Questions and answers are simply mathematics

If you find the study of mathematics dreadfully boring, it is time to play a little. In “Amusements in Mathematics” by Henry Ernest Dudeney (published by David Gaddy, Nov 2011),  plenty of mathematical fun is crammed into 640 pages. According to the author, this collection of puzzles and mathematical problems was created so that the user of the book could tap into the pleasure of “doing math”.

Henry Ernest Dudeney (1857-1930), an English mathematician, is best known as a master of logic puzzles. The author views mathematical puzzles as perplexing questions begging our answers. The reader is drawn into the hunt for solutions and answers to these questions. Asking and answering questions is a part of human life, and comes naturally to us all. When mathematics is viewed as the process of asking and answering questions, we allow ourselves to bypass any existing “number” prejudices and start to enjoy what comes naturally.

Amusements in Mathematics” also includes a discussion on the psychology of puzzles and the application of math in our daily lives.  It is an excellent resource for mathematics teachers seeking a readily accessible collection of “questions” that will spice up a lesson. However, this puzzle book is just as useful to anyone seeking a little mental stimulation – after all, we can all answer questions and should not shy away from the challenge of doing so often. This extensive collection of puzzles and problem-solving exercises is now available from  The book can be purchased at a saving of 20% until the end of February 2012 using the following coupon code: 20% off books – Enter code FEBBOOKS12 – Save up to $25 – Offer ends 2/29/12


Does withholding knowledge stimulate or stunt learning?

Does refusing to share knowledge truly stimulate learning? I love to learn new things, and am constantly on some mission of discovery.  Over the years, I have tried to share my enthusiasm for learning with my students, and anyone else who will allow me to indulge my love of learning.  I have just as eagerly shared what I have learned as I have shared my enthusiasm for learning.  One of my greatest thrills as a teacher is to see curiosity light up the eyes of a student, and watch them begin their own journey of discovery. I don’t believe we are ever too old to learn new things.  I do believe that as soon as we choose to give up the quest for knowledge and understanding we limit our relevance to society.

Earlier today, I interacted with an intelligent, interesting individual who often writes some thought-provoking articles.  A recent article of his stimulated some study on my part and raised some questions, so I addressed those questions to the author, in the hope that he would help me understand his thought process better.  He responded in a rather unexpected way.  He indicated that he did indeed have the answers to my questions, but felt that sharing what he knew would discourage me from thinking independently and stunt my ability to aquire or generate knowledge.  If he answered my questions, that would somehow make him guilty of spoon-feeding me. 

How often has an intelligent, educated, and seemingly-wise teacher with a vast and valuable knowledge- and understanding-base quenched the desire that a student may have to learn simply by not embracing a desire to share?  How often is the learning process retarded, because those who have the knowledge will not share it with those who do not have it?  I have, at times, experienced this “what is mine is mine, and I will not share” attitude in the highly competitive research environment where it is believed by some that withholding knowledge grants power, and sharing knowledge weakens your position to dominate as a researcher.  How often does this attitude seep down into the classroom environment where the goal should be to encourage everyone to learn as much as they can?

Are there teachers who withhold answers just to ensure that the students do not grow to know more than they do?  Is this restricted sharing environment comforting for the teacher, and effective in stimulating the students to seek their knowledge elsewhere?  Are there teachers who are not motivated to take up the torch of lifelong learning?  Do our formal learning environments still accommodate teachers who have no interest in growing and developing, so they always have something new to share with their students?


Teaching Creative Problem-Solving to Children

Bob Eberle and Bob Stanish agree that creative problem-solving is a basic skill and a good sense approach to modern day living and learning. As a practical style of learning, creative problem-solving has significant transfer value.

CPS: Creative Problem-solvings for Kids In their book, “CPS for Kids: A Resource Book for Teaching Creative Problem-Solving to Children”, Eberle and Stanish share their 6-step approach to creative problem-solving. They show how to start with becoming more alert and developing an awareness which stimulates recognition of situations or conditions that need improvement or correction. From this starting point of becoming more observant, the reader is led to the point of generating creative ideas with potential solutions to the problems at hand. But the process doesn’t end with an idea. No, it takes the reader all the way through to a final step that is often omitted when problem-solving techniques are taught. Solution-finding is only part of the end product. Implementing a workable solution is the rest of the end product, and the final step in Eberle’s and Stanish’s process. The reader is taken all the way from waking up to the call for solutions, to developing the final plan to implement their best solution.

While this book emphasizes application in the elementary school environment, its value in teaching at all levels should not be under-estimated. Students need to be challenged to think, and this book helps teachers, parents, and students alike to seek out those challenges and to embrace them enthusiastically.


Where is the gap in my education?

As a teacher of Physics, I have spent years searching for ways to make complex concepts simple to grasp. I have looked for ways to make the learning process easier. And I have studied my students, listened to them, watched them, and experimented with different ideas to see which will enhance their understanding. In this process, one thing has never ceased to amaze me. In speaking to colleagues in similar study fields, I discovered that I was not the only one to notice this strange “phenomenon”. What astounded me was the gaping hole in the education of my students, and the frightening thing about it was that most parents and students didn’t seem the least bit concerned about it. What was missing? Common sense. Common sense? Surely I am mistaken? Everyone has common sense – it comes with the being human, right?