**Program Design**

Most educationists promote the ‘currently popular model of good school’, which sees **effective school as a team of capable/ dedicated teachers, headed by a good principal, who are provided good incentives as motivation and reasonable capital infrastructure to operate in.** This model has shown good results in the setting of elite well managed and well resourced schools, mostly in private sector in India, but also in government/ public sectors in OECD and East Asian countries. This model has historical and exemplary sanctity, and most policy makers-influencers that come from top 1-2% socio-economic category of Indian population, have personally experienced efficacy of this model, having studied in schools based on this model.

Official policy in India has tried to operationalize this model in Govt. schools by (i) now allocating proportionally as much funds to elementary schools as in OECD countries, as % of GDP, which is higher than of East Asian countries, (ii) raising financial incentives to school teachers to a level highest in the world in terms of per capita GDP, (iii) specifying teacher education/qualification norms comparable to OECD/ East Asian countries, and (iv) providing time-resources for mid-career teacher training-support, which is most extensive in the world, under DPEP/SSA/ RTE policy regime, post 1995. Gyan Shala recognized that this model will be able to serve 5% of children in India, but will fail to meet educational needs of the rest 95% children, belonging to low and medium income, local language speaking families. For a complex set of reasons, resulting in ineffectual teams of teachers-principal, this traditional model has, in fact, not worked, in general, in India.

Gyan Shala, therefore, is an attempt to evolve-implement-demonstrate a __new model__ that would ensure a quality of education for 95% of Indian children, which currently only top 1-2% category, is availing. Core features of this model are:

- Placing
__relatively greater emphasis__on harnessing nature given capacity of a child to learn for improvements in learning outcomes, than on improving teacher effectiveness. (Both elements, though, are always present in every school situation). Other than designing class processes towards such prioritization, this means spending proportionately larger share of funds/ cost on ‘learning material for children’ than on teacher incentive-education, compared to the traditional model. - Recognizing that ‘in class time and work by children’ is the most important instrumentality for improving learning, and making best design-efforts to improve efficiency/ efficacy of in-class work.
- Treating ‘short-term training and immediate on the job training-support to teachers’ as more effective instrument to raise teaching effectiveness than the long-term teacher-education.
- Demystifying ‘great teacher capability’, by re-engineering it as the joint efforts of a six-tier team of easily available talent, for providing academic support to children.
- Ensuring accountability by accepting linking of resource support to the school with results of ‘independent assessment of learning outcomes’.
- Designing-managing large scale schooling by relying on management design-lessons from large effective corporate entities with proven record of success in comparable contexts.
- Adopting State-national curriculum goals, but supplementing these with few others that are recognized as important in emerging internationally accepted analysis/ views of education. These include fostering ‘critical thinking ability’, and ‘creative problem solving’.
- Foster ‘learning culture’ not only in the class-rooms but throughout the ‘school system’.

**Local Language Curriculum & Pedagogy**

Gyan Shala recognizes that when a child comes to it at an age of 5+ years, she already has fairly developed understanding of her first language, though only in oral, not the written, form. We accept that the first priority of a language module in a school system is to move from oral to written mode of language, and, therefore, its primary purpose is to help child ‘learn to read’. Gyan Shala, however, also recognize that the language is a primarily an instrument for communicating a meaning. Therefore, ‘reading to learn’ is as, or even more, important as ‘learning to read’. Developing the language module in a manner that optimally combines the two tasks, i.e. learning to read, and reading to learn, in an optimal manner, is recognized as the primary and an ongoing design challenge for local language curriculum.

Gyan Shala will aim that a child learns to recognize all alphabets and learns to read/ write individual words with meaning in a short age appropriate text, by the end of first year. In the second year, the focus will shift to understanding the meaning of text and writing a text to communicate some meaning. Even the first year language module is so handled that child starts internalizing the inherent concept that a text is linked to some meaning. By the end of the third year, Gyan Shala will aim that a child can read a new simple text with comprehension, have substantial sight memory of words needed for effective reading, and also write a simple text, such as a letter, story, narrative and a report, using words common in her/his context. In the third year, local language newspaper is used as the basic text for a part of the year in the classroom, so children become comfortable in reading with comprehension an unfamiliar text of relevance to them. Throughout, emphasis is placed on using such a text that is appropriate to the context of children, and interesting to them. The text of different variety is used, including short narration, story, poem and rhyme.

