STATEMENT OF PERMISSION TO COPY In presenting this professional paper in partial fulfillment of the requirements for an advanced degree at Montana State University, I agree that the Library shall make it freely available for inspection. I further agree that permission for extensive copying of this profes¬ sional paper for scholarly purposes may be granted by my major professor, or, in his absence, by the Director of Libraries. It is understood that any copying or publication on this professional paper for financial gain shall not be allowed without my written permission. A SURVEY OF MINI-MATH COURSES IN THE MATHEMATICS CURRICULUM OF MONTANA'S SECONDARY SCHOOLS by A professional paper submitted in partial fulfillment of the requirements for the degree of 1IASTER OF EDUCATION with concentration in Secondary Education ✓/ JOHN WILLIAM HEMMER Approved: MONTANA STATE UNIVERSITY Bozeman, Montana August, 1974 iii ACKNOWLEDGMENT My appreciation is extended to Dr. Robert J. Thibeault, Head of the Educational Services Department at Montana State University, whose constant help and encouragement kept me going and caused this paper to be finished. TABLE OF CONTENTS Page LIST OF TABLES vi ABSTRACT . vii Chapter 1. A STUDY OF MINI-COURSES HI MATHEMATICS Statement of the Problem Need for the Study Solution of the Problem. Definition of Terms Summary 2. REVIEW OF LITERATURE CONCERNING MINI-COURSES IN THE * SECONDARY SCHOOL . Non-academic Mini-courses. Academic Mini-courses Summary. 3. PROCEDURES . . .......... Instrument ..... Procedures Analysis of Data Summary 4. ANALYSIS OF DATA Analysis of Questions. • • • 1 1 1 2 3 4 5 5 7 12 13 13 14 15 15 16 17 Summary, 24 V Chapter page 5. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS. ........ 25 Summary 25 Conclusions. 25 Recommendation 27 APPENDICES . 28 APPENDIX A: Cover Letter. 29 APPENDIX B: Questionnaire 30 LITERATURE CITED 33 vi LIST OF TABLES Table . Page 1. Schools Responding to Questionnaire ...... 16 2. Use or Planned Use of Mini-courses. ............ 17 3. Length, or Planned Length of Mini-courses in Weeks ..... 18 4. Comparison of Mini-courses Taught As Separate or Integrated Classes. 19 5. Grade Levels at Which Mini-courses Were Used . 20 6. Ability Levels at Which Mini-courses Were Used 22 7. Number of Mini-courses Offered 23 o vii ABSTRACT The purpose of this study was to determine the extent to which mini-courses were being used in the mathematics curriculums of Montana's secondary schools. A closed form questionnaire was mailed to each secondary school in Montana and completed questionnaires were received from 81.6 per cent of the schools polled. Research into the use of mini-courses showed them to be used in the non-academic area as enrichment courses or as a trial period for courses to be instituted at a later time. Mini-courses were used in the academic area to give students more options and experiences. It was felt that mini-courses better utilized staff strengths as well as provided for individual differences. This study showed that the use of mini-courses in the mathema¬ tics curriculum was an increasing trend in Montana. About one-half of the schools responding to the questionnaire used or planned to use mini¬ courses in their mathematics curriculums. The most popular length for mini-courses was found to be six to nine weeks. Courses less than six weeks in length tended to be integrated into normal classes, while courses six weeks or longer tended to be taught as separate classes. Credit for these classes corresponded with the length of the class and was given on a semester basis. Mini-courses were found to be used at all grade levels and for all ability levels. Courses designed for the below average student tended to be offered in the first two years of high school, while those designed for above average students were usually offered in the last two years. Some concern was expressed in the area of using mini¬ courses for the college-bound student. Schools were afraid such courses might take away needed time and cause students to miss needed mathema¬ tics background. Schools seemed more willing to allow students a choice of which mini-courses they would take rather than a voice in the content of such courses. The opportunity to choose was dependent upon the number of mini-courses the school offered. This opportunity was reduced in schools offering less than five mini-courses. In view of the increased use of mini-courses, the investigator recommended that secondary schools in Montana explore the possibilities of using mini-courses in their mathematics curriculums as a tool for better meeting the needs and abilities of students. i Chapter 1 A STUDY OF MINI-COURSES IN MATHEMATICS The problem of providing a student with knowledge which will help prepare him for future life is a problem that has consistenly shadowed the curriculum of our secondary schools. Is it possible to take into account the student’s interests and abilities and at the sane time be practical in nature? Some