Aspects learnt from the Shanghai visit.

This report is constructed from the visit of 17 primary headteachers to Shanghai in March 2015. The teachers visited 9 primary schools in four days. Some primaries were visited more than once and this allowed elements to be re-explored.

Several aspects were considered during the visit. This report covers those aspects pertaining to the teaching of mathematics in the schools. It is fair to say that there was a lot more learning from the visit. The hospitality of the schools was of the highest standard and the schools took a lot of effort to ensure that the headteachers were able to investigate all the aspects that they wanted to.

Design of lesson -

There seemed to be 3 'patterns' of lesson - new, review, practice. The new material lesson is sometimes referred to as a concept lesson.

The lessons are scaffolded in very small steps with attention to micro detail.

The schools are all working on developing discussion. They use techniques such as :

My turn your turn Partner talk in twos Learning group in 4s, mixed ability helping each other - think, do, discuss. (This was in a

teaching school that has won awards - school B)

They also ensure that the children internalise ideas by getting the children to say them out loud or whispering them to themselves. They see this as ensuring that the children have internalised key ideas. There is a heavy emphasis on the children using the correct language and talking in sentences.

The teacher spend a lot of time considering the difficulties that children might have.

The model of most lessons encourages pupils to have a go and then to receive feedback.

Mini plenaries are used in all lessons- in these mini plenaries the visualiser is used a lot to encourage pupils to share their work. The teacher can look for particular examples to illustrate a point and to show a range of ideas or they might want the child to explain the mathematics. They think this should be done by more than one child to ensure that the class hears an explanation in more than one way or has the explanation reinforced. When this wasn’t done in a TRG class the teacher was offered the advice to ensure that she got more children to explain their ideas.

The lessons are about the quality of understanding they were not about the quantity of exercises that the children did. Owing to the nature of the visit lessons were seen that were about building concepts. So quantity of exercises might be greater in practice lessons and is also covered with the use of homework. (see later)

The lessons are sharply focused. Each lesson is 35 minute only then a 10 minute break - some children choose to finish their work in this ten minute break. The 35 minutes is a carefully researched time. They know this is the right amount of time that ensures that children give full attention.

Planning

There are different expectations in schools visited.

Planning could take the following forms:

- planning separate to text book - pages & pages

- annotations on the text book

- creating plans based on the text book

In one school 1 plan per week presented at a teacher meeting and discussed. In another school the teachers gave the plans for two topics to the subject leader for perusal.

Differentiation -

One school suggested that the homework could be differentiated to ensure there was challenge for the most able-another said their homework included a compulsory part and a challenge. Another school said this challenge was only marginally harder.

It was hard to get a sense of this as we only saw TRG lessons which did not concentrate on practice. One school has said they will send us a video of the practice lesson.

What we saw was children all doing the same thing. Teachers didn't do much checking of individual children (School A) but said that they do assessment through marking homework and then ask targeted children to stay behind after school for catch up. We had evidence in other schools of the teachers being very aware of who hadn’t got the concepts. Schools seemed to use times such as lunch times or after school to offer support for children who had not got the principles.

One school which wins prizes for being the best school in China said they differentiated by having extra lessons for some children to broaden their understanding. This was done at two levels. The first was that children could volunteer for extra mathematics in some time set aside for choosing an aspect of the curriculum to study and the second was a time when children were selected for extra mathematics.

Homework as a word seems to have a different meaning in that some of the schools said that most children did written homework in school. This might be in time between lessons or in the lunch time when they might be offered support to do this.

Shanghai had decreed that Grade 1 and 2 should not be given homework. This is line with China’s National Plan for Medium and Long-term Education Reform and Development (2010-2020) (see extract in appendix ).This meant that in some schools they were only given oral homework which involved sending home a tape to do with your child.There was a tension for some of the schools who agreed with the no homework policy but felt compromised by the fact that the curriculum still had the same demands.

The homework was handed in at 8 o’clock in the morning so that the teacher could mark it before that day’s lesson.

One school said they only expect 80% of children to get it before moving on and do intervention catch up once a week to help the children not getting the idea. Other schools were very concerned to ensure that all children should have chance to understand. There was often a sense that if you didn’t get it you should practice more to ensure that you do.

