or conditions which benefit society as a whole can be created if inequality is required.inequalities of access to basic education of adequate quality linked to identity or location are not included in fair inequalities.Fair inequalities of outcome can only be achieved if there is equality of opportunity and society must level the playing field.

Society should focus on providing opportunity first for those who need it the most, according to the equity paradigm sketched above.It is for policy-makers and social scientists to figure out how to make provision when the target group is very large and resources are scarce.There is more disagreement in the global education discourse about how to reduce inequity than about the paradigm itself.Policy-makers in countries where the group of pupils with low learning outcomes amounts to a majority face a considerable challenge in raising the outcomes.It may be less costly to reach children in urban areas than it is in rural areas.If both groups in low-performing countries have poor opportunities to learn, the gaps in learning outcomes need not be large.

Difficult decisions must be made regarding which levels of education and which pupils to focus on (for example, whether to divert higher education subsidies to basic education), as resource scarcity ensures that developing countries are constrained in terms of how much education can be provided to whom.More equity will always be preferred to less, while the preferred distribution of opportunity must be achieved as efficiently as possible to ensure that opportunities are extended as widely as is feasible within the relevant resource constraints.

It is less obvious that fair inequality is preferable to unfair equality.Consider a poor quality education system with low learning outcomes.The system is inequitable because it gives unfair and unjust outcomes to everyone.The introduction of a small number of high quality schools in disadvantaged areas into such a system would arguably reduce inequity, at least in the absolute sense, by providing worthwhile and fair opportunities to develop the capabilities of some children.It would increase inequality of opportunity.Providing high quality education to all would be a more straightforward way to improve equity.When compared to the situation of universally poor outcomes, there would still be an increase in inequality.

The case for equal access as the desired distribution may be strengthened by the promotion of access to basic education.Based on the benefits of education, both monetary and non-monetary, one may reach a slightly different conclusion, particularly where the distribution of higher levels of educational achievement is concerned, and where it is dependent on scarcity.If the supply of decent jobs is fixed and educational attainment increases, then the price of such jobs may be raised.The subsidy of higher levels of education in the public sector may be argued to serve to widen inequality and improve social justice if it is linked to economic rents rather than productivity benefits.If educational access is to berationed, it must produce fair inequality.

It could be seen as inequality linked to effort or merit rather than background advantage.Without unlimited resources, educational progression must be limited, to the extent that the state meets the costs of provision, and the ways in which limits are applied.

The benefits of basic education are non-positional.Lower fertility, lower child mortality, better adult health, and better parenting are all linked to more education.The extension of these benefits to any individual does not reduce their value to anyone else.Better democratic participation, improved gender equity, and reduced crime are some of the benefits that may be argued for.The notion of a right to basic education is straightforward to defend on the basis of these important benefits.A child whose education does not provide for adequate basic skills of literacy and numeracy, of whom there are as many as 250 million, is denied important benefits and opportunities to develop capabilities, which may be considered an individual injustice, contributing to wider absolute injustice at both national and global levels.

In this section, we look at the contributions to inequality of horizontal or ascriptive factors such as gender, location, or socioeconomic status compared to some common benchmarks and to pure inequality.

Data on the sources of inequality isn’t always presented in international assessments.There is a Grade 6 assessment in reading and mathematics applied mostly in Southern and Eastern Africa.It shows the difference between being rich or poor, being a boy or girl, or being in a rural or urban area.The sources of inequality are shown in Figure 1.It shows the average across all countries.

The biggest source of inequality is the fact that children who score at the 75th percentile are more likely to score 25th in the assessment.The difference between rich and poor, and the differences between the highest- and lowest- scoring geographical regions, are important.The effect size of 0.25 shows the difference between rural and urban areas.The difference between boys and girls is real, but not very large, and in one case disfavours boys, in the other case girls.