schools are attempting to make advances in this direction with the introduction of prime interest short-term courses called mini-courses. Statement of the Problem The problem of this study was to determine the extent to which mini-courses were being used in the mathematics curriculum of Montana’s secondary schools. Need for the Study * ' The need for this study became evident when the school in which the investigator is employed became interested in using the mini-course concept. It was felt that it would be useful to know how many schools were using mini-courses in their mathematics curriculum and the general organization of the courses. With the knowledge obtained from this study, it was hoped that the investigator would be able to use this knowledge in establishing a more effective mini-course system in the mathematics curriculum of the 2 investigator’s school. If determined that the mini-course concept is a trend developing in Montana, the length of time the mini-course is used on a trial basis in the investigator’s school would be affected. The general questions to be answered by this study include: 1. What percentage of high schools in Montana have mini- courses in their mathematics curriculum? 2. What is considered as average length for a mini-course? 3. Do mini-courses tend to be academic or non-academic in . organization? 4. How many schools are planning to initiate mini-courses in their mathematics curriculum? 5. Do mini-courses tend to be organized for any particular grade level? 6. Do mini-courses tend to be organized for any particular ability group? 7. Do students play any part in the organization or content matter of the mini-courses? 8. Are students able to choose from a variety of mini-courses? 9. Which grading systems tend to be used in mini-courses? Solution of the Problem The solution to this problem was in the form of a questionnaire which was sent to a mathematics teacher on the staff of each of Montana’s secondary schools. Each teacher was selected from a list 3 obtained from the State Department of Education and was asked to complete the questionnaire to the best of his knowledge. After the questionnaires had been returned to the investigator, the results were compiled and conclusions drawn. The investigator did not feel that any limitations were inherent in this study. The study was confined to the schools of Montana, and no attempt was made to infer to any larger group or any grade level , other than secondary. Definition of Terms The following terms can be used in many different areas and may have different meanings to different people. For this reason, the following terms are defined as they are used in this study. Mini-course. Any course of short duration, usually two to nine weeks, which may be academic or non-academic in which the student may or may not be involved in the planning of such course. Academic course. Any course for which the student receives credit which may be used to meet state graduation requirements. Non-academic course. Any course in which no credit is given but is taken as an enrichment idea in which the student wants to broaden knowledge in a certain area. 4 Summary . In studying the extent of mini-courses in the mathematics curriculum of secondary schools of Montana, it was hoped to determine if schools were using the mini-courses as a method of providing a more practical curriculum for the high school student. Information obtained was used by the investigator in the planning and instituting of mini¬ courses in the mathematics curriculum of his school. Chapter 2 REVIEW OF LITERATURE CONCERNING MINI-COURSES IN THE SECONDARY SCHOOL Research into the use of mini-courses in the secondary school found them serving two main purposes. Some schools used them merely as an enrichment idea or to fill in time at the end of the year when other work had been completed. These were considered to fall under the non-academic area. Other schools used them as credit toward graduation in which the student was able to cover topics not always covered in a textbook. These were considered as academic mini-courses. Non-academic Mini-courses In the non-academic area, the mini-course has been used for different purposes. Bazelli (1970) reported that in some of the inner city schools that have many students from the ghetto areas, the mini¬ course has been used to teach skills and understandings which are normally taught in the home but are found to be lacking among these students. These courses were used in the categories of communication, home and family, personal and social, citizenship and career, and cultural. They were set up to run an hour a day for nine or ten weeks. They varied in length so that a student would select two or four in any one semester. Hayward (1969) reported the mini-course being used as a program for seniors during the last few weeks of school when regular course 6 work had been completed or during semester breaks. Students were allowed to suggest the areas that they were