Top 100 things to write about

This Privacy Policy describes the information we collect about you online, why we collect it, how we use it, and when we share it with third parties. This Privacy Policy also describes the choices you can make about how we collect and use certain of that information.

Top 100 things to write about

This work is available here free, so that those who cannot afford it can still have access to it, and so that no one has to pay before they read something that might not be what they really are seeking. But if you find it meaningful and helpful and would like to contribute whatever easily affordable amount you feel it is worth, please do do.

I will appreciate it. The button to the right will take you to PayPal where you can make any size donation of 25 cents or more you wish, using either your PayPal account or a credit card without a PayPal account.

The Concept and Teaching of Place-Value Richard Garlikov An analysis of representative literature concerning the widely recognized ineffective learning of "place-value" by American children arguably also demonstrates a widespread lack of understanding of the concept of place-value among elementary school arithmetic teachers and among researchers themselves.

Just being able to use place-value to write numbers and perform calculations, and to describe the process is not sufficient understanding to be able to teach it to children in the most complete and efficient manner.

A conceptual analysis and explication of the concept of "place-value" points to a more effective method of teaching it. However, effectively teaching "place-value" or any conceptual or logical subject requires more than the mechanical application of a different method, different content, or the introduction of a different kind of "manipulative".

And it is necessary to understand those different methods. Place-value involves all three mathematical elements. Practice versus Understanding Almost everyone who has had difficulty with introductory algebra has had an algebra teacher say to them "Just work more problems, and it will become clear to you.

You are just not working enough problems. Meeting the complaint "I can't do any of these" with the response "Then do them all" seems absurd, when it is a matter of conceptual understanding. It is not absurd when it is simply a matter of practicing something one can do correctly, but just not as adroitly, smoothly, quickly, or automatically as more practice would allow.

Hence, athletes practice various skills to make them become more automatic and reflexive; students practice reciting a poem until they can do it smoothly; and musicians practice a piece until they can play it with little effort or error.

And practicing something one cannot do very well is not absurd where practice will allow for self-correction. Hence, a tennis player may be able to work out a faulty stroke himself by analyzing his own form to find flawed technique or by trying different things until he arrives at something that seems right, which he then practices.

But practicing something that one cannot even begin to do or understand, and that trial and error does not improve, is not going to lead to perfection or --as in the case of certain conceptual aspects of algebra-- any understanding at all. What is necessary to help a student learn various conceptual aspects of algebra is to find out exactly what he does not understand conceptually or logically about what he has been presented.

There are any number of reasons a student may not be able to work a problem, and repeating to him things he does understand, or merely repeating 1 things he heard the first time but does not understand, is generally not going to help him.

Until you find out the specific stumbling block, you are not likely to tailor an answer that addresses his needs, particularly if your general explanation did not work with him the first time or two or three anyway and nothing has occurred to make that explanation any more intelligible or meaningful to him in the meantime.

There are a number of places in mathematics instruction where students encounter conceptual or logical difficulties that require more than just practice. Algebra includes some of them, but I would like to address one of the earliest occurring ones -- place-value.

From reading the research, and from talking with elementary school arithmetic teachers, I suspect and will try to point out why I suspect it that children have a difficult time learning place-value because most elementary school teachers as most adults in general, including those who research the effectiveness of student understanding of place-value do not understand it conceptually and do not present it in a way that children can understand it.

And they may even impede learning by confusing children in ways they need not have; e. And a further problem in teaching is that because teachers, such as the algebra teachers referred to above, tend not to ferret out of children what the children specifically don't understand, teachers, even when they do understand what they are teaching, don't always understand what students are learning -- and not learning.

There are at least two aspects to good teaching: It is difficult to know how to help when one doesn't know what, if anything, is wrong. The passages quoted below seem to indicate either a failure by researchers to know what teachers know about students or a failure by teachers to know what students know about place-value.

If it is the latter, then it would seem there is teaching occurring without learning happening, an oxymoron that, I believe, means there is not "teaching" occurring, but merely presentations being made to students without sufficient successful effort to find out how students are receiving or interpreting or understanding that presentation, and often without sufficient successful effort to discover what actually needs to be presented to particular students.

That is not always easy to do, but at least the attempt needs to be made as one goes along. Teachers ought to have known for some time what researchers have apparently only relatively recently discovered about children's understanding of place-value: Jones and Thornton, p.

13 Things Men Need to Know About Pregnant Women - The Daddy Files

His [sic; Her] investigation showed that despite several years of place-value learning, children were unable to interpret rudimentary place-value concepts. It should not be surprising that something which is not taught very well in general is not learned very well in general.

The research literature on place-value also shows a lack of understanding of the principle conceptual and practical aspects of learning place-value, and of testing for the understanding of it. Researchers seem to be evaluating the results of conceptually faulty teaching and testing methods concerning place-value.

And when they find cultural or community differences in the learning of place-value, they seem to focus on factors that seem, from a conceptual viewpoint, less likely causally relevant than other factors. I believe that there is a better way to teach place-value than it is usually taught, and that children would then have better understanding of it earlier.

Further, I believe that this better way stems from an understanding of the logic of place-value itself, along with an understanding of what is easier for human beings whether children or adults to learn.

A teacher must at least lead or guide in some form or other. How math, or anything, is taught is normally crucial to how well and how efficiently it is learned. It has taken civilization thousands of years, much ingenious creativity, and not a little fortuitous insight to develop many of the concepts and much of the knowledge it has; and children can not be expected to discover or invent for themselves many of those concepts or much of that knowledge without adults teaching them correctly, in person or in books or other media.

Intellectual and scientific discovery is not transmitted genetically, and it is unrealistic to expect 25 years of an individual's biological development to recapitulate 25 centuries of collective intellectual accomplishment without significant help.

Though many people can discover many things for themselves, it is virtually impossible for anyone to re-invent by himself enough of the significant ideas from the past to be competent in a given field, math being no exception.I absolutely LOVE your Blog.

Thank you for writing it. I poured over this list, delighted to have discovered it. Never having been to Italy, but knowing I will be making the trip to visit a new friend and associate I have been immersing myself in learning.

Sep 12,  · Blog Topics I Hope YOU Write People often ask me how I come up with things to blog about, and I find the question strange, because my problem is the opposite. I have too much to blog about.

top 100 things to write about

In one of my favorite Stephen King interviews, for The Atlantic, he talks at length about the vital importance of a good opening line. “There are all sorts of theories,” he says, “it’s a tricky thing.” “But there’s one thing” he’s sure about: “An opening line should invite the.

The Best Books: The Top Novels of All Time A contemporary list, with an international flavour and a respect for the classics, The Best Books: Top Novels of All Time list contains many of the great works of fiction you'd expect, but with a few surprises to add a little spice to the collection.

Things To Do In Charleston Top 10 Best: Favorites from Locals & Tourists! Everyone's invited to chime in! Vote for your favorite things to do in Charleston Top 10 Best by filling in the form below.

This list is things to do before you die - just some ideas on what you can put on your bucket list. saving Travel Movies Books Food Other Make a List. Sign Up / Log In. Top K-Dramas. , Top Songs of the 80s. 79, Albums You Must Hear Before You Die. 26, Things That Make Michael Happy.

Things to Write About