The problem of this study was to compare arithmetic performance scores of pupils who had been presented tape-recorded instruction with arithmetic performance scores of pupils who had received the same instruction by means of traditional teaching methods.

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The effectiveness of the Touch Math method of instruction was examined in count-all addition procedures with Down Syndrome children. Four children with Down Syndrome were selected for a multiple probe design study. The participants, two male and two female, are students at a school for intellectually handicapped children and adolescents. They were ascertained to have the minimum required skills in rote counting, one-to-one correspondence, and recognition and identification of numbers. In a multiple pretest procedure with 15 simple addition problems, they demonstrated ineffective addition strategies such as guessing and averaged less than 35% correct. / The Touch Math program was then implemented during the regularly scheduled math period four days a week for 40 minutes each day. Students progressed through an incrementally more difficult series of simple addition worksheets. During each session the student received training on the problems and then was administered the worksheet. / Results indicate that the Touch Math method has been successful for the teaching of simple addition with these students. Scores on the worksheets progressed from 0% to 100% correct and probe results improved from less than 35% correct to greater than 86% correct following completion of the program. Subjects completed the program in 5 to 16 days.

This study was designed to see if children with intellectual disabilities could be taught to add pairs of single-digit numbers using the Touch Math method. Three intellectually disabled students who could add only by using physical representations of numbers were selected for the study. A multiple-probe design across the 3 students was used to evaluate the effectiveness of the intervention. The intervention consisted of a three-step addition program that was planned to teach students to add by counting the faded touch points of the smaller addend starting from the larger addend. The data show that the 3 children were able to master the program and to retain the Touch Math method from 1 to 5.5 months following completion of the program. Suggestions for future research and for teachers are discussed.

The present study was designed to see if children with learning disabilities could be taught three-row, double-digit addition problems using a dot-notation method. Three children with learning disabilities were selected for the study. Prior to the intervention, these students used a combination of count-all and count-on strategies when solving addition problems and used concrete referents such as fingers or tallies. A multiple-probe design was used to evaluate the effectiveness of the intervention with the 3 subjects. The experiment consisted of a teaching phase where students were taught to touch and count the dots on numbers 1 to 9 in a specified pattern and an intervention phase where students progressed through nine levels of addition problems. The final stage consisted of three-row, double-digit addition problems requiring regrouping with touch points removed. Results indicate that the 3 subjects were able to learn and apply the dot-notation method successfully and were able to retain the method from one and a half to four and a half months after completing instruction. Suggestions for future research and for teachers are discussed.

Research indicates that many children finish primary school in Southern Africa still reliant on inefficient counting strategies. This study extends the research of the South African Numeracy Chair project to early mathematics intervention with Grade 2 learners. It investigated the possible adaptation of the Mathematics Recovery programme to facilitate learner progression in early arithmetic strategies. This study aimed to investigate the possibility of adapting the Mathematics Recovery programme for use in a whole class setting, and to research the effectiveness of such an adapted programme. This study also aimed to investigate the extent of the phenomenon of unit counting and other early arithmetic strategies used in the early years in Zambia. This study was conducted from an emergent perspective. A review of the literature indicated that children who become stuck using unit counting face later mathematical difficulties, and that teacher over-emphasis on unit counting in the early years of schooling may be a contributing factor. This study used a qualitative design research methodology that consisted of a preparation phase, teaching experiment and retrospective analysis. The context of this teaching experiment was a seven week after-school intervention with a class of Grade 2 learners aged seven to eight in a rural Zambian primary school. Data collection and analysis focused on video recordings of a sample of 6 learners. The experimental teaching content focused on the Early Arithmetic Strategies aspect of the Mathematics Recovery programme. Although limited by time and research focus, this study found that all learners made some progress in early arithmetic strategies, and indicates that the Mathematics Recovery programme has potential for adaptation for early intervention in whole class teaching to address the mathematical education challenges in Zambia and beyond. This study also found that unit counting predominated in the sample learners, but that strategies were not yet entrenched, indicating this was a suitable age for early intervention. This study makes methodological contributions to a growing body of research into the adaptation of the Mathematics Recovery in Southern African contexts and suggests avenues for possible further research.

Jean Piaget describes three stages in the development of that aspect of quantitative thinking which he named conservation of number. In the first stage, a child is quite unaware that one-to-one pairing of two sets implies equivalence of the sets. He is unable to make a correct one-to-one correspondence, and if presented with two sets of objects which have been matched unit for unit, believes that one set has become greater if its units are spread out, or smaller if they have been compressed. In the second stage, the child is able to make a correct correspondence, but does not believe in the continued equivalence of the sets when one is spatially rearranged. In the third stage, the child maintains that the matched sets remain equivalent even though the units of one set have been rearranged, that is, the child conserves number. Piaget postulates that conservation is a necessary condition of mathematical understanding. In this study, it was hypothesized that children who are in Stage 1 at the beginning of their Grade 1 year, and who are still in Stage 1 at the beginning of the second term show low achievement in arithmetic at the end of the school year. It was further hypothesized that each stage in conservation is associated with corresponding levels in terminal achievement in Grade 1 arithmetic. One hundred fifty-six children received an individual conservation test in October of their first grade year, and were thereby classified as being in Stage 1, Stage 2, or Stage 3 in conservation development. In January, those classified as Stage 1 received a second conservation test, and were again classified according to their stage in conservation development at that time. In May, the arithmetic sub-test of the Stanford Achievement Test, Primary I Battery was administered to all groups. A significant proportion of the Stage 1 group selected by the January conservation test had achievement scores which fell below the median for all subjects, while a significant proportion of the Stage 3 group selected by the October test had above-median achievement scores. Mean achievement scores for the two Stage 3 groups did not differ significantly from each other, but were higher than mean achievement scores for the Stage 1 and Stage 2 groups. No significant differences were found among mean achievement scores of Stage 1 and Stage 2 groups. The results were interpreted as being consistent with Piaget's theory. The superiority of the mean terminal achievement of early conservers over that of children who had not developed conservation by January appeared great enough to be of educational importance. Some individual scores showed marked deviation from the pattern derived from the group data, however, and caution in use of the conservation test as a predictive instrument was recommended. It was proposed that the conservation test could be a useful diagnostic procedure for the teacher. / Education, Faculty of / Graduate

This comparative study of methods used in teaching arithmetic was carried out in the La Vega Public School, McLennan County, Texas, during the 1941-1942 school term.

This thesis describes the experiment made by the author in two of her seventh-grade arithmetic classes comparing the effectiveness of the formal and activity methods of teaching on the progress of the students.