don't give up yet!!!

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Don't Give Up Yet!!! Author(s): Beth Ellen Lazerick and Carolyn Karafin Harris Source: The Arithmetic Teacher, Vol. 26, No. 3 (November 1978), pp. 42-43 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41187677 . Accessed: 13/06/2014 00:19 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to The Arithmetic Teacher. http://www.jstor.org This content downloaded from 91.229.229.203 on Fri, 13 Jun 2014 00:19:38 AM All use subject to JSTOR Terms and Conditions

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Page 1: Don't Give Up Yet!!!

Don't Give Up Yet!!!Author(s): Beth Ellen Lazerick and Carolyn Karafin HarrisSource: The Arithmetic Teacher, Vol. 26, No. 3 (November 1978), pp. 42-43Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41187677 .

Accessed: 13/06/2014 00:19

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.

http://www.jstor.org

This content downloaded from 91.229.229.203 on Fri, 13 Jun 2014 00:19:38 AMAll use subject to JSTOR Terms and Conditions

Page 2: Don't Give Up Yet!!!

Don't Give Up Yet!!! By Beth Ellen Lazerick and Carolyn Karafin Harris

Children who experience difficulty in understanding basic mathematical con- cepts and in learning standard al- gorithms are probably sitting in every classroom. Sometimes these children are labeled "slow" and show symptoms of a child with learning disabilities or brain injury. Other times these children are the ones who have simply not been "reached" by teachers and they exhibit signs of frustration and a distrust of mathematics in general. Although the children who are working appropri- ately with grade level material may 'f need continued review, practice, and ' reinforcement with materials and expe- riences to learn concepts, children who are having difficulty with learning basic mathematics with conventional teach- ing materials and methods may need different or special techniques and aids ' to augment learning.

All of us try various methods to teach students and we are always look- ing for new and better approaches. The following "What Ifs" state possible problems in the classroom and each is accompanied by some suggestions that may prove successful for remedial or conventional use. Like all teaching ideas and aids these suggestions may not work for all students in all classes. However, based on a knowledge of the student, prior history, and a certain amount of experimentation, the teacher should be able to determine whether any of these suggestions is best suited for a particular student. Further- more, as students begin to learn mathe- matical concepts and algorithms, teaching aids which may not have worked before may become more effec- tive.

Beth Lazerick teaches mathematics and science at Agnon School in Beach wood, Ohio. She also teaches at Cuyahoga Community College and at Cleveland State University and serves as a mathe- matics consultant to the Greater Cleveland Teach- ers Center and other area groups. Carolyn Harris has worked extensively with children with learning disabilities in the Greater New York area and is now serving as a supervisor-consultant in and near Pittsburgh, Pennsylvania.

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Page 3: Don't Give Up Yet!!!

1 . What if your student has been unable to establish the idea of one-to-one corre- spondence?

The teacher can present the concept of number by pairing the spoken num- bers with written numerals and with objects that appropriately suggest the specific number. For instance, the con- cept oïone can be paired with "one nose" or "one head"; the concept of two with "two eyes" or "two hands"; three, with the three wheels on a tri- cycle; four, with the four legs on a chair 'five, with five fingers; six, with the six dots on the familiar domino; and so on. Continued association of number, an abstract concept, with con- crete reminders may help some chil- dren.

2 . What if a primary grade child is still reversing numerals?

Some familiar ideas may help some children. Sandpaper numerals, which children can trace with a finger, will give children a feel for the shape of the numeral. The use of sand trays, finger paints, or even chocolate pudding (in which children can "write" numerals) will provide tactile writing practice and experience that will help certain chil- dren to write numerals better. Just be sure to work with only one numeral at a time. To get children started writing a numeral the right way, a green mark iovgo may be drawn on the side of the sheet of paper on which the child should begin the specific numeral. For the numeral, 3, for example, place the green mark on the left side of the pa- per. One caution - try not to prompt a child by saying such things as, "Start at the side nearest the door." Great trag- edy can arise if the room arrangement is shifted. A stencil or template is easily used; the cutout portion creates the shape of the problem numeral and the student only has to trace it with his finger, crayon, or pencil.

3 . What if the student is still reversing some numerals after learning addition of whole numbers?

This student may be able to function quite well if he or she uses a flannel board with precut numerals. (Such nu- merals must have a clearly identifiable correct side so that children do not re- verse these figures also.) Plastic, mag-

netic, or paper numerals can also be effective in this case. Some commercial materials are available. The strategy here is for children to see the numerals in a consistently correct position so that they will begin to internalize the appropriate configurations.

4. What if a child cannot control the size of his or her numerals?

Unlined paper may be useful ini- tially, then paper with wide lines. Large-square graph paper will encour- age children to keep pencil marks within the squares. Guides using color codes can be added to further clue chil- dren in to correct sizes (fig. 1). If the child cannot stop where the bottom line is, then tape may be placed at the bottom line.

Fig. 1

5. What if the student is writing the teen numbers (13-19) in reverse but gets the others correct?

The teen numbers are the only ones that do not fit a logical pattern. All other two-digit numbers (except multi- ples of 10) that are greater than 20 are named by saying the left-most digit first, followed by those to the right. For instance in "21" we say "twenty" and then "one." To help children with this specific reversal problem a teacher might explain that 13 through 19 are "funny" numbers. One highly regarded university professor has privately advo- cated that we rename "13" as "tenny- three" and "14" as "tenny-four." It might just work!

6. What if a child cannot remember multiplication and division facts?

Traditional ideas can be of help in memorizing facts. Students can be given hints such as, in every multiple of nine the sum of the digits is nine. (6 X 9 = 54 and 5 4-4 = 9) Also, some chil- dren do not realize that all multiples of five end in either zero or five. The con- tinued use of a matrix will also even-

tually help children to learn facts. One nonconventional technique involves triangular flash cards. The product is in one color at the top of the triangular region and the factors are on the other two points (fig. 2). One point of the flash card is covered at a time and the children have to name the missing fac- tor or product. When a factor is cov- ered, a division fact is created. The suc- cess of this sort of flash card lies in the fact that numbers do not disappear as they do on regular cards. Teachers might also take note that after division is introduced to some children, diffi- culties with multiplication facts often begin to disappear.

Fig. 2

7 . What if an older child has visual or spatial problems that interfere with his or her computational ability because the child is unable to keep numerals lined up correctly in long division?

This particular type of student often understands the process and knows that a specific arrangement of numerals has meaning, but the student needs some help in getting and keeping the appropriate arrangement. The student can turn his paper sideways so that the lines are vertical instead of horizontal. This should immediately give the stu- dent some additional support and may help him or her to function more ade- quately. Squared paper also might be used.

8. What if none of these ideas is new or what if none is successful?

Talk to other teachers. Talk to people who work in the ever-expanding system of teacher centers around the nation. Ask teachers of younger or of older children what they have done or do. Use the ideas presented here as springboards for developing your own ideas to help children who are not hav- ing success in mathematics. Just don't give upyet!!!D

November 1978 43

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