interested in and then select the courses they wanted to take. It gave them a chance to suggest innovations and cause change through a democratic process. They usually suggested that grades and required homework be the first things dropped. When found in the non-academic area, the mini-course tended to be used as an enrichment course. Scheduling varied from one day of mini-courses, in which the instructor could use up to two or three blocks of time if he felt it was necessary (Youngren, 1973), to one hour a day for nine to ten weeks in which students were released from study hall or other non-class time (Bazelli, 1970). The non-academic mini-course was also used to test some course which may be later integrated into the curriculum (Turner, 1972). Monument Mountain High School in Stockbridge, Massachusetts, set aside one week to propose and try new ideas in what to .teach and study. Everyone submitted ideas and a committee then decided what would be offered. Afterward some of these courses were integrated into their academic curriculum. The teaching corps for the non-academic courses tended to come from three main areas and in each case certain conditions had to be met. Teachers were found on most faculties with special interests which were used outside of curricula offerings. In this case, teachers 7 usually wanted the classes limited to those students genuinely inter¬ ested. Instructors needed the time to teach made available from their planning periods. In some cases, as reported by Hayward (1969), parents offered to monitor study halls to free teachers for the mini¬ courses. In the secondary school, many students can be found who have special interests .that they want to share. They must demonstrate competency in those interests and should have adequate supervision. In areas of special interest to students in which no regular staff member was familiar, the secondary school was able to obtain instructors from the local community. A faculty advisor was appointed in this case to help the patron with normal school practices. Fenwick (1970) warned that the schools should be careful about searching the community for resource people before checking out the resources within the school. Academic Mini-courses When mini-courses were integrated into the regular academic offerings of a secondary school, the problem of scheduling was one of the hardest to overcome. Fenwick (1970) reported that the mini-course was most easily integrated into a school that already had a flexible schedule rather tlian one with a more structured curriculum. Lincoln-Sudbury Regional High School in Sudbury, Massachusetts found their introduction of mini-courses to follow four stages of 8 development (Bronson, 1971). First, the teacher load was reduced to four classes plus a conference period to work with the students. They found poor results at first on the voluntary use of the conference period. Second, a program of independent study was started and, again, a small amount of student participation was noted. Third, an honors program was instituted which provided credit to individuals involved. Finally, an introduction of elective courses to parallel the regular courses was instituted. The purposes of mini-courses in the secondary school varied according to the subject areas they were used in. Farrell (1972) reported on the use of mini-courses in vocational education as an attempt to solve two basic problems. Students tended to have low motivation and an opinion that regular courses were not relevant to their needs. This school also had a lack of enrollment in vocational classes. Mini-courses can help a student make a career choice by exposing him to a greater number of vocational possibilities than regular courses. Paldy (1970) reported the mini-course to be used in the physics curriculum in an attempt to increase enrollment. He found that students may be wary of signing up for a year course in a subject area that they are uncertain about. The mini-course gives them a chance to try a sampling of the course and, if they become interested, to continue in the program. The courses can be scheduled so that the students do not 9 have to take all of the physics mini-courses in one year, but could take different topics in different years. The purposes of mini-courses as viewed by principals were shown in a survey of 440 Kansas High Schools (Guenther, 1973). Of the 379 who responded, it was found that 28 per cent offered mini-courses in their curriculums. The following are the purposes as viewed by these princi¬ pals with the percentage who felt it fit their needs. 