Concrete Teaching Research Articles

Children's conditional reasoning

This study stemmed from a desire to redress the distorted view of mathematics in the elementary curriculum, created by the current imbalanced emphasis on computational rules and some applications, but very little logical analysis. The study is intended to show that fifth-grade students can significantly improve their use of logical analysis through a suitable instructional unit taught under ordinary classroom conditions. Concrete teaching materials were developed, through several trials and revisions, to familiarize students with the distinction between the valid inference patterns — Modus Ponendo Ponens and Modus Tollendo Tollens (AA, DC), and the fallacious ones — Affirming the Consequent and Denying the Antecedent (AC, DA). No formal rules were taught. The experimental unit was implemented four to five times a week for 23–25 sessions, by 4 fifth-grade teachers in their ordinary classes. The teachers participated in a twelvehour pretraining workshop. A pretest/posttest treatment/no-treatment design was applied to assess resulting improvement in students' conditional reasoning ability. The sample consisted of 210 fifth graders in a suburban area, 104 in 4 experimental classes and 106 in 4 control classes. A written group test was developed, through trials and revisions. Test items are formulated with a reasonable hypothetical content. Each item includes two premises: the first a conditional sentence, and the second either its antecedent, its consequent, or the negation of one of these, thus determining the logical form: AA, DC, AC, or DA. The question following the premises is stated positively. AA and DC are answered correctly by ‘yes’ or ‘no’: AC and DA by ‘not enough clues’ (NEC). The test contains 32 randomly-ordered three-choice items, eight in each logical form (two of the eight in each of the four possible modes in which negation may or may not occur in the antecedent or consequent). No sentential connective other than negation and conditional appears in the premises. Test/retest reliability was 0.79. Experimental and control group pretest performance levels did not differ (α=0.05). More than 78% of the answers on AA and DC, and fewer than 33.1% on AC and DA, were correct. Overall pretest mean scores were 54.3% and 53.8% for the experimental and control groups respectively. There was a significant difference (α=0.01) between the experimental and control groups' posttest overall performance—74.7% and 55.4%, respectively. There was no significant change in the control group's pretest and posttest performance levels on any logical form, or for the experimental group's on AA and DC. However, on AC and DA the two groups' gain scores were found significantly different. Negation mode, unlike logical form, was not found to be independently influential in analyzing test scores, but interacted with logical form. There was a pretest/posttest increase of 3.5 in experimental group frequency (percentaged) of incorrect NEC answers (AA and DC). As NEC appeared infrequently on the pretest, this increase was interpreted as learning that NEC is an acceptable answer. Separating out this effect from the percentaged frequency of correct NEC answers (AC and DA) left a pretest/posttest average increase of 37.8. This increase was attributed to learning when NEC is correct. Teachers were excited at the beginning, frustrated in the middle, and felt competent and involved in the project at the end. They felt the teaching should be less condensed. The majority of the students reacted positively to most parts of the experimental unit. However, some thought the unit as a whole was too repetitive and boring. No correlation was found between learning logic through the experimental unit and standard school achievement as measured by the Stanford Achievement Test (SAT). High, average, and low SAT achievers of the experimental group did not differ significantly in their pretest and posttest gain scores. Results of the study call for further investigation of the value and usefulness of teaching various parts of logic as an ordinary part of the elementary mathematics curriculum.

Helping Beginning Teachers Manage Classrooms

This article provides a framework for defining and analyzing classroom management problems of beginning teachers. It also includes a practical illustration of the application of this framework to the solution of a concrete teaching problem.

身近な地域学習と大縮尺地図指導の位置づけ

The curriculum of social study edited by the Ministry of Education in 1948 has been revised four times. The forth edition in 1969 includes that study of “home community” were changed into “Community, its land and people” for the sake giving weight to the way of regional study.According to “the Principle and the Way of Teaching Geography” written by Professor Toshio Kikuchi of Chiba University, the study of “home community” has been changed little by little since Meiji Era with the change of the educational thoughts and social need.The writers examine, the problems of study community under his thought as follows;1. The meaning of geographical view-points and its way of thinking in the study of community this unit.2. How to teach geographical view-points and its way of thinking in this unit and role of this unit in the course of study of geography teaching.3. Teaching plan and the concrte teaching of this unit to cultivate pupils' geographical way of looking and thinking.4. How to teach the maps on large scale and what to be taught in lower secondary school, and map teaching in pupils' education through elementary school to higher secondary school and to their life-long education.5. Planning and concrete teaching of the maps on large scale about the place they live.In order to solve these five problems, the writers examine both the new and old curriculums and some other reports concerned, then they make out the methodic role of this unit.They give the pupils so-called paper tests to examine how pupils studied through field observation in their elementary school days, how much experience of reading large scale maps they had and to what extent they could read maps.Later, we had an interview research, too. After those examinations, the writers show a model of planning and everyday lessons for this unit.The above those researches show us that geography teachers should give pupils as many chances of field observation as possible in the community area; they should select very carefully the typical and selected materials so that pupils can study their community area directly.The study of community should be repeated effectively, in adquate times, in the study of regional geography and Japan in the world. It is important for training technics of regional study and developing a purpose of social study.In teaching how to read the maps on large scale in lower secondary school, teaching should be begun with the study of contour lines, because they had only a little experience of studying contour lines in their elementary school days.According to the result of the writers interview research, the writers admit that pupils are much better after studying their community in this way in lower secondary school than before.But they are at a loss if they were asked to explain some different points connectedly; to explain a certain district collectivly and macroscopically comparing with other districts.Therefore, the writers find that geography teachers should not expect too much ability of reading maps by teaching the community, they should not forget to teach them reading maps at any time in the whole curriculum of teaching geography.