Understanding Of Arithmetic Research Articles

Intra-class grouping for arithmetic instruction: critique and criteria

Attempts to meet the problem of adjusting arithmetic instruction to pupil differences frequently involve the organization of instructional groups of pupils witilln the classroom. The major purpose of subgrouping in arithmetic classes is to provide for individual differences by bringing pupils of like arithmetical backgrounds, skills, understandings, and concepts together into small groups so that they can study and work effectively at rates and levels that are closer to their own abilities and characteristics. Closely related to the possibility of adjusting instruction to pupil differences are other reasons why intra-class grouping for arithmetic instruction could increase the efficiency of the learning situation or increase the productivity per man-hour of teaching and learning. These reasons generally pertain to the interactions and communications witilln the class or to the desirability and effects of pupils succeeding at their own levels.

In the classroom: The use of overlay charts: A device for teaching some number concepts

The teaching device described is based on a hundred chart and a series of overlays. I used a portable flannel board and inserted several hooks on top from which the overlay papers were suspended. The paper used was 24“ by 18” construction paper. A different color was used for each overlay to make the project attractive to the children. The children were second-graders with an excellent understanding of arithmetic. Counting in multiples, odd and even numbers, and bases other than base 10 were the understandings which were explored with this teaching aid.

Arithmetic instruction changes pupils' attitudes toward arithmetic

The fact that pupils in all arithmetic classes differ in such ways as understanding of number operations, rate of learning, background of experience, and interest in the subject indicates that arithmetic instruction should be adjusted to provide for the apparent variations in pupils. Authors of texts concerned with the teaching of arithmetic recognize that these pupil differences exist and suggest methods of teaching and classroom organization to provide for them. Classroom teachers are also aware of the extent of these differences and are concerned with methods of instruction which will meet the needs of all the pupils in their classrooms. The adjustment of arithmetic in truction to variations in pupils has become a major aspect of arithmetic in truction. Most of the proposals and methods for adjusting arithmetic instruction to pupil differences in arithmetical abilities and understandings are concerned with some organizational procedure and involve some type of ability grouping or some type of individualized program.

Arithmetical Understandings of Elementary-School Teachers

Educators and laymen alike have become more and more concerned about the effectiveness of arithmetic instruction in our public schools. It is not enough merely to calm the critics. Today it is imperative that all citizens attain mathematical literacy to carry out the responsibilities and use the opportunities of effective citizenship in a modem technocracy. This responsibility cannot be left entirely to teachers in junior and senior high school. Elementary-school teachers must recognize and assume their share of the responsibility. A firm grasp of basic arithmetical concepts and processes is essential to teach arithmetic meaningfully. Teachers cannot teach understandings that they themselves do not have. Effective instructional methodology will not automatically follow understanding, but certainly effective teaching methods are inescapably rooted in understanding. One prerequisite for any program to further develop essential understandings among teachers is to determine what teachers bring to the teaching of arithmetic-their understanding of the subject, their attitudes toward it, and their recognition of possible need for improvement. To measure these facets of the classroom teacher's background was the purpose of a study recently completed under the direction of the writer and the sponsorship of the Utah Educational Research Council. The instrument selected to measure elementary-school teachers' understanding of basic arithmetical principles and concepts was Glennon's Test of Basic Mathematical Understandings, which consists of five sections:

The Arithmetic Teacher

The Arithmetic Teacher is a quarterly journal published by The National Council of Teachers of Mathematics, a professional organization devoted to the improvement of the teaching of mathematics at all levels of instruction. This new publication should make professional reading on the teaching of arithmetic more accessible to elementary school teachers and as a result, the thinking of leaders in this field should be more readily reflected in school practice. Devoted to the improvement of the teaching of mathematics in the kindergarten and the grades of the elementary school, THE ARITHMETIC TEACHER will bring to teachers direct help on how to improve the teaching of arithmetic and knowledge and understanding of the application of new ideas to classroom work from day to day.