Achievement Test Report (ATR)

 ATR (Achievement Test Report)

 

Definition

 

1.     Any test that measures the attainments and accomplishments of an individual after a period of training or learning”-N M Downie

2.     The type of ability test that describes what a person has learned to do’–Throndike and Hagen

3.     “A systematic procedure for determining the amount a student has learned through instructions”–Groulund

 

Teacher teach and help learners to learn. The learning that takes place is assessed or evaluated for the benefit of learners as well as for teachers to evaluate his/her own work. At the end of a lesson or a group of lessons, the teacher needs to get feedback on what the learner has achieved or to assess his/her own achievement as a teacher.

Purpose

1.     To measure whether students possess the pre requisite skills needed to succeed in any unit or whether the students have achieved the objective of the planned instruction

2.     It provides basis for promotion to the next grade

3.     To find out where each student stands in various academic areas.

4.     To monitor students’ learning and to provide ongoing feedback to both students and teachers during the teaching learning process.

5.     To identify the learning difficulties

6.     To assign grades

Steps

Planning of test:- To determine the objective of test and determine the maximum time and maximum marks.

Instructional objectives:- For Science, SST and Math the major objectives are – knowledge, understanding, application and skill while in languages the major objectives are – knowledge, comprehension and expression

Design:- It specifies weightage to different –

 a) instructional objectives

 b) types of questions 

 c) units and sub units of the course content

d) level of difficulty

Weighted of Instructional Objectives

Knowledge – 20%                                             Understanding – 35 – 40 %                       

Application – 20 - 25%                                      Skill – 25%

Weighted of Difficulty level

Easy – 25%                   Average – 55 %                         Difficult – 20

Blue Print :- the policy decisions as reflected in the design of question paper are translation into action through Blue Print. A question setter decides –

a)     How many questions are to be set for different objectives

b)     Under which unit a particular question is to be set

c)     Types of questions

d)     Distribution of question over different objectives

Number in bracket indicates number of questions

Writing of question:- Writing appropriate questions in accordance with the syllabus prescribed in the blue print. You can write the questions in several ways –

a)     Writing all question belonging to one objective each at a time – knowledge/ understanding/ application

b)     Taking up questions according to their form or type -LA , Essay type, VSA, SA

Marking Scheme

It should have three columns. 

1 . Serial no 

2, Detailed solution with steps

3. Bifurcation of Marks

                                        (Sample Marking Scheme only for reference purposes)

Question Wise Analysis

Student have to analyse each question on the basis of its difficulty level.

Question no	Content	Objective	Level of question	Marks
1	Area	Knowledge	Easy	1
10	Volume	Application	Average	2
12	Statistics	Skill	Difficult	4

The purpose of question wise analysist to know the strength and weakness of paper.

Highlight of a good marking scheme:-

a)     It consists of three column – Serial number of question paper, expected answer and marks allotted to each value point under column 2

b)     For LA – i) answer should be complete and cover all major areas as demanded by the questions ii) clearly indicate each expected points or the parts      iii) indicate marks for each expected points

c)     SA – For short answer questions answer should be provided in break up with break up of marks

After the test Prepare detailed result of each student.

Thanks a lot

 

17th National Math Convention at Delhi World Public School Bhatapara (Chhatisgarh) in December 2023

17th National Math Convention 2023

All India Ramanujan Maths Club in association with Delhi World Public School.  is going to organize the 17th National Maths Convention 2023 at Bhatapara (Chattisgarh) on 30-31th December 2023 

Last Date of Registration = 2nd November 2023

A school can register in maximum 3 events. Each event (Quiz/Puzzle/ Model/ Poem and Essay) can be participated by two students. Maximum 8 students and 1 teacher from one school can register. The organizer will provide all the support at the venue (Boarding/Lodging on sharing basis). Participants have to bear the cost of their own ticketing.

Details of events are as follows:- 

    Quiz Competition

Syllabus :-  General Mathematics

                          History of Mathematics

                         Know your Mathematicians

                          Identify Mathematical Shape/ Curve/ Film / Book

Question on the mathematician that you can check on the blog page itself. In the past we have conducted several quiz on Aryabhata and Ramanujan so get an idea of what type of question will be asked in quiz section.

Level 1 :- Written test through Google Form will be conducted in the first phase. 12 students with maximum correct answer will be selected for Final round.

1st level Exam will be held on 30th December. Only registered students can participate in the exam.

Level 2 : PPT Round with selected students

                 Mathematical Model Topics (Junior/Senior)

3 D model making - Topic and instruction will be given at the venue. Students have to bring 3-4 A-4 sheet, pencil, scissor, tape, glue with them.

Besides that, students can bring their own working/non working Mathematical models with them to be showcased their. The top 3 models will win prizes. 

