A study of some of the most difficult topics identified in teaching mathematics in grades four to eight: in three elementary schools

McGrath, John Patrick (1977) A study of some of the most difficult topics identified in teaching mathematics in grades four to eight: in three elementary schools. Masters thesis, Memorial University of Newfoundland.

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Abstract

This study attempted to make use of the expertise and experience of teachers to identify some of the most difficult topics in teaching mathematics in grades four to eight in three particular elementary schools. It also sought teachers’ opinions as to why the difficulties exist, asked the teachers to share their classroom-tested techniques for overcoming these difficulties, and then attempted to determine trends of difficulties across grade levels. -- The procedure involved classroom visits, teacher interviews and two questionnaires administered to teachers at each grade level. The investigator observed five grade four classes, seven grade fives, ten grade sixes, eight grade sevens and nine grade eight classes. He worked with thirty-eight teachers who are directly involved with the teaching of elementary school mathematics. -- The first questionnaire listed topics appropriate to each grade level and asked teachers to rate them from 1 – no difficulty, to 5 – extreme difficulty. Using the results of the first questionnaire, a list of approximately eight of the most difficult topics was prepared for each grade level. On a second questionnaire, teachers were presented with these eight or so topics and asked to select the three most difficult. They were also asked to indicate the specific aspects of the difficulties, their reasons for the difficulties, and suggestions for dealing with them. The resulting information was analysed for each grade level and trends across grade levels were determined. -- Topics such as world problems, division, multiplication number facts, fractions, and geometry were indicated as major problem areas at all grade levels. Difficulties with such topics as place value, work with other bases, percent, and areas and volumes were specific to particular grade levels. -- Reasons for the difficulties ranged from very general to very specific. Lack of reading comprehension skills was often given as a reason for the difficulty with word problems, whereas, not having multiplication number facts mastered was often given as one reason for the difficulty with long division. -- Teaching techniques offered ranged from general suggestions such as making greater use of manipulative materials, to specific suggestions such as allowing the use of multiplication fact cards for work with division. Some suggestions were very explicit in that they outlined step-by-step procedures for dealing with certain problem areas.

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