Disproof by Counterexample

If a statement is made on several numbers or objects and it is untrue, we can easily disprove (i.e. prove that it is false) by using a counterexample. If we show that the claim does not hold for any one of numbers or objects, our job is done.

This method also help us in solving some questions in competitive exams like JEE. How? Watch the video till end. Don’t forget to subscribe the channel and comment your views.

Re-Introduction to Mathematics

Re-Introduction to Mathematics. Because you have studied this subject and know it. But do we know it’s true nature? I think, it will take a lifetime or more to do so. Let’s start now and see how far we can go. Find the video lecture on this topic. (In this video, the sound quality is a little low and there is noise. We will fix that from next videos. For now, I request you to focus on topic.)

Outline of Lecture:

(Part I)

1) What is mathematics?

2) Axioms and Theorems.

3) Implication and Double Implication

(Part II)

4) Proofs and Types of Proofs

5) Examples

6) Are axioms always true?

Study Techniques

What is the most effective way of reading or of taking class notes? Can one master this methods to achieve better learning and results?

The answer is yes. Experts have studied different study techniques over the years and presented better versions to us. I have tried to put some of it together, with my own experience. I hope you will find it useful. (I also arrange the one-day workshop on this topic. Contact me if you need more info on it.)

I have divided the lecture in two parts.

Part I consists Note Taking Techniques. I have discussed Cornell System, Outline Method, Charting Method and Concept Map.

Part II consists of Reading and Comprehension Techniques and brief on memory Techniques. In Reading and Comprehension I have shared my own experiences and also discussed SQ3R method.

Thanks !

(Don’t forget to comment and share your views.)

काही मनांत ज्योत पेटावी म्हणून…

जगण्याला धार असली पाहीजे,

कड्यावरून कोसळणाऱ्या पाण्यासारखी,

पाजवलेल्या पात्यासारखी,


ताज्या खोल जखमेतून उसळणाऱ्या,

उष्ण रक्तासारखी,


कुठल्यातरी कारणानं,

हृदय कायम ढोल बडवत असलं पाहीजे,


छातीचा भाता,

शब्दांनी, श्वासांनी,

कायम पेटवत असला पाहीजे,

पेटत असला पाहीजे,

जग जाळण्याठी नव्हे,

काही मनांत ज्योत पेटावी म्हणून…

Trying to fit in?

Why am I trying to fit in? With every passing day, I find more of my energy is being wasted in trying to obey popular rules framed by the clueless society. Nonetheless, I have tried to defy few of them. And my conscious asks me sarcasticly, ‘Oh really?’.

The desperation to try to fit in is equally pathetic to trying to be different. Traveling is the time when I honestly introspect, and I have just realized, I suck at being myself for sometime now.

I never used to think of what I am wearing or what ideas do people conceive from appearence, what should be ideal bite size when I am eating or is sauce/butter sticking to my face somewhere, what will someone think if I am initiating conversation for no reason and so on. I should go through my decision making and thought process to settle down this uneasiness for once. Either embrace my raw approach and leave opinions of others for their own or try to be sophisticated and fit in. Or simply do whatever what I want and don’t give a f***about anything else.

What I have decided?

To not to think much when it comes to personal !

And first test comes soon after.

Should I publish this post or not.

The draft is saved.

(After two hours, I am sitting in a Restrobar and anwer is on one of its walls… 🙂 )

Thumb rules of Good Parenting

(The following article contains bullet points from Parenting Seminar I delivered at couple of schools. Hope it will be helpful.)

Dear Parents,

• Of all the organizations we are part of, the most underestimated and neglected organization is our family. We all need to find a way out to utilize most of the potential of this team called family. We need to take time to sit together regularly, set goals and help each other out to achieve more individually as well as a team.

• The youngest members of this team, children, are the ones ‘our beloved organization’ need to invest most of our efforts and time in. To raise a child to his/her full potential is the best way to contribute to the nation and the world.

Be involved in your childs life. Take out time to talk, read and play with them.

• To raise a child properly, parents must shape themselves up. Development of a child and parent goes hand in hand. (Take time to read and learn.)