**Components of Language class work**

Gyan Shala classes have four types of exercises in local language module.

- Story telling/ listening (10 minutes/ day- for the whole class) that focuses on linking meaning to the text and its communication.
- Subject teaching/ learning (15 minutes/ day- for the whole class). In the first year, this focuses on explaining the shape/ sound of alphabets, the pronunciation and writing of these, and using the words in different context. From the second year, this is used for learning to decode/ interpret the meaning of a text and to answer questions based on the text.
- Work sheet (15 minutes- individually work by each child). These provide exercises to the children to practice the lesson learned in the subject teaching and story listening modules.
- Group tasks/ activities (10-12 minutes- for each group of 6-8 children), this reinforces the teaching session and worksheet exercises.

**1. Story telling/listening module**

Gyan Shala team has composed text stories based upon a set of chosen picture-books, eight or nine for grade I and II each. Typically, each picture frame carries either one or two sentences text with the total story having 20-30 sentences only, for grade I story. In grade II, a picture frame may have 2-3 sentences and the whole story up to 40. In both the grades, these sentences are kept only 3-6 words long, at most, and many of the sentences are often a single clause. So far, Gyan Shala uses books published by the National and Children Book Trusts (NBT & CBT) but superimposes its own text to prepare its story books in children’s local language.

One story is used for 2-3 weeks, and each day of storytelling covers 1 or 2 picture frames. While telling the story, the teacher uses the picture to describe the situation, helps the children to internalize the meaning of the situation depicted in the picture, focuses attention on a chunk of meaning/ expression, and then links this chunk to the 1-2 sentences/ clauses written on the pages. The purpose is that the children should be able to understand the meaning of whatever is written, in its total context. The relationship of the sentences/ chunks of meaning on a picture frame are linked to those on the preceding and succeeding pages and thus the total story is told, as a series of chunks of meaning embedded in the sequences of picture frames. Children’s attention is drawn to matching sound with the shapes of words, but the focus is not on explaining the meaning of word, but on linking the whole clause/ sentence to a chunk of meaning/ expression.

In the 3^{rd} grade, Gyan Shala uses standard textbook prescribed by the government for its primary system. The story telling module in this grade is used to read/ understand the text/ lesson given in these books. Typically, a story/ essay/ poem is divided in para/ couplets. On any day, a given para/ couplet is covered in the class. The teacher is trained to divide the para/ couplet in not only sentences but also small clauses. Children, by then, have learned to identify the shape of letters/words and read the words. They are now trained to read a sentence as composed of clauses, with each clause itself containing an independent chunk of meaning. More than one clause read together completes the meaning of the sentence. Many sentences together complete the para/ couplet and many of these together then complete the essay, story or poem. For around 40 per cent of third grade, a local language newspaper is used as the core text for language module.

**2. Subject Teaching Module**

In the grades I, the subject teaching session is held every alternate day. Typically, one word from the story being covered is picked up and children are taught its shape, sound and meaning. The words are so chosen that over the first year, all the letters in the alphabet, both consonants and vowels, get covered in the chosen words, and these describe not only a range of objects but also common feelings/ thoughts/intangibles. While explaining its meaning, its application in many situations is illustrated and its difference from other similar or opposite meanings/ words is pointed out, which becomes the foundation of synonyms and antonyms. Special attention is paid to the stroke pattern for writing the word correctly/ neatly.

On completion of a story, one week is devoted to teach the reading, identifying, writing, and using a set of basic alphabets that have been covered in the words taught during the story module. The general nature of alphabet is illustrated by showing its use in not only the words covered in the story but in many other familiar words. All basic alphabets get covered in the grade I itself.

In grade II, subject teaching session is held five days a week. The explanation of words meaning and application continues on the above pattern, but in addition, the application of antonyms and synonyms is illustrated with greater depth. An attempt is made that children start putting together the meaning of different sentences to make sense of a whole para, to understand the topic, issue and context. This, in turn, should enable the children to answers simple questions that can be framed to elicit their understanding of the contents of the text.

