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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.Jan 03, · Does anyone have a template page for 5 ways to write a number?
Word form, expanded, place value blocks, standard-- and I feel like there is another way to write . November Every-Day Edits Use Every-Day Edits to build language skills, test scores, and cultural literacy.
Be sure to see our tips for using Every-Day Edits in your classroom. Write “five thousand” instead of “five K.” Commas add clarity: When using numerals and a number has four or more digits (in the thousands or more), use a comma to help the eye quickly process the number.
Apr 20, · By Chris Mooney, a science and political journalist, blogger, podcaster, and experienced trainer of scientists in the art of communication. He is the author of four books, including the just. These are the five leadership traits or leadership qualities that followers say they most want to see in a leader.
These traits can improve your quality of leadership. Mar 16, · Write the imaginary number part. Combine the value you just calculated with the imaginary number indicator, i.
When written as a whole, these two pieces make up the imaginary number part of the standard form. Example: √() = 8i. The i is another way to write: √(-1) When you consider that √() = 8 * √(-1), you can see that it 24%(18).