1. Give students more options, varying experiences, and more flexibility—66 per cent. 2. Utilize staff strengths—51 per cent. 3. Provide for individual differences—46 per cent. • 4. Revitalize interest in a particular area—33 per cent. 5. Develop more contemporary, relevant offerings—28 per cent. In response to whether they thought that mini-courses were a good idea, 19 per cent responded that it was too early to tell. Of the principals polled, 43 per cent claimed that their teachers thought mini-courses were good or excellent. The uses of mini-courses in a mathematics class was found by Lee (1973) to supplement the regular curriculum by providing a variety of educational experiences which the students select and explore. The units consisted of two to three week courses which were based upon one or more skills that were presently being taught in the regular mathema¬ tics curriculum. 10 The planning and conducting of the mini-courses were similar in both academic and non-academic areas. In some cases the teachers listed topics and allowed students to list their preferences. This method was most prevalent in the academic offerings (Lee, 1973). In the non- academic area, the list of offerings usually was obtained by polling the students to determine their interests. Students were then allowed to pick the courses they wanted and those with enough student interest A were taught. The. courses tended to be exploratory in nature and seemed to be vocational skills that could be used with increased leisure time (Engle, 1972). When used in this manner, it was found that the number of mini-courses became almost limitless. One school reported as many as 400 mini-courses being offered ("Flirting with Free Forming," 1972). In the non-academic mini-course, the first things deleted were homework, tests, and grading. If used as an academic course where a grade was necessary, the school system usually went to a pass-fail system, with the grade dependent upon attendance and tardiness alone. In some cases taking attendance was mandatory in order to comply with state laws ("Flirting with Free Forming," 1972). In a nation-wide survey conducted by the National Education Association Research Division in 1970-1971, school systems were polled as to whether the system had any free-form courses or mini-courses, either outside the regular'curriculum or as electives within regular required courses, in which students were able to choose their own topics 11 or be allowed to pick from a variety of unit topics. The results showed that about one out of four school systems had mini-courses offered. This was further broken down into one out of five at the high school level, one out of ten at the middle or junior high school level, and one in twenty-five at the elementary level. In addition to showing that the high schools were more apt to have mini-courses, it also showed that these courses were more prevalent in the larger schools ("Free- Form Education," 1972). The advantages of mini-courses were felt to be almost as many and varied as the number of courses themselves. Transfer students seemed less affected because they had a broader background to take to their new school and incoming transfer students became better adjusted since the variety of subjects eliminates repetition (Lohut, 1973). Teachers learned to cope with a variety of groupings and felt their work was more demanding and rewarding (Bronson, 1971). Teachers felt that they were reaching the middle student more effectively. Teachers felt that .the grading was more equitable in their mini-courses than in regular classes. It was found that the cost of the materials used in mini-courses was less than that of regular textbooks. Students felt that it was an advantage to be able to choose from a variety of courses rather than having to stay within the struc¬ tured curriculum. Although seen as an advantage by students, the selection of courses was found by Gudaitis (1972) to be based on title 12 and description instead of content. Students also based their selection of classes on the instructor of the class rather than its usefulness to them. Another benefit of mini-courses reported by Engel (1972) and reinforced by Hayward (1969) was that they seemed to improve relations throughout the school as well as bringing the schools closer to the community. This, of course, was most noticeable when people from the community were brought in to teach such courses. School relations were also aided by the amount of planning and flexibility required. Teachers found that it was necessary to communicate with others and seek coopera¬ tion on many levels. Summary It appeared that the mini-course can be part of a solution to the old problem of a constant demand to obtain a more relevant curricu¬ lum. It can offer the student a chance to explore some area which may be outside the traditional curriculum but still of high interest to him. As stated by Hayward (1969), "Being allowed to learn instead of being made to learn changed everyone's attitude." Chapter 3 PROCEDURES The impetus for this study came when the Columbia Falls High School mathematics department, Columbia Falls, Montana, became inter¬ ested in using mini-courses in its mathematics curriculum. The main purpose in instituting mini-courses was to help the less able mathematics student achieve the two years of mathematics which is required by the state of Montana for graduation