Children are taught to use punctuation marks, and writing of words with proper spacing. They are taught to write up to five sentences on a topic, by illustrating that any topic/ issue has many aspects, each of which can become the subject of one or two sentences. The proper structure of a sentence is explained by giving examples of correct sequencing/ ordering of different words, including the object, subject, verb, adverb, proposition etc. The changes in sentence structure with past or present tense, with singular or plural subjects/ objects, and gender changes is explained. The order of alphabets is taught so children could arrange the words/ letters as per alphabetical order and search for the word meaning in a dictionary. The concept of joint word is explained which is a distinctive feature of Indian languages.

In grade III, the subject teaching is held all six days a week. The understanding of all aspects covered in grade II is deepened. Children are encouraged to give longer and detailed answers to the questions based on the text, and explain the cause-effect relations. The common phrases used in the text and their application in other situation are covered. Children are trained to write alternate stories based on a sequence/ set of pictures. They are asked to use given two words together in a sentence, and replace a set of words with single word (traveler for one who travels). Children are given greater practice in using a dictionary, and understand/ use idioms and literary/ colloquial expressions. The writing of essay, letter and application to some public authority is taught, both in terms of format and content formation. Last, children are taught to write a report based on observations and data/ information available in newspapers.

**3. Worksheet Exercises**

Children typically complete one page each day. In every grade, each child gets four volumes of worksheets, each volume containing around 60 worksheets.

In grade I, the first and primary purpose of worksheet is to give children a practice to read and write the whole word and identify it in a cluster, thus building site-vocabulary. In doing writing practice, children start writing on dotted shape and move to free-hand writing. The size of font starts at 24 and reduces gradually to 16. In the beginning, children write just one word, but later they are asked to write a clause of 3-5 words. Regarding the basic letters, the practice entails relating its presence in a word with the place of sound in the pronunciation of the word. They practice identification of alphabets both in written and spoken form. Some exercise of filling in a word in a familiar clause/ sentence is given.

In grade II, the worksheets are mainly to enable children to provide written answer to written questions based on the text covered in the class. Later, they are given a new text on which they should be able to answer simple queries. They are asked to identify the antonyms or synonyms from alternatives available, while later they are asked to recall these from memory. Children write/compose up to five sentences on a topic/ theme covered in the class, and write similar picture-frame description. They are asked to use phrases. Children are asked to arrange words in alphabetical order. Children are asked to modify structure of sentence as per changes in tense, gender, and numbers.

In grade III, children are given questions based on the text that requires a long answer. Different types of material are given to children for this purpose, which could be a marriage invitation, invitation for a competitive event, advertisement or typical story/ poems. Children should be able to fill gaps in an incomplete poem/ text taught in the class. They are asked to write longer and more elaborate stories from a set of picture-frames, essays, letters and applications. They write 6-7 sentences on a topic covered in the text.

**4. Group Activities for Language Practice**

Group activities are meant to repeat and reinforce the exercises covered in the worksheet or taught through subject teaching. Group 6-8 children complete the task assigned by the teacher who provide feedback and help correct the mistake if any.

In grade I, the main group activities include reading/ identifying from a set a word-card that is called by the teacher and then speak up to two sentences by using the word. In another activity, they are to identify and pick up all the words in a clause and compose these in the correct order. In another activity, children are given a topic on which they speak or ask questions, in turn. Children compete in telling the antonyms or synonyms, and take dictation of words covered. Children sometime also compete in locating the word/ clause spoken by the teacher from the given text. Similar competition is held in reading a new word, by using alphabetical pronunciation. Children compete in groups in finding words that starts with or include the given letter. Children provide picture frame description sometime with supportive prompts by the teacher.

In grade II, most of grade I activities are repeated with greater complexity. They also make story based on a picture set. Dictation is given of full sentences along with punctuation marks. An unfamiliar text is given for children to read and answer questions there of.

In grade III, the above activities continue at higher level of complexity. For example, children are required to make a chain story. Dictation is given for full para and reading practice covers the text written by other children, not only the printed version. Reading and comprehension of news-papers headlines is undertaken. Use of dictionary is practiced. Greater emphasis is on reading of various types of text material, with emphasis on the use of punctuation marks.