• The way we behave with our children or to other in their presence is the thing which impacts their personalities most. What we do matters. We need to stop our abrupt and agitated responses. Our responses should be calculated ones to have desired effects and learning for the child.

• Love your child. But love doesn’t mean lowered expectations or gifts. We often replace our love for child with the facilities, material possessions etc. Motivate them to achieve more without pressurizing.

• Be involved in your childs life. Take out time to talk, read and play with them. Give your undivided attention to them for some fixed time daily. Don’t do their work, but be there to support and guide them.

• Pay close attention to your childs special needs if any. Many a times, underperformance is caused by some learning disability. Take professional help in these cases.

• Results are like the Pathological Results. It tells us where the improvement is needed. Don’t use the results to only shout at your child. Results depend on way of evaluation too. (Don’t run after artificially perfected results only to satisfy you.) It’s okay to get less percentage, just ensure your child is learning. Can understand what he/she heard or read in lines and further, between the lines.

• We should set and follow the rules of behavior. Involve your child in making policies on use of TV, mobile etc. Don’t micromanage your child and his behavior, but establish broad guidelines.

• Nurture you child. Create an environment which helps him/her to be sensible person of independent thoughts. Remember, independence and voicing opinions is not disobedience. These are virtues, not vices.

• Develop your child to be patient, to listen to others, to help others and to coexist. Make him/her understand importance of ecology, water, soil conservation.

• Be consistent with your efforts as parent.

• Avoid harsh disciples. Never hit your child.

• Explain your rules and decisions, in age appropriate manner. Satisfy their queries.

• Treat your child with respect. It’s equally important to treating our elders respectfully.

प्रभावी शिक्षकाचे प्रमुख गुण

मूळ लेख  Top Qualities of Effective Teacher (http://rupeshghagi.com/top-qualities-of-effective-teacher/)  चे चैताली दंदेशरद कळस्कर यांनी केलेले भाषांतर.

एक  प्रभावी शिक्षकाचे उत्कृष्ट गुणविशेष काय आहेत? कोणत्या गोष्टी त्यांना इतरांपेक्षा वेगळे बनवते?  हे प्रश्न आम्ही दिशा एज्यु पॉइंट येथे दिनांक ०८ मे २०१८ ला झालेल्या शिक्षकांच्या सभेत चर्चेला घेतले आणि मी या ठिकाणी त्यासंबंधी महत्त्वाचे मुद्दे ठेवण्याचा प्रयत्न करीत आहो.

शिक्षक हे राष्ट्राच्या निर्मितीचे आधारस्तंभ आहेत कारण आपण भविष्यातील नागरिक, तंत्रज्ञ. वैज्ञानिक सनदी नौकर, राजकारणी आणि व्यवस्थेतील इतर सर्व घटकांना आकर देतो. त्यासाठी आम्ही सर्व शिक्षकांनी अत्यंत सुष्म पद्धतीने जास्तीत जास्त प्रभाव निर्माण करण्यासाठी आमची कौशल्य वृद्धिगत व धारधार केली पाहिजे. म्हणून प्रभावी शिक्षक होण्यासाठी काय गुणविशेष असले पाहिजे किंवा मिळविण्याच्या प्रयत्न केला पाहिजे,  ते सांगण्याचा मी  प्रयत्न करीत आहो.

१) शिक्षक हा विद्यार्थ्यांना दडपणातून मुक्त करून त्यांना सहज करण्यास समर्थ असला पाहिजे. ज्ञानार्जन करणाऱ्या विद्यार्थ्यांचा विश्वास शिक्षकांना वर्गात व वर्गाबाहेर सकारात्मक वातावरण निर्माण करण्यास मदत करतो. लक्षात ठेवा अभ्यासतंत्र तेव्हाच जास्त फायद्याचे असते जेव्हा प्रत्येक जण त्यात कोणत्याही दबाव न येता सहभागी असतो. विद्यार्थ्यांना शिक्षकात मित्र, तत्वज्ञ व मार्गदर्शक सापडला पाहिजे.