from high school. The design for the study grew out of a need for the researcher to obtain information regarding the use of mini-courses by other mathematics departments in secondary schools of Montana. In this way it was hoped that the results would help the researcher’s school in determining the best procedure in using its mini-courses. In this chapter, the researcher will discuss the instrument being used in the study, the research procedures being used, and how the data will be analyzed. Instrument The basic instrument used to gather data for this study was the questionnaire, shown as Appendix B, pages 30-32* It consisted of eleven questions, each of which was used to help answer one of the nine questions to be answered in the study. The closed form of questionnaire was used with a comment section provided at the end of the questionnaire 14 for any additional infomation that an individual felt was important to the study. Procedures The list of all high schools in Montana was obtained from the Montana Educational Directory (1972-1973). A list of mathematics teachers for these schools was obtained from the state office of the Superintendent of Public Instruction. In those cases where a departirient head was designated, the questionnaire was sent to that person. In all other cases, a questionnaire was sent to one of the mathematics teachers listed. The population of this study was 185 secondary schools in Montana. Mailed questionnaires were sent to every member of the population so that no sampling procedures were necessary. A cover letter (Appendix A, page 29) accompanied each questionnaire explaining the purpose of the study and the questionnaire. A self-addressed stamped envelope was included with each questionnaire. The questionnaire was mailed to each member of the population on March 20, 1974. Each member was asked to return the completed ques¬ tionnaire before April 12, 1974. On April 30, 1974, a follow-up questionnaire was sent to all members of the population whose response was not received. 15 Analysis of Data Upon receipt of the questionnaires, the data was analyzed and presented in tables. The number of members answering each question was given along with percentage totals. The totals and percentages were given in separate tables for each class of school. Any answer in the space provided for comments was summarized in such a manner as to include all ideas presented. Summary In an effort to obtain information about the use of mini¬ courses in the secondary mathematics curriculums of Montana, the researcher mailed a closed form questionnaire to all the secondary schools in Montana. The results were presented in table form showing both totals and percentages where meaningful. Chapter 4 ANALYSIS OF DATA In an effort to determine the extent to which mini-courses are being used in the mathematics curriculums of the secondary schools of Montana, the questionnaire (Appendix B, pages 30-32) was sent to each of 185 schools on March 20, 1974. The completed questionnaire was received from 122 schools within three weeks. As this was only 66 per cent of the population, a follow-up questionnaire was sent to those schools not responding on April 20, 1974. The^respondents to the second request totaled twenty-nine and brought the total percentage of those responding to 81.6 per cent. The number and percentages of schools responding to the ques¬ tionnaire is shown in Table 1. Determination of school classification was made from the Montana High School Association Handbook (1973-1974). Table 1 Schools Responding to Questionnaire School Classification Number of schools Number of returns Per cent return AA 14 14 100.0 A 32 28 87.5 B 39 33 84.6 . . . c. 100 76 76.0 Totals 185 151 81.6 17 Analysis of Questions The number of schools using mini-courses in their mathematics curriculums was shown to be about one out of every five. A few schools commented that other departments within their school were using mini¬ courses, but the mathematics department had not yet done so. Of the schools which reported that they were not now using mini-courses, about one in every four indicated that they were planning to institute some system of mini-courses in their mathematics depart¬ ments in the near future. School responses to whether they were using mini-courses in their mathematics curriculums or planned to do so in the near future are shown in Table 2. Table 2 Use or Planned Use of Mini-courses School Classification Number Using Mini-courses Per cent of Schools Responding Number Not Using Mini-courses But Planning To Per cent AA 6 42.9 4 50.0 A 2 7.1 9 34.6 B 6 18.2 5 18.5 C 16 21.1 12 20.0 Totals 30 19.2 30 24.8 18 Of the schools now using mini-courses in their mathematics curriculums, the length of such courses varied from two to eighteen weeks. The most common length was found to be nine weeks or less. This length would correspond to the length of the grading periods in most schools. Schools teaching courses of eighteen weeks in length would