**Math Curriculum and Pedagogy**

An important goal of math module in elementary stage is to eliminate the fear of math and dealing with numbers that is found in so many children. The module is designed to not only make children skilled in basic arithmetic operations, but also feel comfortable in handling numbers and their application in real life.

The math module attempts to help children use numbers not only to count but also see relationship among numbers as elements of an ordered set. While understanding, for example, that 4 is smaller than 5 by one and larger than 2 by 2, or that it comes in between 3 and 5, the essentials of addition or subtraction are introduced/ internalized. The children are taught to not only perform basic arithmetic operations, but also use alternate counting/ computational technique/ algorithms, and to cross-check the answer. They begin to understand the relationship among different operations, e.g. that the addition and subtraction are opposite; multiplication is repetitive addition; and the division is repetitive subtraction. Special emphasis is placed on understanding the place value, how it is used to represent larger numbers, and how this is operationalized in various standard procedures used in mathematical computations.

The sequencing of lessons, time devoted to each section/ stage, teaching guidelines, sequencing and composition of worksheets are all important elements in achieving above objectives. The worksheets and activities are so designed that besides getting adequate repeat practice, the children learn to substitute the lazy habit of pattern formation with exact computations. Exercises are set out in a way that requires children to examine alternate hypotheses before choosing the correct one, and to find pattern under a jumbled set. Children are enabled to estimate the size of a set of objects, with the number scheme providing exact measure of the estimate. Similarly, children are enabled to convert problems/ questions in daily life into questions involving arithmetic operations.

**Examples of Pedagogical Approach Employed:- **

**1. Counting by using Objects:** The child is to pick up a number card and correct number of counters according to the number spoken by the teacher. The child is also asked to add or reduce one counter from the set and choose corresponding number card.** **

**2. Shop keepers and Buyers:** Children are formed in pairs. One is to act as the shopkeepers and other buyers. Byers give number card to the shop keepers and shopkeepers gives correct number of counters to the buyers.** **

**3. Which number is after and before me:** Speak a number and ask child to show a number card either after/ before number of that number and put correct number of counters or Ask child to pick up number card and put correct counters accordingly to the number spoken by the teacher. Ask them to find either after/ before number of that number and put correct number card.** **

**4. How I can make:** Ask child to put correct number of counters accordingly to the number spoken by the teacher. Teacher speaks a number that is + or – 3 of that number .Ask child to pick up that number card and ask them to make this number using correct number of counters** **

**5. Sort and Count different object and link with Number Card:** Ask child to sort and count the different object kept on a box and match it with number card.** **

**6. Sequencing: **Ask children to speak numerals in different sequences ex. 1,2……,10 or 1,3,5…9 or 2,4,6……10 . The child who will make mistake will be out.** **

**7. Comparing any two number using objects: ** Ask child to pick up two number cards and put correct counters accordingly to the numbers spoken by the teacher. Ask them to find out smaller and larger sets through one to one correspondence. Ask to find out how many less in smaller sets than larger sets and the same way how many more in larger sets than a smaller set.** **

**8. Which number is smaller / larger number than me:** Ask child to pick up number card according to the number spoken by the teacher. Ask them to find smaller/ larger number to that number.** **

**9. Comparing greatest and smallest number using objects:** Ask child to pick up four number cards and put correct counters accordingly to the numbers spoken by the teacher. Ask them to find out greatest and least number through one to one correspondence.** **

**10. Arrange numbers in ascending and descending Order:** Ask child to pick up four number cards and put correct counters accordingly to the numbers spoken by the teacher. Ask them to arrange numbers in ascending or descending order through one to one correspondence.** **

**11. Understand Zero using Counters:** Ask child to pick up number card and put correct counters accordingly to the number spoken by the teacher. Ask them to reduce counters accordingly to the number spoken by the teacher. This will be repeated till no counters will left with children and ask them to show correct number card.** **

**12. Understand Zero using Counters:** Ask child to pick up number card and put correct counters accordingly to the number spoken by the teacher. Ask them to reduce the same number of counters all together and ask them to show correct number card.** **

**13. Counting using fingers/ finger Cuts:** Ask child to pick up number card and show correct number of fingers/ finger cuts according to the number spoken by the teacher.