Use of textbook and workbooks

Pupils workbooks -

These help children to quickly spot each other's mistakes because they're all working with the same page set up

The book provides good quality modelling

Children seemed motivated to complete the page during their free 10 minutes time.

There are Teachers guide– these were only in Chinese and it was therefore difficult to understand their value but they were appreciated by the teachers.

Children can annotate the textbook. The textbook might also be a support to help you remember the concepts or teaching points. It was difficult to get evidence of whether the children used it for this.

Parents can buy the textbooks. This is not necessary when your child is in a grade as each child is issued with a textbook but it could be that some parents buy them before the child goes into the grade to get them ahead.

Variation

There was a lot of evidence of teachers using variation.

This came in different forms.

1) Variation used in that just small aspects of a problem were changed to ensure that more and more complicated aspects could be understood.a) A car and a bus are driving to Beijing, the car is travelling at 108km/hr and the bus at

92km/hr. If the bus has an 18.4 km head start, after how long do they meet? b) A car and a bus are driving to Beijing, the car is travelling at 108km/hr and the bus at

92km/hr. If the bus has an 0.2 hour head start, after how long do they meet? c) A car and a bus are driving to Beijing, the car is travelling at 108km/hr and the bus at

92km/hr. If the bus has a 0.2 hour head start, after what distance do they meet? d) A car and a bus are driving to Beijing, the car is travelling at 108km/hr and the bus at

92km/hr. If the bus has a 0.2 hour head start, after how long will the car be 13.6km ahead of the bus?The problems were done in order and each discussed in turn

Using different resources to solve or prove the same aspect. o Show why 0.3 is the same as 0.30 using a 10x10 hundred square and a number lineo Explain how to order decimals by using the number line or paying attention to the

digits Finding a range of methods of getting the answer

o How many different ways can I do 198x112 horizontally and then looking at how to get the answer using a vertical method

Throughout all the lessons careful attention was given to the examples used to ensure that children had a full understanding of the different aspects. So in a lesson on why 0.30 is the same as 0.3 the teacher used a full range of numbers that had zeros in different places to ensure that children had discussed all possibilities, eg 1.20, 1.02, 0.7, 0.70, 10.7,10.70.

The Use of the Teacher Research Group

This is a very impressive element of the work that is done in schools. This has been a government requirement since 1952 and so is a very established element of schools. All schools used it very regularly-once a week. As was apparent in a lot of the things seen in school it is both the attention to the detail and the persistence of approach that grabs the attention. (Children doing the same physical and eye exercises every day for the six years of their primary education is an example of how persistence is established).

One possible structure for the organisation of TRGs is that initially the meeting will look at the plans for the term. The next meeting looks to plan in greater detail with an emphasis on possible difficulties that children might experience. The next TRGs could follow some of the patterns from below:

The teachers all watched the lesson. In the TRG the teacher explained the purpose of the lesson. Teachers then in turn gave a critique of the lesson which included advice for how to improve or what to do next in the lesson. The advice was very detailed and very specific and the lesson was dissected in minute detail. This could lead to very serious discussion.

The teachers all watched the lesson. In the TRG the teacher explained the lesson with particular emphasis on the aspect of research that the grade was doing. The programme of research was:

Grade 1 looking at how to ensure that children listen Grade 2 looking at how to develop children working in a group Grade 3 looking at how to develop the children as question askers (ensuring the

questions are relevant to what is being taught) Grade 4 looking at children previewing their lesson so that they arrive with

questions

The TRG sits in the system where teachers are expected to take responsibility for their own development which is then supported by the TRG. A teacher can move between different levels of teaching by taking exams, being observed, taking part in research and acting as a mentor. The levels were explained as:

Beginner teacher- this could last many years. In the initial year the teacher would have a mentor who would help with planning and also observe the teacher. One teacher told us she had been observed about 30 times by her mentor and that the mentor gave no notice of this observation.

Lead teacher school Lead teacher district Senior High Teacher

It was essential to have done some research to move between levels of teachers and the higher levels were expected to take a lot of responsibility for mentoring other teachers. This research needed to be on a specific topic and relate to specific content. It needed to have a fixed time and place.

Teachers to move levels are evaluated on their planning, their tutoring, on developing tests as well as delivery in the classroom. In the classroom they were evaluated on their questioning, the quality of the hook to gain pupils attention, their ability to listen to and use pupils’ responses, the ability to engage the interest of children and the careful thought given to the next steps for each child.

