practice

On How To Solve It

I recently finished reading How To Solve It – A New Aspect Of Mathematical Method – by George Polya.

Below are key excerpts from this book that I found particularly insightful:

A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery. Such experiences at a susceptible age may create a taste for mental work and leave their imprint on mind and character for a lifetime.

Studying the methods of solving problems, we perceive another face of mathematics. Yes, mathematics has two faces; it is the rigorous science of Euclid but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself. But the second aspect is new in one respect; mathematics “in statu nascendi,’ in the process of being invented, has never before been presented in quite this manner to the student, or to the teacher himself, or to the general public.

Trying to find the solution, we may repeatedly change our point of view, our way of looking at the problem. We have to shift our position again and again. Our conception of the problem is likely to be rather incomplete when we start the work; our outlook is different when we have made some progress; it is again different when we have almost obtained the solution.

Where should I start? Start from the statement of the problem. What can I dot Visualize the problem as a whole as clearly and as vividly as you can. Do not concern yourself with details for the moment. What can I gain by doing so? You should understand the problem, familiarize yourself with it, impress its purpose on your mind. The attention bestowed on the problem may also stimulate your memory and prepare for the recollection of relevant points.

It would be a mistake to think that solving problems is a purely “intellectual affair”; determination and emotions play an important role. Lukewarm determination and sleepy consent to do a little something may be enough for a routine problem in the classroom. But, to solve a serious scientific problem, will power is needed that can outlast years of toil and bitter disappointments.

If you cannot solve the proposed problem do not let this failure afflict you too much but try to find consolation with some easier success, try to solve first some related problem; then you may find courage to attack your original problem again. Do not forget that human superiority consists in going around an obstacle that cannot be overcome directly, in devising some suitable auxiliary problem when the original one appears insoluble.

The future mathematician should be a clever problem-solver:; but to be a clever problem-solver is not enough. due time, he should solve significant mathematical problems; and first he should find out for which kind of problems his native gift is particularly suited.

In closing:

Going around an obstacle is what we do in solving any kind of problem: the experiment has a sort of symbolic value. The hen acted like people who solve their problem muddling: through, trying again and again, and succeeding eventually by some lucky accident without much insight into the reasons for their success. The dog who scratched and jumped and barked before turning around solved his problem about as well as we did ours about the two containers. Imagining a scale that shows the waterline in our containers was a sort of almost useless scratching, showing only that what we seek lies deeper under the surface. We also tried to work forwards first, and came to the idea of turning round afterwards. The dog who, after brief inspection of the situation, turned round and dashed off gives, rightly or wrongly, the impression of superior insight. No, we should not even blame the hen for her clumsiness. There is a certain difficulty in turning round, in going away from the goal, in proceeding without looking continually at the aim, in not following the direct path to the desired end. There is an obvious analogy between her difficulties and our difficulties.

A highly recommended read in the area of problem solving.

On SPIN Selling

I have recently read SPIN Selling, The Best-Validated Sales Method Available Today. Developed From Research Studies of 35,000 Sales Calls. Used by the Top Sales Forces Across The World. by Neil Rackham.

The main premise of this book is best summarized by the author in the first chapter of the book: “The traditional selling models, methods, and techniques that most of us have been trained to use work best in small sales. In this book I’ll be showing you that what works in small sales can hurt your success as the sales grow larger—and I’ll be sharing with you our research findings that have uncovered new and better models for success in large sales…One of the simplest models of a sales call does seem to be applicable to any size of sale; almost every sales call you can think of, from the simplest to the most sophisticated, goes through four distinct stages 1. Preliminaries: These are the warming-up events that occur before the serious selling begins…2. Investigating: Almost every sale involves finding something out by asking questions…3. Demonstrating Capability: In most calls you will need to demonstrate to customers that you’ve something worthwhile to offer…4. Obtaining Commitment: Finally, a successful sales call will end with some sort of commitment from the customer…We decided that the focus of our research would be to develop new and positive questioning models that could replace the old ones, which were proving so unsatisfactory…We found that questions in the successful call tend to fall into a sequence we call SPIN. In summary the SPIN sequence of questions is: 1) Situation Questions: At the start of the call, successful people tend to ask data-gathering questions about facts and background…. 2) Problem Questions: Once sufficient information has been established about the buyer’s situation, successful people tend to move to a second type of question… 3) Implication Questions: In smaller sales, sellers can be very successful if they just know how to ask good Situation and Problem Question…4) Need-payoff Questions:Finally, we found that very successful salespeople ask a fourth type of question during the Investigating stage… is that they get the customer to tell you the benefits that your solution could offer.”

Below are key excerpts from the book that I found particularly insightful:

1- “The psychological effect of pressure seems to be this. If I’m asking you to make a very small decision, then—if I pressure you—it’s easier for you to say yes than to have an argument. Consequently, with a small decision, the effect of pressure is positive. But this isn’t so with large decisions. The bigger the decision, the more negatively people generally react to pressure.”

2- “By forcing the customer into a decision, closing techniques speed the sales transaction…Closing techniques may increase the chances of making a sale with low-priced products. With expensive products or services, they reduce the chances of making a sale.”

3- “The first step in successful closing is to set the right objectives. The starting point for obtaining a commitment is to know what level of commitment from the customer will be needed to make the call a success.”

4- “So what’s the test of closing success? What’s the result, or outcome, that allows us to say that one call has been successful while another has failed? The method we finally chose involved dividing the possible outcomes of the call into four areas: 1)Orders: Where the customer makes a firm commitment to buy… 2)Advances: Where an event takes place, either in the call or after it, that moves the sale forward toward a decision… 3)Continuations: Where the sale will continue but where no specific action has been agreed upon by the customer to move it forward…4)No-sales: Our final category is where the customer actively refuses a commitment.”

5- “Obtaining Commitment: Four Successful Actions 1. Giving attention to Investigating and Demonstrating Capability…2. Checking that key concerns are covered..3. Summarizing the Benefits… 4.Proposing a commitment”

6- “The purpose of  questions in the larger sale is to uncover Implied Needs and to develop them into Explicit Needs.”

7- “Demonstrating Capability Effectively: 1.Don’t demonstrate capabilities too early in the call…2. Beware Advantages…3. Be careful with new products.”

8- “Making Your Preliminaries Effective: 1. Get down to business quickly…2. Don’t talk about solutions too soon…3. Concentrate on questions.”

9- “The Four Golden Rules for Learning Skills Rule 1: Practice Only One Behavior at a Time Start by picking just one behavior to practice…Don’t move on to the next until you’re confident you’ve got the first behavior right…. Rule 2: Try the New Behavior at Least Three Times…Never judge whether a new behavior is effective until you’ve tried it at least three times…Rule 3: Quantity Before Quality…When you’re practicing, concentrate on quantity: use a lot of the new behavior. Don’t worry about quality issues, such as whether you’re using it smoothly or whether there might be a better way to phrase it. Those things get in the way of effective skills learning. Use the new behavior often enough and the quality will look after itself…Rule 4: Practice in Safe Situations…Always try out new behaviors in safe situations until they feel comfortable. Don’t use important sales to practice new skills.”

10- “The most important lessons come from the way you review the calls you make. After each call, ask yourself such questions as these: Did I achieve my objectives? If I were making the call again, what would I do differently? What have I learned that will influence future calls on this account? What have I learned that I can use elsewhere?”

Regards,

Omar Halabieh

SPIN Selling