Have you done your homework? Många lärare ger läxor och många elever läser läxor. Men om vi ber lärare berätta om sin undervisning är det få som nämner läxor. I stället talar man om skolan man arbetar vid, ämnet man undervisar i, sina elever, lektioner, praktiskt arbete, diagnoser och prov. M. Allyson Macdonald, Holar Agricultural College, 551 Sau∂árkrokur, Island, redogör för en undersökning om läxor och läxläsning – om varför man ger och gör läxor.

What I wanted to do was to find out if some common assumptions about homework were indeed true. For example, were the following true? • Students do better on their courses if they do a lot of homework. • Good homework is not necessarily just going over what was done in class. • Teachers should comment on homework and return it as soon as possible. Questionnaires for teachers and students in secondary schools in Iceland were prepared similar to one used in Israel for students (Tamir, 1985), though some questions were omitted and others added. Both teachers and students answered similar questions about homework. The questionnaire was sent to all members of the Association of Science and Mathematics teachers (LMFK) and to department heads. Completed questionnaires were returned by 70 teachers, estimated to be about 20% of all current secondary science and mathematics teachers in Iceland. Most of these teachers indicated that they were willing to administer a student questionnaire, which was then mailed to the first thirty-five teachers to respond. Information was thus obtained from 281 science students (13 science teachers) and 110 mathematics students (7 mathematics teachers). The student sample is a young adult Nämnaren 100

population with 228 males and 154 females in the age range 16-22 with over half aged 18, 19 or 20 and a few older than 22. Over half of the students are specializing in science or technology-based courses or courses requiring a good mathematics background. The courses described by the teachers included introductory, general and advanced courses in mathematics, biology, chemistry, geology and physics. The courses described by the students were similar to those discussed by their teachers, but the range was not as great. Only one physics class (of five students) was available and in general the physics teachers showed the least interest in the survey. Mathematics teachers obtained replies from students beyond the introductory level, perhaps because student responses were returned in the spring term. There were a range of student data available from biology and chemistry classes.

Interpreting questionnaire results There were 30 questions grouped into four categories: Teacher-initiated: Type of homework and Feedback and evaluation Student-controlled: Doing homework and Learning

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Table 1 List of questions sent to students. The questions to teachers were similar, except in two cases (9 and 10). Type of homework 1. Does the teacher set homework in order to let you go over that which was covered in class? 2. Does the teacher set homework in order to let you learn material which was not covered in class? 3. Does homework require observation and/or experiments? 6. Does the homework require watching of a videotape? 8. Does homework require use of a computer? 10. Do all students get the same homework? (Students) 10. Is the homework set in accordance with the abilities and interests of students? (Teachers) 12. Does the homework require critical thinking and/or solutions to problems, rather than direct practice (exercises on particular methods)? 16. Does the homework require writing? 18. Do you prepare for the next lesson at home (e.g. by reading the textbook)? 26. Does homework you are given require reading? Feedback and evaluation 14. Are you interested in the teacher's comments on homework? 17. Do you hand in homework only because it is part of the course grade? 19. Are you expected to report on your homework to the class? 22. Do you get a grade for homework? 24. Are you interested in getting a grade for homework? 27. Is homework gone over in class? 28. Does your teacher take students' homework home to correct it? 13. Are quizzes used to check your grasp of material related to homework? Doing homework 5. Do you do your homework conscientiously? 15. Do you do your homework with friends? 20. Do you use help from the teacher with homework? 21. Is there cheating on homework, e.g. such as copying from others when you come unprepared to school? 30. Do you get help from others not in your class with your homework? 29. Do you have access to reference materials? 9. How many hours do you spend on homework in this course per week? (Students) 9. How many hours do you think students should spend on homework per unit per week? (Teachers) Learning 4. Does homework help you understand the course material better? 7. Does the homework lead to more enjoyment of the course in class? 23. Do you tnink that homework helps you master the material? 25. Do you like doing homework? 11. Do you want homework in this course?

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An example of the student questionnaire is given in Table 1. Where the substance of the teachers' questions differed these are also given (questions 9, 10). Responses were almost always of the Never-Sometimes-Usually type, though a few were YesNo. These were assigned a score of 1-2-3 or 1-2 for statistical analysis using SPSS (Norusis, 1986) on an IBM PC. The correlation between teachers' and students' responses on the 30 items in the questionnaire was very good, with r = 0.9. This indicates that the results can be considered as valid i.e. that they do reflect the homework practices in some secondary science and mathematics classes in Iceland. Teachers received additional questions concerning their education and experience and were asked to describe certain aspects of a course they were currently teaching. Teachers and students were asked to write short paragraphs on two topics. One was to describe typical teaching of a topic in the course, and the other to discuss the purpose of homework in the course. All teacher paragraphs and three student paragraphs per school (randomly selected) were subjected to an item analysis where the number of times different items appeared were counted. Some paragraphs included more than one item. These data are not summarised here but are referred to as needed. These additional questions provided further evidence of the validity of the questionaire responses. Since I was interested in the relationship between homework practices and learning, responses to the questions in the categories concerning type of homework, feedback and evaluation, and doing homework were tested for correlation with responses in the learning category. This was done separately for the student groups but for the teachers as a whole, since there were few significant differences between the two teacher groups. The frequencies of response to the questions discussed later and the related correlations are not given here but

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are obtainable from the editor. (The adress is given at the beginning of the article).