                                                                    Mathematical Poem Topic (Junior/Senior)

                Role of Mathematic

                 Zero

                Number game

                Ramanujan

             Mathematics in daily life

               Why do I love Math?

                                      Word Limit for Poem :- 100 - 200 word

                    Mathematical Essay /Poem Topic (Junior/ Senior)

 a ) Relevance of Ramanujan in today’s world

b)  If I were Aryabhata/ Brahmagupta

c) Mathematics in Kitchen

 d) Importance of Numbers

 e) India the country of Numbers  

 f) Contribution of Indian Mathematicians in Freedom Struggle

g) Use of ICT in Mathematic

h)Math Phobia : How to address it

i) Journey of Pi in 100 years

j)Career in Maths

k) Had the shape of Ice-cream cone be Spherical?

l) Indian women  mathematician at a glance.

m) Why don't we respect our Mathematicians/Scientists at par with Actors/Politicians

n) Why mathematics is considered the most insipid subject?

                                                      Word Limit :- 350- 500

Link for Registration

                              EVENTS FOR TEACHERS

  Extempore: - A teacher has to present his view on the topic given on the spot. The maximum time allocated is 7 minutes for presenter and 3 minutes for judges. Topic of Extempore are ---

Ramanujan

 Indian freedom struggle and contribution of Mathematicians

 Mathematicians you would like to be

Mathematics in War planning

 Cryptography and Maths

Use of Mathematics in preserving monuments

History of Indian Mathematics

Zero

Career in Maths

Women Mathematicians of India 

Mathematicians from MP/Chhatisgarh

An innovative Practice to teach Algebra in your class room.

Mathematical Exam conducted by different organizations across world

 Paper Presentation: - A researcher/ teacher can present his paper on the given topic in virtual mode if selected. A 200-300 words write up (Abstract) need to be sent well before the due date. The top 10 entries will get a chance to present their paper live on the designated day. 

Use of ICT in teaching Maths

Mathematics in Gaming

Maths in NEP, Your take

 Practical use of Imaginary Number 

Anecdotes :  Relevance in teaching Maths

Award :- Every year we select 6  Teachers across India for National Best Teacher Awards. This award is for working teachers in Govt/ Non Govt Sector School only.

 Apart from that we confer 1 Ramanujan and 1 Aryabhata Award and 1 Innovative Teaching Award to teachers working in Govt Sector / NGO/ Coaching/ College/ Universities. 

You can apply for the same by clicking the link given below. 

For Aryabhata Award and Ramanujan Award you must have at least 15 years of teaching experience, minimum 3-10 research paper published

READ ABOUT APPLYING DIFFERENT AWARDS

For any information you can send your messages/whatsapp on 

Dr Chandramauli Joshi - Chairman -- 9825166956

Dr Rajesh Kr Thakur - Secretary - 9868060804

Check our website for more information --- 

News of National Convention

Convergent vs Divergent Thinking - K Bhanumoorthy

 

Thinking Mathematically Part - 3

Convergent vs Divergent Thinking

 “It is clear that the chief end of mathematical study must be to make the students think.”

                 ----- John Wesley Young, American mathematician.

 

Courtesy :- Convergent Vs. Divergent Thinking: Know the Real Difference (pinterest.com)

                                                                   Convergent Thinking: 

Converge means coming closer together/come to/ towards the same point, with reference to psychological aspects mean to follow only on well-established facts. In biological aspects means evolutionary convergence. In mathematical terms, given a series approaching a definite limit in case a more number of terms are added. There are logarithmic series, exponential series geometric series, other kind of series. All human beings use convergent thinking in some process of our daily life.

Courtesy:- https://www.sketchbubble.com/en/presentation-convergent-thinking.html

 An example as x tends to infinity implies 1 / x tends to zero (0).

Y= 1 /x, converges to zero as x increases, the limiting value of y is zero since y can be made as small as one thinks of. The line y = 0 (the x axis is known as asymptote of the function.

Let me give another example. Observe the sequence 128,64, 32, 16, 8,4, 2,1, 0.5,0.25. ---

Every number is half (1/2) of the previous number, the limiting value is zero (0), in other words come closer to zero.

Observe the sequence, 3,6,12,24, 48,96, 192, 384, 768, 1536, ----, every number is double the previous number. In this case the limit tending to infinite.

 Convergent thinking helps an individual or in other terms allowing to connect different elements in a question. It is nothing but choosing a correct/ opt method, to solve the problem. It’s a matter of befitting/ correct strategies.

Divergent thinking: 

Divergent means be different from, varying/ dissimilar/ unlike/ unalike. If we think on psychologically, it is variety of thoughts, assumption more in numbers. Mathematically to say increase indefinitely, moving away from normal path. It’s a process /method used to generate creative ideas, finding out many possible solutions Divergent thinking had been coined by Mr. P Guilford in 1956. 