The 2015 application of PISA, an assessment that is applied mostly inOECD countries but increasingly in developing countries, contains the possibility of some interesting contrasts in terms of gender inequality and inequality associated with being rich or poor.One can appreciate the relative size of the differences if the graphics in Figure 2 are scaled the same.The standard deviation and effect size of 0.25 are shown in each graph so that one can compare the differences.Pure inequality, which can be accounted for by differences between the rich and poor or between boys and girls, is the biggest source of variation.It is equivalent to three to four grades worth of difference.The differences between rich and poor are significant, but the difference between boys and girls is less significant.

Test score data from Young Lives allow an indicative comparison of between- and within-country inequalities.The chart shows that raising girls learning outcomes to the average for boys in India could reduce the performance gap between India and Vietnam by 20 percent.Raising rural pupils to the level of urban pupils in India would reduce the gap between rural and urban performance by 50 percent.Raising the level of the highest performing district in the India sample would have the same effect as the Vietnam average.Raising attainment to that of the wealthiest tercile of pupils or the most advantaged social group would close the gap.To reach the average levels of Vietnam, all achievement in India needs to be raised to the level of children whose mothers received university education.Clearly, children with university educated mothers in both contexts are a comparatively rare and much advantaged group.The implication is that for the most part, horizontal inequalities due toscriptive factors such as gender, wealth, and location are only a partial explanation for low learning levels.The indicative comparison shows that closing some large and important attainment gaps in India may be expected to reduce the gap with Vietnam by only around half, leaving an equal amount of difference in unexplained attainment between these two systems.

Individual child factors, home advantage and school quality are shown in Figure 3 to be a factor in Vietnam and India having more advantaged pupils.The pattern of school supply in many contexts is that less advantaged pupils attend poorer quality schools, either in terms of resources or effectiveness, that adds value to their learning outcomes.If the impact of school quality is heterogeneous, disadvantaged children may benefit less from the quality of education.When compared to their more advantaged peers in the same schools, disadvantaged children make less progress as a result of school quality, other things being equal.This could lead to a triple disadvantage in the form of (i) disadvantaged home background, (ii) segregating into a lower quality school, and (III) benefiting less within a school than more advantaged pupils.The institutional features of the system may contribute to the differential school effectiveness for different groups of pupils.

Figures 4 to 6 show the relationship between home disadvantage and school effectiveness in math in India.The bars in Figures 4 and 5 represent the mean school value added estimates with and without conditioning on the pupils’ background, grouped by gender and category of mothers’ education.One hundred points on the scale is equivalent to around three years of average schooling, so the figure shows that children whose mothers attend schools that improve their test scores by up to 0.2 standard deviations more than those who don’t.

According to four key school types in India, Figure 6 shows the relationship between home advantage and school performance.There is a strong general pattern according to which more advantaged pupils attend higher performing schools.There is more variation in school performance for more disadvantaged children.State government schools are more variable in performance but it is notable that even within the category of private aided schools, there is more variation in their performance.There appears to be no pattern among state government schools, while there are no schools which are attended by more advantaged pupils.Due to their more disadvantaged pupils, a large proportion of state government schools have lower performance than almost any private school.Affected by greater uncertainty with regard to school performance, disadvantaged pupils in socio-economic terms attend schools which are less effective.

The figures show that on average boys attend more effective schools, suggesting that school choice is operating in favour of boys.The effects of home advantage are compounding the differences in school quality in the case of mothers’ education.The effects of differential school quality are not included in the figures.The study used Young Lives data to compare school effects for advantaged and disadvantaged children, controlling for a variety of child and household factors.When compared to non-native speakers, the impact of school effects is higher in math and Spanish.

The data show that pure inequality between the two countries and between schools based on their effectiveness is large, especially compared to inequality linked to factors such as gender.The factors separate from individual and household disadvantage may compound inequalities substantially.