२) शिक्षकाने व्यक्तिशः प्रत्येक विद्यार्थ्यांचा आदर केला पाहिजे. तसेच जेव्हा केव्हा आपण विद्यार्थ्यांशी संवाद करतो तेव्हा आम्हाला आमच्या मर्यादा समजवणे गरजेचे असते. आपले  प्रयत्न विद्यार्थ्यांना प्रेरीत करण्यासाठी, अन्तर्मुख होऊन स्वतःच्या चुका ओळखून त्या सुधारण्याची क्षमता त्यांच्यात यावी  यासाठी असावे.

३) शिक्षकाचे व्यक्तिमत्त्व काळजी घेणारे व दयाळू असले पाहिजे. शिक्षकांनी मेहनती, सहनशील व सहानुभूतिपूर्ण असावे. ते सहनशिल श्रोते असावे. तुम्ही जेव्हा जबरदस्तीने बळजबरीने बदल घडवून आणण्याचा प्रयत्न करता तसे क्वचितच घडते पण त्यामुळे संवादाची साखळी सुद्धा भंग पावतो. शिक्षकांनी विद्यार्थ्यांना चर्चा करण्यासाठी प्रश्न विचारण्यासाठी अणि असहमती दर्शविण्यासाठीसुद्धा उत्तेजन दिले पाहिजे.

४) एक उत्तम शिक्षक नेहमी शिकण्याच्या प्रक्रियेत विद्यार्थ्यांना सहभागी करण्याचा मार्ग शोधत असतो. उदाहरणे कथा, विनोद, प्रात्यक्षिक इ.  अनेक साधने उपलब्ध आहेत. शिक्षकाने त्यांचा योग्य पध्दतीने वापर करावा.

५) शिक्षक चांगला संप्रेरक असावा. अवाजाचा चढउतार आपला मुद्दा प्रभावीपणे मांडण्यासाठी सहाय्यभूत ठरतो. परंतु घटक, सामग्री, शब्दांची  निवड, लहान सोपी वाक्ये आणखी जास्त महत्वाची आहेत शेवटी आपले ध्येय विद्यार्थांना शिकण्यासाठी मदत करणे आहे, त्यांना प्रभावित करणे नाही.

६) शिक्षकांना विद्यार्थ्यांच्या सामाजिक, भावनिक आणि मानसिक क्षमतेची जाणिव असावी. शिक्षक लाजाळू विद्यार्थ्यांसोबतही योग्य संवाद साधण्यास आणि त्याचा आत्मविश्वास वाढविण्यास सक्षम असावा. भावनिक स्थिती हाताळण्याची विद्यार्थ्याची क्षमता त्याच्या शैक्षणिक प्रगतीवर प्रभाव पाडते. शिक्षकाने प्रत्येक विद्यार्थ्याच्या आकलन क्षमतेनुसार अध्यापनाची दिशा ठरवावी. प्रत्येक मुल वेगळे आहे. आपण जर त्याला समजून घेवू शकलो व त्याच्या शिक्षणविषयक गरजा ध्यानात घेवून शिकविण्याचा प्रयत्न केला तर शिक्षक आपले कर्तव्य उत्तम पद्धतीने पार पडू शकतात.

७) शिक्षकांनी विद्यार्थ्यांकडून उच्च अपेक्षा ठेवाव्या. विद्यार्थ्यानाही आधिक  उत्तम शिकण्यासाठी व स्वत:कडून उच्च अपेक्षा ठेवून प्रयत्न करण्याचे वळण लावावे. उच्च अपेक्षा आणि स्वत: ठरविलेले ध्येय्य विद्यार्थ्यांना यशस्वी होण्यासाठी प्रेरणा देतात.

८) शिक्षकाला त्याच्या विषयाचे परिपूर्ण आणि अद्ययावत ज्ञान असणे आवश्यक आहे. ते शिकविण्याच्या विविध पद्धतींचा अभ्यास व चिंतन करीत असावेत. त्यांनी वर्गात व वर्गाबाहेर करता येणाऱ्या व्याख्यान/प्रात्यक्षिक/चर्चा/उपक्रम अशा अनेक माध्यमांतून परिपूर्ण असा शैक्षणिक अनुभव तयार करावा.