Christopher Danielson had written a number of books where he mentioned   about divergent thinking. Divergent thinking helps in self-entrepreneurs, and also the people who lead the organizations. Creative thinking helps divergent thinking. Open ended questions, brain storming questions generate divergent thinking. It’s a journey of thinking, how one ‘s mind works. In brief I would say thinking outside the box. In mathematics, activities promote divergent thinking. The ideas that flow through one’s mind are in flexible way and displayed. 

Different age people think /respond in different ways. Divergent questions, have no specific answers, also generate divergent thinking and encourage students to think more. Brain storming sessions in a class shall develop divergent thinking skills. Even this can be tried out, a topic may be given to students, may be asked to submit their ideas, children’s creative play also develop divergent thinking. There is a playful approach in this sort of questions. One who thinks what to count is matter of thinking, rather how does one view.

Courtesy:- Divergent Thinking PowerPoint Template - PPT Slides (sketchbubble.com)

An example: we know 1+1 =2.  Suppose I write 1+1 = 6, how,  

In what way it is true.  1car + 1 scooter = 6 wheels.

1 goat + 1 man = 6 legs. In the same manner we can think of plenty, yes, a sort of divergent thinking.

Another example: given 123456789. = 100. One can use any fundamental operations of arithmetic (+, -.X, ÷) How then, the answer is given below.

1+2+3+4+5+6+7+8x9 = 100.

                  Courtesy:-  Convergent Thinking PowerPoint Template (sketchbubble.com)

IN 1887, Emmit invented folding bike. There are quite number of things, to use the optimum space in aa house/any place, many, like, folding chairs folding dining tables, folding cots, folding cup-boards, folding cycles, plenty of things so to say. All these things emerged out, on account of divergent thinking. Could I say! .

To conclude human beings are blessed with thinking skills, one among the 6 senses. Let us utilize them with positive thinking  in a proper way, utilize them for the benefit of humanity and make this beautiful land of earth, sustain peace, happiness prevail in the whole universe.

A quote from Lao Tzu.

“Kindness in words creates confidence. Kindness in thinking creates profoundness. Kindness in giving creates love.”

 

Thinking Mathematically Part - 2 By K Bhanumoorthy

   Thinking Mathematically Part - II

 “No problem can be solved until it is reduced to some simple form. The changing of a vague difficulty into a specific, concrete form is a very essential element in thinking.” ----    J.P Morgan

 Concrete Thinking: The word concrete means definite/ real/ genuine/ factual/substantial/ solid/ tangible so on. It is centered on one’s observations, feeling, and experiences felt in the present non-abstract concepts. It is part of leaning process, possible be developed at workplace. It impacts the way people perceive the world. Jean Piaget, a noted Psychologist, said young children do move gradually from concrete to abstract thinking. It is nothing but reflecting one’s experience; they believe in what do they see and hear, trust the words what they hear. They would accept what one says, there is no question of asking questions. It is also called literal thinking, look for physical objects for proper understanding.

Example: Giving directions to others one has to use the language carefully. “Put the book on the table/ red book on the table.” The complex ideas are divided into small, parts /components and then each is concentrated separately, stay more mindful. problems are solved efficiently. In base ten for addition blocks of ten be used to carry out the addition. Using teaching aids make the learning easy, the ideas are made by simple showing objects. 

Example: To show a cube, defining what is an edge, face, vertices, can easily how many edges, faces, vertices are there in a cube. (E 12, F6, V8); 

Another example 4x3 ie 3 times of 4 can be shown by diagrammatic representation, 4things in a group, for 3 groups as 4 + 4+ 4 = 12. Multiplication as repeated addition.

Abstract Thinking: The word means theoretical /having no material existence/ notional / philosophical. There is abstraction in Mathematics, separated from physical and social world. Algebraic concepts are abstract. We say variables (dependent, independent) functions (onto, into one-one), equations, degree of equation, polynomials so on. When we count a number of objects after counting, we represent by a number (a symbol). The number can be representing the number of animals, tables in a class room, the number of days, the number of fruits, so on.  Abstract thinking is an ability to absorb through our senses, high order reasoning skills. It could be humor, wisdom, success, love, happiness, imagination. In brief a way of thinking not connected with physical objects. An example I would like to give. Suppose a project is given, to be completed. Normally one shall look for required steps and go ahead to complete. The question why this project is carried out, the purpose/need, is abstract thinking.

Lateral Thinking: It means indirect /finding other alternatives. It is essence of creativity. It is nothing but moving from known area to new areas. Lateral thinking is linked with Edward Do Bono. In fact, he popularized this kind of thinking. Another popular mathematician from Hungary George Polya. He had written a book “How to solve it”. A problem can be solved in different ways using different methods. Now a days we call it as an open-ended approach. In brief I would say, finding other alternatives to solve or find the solution.