In this section, we look at whether countries seem to improve average learning outcomes by reducing the proportion of children with low achievement or by increasing their proportion with high achievement.We want to know if improvement in averages is consistent with either increasing equality or reductions in cognitive skill poverty, and if this depends on the level at which the countries start?

If countries want to improve their average performance, they can either reduce or increase the percentage of children who have poor performance.The evidence suggests they do.

There is no assessment that includes a sample of countries in the world.Lower-middle income and low-income countries are not included in most of the global assessments.Few of the lowest-income countries participate.It is not possible to compare the assessments that work in high-performing countries with the ones that do not in low-income countries.All of these arguments are not perfect, and will remain so for a long time.

With the information at hand, we would argue that most countries improve their averages from low to middle average performance by reducing the proportion of children with very low performance, and then improve again from middle to high performance.We think that differences between countries at any point in time can tell us a lot about how countries progress.

The situation is illustrated in Figure 7 by the results of the mathematics assessment.The red line shows the percentage of children at each level of performance, from lowest to highest, for the three countries that have the lowest average performance; the green and blue lines show the same thing for three other countries.There is a bulge of students at the left of the distribution.The graph shows that countries cut the percentages of children in the two lowest performance levels from about 55 to 10 percent and from 25 to 15 percent, but don’t increase the percentage of kids in two highest levels.Less than 10 percent of children are moved into the top two categories.In order to increase the proportion of children in the two highest performance categories, countries have to go from mediocre to high performance.The bulge at the left of the learning distribution can be reduced.

Sometimes this pattern is not the case.For example, in the grade 6 reading assessment in Southern and East African countries, we find a similar pattern, but the pattern is much weaker than for PISA 2015.There is a drop in the percentage of children who are at the lowest levels of performance when going from low average performance to mediocre performance in Figure 8.One should not read too much into the difference between PISA and SACMEQ, as it may be due to the easier assessment for the worst-performing countries.The table in Appendix 1 makes it clear that the case is more of an exception than a rule.

Is it possible to decompose the inequality?There seems to be a lot of inequality in learning achievement between countries.What are some of the consequences of what we find?

This may seem like an academic question.At least for international development agencies, it has policy relevance.The question is related to the one immediately above.If countries move up from the bottom, in terms of average achievement, by reducing the proportion of children with very poor performance, and if a lot of worldwide inequality is within countries, then it seems logical for international development agencies to help them.This is consistent with the notions of fairness discussed in section 2 of this note.

The previous question was more difficult to answer.We think it is possible to get some clues from the data.The inequality measures that economists have developed for concepts such as income and wealth assume that one is measuring something that comes in natural units that have inherent meaning, like dollars of income per year or hectares of arable land.This is not the case with the important knowledge assessments.Scales of knowledge are more complex than dollars of income or hectares of land.Not all questions on the assessments are of equal difficulty, so one could use a more natural metric such as percentage of questions answered correctly.If one dollar note in one person’s pocket had more value than a different one.

The standard assessment results data can be used to derive some appealing notions of world inequality.On the vertical axis, you can see the learning outcomes score for children at the 5th, 10th and the highest percentiles of skill in the mathematics assessment.The learning outcomes and percentiles are on the horizontal axis.The percentiles are country specific.The middle child in a lower-performing country is more likely to be in the higher performing country.The yellow double-headed arrow is at the 50th percentile.The lower-performing children in the average country are more likely to perform better than the higher performing children.The lower-performing country is shown as the vertical side of the triangle drawn on the lower right-hand side.The left-most double-headed arrow, equal to the side of the triangle with corners, is the least-learned child.It would be convenient if the difference between countries was summed up by definition or by construct.This isn’t the case, but the sum is correct.

Half of the inequality is within countries and the other half is between countries.

While we are only using TIMSS 2015 Grade 4 mathematics to illustrate this graphically in Figure 9, it turns out that a little more than half of the inequality is within countries.The total worldwide inequality would be half between countries and half within countries if more low-income and low performance countries participated in these assessments.The effect on increasing measured between-country inequality that including such countries might otherwise cause could be mitigated by this.If one could impute low levels of learning to those not even in school, it would likely reinforce the evidence regarding how progress is made.