Aims of the development of the curriculum is that children can explain their procedures for learning and that schools are taking account of the individual nature of learning and so these will be aspects that both schools and teachers will be now expected to demonstrate.

See appendix 2 for a school report on its use of the TRG

Assessment

Summative assessment was used in all schools. Tests were used on a regular basis to identify whether children had understood aspects of the curriculum. These tests were devised by the teachers working in collaboration and were an aspect of professional development (see above).

One Headteacher did say that she used the end of term assessments to evaluate the effectiveness of teachers.

Formative assessment was harder to capture but seemed to be a mixture of observation and marking of homework.

Level of mathematics

Times tables - different expectations in the schools visited. Some children know aspects such as their tables when they start school but schools don't expect it. There was a period of focusing on the times tables (about four weeks in some schools) but this was about teaching the children about the connections between tables. This happened in grade 2 and went to 10x10.

The following gives an outline of the grades. It has been difficult to get a definitive answer to the age of children starting school. It seems that children start grade 1 in the year that they turn 7 years old. However there did seem to be schools were children might be older in grade 1. The government position is that: Any child reaching six years of age should enter the primary school and in places where conditions are not available, the age for a child to enter a primary school could be postponed to seven years old.

Grade 1 - embed addition and subtraction

Grade 2 the emphasis is on multiplication and division

Grade 3 was comparable with UK

Grade 4 learning about decimals - again felt that this was comparable with UK standard

Grade 5 solving algebraic equations, multiplying decimals - above Y6 standard.

Fractions taught at a higher level in UK than Shanghai. E.g. leave multiplying and dividing fractions to middle school

One school gave us a detailed analysis of the curriculum. See appendix for their written explanation of this.

TEXTBOOKS

Grade1

Getting to know numbers to 20 (within 10 first) Getting to know numbers 20-100 and do place value HTU Addition and subtraction to 20. Focus on language (e.g. Subtrahend - subtractor = difference)

(addant + addant = sum) Relationship with addition and subtraction, adding is carrying 1, subtraction borrowing 1 e.g.

9+5 and 14-5 Build up to 2 digit number +\- 2 digit in microscopic steps using vertical form Time - o'clock Shape 3d and square, rectangle and circle. Cube faces are squares Positional language Measuring lines cm and mm Statistics - bar charts with labelled intervals and tally charts, Writing number sentences with simple problems to understand addition and subtraction

Addition and subtraction

Grade2

Numbers to 1000 Numbers to 10000 using manipulatives and place value Multiplication and division within timetables for whole semester (factor X factor = product),

(dividend divided by divisor = quotient) learn division using language. Division with remainders within times tables

4 weeks learning timetables - 10,5,2,4,8 then 3,6,9,7 +\- with 3 digit vertical form Time - hours & minutes Weight (1kg =1000g) Know right angles - right angle or not? Then acute or obtuse Facts about cubes and cuboids - how they link and squares and rectangles - extend onto

naming 3d shapes Directional language (compass) Triangles and parallelogram and name triangles Magic squares Observe shapes in different ways Tangrams Bar charts

Grades 3-5: 6 areas

1) cultivating calculating ability with written methods

2) expanding knowledge of numbers

3) geometry

4) introducing concept of statistics

5) problem solving

6) further questions

Grade 3

Place value 10 000 Knowledge of numbers - introduce simple fractions Vertical form of all operations Km and m

Area and perimeter of rectangles and squares using formula Bar charts Solving problems - speed, time and distance 2 step calculations in solving problems "Planting tree problems" half way between 2 numbers similar to ages Cycle problems e.g. What day will it be in 36 days time? Combination problems - how many different ways

Grade 4

Decimal numbers - learn from fractions 1/100 1/10. Read write and place value Place value up to any number Distributive and commutative laws Fractions - adding and subtracting with same denominator Vertical form with decimals -/+ Circles - facts about them and naming parts Angles measuring and all facts e.g. Triangles, straight line, round a point etc Parallel and perpendicular lines Line graphs Solving 3 step problems Coordinates and position (only in 1 quadrant)

Grade 5

Multiplication & division with decimals (vertical forms) Equations and algebra Area and perimeter of all basic 2d shapes and of compound shapes 3d shapes naming and facts of all and extend to volume Averages from bar charts and line graphs Probability Equations to solve problems Negative numbers

See appendix 1 for greater detail

Appendix

Description of the Curriculum as provided by Cao Guangbiao Primary School

Now, I would like to brief you on the six textbooks used for grade three, four and five.