usually consider these to be semester courses and not classify them as mini-courses. This may in part explain the low number of schools listing eighteen week mini-courses. In the schools which indicated plans to initiate mini-courses in their mathematics curriculums in the near future, the length of six to nine weeks seemed most popular. A listing of the lengths of mini- courses now being used as well as planned lengths is shown in Table 3. Table 3 Length or Planned Length of Mini-courses in Weeks School Classification Now Using Mini-courses Planning to Use Mini-courses Less Than 6 6-9 18 Less Than 6 6-9 18 AA 1 4 0 0 2 0 A 0 2 0 2 4 0 B 2 3 1 10 3 0 C 11 5 1 1 7 1 Totals 14 14 2 3 16 1 19 Those schools having mini-courses of less than six weeks in length, tend to have them integrated into their normal classes rather than taught as separate classes. Courses taught at a length, of six to nine weeks, which adapted well into the regular grading schedule, tended to exist as separate classes and did not correlate to any particular class. The number of schools using or planning to use mini- courses as separate or integrated classes is shown in Table 4. Dupli- l cation of integrated and separate classes in some schools caused figures to be higher than the actual number of schools having mini¬ courses. Table 4 Comparison of Mini-courses Taught As Separate or Integrated Classes School Classification Schools Using Mini-courses Schools Planning Mini-courses Separate Integrated Separate Integrated AA 4 3 1 2 A * 2 0 0 3 B 6 • 1 3 1 C . 10 8 8 2 Totals 22 12 12 8 Of all the schools using or planning to use mini-courses in their mathematics curriculums, only three indicated that credit toward 20 graduation would not be given. In the case of integrated courses, the student may receive credit with, that class but no extra credit as far as graduation requirements. In those schools teaching mini-courses as separate classes, the credit received corresponded to the length of the class. This meant that three six-week or two nine-week courses enabled the student to receive a semester credit of mathematics. All schools counted this credit toward the two-year mathematics requirement for graduation from high school. The use of mini-courses did not seem to be predominant in any particular grade level. Table 5 shows the number of schools using mini¬ courses at a particular grade level combined with those schools which indicated the grade level at which, they planned to use their mini¬ courses. Table 5 Grade Levels at Which Mini-Courses Were Used School Classification 9 Grade 10 Levels 11 12 AA 2 6 8 9 A 0 4 6 6 B 7 8 10 10 c . . 17 17 18 19 Totals 26 35 42 44 21 »• The lower numbers using mini-courses in grade level nine was due in part to the fact that many AA and A schools considered this to be part of the junior high school in a 6-3-3 system. The table shows that mini-courses are used for all levels; however, some schools did have it restricted to the first two years of school while others the last two years. The levels at which mini-courses are used depend to a degree on the ability levels for which the course was designed as well as the purpose for having mini-courses. Courses designed for the below-average students tend to be offered at the ninth or tenth grade level as a substitute for algebra in their mathematics requirement. When the course is taught to above-average students, it is usually taught at the eleventh or twelfth grade levels. In this case it may be used to broaden the students1 knowledge in some area not covered in textbook material but considered useful, especially to college bound mathematics students. Some concern in this area was expressed by a few schools which felt that the introduction of mini-courses might hurt the college-bound student. They were afraid the mini-course might take time away from these students and cause them to miss some of the mathematics background they needed. Discretion would have to be used in this area to see that mini-courses do not do more harm than good. 22 Table 6 shows the ability levels at which the schools perceived their mini-courses as being used. It is a combination of schools using and planning to use mini-courses. Table 6 Ability Levels at Which Mini-courses Were Used School Classification Below Average Average Above Average AA 5 6 6 A 3 4 2 B 6 8 6 C 11 15 17 Totals 25 33 31 The majority of schools felt they had or were planning to have a variety of mini-courses which would enable them to meet the needs of students of all ability levels. This would require some type of grouping on the part of the mathematics teacher to insure that a less mathematically able student did not find himself confronted with a class in which he could not keep up. This would tend to reduce the amount of choice a student might have in mini-courses that he would like to take, since courses designed to cover a wider range of abilities provide access to the greater amount of students. In the questionnaire the schools