We use only the global assessments because the regional ones don’t include high-income countries and would under-estimate the inequality in the world.

The full information from Table 1 is summarized in Appendix 1.

Most of the results presented here are from published data.Primary data analysis could yield different conclusions than what is presented here.Even though our conclusions are underpinned by numbers, we try to use qualitative language.

Producing Superstars for the Economic Mundial: the Mexican Predicament with Quality of Education was written by L. and M.In: Hausmann and others.The Mexico Competitiveness Report was published in 2009.The World Economic Forum is in Switzerland.Sandefur, J.They did it in (2016).Fourteen African countries have comparable mathematics scores.The paper is from the Centre for Global Development.Realizing the Promise of Education for Development is a concept note in the World Development Report.The World Bank Group.

There is research on improving systems of education.RISE is a programme.There is a document available at: http://www.riseprogramme.org/sites.

Refers to Amartya Sen at Harvard University.

As far as average test scores are concerned, India and South Africa were among the lowest performing countries.In both India and South Africa, the difference between the 5th and 95th percentiles of the test score distribution was greater than 300 points.Two Indian States are compared to the worldwide distribution of mathematics achievement.

M. J. Adler.The year 1981.The six great ideas are Truth, Goodness, Beauty, Liberty, Equality, and Justice.

A Hobbesian state of nature refers to a state without law or a social contract in which one is not ignorant.

In India in 2015, rural pupils scored an average of more points than urban pupils in mathematics, but in only one state the urban-rural difference was statistically significant.You can find a PDF of theNASSummary.pdf at http://www.ncert.nic.in/departments/nie/esd/.

There are economic rents and teachers’ salaries in India.The year 2014).Accounting Versus Economic Cost of Primary Schooling in India is a valuetraction in public sector production.The journal is published by the SSRN.

At the risk of being a little technical, whenever we assess strength or size in this note, we will typically reason in terms of proportions of a standard deviation.The most used measure of dispersion is the number on learning results.No number is equal to the average in any set of learning outcomes.There is a typical deviation of each number.This is a good benchmark.If the average difference between boys and girls in a test is 10 points, and the same test has a 50 point difference for rich and poor, then the standard deviation of all the results is 100 points.A cut point is that a difference should be about 14 of a standard deviation to be considered substantively important.It is now somewhat conventional, also, in using these international assessments, to note that somewhere between one third and one half of a standard deviation is equivalent to one grade’s worth of difference in learning achievement.A large difference of one standard deviation is at least one, two, or possibly three grades worth of studies.See the Organization for Economic Co-operation and Development.They did it in (2016).The results are about excellence and equity in education.Paris: Publishing of the Organization for Economic Co-operation and Development.There is a pg.65.

A. Singh.The year 2014).Evidence from India, Vietnam, and Ethiopia show the emergence and evolution of learning gaps.Young lives.The files are available at: www.Younglives.org.uk.

A member of the Intellectual Leadership Team co-authored a paper about the idea of a triple disadvantage.Poor children in India are more likely to be beaten than rich children, but only in public schools.See Desai, Duby, Vanneman, and Banerji.Private schooling in India is new.The India Policy Forum was held in 2008.

The scores are adjusted for age differences.The mean maths test score in India was 531 points and in Vietnam 586 points.Average annual progress in India is around 30 points.

16 Glewwe, P., S. Krutikova, and C. Rolleston were published.There are learning gaps between advantaged and disadvantaged students.There is evidence from Vietnam.Economic Development and Cultural Change.

Tribal and Social Welfare schools are usually located in disadvantaged areas.

This line of argument is similar to the one written by the RISE Research Director.The year 2009.There are educational consequences of blinding weak states.The paper is from the Center for Global Development.