Image Source :- Lateral Thinking (quality-assurance-solutions.com)

Let me give some examples: 

Example :- A null among say 8 people. Let us say this game is under elimination. Every player loses one game. The question is how matches are to be played to find the winner. The answer is 7 matches are to be played. How arrived the answer?

Let us say the competitors be named as A, B, C, D, E, F, G, H. 

To start with, games between A&B, C& D, E&F, G&H ----------------------- 4 matches.

 Assuming B, C, F, H wins, now the games between B&C, F&H ------------2matches.

Assuming C, H wins, now the game will be between C & H    -------------- 1match

So total 7 matches are to be played. This kind of problem quoted by Mathematician---George Polya.

Another example: If electricity goes quite often one could think of UPS, Generator, another alternative. In case of un-employment problem, one can think of starting own business. It is the question, how one could be able to solve not only problems in mathematics but in real life situation too. Education, in that way helps an individual, value-oriented education is preparation of one’s life.

Another example:  Given 9 match sticks, one can easily 4 equilateral triangles, it will be diagram in 2D.

                                    

Instead given only 6 sticks, can we form 4 triangles of same shape and size. Yes, possible if one who thinks, beyond.

3 Dimension, forming a tetrahedron.    ---- be continued.

This article is written by K Bhanumoorthy sir, who is a retired KV Principal. He is a passionate writer and loves mathematics deeply. You can contact him by sending your mail to - <bhanu_haresh@yahoo.co.in>

Thinking Mathematically - K Bhanumoorthy

 

THINKING

“To think is easy. To act is difficult. To act as one thinks is the most difficult of all.” 

                                               ---- Johann Wolfgang Von Goethe.

 Introduction: 

Let me write about thinking. Think means as per dictionary, it means use your mind to form ideas, solve problems, imagine, cogitate, ruminate, ponder, consider, reflect, so on. There are various ways of thinking. I would like to discuss (restricted to mathematics). Thinking could be creative, analytical, critical, concrete, abstract, divergent, convergent, lateral. The way one approaches problems and solutions relies more on how the brain manages processes information rather than the facts presented.

I. Creative thinking: This way of thinking allows anyone to generate new ideas, a new design is formulated to get the required results. There is involvement, artistic, original, being resourceful. Students shall be able to frame own questions, open ended approach in solving problems. It’s matter of divergent skills. Self-imposed conditions are removed. I mean to say overcome fixation.

                                                                        IMAGE SOURCE

An example: a question of this kind. 

I) Find two numbers where the sum is 9, the difference is 2. Ans: 3.5, 5.5.

                                                               IMAGE SOURCE CREDIT - VISIT

ii) There are 3 boys, 3 girls. They are standing in a line. How many students are there? Everyone knows there are 6 students in total. The question can be modified. In how many ways the students can stand in a line. (ans.4x3x2x1= 24 ways). If they are arranged in a line with condition no students of same gender stand together. How many ways can be arranged?  Then the answer is 2x2x2= 8ways.

iii) The volume of a tank is given as 30 Sq m. what could be different measurements? 

One answer is 3m, 2m,5m.

II. Analytical Thinking: This is detailed study. This is very much required in mathematics. Analytical thinking simplifies mathematics learning, especially in proving theorems. Mathematic is language of pattern. Concept in mathematics requires analytical thinking.

Source -  Image 1:- Analytical Thinking Skills for Problem Solving – IspatGuru 

Source - Image 2 :- Analytical Thinking & Problem Solving - SEMINAR BAGUS (seminar-bagus.com)

Example: When we increase the perimeter of a rectangle, does the area increase?

1)      Length 6cm, breadth 4cm. Then Area is 6x4 = 24 sq cm. Perimeter is 2(6+4) 20 cm.

2)      l =8cm, b =3cm, A = 24 sq cm, Perimeter is 2(8+3) 22 cm. Many other possibilities are there.

 We can conclude when we increase the perimeter of rectangle, the area does not increase.

III. Critical thinking: This is an important factor, in solving mathematics problems. It is an ability to analyse the given data and then proceed, to find solution. This kind of thinking we do require in one’s personal life and professional life also. This kind of thinking strengthens an individual to identify the sources and to draw the

Image Source:- CRITICAL THINKING SKILLS. 1. Analytical Part of critical thinking… | by Zaini Mirza | Medium

conclusions. Helps in Mathematics worksheets, puzzles, multiple choice questions, matching questions so on.

Examples: i) An electrical engineer evaluate materials suitable for particular job. Ii) A manager of a company / shop analyses customer feedback for better customer service.

      ii) What do the 4 animals in common? Cat, fox, squirrel, mouse. (Ans: tail.)

      iii) Find the odd man out? Tea, Diesel, coffee, apple juice. (Ans: diesel)

 

                                               ----- be continued

By - K Bhanumoorthy