**Understand place value:**** **

**14. Grouping in to units and Tens:** Ask child to pick up number card and put correct number of tens bundles and loose counters accordingly to the number spoken by the teacher. Add or reduce one counter from it and put correct number** **

**15. Dice game:**

**A. (Using single dice):** Ask child to throw the die and collect from the box a number of counters corresponding to the numeral thrown. As soon as a child has collected 10 counters he can exchange them for a bundle of ten. The winner is the first child to collect maximum bundles.

**B. (Using tens and unit dice):** Ask child to throw two die and collect from the box a bundles of tens and counters corresponding to the numeral thrown.** **

**16. Secret number using arrays:** Teacher will decide a number. Child locate the secret number first by its tens digit, then by its units digit referring to their arrays while making their guesses.** **

**Addition and Subtraction:**

**17. Add or Subtract using counters:** Ask child to pick up number card and put correct counters accordingly to the number spoken by the teacher. Ask child to pick up another number card and add/ reduce correct counters accordingly to the second number spoken by the teacher. Show number sentence using number card and symbol card.** **

**18. Add or Subtract using number line:** Ask child to pick up number card and go ahead on number line accordingly to the number spoken by the teacher. Ask child to pick up another number card spoken by the teacher. and go forward or backward on the number line depending on operation involved. Show number sentence using number card and symbol card.** **

**19. Add or Subtract using fingers/ finger cuts:** Ask child to pick up number card and count fingers / finger cuts accordingly to the number spoken by the teacher. Ask child to pick up another number card and add/ reduce finger/ finger cuts accordingly to the second number spoken by the teacher. Show number sentence using number card and symbol card.** **

**20. Dice game:** Ask child to make a grid in book with number up to 10. Each child throws the die twice and can either add or subtract these two numbers using counters and then they have to cut the resulting number in their grid .The first child to cut maximum grid is the winner.** **

**21. Guess how many: **Teacher puts counters and children will count. She ask them to close their eyes and removes some counters and hides them in her closed hand. Then they open their eyes and look at the remainder and find how many counters the teacher is hiding in her hand .Then again count the counters together to verify. Write number sentence on black board .This will continue for all possible pairing of a given number.** **

**22. Addition and Subtraction in daily life:** Teacher puts counters and child will count It. She ask them to close their eyes and add/ removes some counters. Then they open their eyes and look at the counters and decides which operation involved. Ask them to show number sentence using number card and symbol card. Ask them to make a word problem using number sentence.

**Multiplication**

**23. Equal grouping:** Distribute the counters equally and found out how many counters in a single group and how many groups made.

**24 Multiplication as Repeated Addition: **

Key Concepts linked to Math Skills acquisition up to grade 2.

- Memorize number sounds up to 100.
- Memorize sequence, both forward and backward) of 100 numbers.
- Writing of 100 number names.
- Counting,
- one-to one matching
- non-repetition
- non-exclusion
- bounding the set

- Properties of numbers:
- Which is more or less in a pair
- How much more/ less
- Highest and smallest in a set of n number (compare n! relationships)

- Representation of numbers in decadal order
- Place value
- Use of only ten symbols to write all possible numbers

- Addition / subtraction of two numbers
- Count on/ down
- Finger based procedures

- Addition of a number column.
- Memorize the results of any two single digit additions. (45 results)
- Memorize the results of two single digit subtraction (45 results?)
- There is a lot of remembering in early math.
- Some exercises on geometric shapes recognition and differentiation
- Some exercises on what is common in patterns

**Math curriculum in middle-school Stage:**

An important feature of Gyan Shala math curriculum is its pace, which has been kept different from CBSE curriculum, to better suit Gyan shala children, so they attain terminal competencies of high school on par with excellent CBSE schools, in spite of their unique limitations and handicaps. This is illustrated in the following indicated pace of coverage.