I will proceed in six aspects. 1. Expanding knowledge of numbers; 2. Cultivating calculation ability; 3. Graphs and geometry; 4. Introducing the concept of statistics; 5. Ability in solving problems;6. Further questions

We are using new textbooks compiled under the guidelines of the second-phase curriculum reform of Shanghai. The textbooks are designed in a spiral pattern and with increasing levels of difficulty. Now I’ll give further details by combining those six aspects for the three grades.

1. Getting to know numbersAt grade one to three, students mainly study natural numbers. In the second semester of grade three they learn simple fractions. During the second semester of grade four they start to pick up simple decimals (students get to know decimals by understanding the correlation between fractions and decimals). The second semester of grade five involves study of positive and negative numbers. After introducing the concept of a certain category of numbers, we instruct students to learn the digital sequence table by heart, understand composition of numbers, and read and write them skillfully.

2. Cultivating calculation ability Chinese kids show better calculation ability. They do all the calculations by themselves without any aid in both assignments and tests. Math teachers pay great attention to cultivating students’ ability in getting the

correct calculation results throughout the primary schooling. Calculation questions account for 50% of the total 100 scores in a test. That’s why the calculation sections of textbooks are designed with a more distinct spiral pattern.

At grade one and two students mainly do calculations orally. Vertical formulae are used for answering addition and subtraction questions while multiplication and division questions are handled according to multiplication table. At grade three, students begin to use vertical formulae to answer the multiplication and division questions.

At the first semester of grade three, multiplication questions mainly involve single-digit numbers while division questions only involve single-digit dividers.

At the second semester of grade three, students learn how to do multiplications and divisions involving two-digit numbers. At the first semester of grade four, students study calculation of whole numbers (integers) involving all the four arithmetic operations and some operation laws such as “a+b=b+a”, “ab=ba”, “a+(b+c)=(a+b)+c”, “a(bc)=(ab)c” and “a(b+c)=ab+bcsdf”. Students of this phase also learn to answer addition and subtraction questions concerning fractions with the same denominator. At the second semester of grade four, students begin to learn methods of answering addition and subtraction questions involving decimals.

During the first semester of grade five, we introduce methods for doing multiplications and divisions concerning decimals. We also teach the concept of equation and students can learn how to solve some simple equations.

3. Cultivating geometrical ability At the first semester of grade three, we introduce the concepts of length measurements. Students are supposed to get to know triangle and study how to calculate the area of rectangle and square.

At the second semester of grade three, we explain the concept of perimeter to the students. They are supposed to learn how to calculate the perimeter of rectangle and square.

At the first semester of grade four, students get a general idea about circle, line segment, half-line (ray), and straight line. They learn about angle and angle measurements. They are supposed to know how to calculate the value of an angle.

At the second semester of grade four, students are supposed to understand the positional relations between two straight lines within one plane, including perpendicular relation and parallel relation.

At the first semester of grade five, students learn how to identify parallelogram and trapezoid and know how to calculate the area of parallelogram, triangle and trapezoid. (That is the end of the lessons on planar graphs at primary school level.)

At the second semester of grade five, students learn how to identify solid shapes, including rectangular parallelepiped and cube, and know how to calculate their volume and surface area.

4. Introducing the concept of statistics Grade three: Students can recognize bar charts and draw up simple bar charts;

Grade four: Students get to know broken line graphs and can draw up simple broken line graphs;

Grade five: Students learn how to calculate and apply average numbers and know about the concept of probabilities.

5. Ability in solving problems (also called “application questions” in China)Grade three: Students learn how to deal with application questions aiming at analysis of basic numerical relationships, such as the relationship among unit price, quantity and total price or that among speed, time and distance. Two-step calculation is also involved in such applications.

Grade four: Students start a further study on application questions concerning basic numerical relationships such as the relationship among working efficiency, working hours and output. Three-step calculation is involved.

Grade five: Students learn how to settle an application issue with equation.

6. Further questions Further questions, which are not explained in the textbooks, include some math problems handed down from ancient China such as the “chicken and rabbit in the same cage” question, tree planting question, collocation questions and encoding questions (e.g. implication of each digit of ID number). Ways to identify a location and cycle-related questions are also involved.