were asked if students had a O 23 choice in the mini-courses they would take and also if the student had any voice in what material would be covered. Schools seemed more willing to give the student some choice in the mini-course he would take than any influence on the material the course would cover. Questionnaires revealed that schools planning mini-courses showed more willingness to allow students a voice in course content than those schools presently using the mini-course concept. This may infer that after mini-courses are instituted one realizes that student input in courses is not too feasible. The opportunity for students to have a choice in' the mini¬ courses they will enroll for must depend to a degree on the number of mini-courses offered in the particular program. Table 7 gives an idea Table 7 Number of Mini- courses Offered School Classification Schools Having Mini-courses Schools Planning Mini-courses 0-5 6-10 11-15 Over 15 0-5 6-10 11-15 Over 15 AA 2 2 0 2 1 0 0 0 A 1 0 0 1 3 1 0 0 B 5 1 0 0 2-. 2 0 0 C 11 2 2 1 7 2 0 0 Totals 19 5 2 4 13 5 0 0 24 as to the number of mini-courses being offered in those schools using the concept as well as the number being instituted by those schools planning some form of mini-course organization. Table 7, page 23, shows that most schools are just beginning their mini-course program and do not have a large number of offerings at the present time. Those schools which plan to give credit toward graduation may have to institute a greater number of mini-courses in order for students to receive at least a semester credit under the mini-course concept. With one semester credit for these courses, the students may need to take part of a regular mathematics class to obtain their two- year requirement. Summary The use of mini-courses in the mathematics curriculums of Montana^ secondary schools seems to be just emerging. These courses tend to be six to nine weeks in length with credit given toward graduation. Schools try to give students a choice of courses designed for different abilities at different grade levels. Whether or not the mini-course is found to be an adequate method for serving the needs of students will be told by the test of time. Chapter 5 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS The purpose of this study was to determine the extent to which mini-courses are being used in the mathematics curriculum of Montana*s secondary schools. In addition, information as to general organization of mini-courses was desired. This would include length, grading procedures, and type of student initiated for. A Summary D The use of mini-courses in the mathematics curriculums of Montana*s secondary schools is a growing concept. The general organi¬ zation of such courses is as varied as the number of schools using them. The investigator benefited from the ideas of other mathematics teachers about mini-courses which should help in expanding a current program. Conclusions While the survey revealed that mini-courses are not a major force in mathematics curriculums, it did show them to be a growing one. If the schools which responded that they planned to initiate mini-courses in the near future carry through with their plans, almost one-half of Montana's high schools would have mini-courses in their mathematics curriculums. • The length of the mini-course that seemed most adequate to the 26 schools using them was six to nine weeks. Although those schools planning mini-courses listed six to nine weeks as the most probable length., some felt that one length might be too restricting. Some courses lend themselves well to a length of nine weeks, while others may not have enough material to last even six weeks. Length is one area in mini-courses that requires much flexibility. The decision to integrate mini-courses into regular classes or keep them separate did not depend upon other factors in the survey as much as on the purpose of the course as seen by the instructor. When material covered is closely related to normal textbook work, the instructor may use an integrated mini-course to give more coverage to that particular concept. Separate mini-courses tend to be used when material does not correlate well with normal classwork but is of high enough student interest and practicability to warrant its presentation. Credit was considered essential for mini-courses whether taught as integrated or separate classes. The ability levels that the mini-courses are designed for seemed to depend somewhat on the grade levels the courses were designed for. Mini-courses designed for the ninth or tenth grade levels were usually geared to the average to below-average student. At this level the courses were often used to allow students a method of satisfying the two-year mathematics requirement for graduation without taking a course of less practical use. Mini-courses taught at the junior and senior 27 levels tended to be designed for the average to above average student. Recommendation In view of the increased