I't seems I've stirred a kettle of bees (is this the right phrase?) with this post, and especially the not so subtle (or appropriate) header I used to promote it in the LinkedIn TOC Learning Network group. The ensuing discussion made me think about a few examples of the need and use of examples....

So, first off - why do we need examples? Examples help us make the shift from the stratosphere of theory to 'sea level' practical use. They help us understand the theory and figure out how it's used so we can then apply it. The best example I can find to this is cooking. When I started cooking I used cook books and quickly moved from text only books to those books that had step-by-step demonstration pictures, because the theoretical explanations weren't helping me create the needed results. These pictures helped me progress a bit but I was still messing up quite a few dishes. Once I went into a live cooking demonstration and learnt by example how to perform the techniques, I started getting things right, which then created the basis for more and advanced learning by doing, a.k.a self learning.

Next important point to cover is - why do we need multiple examples? I find that each new example highlights the subject matter from a new angle and increases the clarity of understanding. If, by any chance, a miscommunication has happened between the teacher (be that teacher a real person or a teaching medium) and the learner, more examples increase the chance of surfacing this and getting it corrected. This has happened to me a few years ago when I was helping my son catch up in Math. He needed to learn long addition (I think). I taught him the concept and had him practice on examples I made up. I was pretty sure he got it all. Then we found a workbook and he sat down to use it. He stumbled on one of the most basic exercises. Turns out I forgot to teach him how to handle numbers that had zeros in them (as in 1023). My mistake for sure, but had we not practiced a wide variety of examples we would have missed that.

My last point to make is about the quality of examples - my math experience shows that quantity per se is not enough, we need a quantity of a high enough quality . This means there is a real need for a wide variety of examples. Using the same example over and over - even if we used different numbers and maybe even more digits, is not good enough. For this one I have a somewhat longer story I find funny. If I recall correctly, my brother told us this story and it had happened to him.

My brother majored in Mathematics (yep, those again) in his higher education. One day in class, the professor was teaching a very complex theme. As is the custom in higher education Mathematics, they were learning the theory and so the professor was using X,Y and Z to represent numbers. As the subject was very complex, the students requested a concrete example. After a few minutes of considerations the professor turned to the board, wrote "Let X=A, Y=B, and Z=C" and proceeded to resolve the equation using A,B and C. Now, having grown up with a Mathematics Professor for a dad, I can tell you that guy was, as far as he was concerned, complying with the request, but I'm sure that not only were the students not amused, they were also nowhere nearer to understanding the subject on hand.

Well, having stated my case for a high quality variety of examples, I'd like to discuss example recycling for just a tad. In this post I did talk against recycling examples. Well, like everything in life, this is not a black and white issue. There is one main situation where I would advocate FOR using the same example and that it when you are dealing with a progression of ideas. So, it would make sense to me to use the same example to explain DBR and s-DBR.

So, can anyone share with me other stories that demonstrate why examples are important and what makes an example good?

So, first off - why do we need examples? Examples help us make the shift from the stratosphere of theory to 'sea level' practical use. They help us understand the theory and figure out how it's used so we can then apply it. The best example I can find to this is cooking. When I started cooking I used cook books and quickly moved from text only books to those books that had step-by-step demonstration pictures, because the theoretical explanations weren't helping me create the needed results. These pictures helped me progress a bit but I was still messing up quite a few dishes. Once I went into a live cooking demonstration and learnt by example how to perform the techniques, I started getting things right, which then created the basis for more and advanced learning by doing, a.k.a self learning.

Next important point to cover is - why do we need multiple examples? I find that each new example highlights the subject matter from a new angle and increases the clarity of understanding. If, by any chance, a miscommunication has happened between the teacher (be that teacher a real person or a teaching medium) and the learner, more examples increase the chance of surfacing this and getting it corrected. This has happened to me a few years ago when I was helping my son catch up in Math. He needed to learn long addition (I think). I taught him the concept and had him practice on examples I made up. I was pretty sure he got it all. Then we found a workbook and he sat down to use it. He stumbled on one of the most basic exercises. Turns out I forgot to teach him how to handle numbers that had zeros in them (as in 1023). My mistake for sure, but had we not practiced a wide variety of examples we would have missed that.

My last point to make is about the quality of examples - my math experience shows that quantity per se is not enough, we need a quantity of a high enough quality . This means there is a real need for a wide variety of examples. Using the same example over and over - even if we used different numbers and maybe even more digits, is not good enough. For this one I have a somewhat longer story I find funny. If I recall correctly, my brother told us this story and it had happened to him.

My brother majored in Mathematics (yep, those again) in his higher education. One day in class, the professor was teaching a very complex theme. As is the custom in higher education Mathematics, they were learning the theory and so the professor was using X,Y and Z to represent numbers. As the subject was very complex, the students requested a concrete example. After a few minutes of considerations the professor turned to the board, wrote "Let X=A, Y=B, and Z=C" and proceeded to resolve the equation using A,B and C. Now, having grown up with a Mathematics Professor for a dad, I can tell you that guy was, as far as he was concerned, complying with the request, but I'm sure that not only were the students not amused, they were also nowhere nearer to understanding the subject on hand.

Well, having stated my case for a high quality variety of examples, I'd like to discuss example recycling for just a tad. In this post I did talk against recycling examples. Well, like everything in life, this is not a black and white issue. There is one main situation where I would advocate FOR using the same example and that it when you are dealing with a progression of ideas. So, it would make sense to me to use the same example to explain DBR and s-DBR.

So, can anyone share with me other stories that demonstrate why examples are important and what makes an example good?