CBSE Grade V (To be fully almost completed by 3^{rd} or 4^{th }grades completion in GS)

- Story of normal life and math concepts in that.(Gr.2,3,4)
- Shapes and Angles: In real life, (3/4)
- Finding squares in a shape (Foundation of area) (3/4)
- Parts and wholes (4)
- Similarities and patterns (2/3/4)
- Multiples and factors (4/5)
- Tracing patterns (3/4)
- Mapping your way (4)
- Boxes and stretches (4)
- Tenth and hundredths (4/5)
- Area and boundary, triangles, rectangle exercises, using graph paper (4/5)
- Smart Charts, graphs, bar charts, column-rows, table (3/4)
- Way to multiply and divide: Uses in life (3/4/5)
- How big/ heavy; volume/ density, estimation (3/4)

CBSE Grade VI (All to be completed in GS before the 5^{th} grade)

- Knowing our numbers: Write large nos., estimate – nearest hundred/ rounding off, Use brackets, roman (4/5)
- Whole nos: Operations with and patterns in whole nos., (4/5)
- Play with numbers: Factors, divisibility by 2,5,10, (5)
- Basic geometrical ideas, angles, shapes, (5/6)
- Understanding basic shapes: Polygons (4/5)
- Integers (Number line, negative nos. operations: Add/ subtract) (5/6)
- Fractions Graphic expression, Addition-subtraction rule, LCM, MCP, (4/5)
- Decimals (5)
- Data Handling: Table, bar chart, (3/4/5)
- Measurements: Perimeter, standard unit (4/5),
- Algebra: Mathematical pattern (4/5)
- Ratio and proportion: Interpretation (5/6)
- Symmetry (5)
- Practical geometry: Draw/ measure line, angles, shapes, using compass, protector,(4/5)

CBSE Grade VII (To be completed by grades 5/6)

- All operations on Integers, both positive and negative, number-line, commutative (a+b = b+a)/ associative {a+(b+c) = (a+b)+c} properties of addition & multiplications. (5/6)
- Fractions and decimals: All operations on fractions by integers and fractions. Graphical representation of fractions and operations (4/5/6).
- Data Handling: Tabular, Range, mean, mode, median, bar-chart, intro. To probability (5/6)
- Simple Equations: Formulate and solve simple equation:, 1 variable. (6)
- Lines and Angles: Complementary, Supplementary, Adjacent, opposite, (6) transversal, with parallel or non parallel lines (6)
- Triangles and properties: Equilateral & Isosceles, Right hand, Pythagoras theorem.(6)
- Congruence of Triangles: Identical (6)
- Comparing quantities: %, interest computations, (6)
- Rational Numbers =whole /+integer (Natural +0= Whole+ negatives=integers) (5/6)
- Practical Geometry (5/6)
- Perimeter/ area, (Triangle, Polygon, circle), conversion of unit (6)
- Algebraic expressions, formulation/ interpretation (6/7)
- Exponents and powers (6/7)
- Symmetry, tessellations, (6/7)
- Visualize Solid Shapes, cuboids, cylinder, cube, sphere, pyramid, cone, Volume (6/7)

CBSE Grade VIII (All of this should be over by Grade 7, and some earlier too)

- Rational Numbers: Basic property of numbers and operations, definition?? (No)
- Linear Equations in one variables: Much too simple (grade 5/6)
- Understanding Quadrilaterals: Define Polygon, and use triangle based simple geometry problems (gr. 5-6-7)
- Practical Geometry: Relatively simple triangle shape linked problems (Gr. 6-7).
- Data Handling: Tables, graphs, Pie charts, Introduce chance, (Gr. 5-6-7)
- Square and Square Roots: Simple Arithmetic (7)
- Cube and Cube Roots: Simple Arithmetic (7)
- Comparing quantities: Use of %, Interest computations (7)
- Algebraic expression and Identities: Simple Algebraic manipulation, no formulation/ generalization (6/7)
- Visualizing Solid Shapes: Nomenclature and two dimensional Z-section/ shadow of solid objects (7)
- Menu ration: Area, volume formulae of various shapes/ objects(6/7)
- Exponents and Powers: (7)
- Direct and Inverse Proportion (7)
- Factorization (5/6/7)
- Introduction to Graphs (6/7)
- Playing with numbers (4-7)

Grade 9 (All of this should be over by 8, while some topics of grade 10, particularly geometry would be covered by 8^{th} grade).