use of mini—courses in the mathematics curriculum shown by this study, the investigator recommends that Montana's secondary schools become aware of the possible use of mini¬ courses in their mathematics curriculum. Whenever feasible, these schools should consider the introduction of mini-courses as a tool to help meet the student's needs and abilities. APPENDICES 29 APPENDIX A Cover Letter March 20, 1974 Mr. Joseph Brannon Chester High School . Chester, Montana Dear Mr. Brannon: In an effort to better meet the needs and abilities of the students in the mathematics curriculum, some schools have instituted the mini-course. The mini-course is a course usually two to nine weeks in length which may be academic or non-academic in nature. The courses deal with a variety of topics that are of interest to students Under the supervision of Dr. Robert J. Thibeault, head of Educational Services at Montana State University, I am conducting a survey of Montana high schools in regard to the use of mini-courses in their mathematics curriculums. The attached questionnaire will take about five minutes of your time and the completeness of the study depends upon your cooperation. If you are interested in the results of the study, please check the appropriate place on the questionnaire and the results will be sent to you. Thank you for your time and consideration. Sincerely, John W. Hemmer* 30 APPENDIX B Questionnaire Directions: Please answer the following questions relating to the use of mini-courses in your mathematics curriculum. Check more than one answer if appropriate. 1. Does your school use mini-courses in the mathematics curriculum? Yes No 2. If you are not now using mini-courses, are there any plans to use such in the near future? Yes No If your answers to questions 1 and 2 were both "No," please return the questionnaire in the envelope provided. If either answer was "Yes,'’ please answer the following questions. 3. What is the normal length of your mini-courses? weeks 4. Are your mini-courses taught as separate classes or integrated into normal classes? Separate Integrated 5. Do students receive credit toward graduation for mini-courses? Yes No 31 6. For which grade levels are mini-courses designed? 9 10 11 12 7. Which, systems of grading are'used in mini-courses? Normal grading Pass-fail Non-graded 8. For which ability groups are the mini-courses designed? Below average Average ' Above average 9. Are students able to choose from a variety of mini-courses? Yes No ___ 10. Are students involved in determining the content of mini-courses? Yes No 11. How many different mini-courses do you offer? °” 5 __ 6-10 • 11-15 Over 15 32 12. If you would like the results of this study, please check here Comments: LITERATURE CITED LITERATURE CITED Bazelli, Frank P. 1970. "A Mini-Course Curriculum for Inner City High Schools," Journal of Secondary Education, XLV, 1 (January), 13-15. Bronson, David B. 1971. "The Story of an English Elective Program," English Journal, LX, 8 (November), 1086-1090. Corgan, James X. 1972. "The APSU Mini-Course Program in Earth Science," Journal of Geological Education, XX, 3 (May), 151-152. Engel, Ross A. and Weller, D. David, Jr. 1972. "Mini-Courses: Maxi- Morale," High School Journal, LVI, 3 (December), 142-149. Farrell, Joe. 1972. "The Six Weeks Vocational Block Program," Agricul¬ tural Education, XLV, 3 (September), 69-71. Fenwick, James J. 1970. "The Mini-Course Curriculum," Bulletin of the National Association of Secondary School Principals, LIV, 343 (February), 155-159. "Flirting with Free Forming," Nations Schools, XC, 1 (July, 1972), 25-28. "Free-Form Education," NEA Research Bulletin, L, 2 (May, 1972), 47-48. Gudaitis, Donald J. 1972. "Mini-Courses, Are They Useful?" Clearing House, XXVI, 8 (April), 465-467. Guenther, John and Ridgeway, Robert. 1973. "Mini-Courses: Promising Alternatives in the Social Studies," Clearing House, XLVII, 8 (April), 486-487. Hayward, Robert R. 1969. "Maximum Results from Mini-Courses," Today1s Education, LVIII, 6 (September), 55-57. Kohut, Sylvester, Jr. 1973. "Mini-Courses in the High School Social Studies Program," The Social Studies, LXIV, 4 (April), 169-171. Lee, Carol and Merle, Gary. 1973. "Oogle Google and the Mini-Unit," The Arithmetic Teacher, XX, 2 (February), 99-100. • • Paldy, Lester G. 3.970. "Think Small," The Physics Teacher, VIII, 2 (February), 61. Postlethwait, Samuel N. and Hurst, Robert N. 1971. "Mini-Courses," Library College Journal, IV, 1 (Winter), 16-24. 35 Romey, William D. and Dean, Walter E., Jr. 1971. "Mini-Courses: A Vehicle for Introducing Flexibility into Large Introductory Science Courses," Journal of Geological Education, XIX, 1 (January), 14-20. Turner, Sheila. 1972. "Mini-Course Week," Senior Scholastic, C, 11 (April 24), 20-21. Wiese, Charles R. 1970. "Mini-Courses: New Spark for Student Enrich¬ ment," Nations Schools, LXXXV, 5 (May), 74. Youngren, Robert. 1972. "For a Change of Pace, Try a Mini-Course Day," Clearing House, XLVII, 3 (November), 159-161.