९) शिक्षकाचे आपल्या कामाप्रती उत्कट प्रेम असले पाहिजे. आपल्या विद्यार्थ्यांच्या यशाप्रती समर्पण तुमच्यातील शिक्षकाला अधिक उत्तम कार्य करण्यासाठी प्रेरित करत. त्यातून तुम्ही स्वत:वर मेहनत घेवून अधिक उत्तम शिक्षक बनण्यासाठी प्रयत्नशील राहता.

१०) स्वत:साठी वेळ द्या. वाचन करा. इतरांकडून शिका. चागले शिक्षक होण्यासाठी तुम्ही एक चांगले विद्यार्थी असणे आवश्यक आहे. शिकण्या-शिकविण्याच्या नव-नवीन पद्धती शोधात राहा.

How to create a good lesson plan !

(What are the components of best lecture plan? How can we plan the knowledge delivery to achieve best possible learning in students? This was the questions we asked ourselves in ‘Weekly Teachers Meet’ at Disha Edupoint dated 16th May, 2018. This is my attempt to organize and present what we discussed.)


Is teaching an art or is it a science? How can you impress your audience or win the hearts with your charismatic voice and presentation may be an art, teaching is definitely not just an art. It’s a science. I have seen people with very average speaking and presentation skills master the art of effective knowledge delivery and transform students’ life. A well organized, hard working teacher can perform better than one who relies merely on talent. It’s very important to master art of thorough planning and efficient execution. So here are few tips to design an effective lesson/lecture plan.


  1. Write it down! Many people have confidence that they will remember everything and execute according to plan they have created in their mind. Avoid being the victim of these thoughts which stops you from excelling in your profession. A well written, detailed lesson plan will help you to do your job better. It’s better to also note down the time needed to complete each of the things you are planning to do and optimize.

    Write it down !


  1. Set up the class environment. Greet students properly. Encourage students to participate in discussions and other activities you are planning for better learning outcomes.


  1. Define goals and objectives. What are the skills/knowledge you wish your students should have acquired at the end of lecture? You should be able to state the goal for yourself and it should be clear enough for the students too. After all, students are in-charge of their learning. They should know what is expected of them, so that they can focus their efforts to it.


  1. Keep your anticipatory sets ready. You should have appropriate strategy to tap into prior knowledge of students, introduce the topic and condition their minds for better grasping of what’s to come next. It can include short questions with one word/yes-no type of answers, discussion on popular application of a concept or even the decorative arrangement which induces the thoughts about topic to be learned in students mind. It needs to be short, crisp and aligned to our goal. It may be helpful to introduce learning goals and objectives at this stage too.


  1. Introduction and Connection. This is the time to capitalize on the effects of anticipatory sets and introduce the topic to students. It’s helpful to tell students the connection of topic under discussion to what they have learned earlier and even how the current topic is going help them learn the concepts to follow. You can even add how the topic is relevant, for which exams, what is the weightage of marks it will carry etc.


  1. Expectation and Standards. Teacher should also be clear of what are the standards he/she expects students achieve in that topic. It’s helpful if the standards are aligned to the standards set by board/education department school follows. Teachers should have high expectations and should train students mind to do so. After all, the outstanding performances need the precedence of higher expectations.


  1. Direct Instruction. This is most significant part of a lesson plan, which mistakenly is supposed to be the only part. This is where we actually teach students. You have a great scope to innovate and make your content engaging yet complete. You have to make sure to complete all the concepts, sub-concepts, applications, relevant examples etc. How to make direct instructions more effective? Is the topic for one more group discussion, but we can put down the essentials in short.


  • Use short, simple and clear sentences.
  • Use stories or other engaging methods if possible. Include activities.
  • Deliver at the right pace, with timely pauses.
  • Use the earlier points while going from one topic to other.
  • If possible, use role play/activities. (After all doing is better than just listening)


  1. Guided Instruction/Practice. This is crucial. How to reduce students’ dependency on teacher and build self confidence? The process of handing over the control of students learning curve from teacher to him/herself involves an intermediate step. Here students are given some tasks. Some problems to solve, a write-up or a project to be done in groups/individuals. Teachers are available to help them if required. Teachers won’t do the task for them but help them complete it themselves.


  1. Unguided practice and Assessment. This includes daily practice problems, homework etc. which students can attempt on their own. This can be graded to assess students understanding to plan for re-teaching or other remedial actions as per requirements.  Teacher can even use formal assessment (to be graded) or informal assessments. Subjective, objective type of questions or essay, write-ups or project works to asses students learning.