- Number systems: Gr. 7
- Polynomials, Gr. 8,
- Coordinate Geometry, Gr. 7/8
- Linear Equations in two variables, Gr. 7/8
- Introduction to Euclid Geometry Gr. 6/7/8
- Lines and Angles Gr. 6
- Triangles Gr. 7
- Quadrilaterals Gr8.
- Areas of Parallelograms and Triangles, Gr. 8.
- Circles, Gr. 7/8
- Constructions, Gr. 7,
- Heron’s formulae, Gr. 8, advanced,
- Surface areas and Volumes, cuboids, cylinders, cone, sphere (9)
- Statistics (8-9)
- Probability: Introduction (7/8)
- Profs. In Math: Gr. 8, focus on geometry (7/8/9)
- Mathematical modeling Gr. 8 to start Programming, flow charting (9)

**Gr. X **(Most of the following should be started/ completed in grade 9, with grade X, focusing on more advanced applications, complex problems, more of trigonometry, coordinate geometry, Quadratic equations, probability, Excel based data-analysis, Matrix (?), Mathematical proofs & Programming).

- Real Numbers, Euclid’s division lema and theorems of arithmetic
- Polynomial, geometric meaning, division of polynomials
- Pair of linear Equation for 2 variables, graphical method of solution
- Quadratic equations
- Arithmetic progression (Gr. 8)
- Triangles- similar, Pythogoras theorem (Gr. 8)
- Coordinate Geometry (9,10)
- Introduction to Trigonometry (9/10)
- Some applications of Trigonometry (10)
- Circles-Tangent to circle (9/10)
- Constructions (9)
- Areas related to circle, segment, sector (9)
- Surface, area and volume of combination of solids (9/10)
- Statistics, Mean, mode, median, cumulative frequency distribution (8
^{th}) - Probability (9/10)
- Proof in Math (7-10)
- Mathematic modeling (7-10)

**Project Work – Creative Expression Curriculum module:-**

This module covers the social/environmental studies component of national/state curriculum for the relevant grades-classes, but in addition, this is meant to serve two purposes. First, the design and pedagogy of this module is meant to provide opportunities to children to learn by discovery method, to experience the ‘process part of learning’, besides acquiring the ‘product-knowledge’ per se. Second, this module is designed to give opportunities to children to practice, sharpen and develop multiple human skills, asides from cognitive skills that tend to be the focus of traditionally transected curriculum.

Project work component at Gyanshala is based on the understanding that child should not be treated as merely a storehouse of data and information fed by the books or teacher. Instead, a child should be enabled to acquire the knowledge by his/her own efforts. Such tasks are given to the child where s/he has to go through the process where s/he has to identify the source of information, collect it, record it systematically, analyze it, conclude or establish relation and report it. Child is also given opportunity to communicate his/her views without unnecessary scrutiny.

The focus of this module is help child to acquire functional skills for

- Expression of his/her thoughts in oral, pictorial and written form without hesitation.
- Raise questions
- Seek the required information
- Observe minutely/systematically
- Collect data and organize it in a systematic form
- Analyze/investigate the data to conclude or establish linkages
- Relate school learning with life experiences

**Learning Attainment Goals**

**First Year :- **

(Oral, pictorial and written (?) expression of simple thoughts and life observations)

Child learns to draw simple shapes and color within boundary

- ? Child learns to draw the object-shapes on the basis of observation
- ? Child makes a composite drawing to depict a theme
- ? Depicts a short 3-4 sentence story in pictorial form where the story is
- scribed by the teacher and copied by the child
- ? Child is able to respond to open-ended questions about his life experiences.
- ? Child starts to understand different facets of a given situation (lateral thinking)
- ? Child learns the technique of detailed observation

**Second Year :- **

- Learns to systematically seek and collect information from various sources on a given task /topic
**?**Learns to observe minutely & note down wherever required.**?**Learns to interpret data supplied in the tabular format.**?**Isolates the required information from the very large tabulated data**?**Interprets a line sketch of an area / community.**?**Learn to decipher different patterns and sequences & thus develops logic. (The topic coverage corresponds to national/state curriculum framework)

**Third Year :- **

**?**More of 2^{nd}Year exercises**?**Learns to draw up a plan / project / experiment to know /analyze the scientific / social facts**?**Learns to supply data in the tabular form**?**Learns to draw up a line sketch of his / her own community / area**?**Understand scientific facts and relationships covered in the course**?**Relate some of scientific theory/ facts to life observations. (The topic coverage corresponds to national/state curriculum framework).