Assignment designThe textbook of each grade is accompanied by an exercise book. Each day of school involves a whole page of exercise questions. Of course, an exercise book alone is not enough. The teachers also prepare additional exercises. Besides, we pay particular attention to questions students find difficult to manage in designing the exercise. Sometimes, we also give special assignments to students to help them better understand what they have learned in class.

Appendix 2Professional Development through Diligence and

PragmatismMath Teaching & Research Section of Cao Guangbiao Primary

SchoolWhenever people speak of Cao Guangbiao Primary School, they laud its math

education. Then, what has made math a feature discipline of Cao Guangbiao Primary School within a short period of time? While we truly hope to share the best part of our experience with everyone, we find that the path we’ve taken in building up the discipline is one that features neither the expected “height” nor the expected “depth”. What we have is but a team which is devoted to one shared vision and taking coordinated steps.

I. Profile of the Teaching& Research SectionThe Math Teaching & Research Section of Cao Guangbiao Primary School is a

well-organized team, characterized by reasonable age structure and great teamwork spirit. Specifically, the Section now is composed of 12 teachers in total, 4 under 35 years of age and 8 between 35 and 45. The average age is 36. All the 12 teachers have an undergraduate educational background. Two of them have senior professional title of middle school. Besides, the Section also includes 1 member of the District Central Group, 1 District-level “Leading Teacher” and 3 school-level “Leading Teachers”.

In response to the drive of curriculum reform, we set our goals as below for further development. They serve to embody our faith that “professional development may be achieved through diligence and pragmatism”.

To focus on improving teachers’ overall quality and cultivating “leading” teachers so as to build ourselves into a learned and capable team with high ethical standards;

To build ourselves into a teaching & research section characterized by prudence, flexibility and creativity so as to further improve the performance of teachers and promote the development of students.

II. Experience & Achievements (I) Improve curriculum design and promote disciplinary development Decide on the basic curricula and reasonably integrate textbooks Develop extracurricular programs and individualize teaching according to

children’s aptitudeFun Starter’s Math Class - one period per week, open to all students;

Fun Mover’s Math Class - open every Friday to about 25 students per grade. It is aimed to enrich students’ math knowledge, improve their ability in solving math problems, and broaden their horizons by organizing workshops on special topics.

Fun Flyer’s Math Class – designed for students capable of performing extra study tasks. It is aimed to tap math “talents” and provide service and help for students’ individualized development in math by offering training on contest questions and organizing exploratory study activities.

(II) Strengthen team building and promote disciplinary development (1) Requiring teachers to grow according to their own plan of career development, (2) Requiring backbone teachers to play a guider’s role, and

Over the past years, by playing a guilder’s role with a one-master-one-disciple model, our senior “leading” teachers have helped us cultivate quite a few young and mid-aged new “leading” teachers. They are the cornerstone of the Math Section and collateral for further development of the Math Section.

(3) Requiring teachers to help each otherTeachers of different backgrounds show different personalities. They can join

hands with each other, help each other and learn from each other. That proves to be the most cost-effective, most efficient and most pragmatic way of self-improvement.

(III) Broaden teaching& research functions and promote disciplinary development (1) Determine research tasks and widen research scope

In order to improve teaching and research efficiency, we have established three task groups. Textbook Group compares new textbooks with older ones so as to remove the obsolete contents and retain the useful parts. Class Group studies the method to effectively process and control resources generated during classes. Activity Development Group plans students’ extra curriculum activities and studies how to better use math education to serve the overall quality of students. Apart from routine meetings on teaching and research, teachers also have exchanges and discussions by themselves “anywhere, anytime and spontaneously”. That’s a great way to share and cooperate among teachers. We call them “informal” teaching and research activities. Such “informal” activities, once becoming a common practice, symbolizes that teachers begin to take initiative in performing their teaching and research tasks. That’s something we are pleased to see.

(2) Enrich the contents and improve the efficiency of teaching& research Strengthen regular teaching and researchLecture preparing: We study how to better prepare class lectures through an “experience sharing – companion help – self-improvement – exchange and check” model.

Experience sharing: At the beginning of each new semester, teachers who have just finished teaching a subject last semester are required to share their experience in teaching the subject, including their views on textbooks, with teachers who take over the subject in the current one and put forward advice on teaching.