It’s very essential to gauge what students have learned. Have the lecture plan mate its goals. It will help us analyze the effectiveness of lecture plan, think of modifications to be done if any or use differential instructions if needed. (Every student has different learning abilities, grasping power etc. A teacher should try and accommodate them with different mode of instructions and/or utilize extra time/resources.)


  1. Exit plan. Closure of the lecture in important. It’s important to end the lecture on high note. A cumulative demonstration of what students learned, the write-up or some innovative way would be helpful. It is important to summaries the days learning and helps continuity with topics to follow. Every lecture should be complete it itself yet be part of continues flow of the learning curve.


  1. Keep equipment, resources to be used in class handy and ready to use. While you plan your lecture, you may also plan for little demonstration, short quiz or some reading material to be shared with students. Also a chalk, projector, some electronic material might be the part of what you will need in class. Make sure it is in place before you enter the class.



This is how we have been preparing our lecture plans and will try to do it more effectively to ensure better learning outcomes.

(You can mail your views or questions in any at ghagi.rupesh@gmail.com)

Top qualities of ‘Effective Teacher’ !

(What are the top qualities of an effective teacher? What makes them stand out? This was the question we asked ourselves in ‘Weekly Teachers Meet’ at Disha Edupoint dated 8th May, 2018. We had a great group discussion and I am trying to put down the crux of our discussion here.)


Teachers are nation builders. Because we shape future citizens, technicians, scientists, bureaucrats, politicians and all the building blocks of the system. Hence, we teachers need to sharpen our skills to create maximum impact in very subtle way. So what are the qualities a teacher should have or strive to acquire to become ‘Effective Teacher’?


  1. A teacher should be able to develop a friendly relationship with students. Earning students trust helps a teacher to create a positive environment in and out of classroom. Remember, learning sessions are more productive when everyone is into it and it cannot be forced. Students should find a friend, philosopher and guide in teacher.


  1. A teacher should respect the student as an individual. Hence whenever we are interacting with students we need to understand our limits. We have to make sure, our efforts are motivating her/him to introspect, identify own mistakes and improve.

    Richard Feynman


  1. Teachers should have caring and kind personality. Teachers should have a practiced patience and compassion. They should be patient listeners. When you try to bring about the change forcibly, it’s very unlikely to happen and also damages the communication channel. Teachers should encourage the students to discuss, ask questions and even disagree. It’s ok if we don’t know answers sometimes and asking students permission to answer it later.


  1. A great teacher always finds a way to get students involved in process of learning. There are many tools like examples, stories, humor, live demonstrations etc. A teacher used them wisely.


  1. A teacher should be a good communicator. Modulations of sound help to put forth our point effectively. But content, selection of words and small simple sentences are more important. Ultimately, our goal is to help the student learn and not to impress her/him.


  1. Teacher should be aware of social, emotional and cognitive abilities of a student. Some students cannot communicate due to lack of social skills. Teacher should be able to communicate properly with shy students too and develop their confidence. The emotional strength also affects how a student learns. Teachers should also consider the cognitive ability of the individual to set her/him on the best suited learning curve.

Every child is different. If we understand her/him and then try to teach taking care their individual needs, we do better as teachers.


  1. Teachers should have high expectations from students. It should motivate student to do better and have higher expectations. It fuel student’s efforts to succeed. Teacher should develop this skill where he can inspire students to do better and not get discouraged by where he stands.


  1. A teacher must have very good and updated knowledge of his subject. He/she should keep reinventing the method of instruction he/she use to teach. He/she should be able to construct a complete learning experience, which does not only include the lecture but other innovative tools/activities to be used in and out of the classrooms. Students learn more by doing rather than just listening and watching.


  1. Teachers should be passionate about their profession. Dedication towards teaching will bring out best in you. When you want your students to succeed, you will find the ways to make yourself more effective.


  1. Give time for yourself. Read. Learn from others. A good learner is a better teacher. Think on your strategies. Reinvent !


(You can mail your views or questions in any at ghagi.rupesh@gmail.com)