SUMMARY custom research writing service, CONCLUSIONS AND RECOMMENDATIONS The purpose of this study was to determine the effect of instruction to promote mental computation on third grade students. A series of activities was designed to facilitate the development of different visualizations of numbers and their properties through varied number models and activities to aid in the development of number sense. These activities offered the students opportunities to develop creatively and share their strategies for computation in order to encourage mental computational development and promote number sense. The teachers were asked on various occasions about the meaning of number sense. While the treatment teacher received information about number sense husband essay, the control teacher did not receive any information from the investigator. It would seem that the control teacher looked for information elsewhere after having been asked about number sense in various occasions. At the time of the last interview both teachers understood clearly what number sense involved. At no time did the activities or the investigator emphasize time in the course of the study except when administering the timed mental computation instrument, for which 9 seconds proved to be sufficient. The teachers major concern seemed to be with the timed assessment of their students by external testing. They felt that their job was to prepare the students for these test; however, the treatment teacher indicated that this was not the sole purpose of teaching mathematics and that helping students to learn how to think was important. She felt that, in this way, mathematics was portrayed not only as procedures and basic facts but also as a way of thinking. This change could be attributed to the use of the treatment activities. From a constructivist view, mental computation is a higher order thinking skill, where the making of the strategy is as important as the using of the strategy. Choosing efficient strategies and inventing nonstandard ways that use number properties to a good advantage improving critical thinking skills in students, are considered manifestations of number sense by recent studies. The teachers that participated in the study were found to have certain beliefs, two of which changed during the course of the study and one was added at the end of the study. These were, the meaning of number sense get your essays written for you, which neither teacher understood before participating in the study, and the belief that mathematics was equivalent to basic facts and procedures. A belief that was added after the last interview was that "speed is important in mathematics." The mental computation instrument could be used by the classroom teacher to determine mental computation skills in third grade students. The investigator suggests that the test could be incorporated into video or computerized form to facilitate its use by classroom teachers. The application of the mental computation instrument developed for the study to a larger sample, could provide benchmarks that facilitates data for curricular and instructional decision-making in the area of mental computation such as the performance level of third grade student in a certain school district. Using a larger sample of teachers, pretreatment shared beliefs could be studied in further detail to determine common views of elementary school teachers. The pre/post treatment measures and the results of the on the clinical interview questions reflect that the treatment did not affect the high achiever groups significantly but seemed to have helped the low achiever group. This effect could also be attributed to the greater amplitude of their potential gain when compared to the high achiever group. The gains appeared greater for both treatment groups when the pre and posttest were compared by items.
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