**Science Curriculum for Middle School (Grade 4-8) :- **

- The middle school curriculum (grades 4-7) would target to achieve the terminal competencies outlined in national/ global curriculum framework for grade 7, although it would be interpreted in the light of what a child should learn, to be ready for doing well in high school (grade 10) examination with another three years of schooling input. Annex I- summarizes this in the light of Australian/ Singapore science curriculum for middle school stage. The high school science curriculum would have more advanced conceptual, analytical-numerical and experimental science topics. The specific curriculum for grades 4-7 will broadly follow but not exactly cover the issues/topics listed in SCERT or NCERT books for the concerned grade. Instead year-wise adaptation would be made to suit the needs of children/ teachers, while conforming to the terminal goal.
- Gyan Shala agrees with the constructivist paradigm of learning/ pedagogy but does not take the position that the only way for a child to construct knowledge is through self-interpretation of experiments controlled or conducted by her/him. Instead, one effective way is through adult support whereby the explanation of concepts and theories/ relationships is used to interpret life experiences, and to examine the validity of the concept/ theory in answering questions that comes to a child’s mind. Gyan Shala also considers Enquiry-evidence based mode of acquisition of knowledge as a critical skill to be nurtured by Science curriculum. At the same time, it considers expository/ deductive learning as the central mode foe the bulk of knowledge acquisition. While not rejecting the utility and validity of controlled/ designed activity/ project by the child in laboratory environment as an aid to learning, Gyan Shala believes that this can be inefficient and even highly erratic in the absence of high quality laboratory and highly skilled adult guidance, which are often not available in the context of mass education. Gyan Shala, therefore, would emphasize the application and interpretation of concepts by the child and teacher in the light of normal life observations.
- We have reviewed the curriculum and learning material in science streams of Singapore, South Australia, Homi Bhabha Centre for Science Education and new NCERT books. We found that all these focus on explaining phenomenon encountered by a child in his/her normal life and environment. This helps root the science curriculum in child’s life experiences and trains the child in scientific processes of careful observation and analytical explanation. We feel that along with this approach of treating science at the primary level, it is useful to introduce some scientific terms while focusing on description/classification, thus starting elements of basic science concepts. This could help in gradually building a structure of scientific hypothesis/ explanation in child’s mind. We remain sensitive to the danger of rote memorizing of the concept names/ definitions, and therefore, this exercise is carefully calibrated.
- Gyan Shala pedagogy places emphasis on introducing/ clarifying basic concepts, through illustration and examples, and by helping children examine both the examples and contra-examples. Clarifying the basic concepts with ever deeper explanation would continue throughout the middle school years, the child-task would be designed to help her accomplish this.
- In explaining the theories, Gyan Shala will take a gradual approach by first clarifying the directionality of relationship among the concepts, and only much later expounding the theoretical proposition.
- Typically, a class session would have three distinct modules to be followed by individual work to be done by the child outside the class. The first module would be devoted to the introduction/ explanation by the teacher. The second module would require the children to try answering the questions framed by themselves or supplied by the teachers, which would require consultations or discussions with fellow children in the class. The last module would constitute the summary exposition by the teacher, and handing out of individual task to be completed by the child that would require him/ her to refer to text books or make/ interpret observations regarding the specific features of her world experience.
- Asides from the typical science module, Gyan Shala curriculum would have a ‘project module that would enable the children to undertake scientific processes of observation and analysis, and link the science with their environment. This would emphasize: Observes, Chooses, describes, classifies discusses, finds, makes models, creates, records, data-analysis, sort, makes hypothesis, identifies differences/ similarities, compares, measures, observes, experiments, explains, identifies ways of …, investigates, demonstrates/ shows, communicates, constructs, predicts, orders, measures by using apparatus, communicates, generates, evaluates.