Companion help: Teachers teaching the same subject prepare their lectures together, including coordinating teaching progress, studying textbooks, setting teaching goals, identifying the focus and challenge for teaching and designing teaching procedures.

Self-improvement: Teachers work out individualized teaching plans according to the characteristics of students.

Exchange and check: Teachers reflect their class performance after class and exchange minds with each other promptly in all possible ways. Each semester, two lecture notes check sessions are conducted to allow teachers to share experience and overcome shortcomings.

Assessment and evaluation: We try to improve the efficiency of student assessment by “ensuring the quality of exam questions and analyzing students’ performance in exams”. We also try to reduce students’ burden and improve teaching efficiency.

Studying exam questions: We always set clear goals in preparing unit quiz questions (by Teaching & Research Section) and quality survey questionnaires (by Dean’s Office at mid-term and end of term) so as to ensure that the questions are more reasonable.

Analyzing students’ performance: After each unit quiz, teaching & research sections will put together students’ scores of the entire grade and analyze their performance on some typical questions so as to form the basis for identifying the teaching focus in later class activities. At midterm and end of term, the teaching & research sections and Dean’s office prepare quality analysis report based on the performance of each grade and conduct disciplinary quality analysis meetings. The results of the meetings will serve as guidance for teachers in their later teaching activities.

Build a characteristic teaching & research sectionWith a view to helping solve teaching and research problems, we organize all

kinds of activities:

Ontology study: By studying math-related ideas and methodologies and exchanging ideas on problem solving, teachers learn more about the nature of math. That helps teachers better understand the textbooks and handle problems related to them.

Exchange on special topics: We have adopted the model of “identifying the topic – conducting discussion – self-reflection and exchange” to handle difficulties and urgent problems that teachers have come across in teaching activities. Specifically, we regard each of such difficulties and problems as a special topic and organize all teachers to provide information and data and give opinions on it; and teachers also actively explore into the topic through class practice. Such a way of solving problems helps up get more concentrated on specific problems.

Scientific research: Adhering to the principles of “training, practice, research and improvement side by side”, our Section is making great efforts to carry out innovation research concerning education and teaching.

(3) Adopt more approaches to exchange, improve teaching and research efficiency

Online exchange: posting topics – posting replies – research & discussion – ◆achieving agreement

School-wide discussion: learning from demo class – exchange and self-reflection ◆– practice in class

Presentation and report: experience introduction – case study – Q&A and ◆discussion

Appendix 3Extract fromOutline of China’s National Plan for Medium and Long-term Education Reform and Development (2010-2020)

Heavy schoolwork is harmful to the mental and physical well-being of youngstersand children. Reducing the schoolwork burdens on students is the society’sshared responsibility. Governments, schools, families and communities mustjointly address the problem by addressing both its symptoms and root causes.Schoolwork burden reduction shall be implemented at primary and middleschools. We shall enable the students to learn in lively ways and grow up happilyand healthily. Primary school students should be the first to have their heavyburdens cut down.

Governments at all levels shall regard reducing heavy schoolwork burdens as amajor task for education work, as well as a goal that calls for overall planning andall-dimensional implementation. Textbook contents shall be readjusted and theirdegree of difficulty redesigned on a scientific footing. The ways and means to testand evaluate student performance and to appraise school operation shall bereformed. School-running operations shall be standardized, and a frameworkshould be instituted to monitor students’ schoolwork burdens and inform thepublic of it. Schools can neither be ranked according to rate of students’admission to higher schools, nor the enrollment indexes. Preparatoryorganizations and tutorial markets should be regulated. We shall also strengthenthe construction and management of venues for extracurricular activities, toenrich the extracurricular activities for students.

Schools should reduce students’ schoolwork burdens so as to give studentsenough time to learn about the society, think deeply, practice more, and doexercises and amuse themselves. It is imperative to improve teachers’

professional quality, their teaching methods and efficiency, while cutting down onhomework and classroom examinations. Students’ interest in studies andhobbies should be nurtured. The curricula and syllabi should be followed strictly,and on no account should teaching hours and lessons’ difficulty levels beincreased. The scores of graded examinations and competitions of various kindsshall not be used to in school enrollment and advances to higher grades duringcompulsory education.