Is homework included? Teachers were asked to describe how they taught a topic in their courses. A short lecture followed by student exercises were common in almost all mathematics classes. The surprise was how few teachers mentioned homework as being part of the teaching in a topic. In 26 mathematics paragraphs, going over homework was only mentioned three times. Only two hinted at setting homework. Students mentioned it even less often in their paragraphs. Yet in the 26 mathematics courses described by the teachers, homework was set after every lesson in over half the courses and once a week in another 20%. Only three teachers never set homework. In the same course descriptions, homework formed part of the final grade in over 40% of the courses. When the question "Is homework gone over in class?" was asked directly, about 55% of mathematics teachers said sometimes and about 22% said always. Thus the first result is that homework seems to be a largely invisible part of teaching. Although most teachers use homework in their courses, they did not indicate that it was an integral part of their teaching plans.

What sort of homework? Teachers and students were asked about the purpose of homework in the courses they were teaching or were enrolled in. An item analysis on these paragraphs showed that teachers seemed to respond in two ways. On the one hand they mentioned specific tasks which were undertaken, and on the other hand they referred to more general aims. Some teachers mentioned both in their responses. In 26 paragraphs by mathematics teachers on the purpose of homework, the follo-

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wing tasks were mentioned: – developing skills 15 times – doing exercises 10 times – going over course material 5 times – setting up problems correctly 4 times The aims mentioned included: – Learning to work independently5 times – improving understanding 4 times – providing feedback 2 times Other items mentioned once or twice included giving students time and students needing time, control over students and encouraging them. Most mathematics students mentioned either developing or practising skills and increasing understanding. There seemed to be a reasonable match between student and teacher perceptions of the purpose of homework. In 39 paragraphs by teachers on the purpose of science homework, the following tasks were mentioned: – reading 11 times – preparing for lessons 9 times – doing problems 9 times – practising or developing skills 8 times – going over course material 8 times – writing reports 4 times Regarding general aims the following were mentioned: – learning to work independently 4 times – help understanding 5 times – help learning 3 times Other remarks mentioned once or twice included that there was not enough time in class or that homework could spread the workload more evenly, and that it could be used to collect extra information, could help students connect the course with reality, should demand insights, or encourage thinking. Do teacher set homework in order to let students go over or consolidate what has been covered in class. About 50% of mathematics students and teachers say this type of homework is usually the case, about 35% say it is sometimes the case and the responses correlate significantly with four 74

of the five statements in the learning category. For science students about 30% say the going over type of homework is usual, about 56% say it occurs sometimes, but there is no correlation between the science students responses concerning consolidation and learning. Does homework involve preparation for a coming lesson? A full 40% of mathematics students never do this, while only 23% of science students never do this. The responses of the science students correlate well with four of the five learning questions, but there are no correlations with learning for mathematics responses. When homework involves required reading, 60% of science students say this is usually the case and only 20% of mathematics students say this is so. Again, for science students there is a correlation with the learning questions concerning understanding and mastering material, but none for the mathematics students. So the second result is that there is a difference in the type of homework tasks which lead to learning in mathematics and science courses.

What does feedback mean ? In mathematics classes, half of the graded homework is end-of chapter and two-thirds exercises for the next lesson, and in about a quarter there are grades for projects or essays. Ungraded homework includes exercises in about half the classes, and reading or data collection in about a third. A lot of homework is graded. What is the student reaction to homework being graded or not? Most students are interested in getting a grade for homework and in obtaining comments for it. About the same amount of homework is checked in class as is taken home for grading (which agrees with the results that homework counts for the course grade in a little over half the courses). Students are seldom expected to report on their homework to the class and if so, it is only in science classes. Nämnaren 100

What is the connection between grading or commenting on homework and learning? One American study has reported that homework which is corrected with comments is more effective than that with no comments and that graded homework is superior to non-graded homework (Paschal et al., 1984). Our results seem to indicate that the effects can be more subtle than this. Many mathematics students are interested in teacher's comments on homework and are interested in getting a grade. Completing homeworkit is correlated with understanding and enjoying the subject. What is also interesting is that doing homework for the grade is not correlated with mastering the material. Perhaps they feel homework should count towards their final grade but that they can monitor their own mastery i.e. they know when they have mastered material and do not need a grade to tell them this. They do however want their work graded as a reward for their efforts. Science students on the other hand are very interested in the teacher's comments on their homework and this desire correlates with both understanding and mastery. Wanting homework is not significantly correlated with wanting it graded. The value of the homework is that it leads to understanding, but since the attempted homework itself may be incorrect then a grade may be an unfair reward for effort. The third result is then that though many students are dependent on teacher's comments for learning, mathematics students are keener than science students on obtaining a grade for their efforts.

What time is spent on homework? Is it worthwhile? Only about a third of the students claim that they do their homework conscientiously on a regular basis, and only about a third admit that they sometimes cheat on their homework by copying answers from others. The teachers obviously feel that there is more copying than the students acknowledge. A little over a Nämnaren 100

third sometimes get help from others not in their class on their homework, but about half say that they sometimes do their homework with friends and only a handful always do this. Over a third are loners when it comes to doing homework. The time spent on homework is the one variable which is frequently discussed in the literature as affecting learning. Comparing Icelandic results with those from other countries can be a little tricky as the school system is different from many others. Teachers were asked how much time students should spend on doing homework. Over half of them said that there should be about half an hour to an hour per unit. Since the courses described by them are mostly 3-unit courses, then for these teachers the amount of homework in their own courses should be one and a half to three hours a week. Another quarter said that there should be one to two hours per unit i.e. three to six hours per course. Students may be enrolled in 18 units a term. Students were asked how much time they spent on homework in the science or mathematics course under consideration. This question was answered about halfway through the course. Science and mathematics students differed, with about 65% of science students spending less than two hours, but 56% of mathematics students spending more than two hours. Tamir (1985) reports Israeli studies in which students spent about two and a half hours a day on homework and spent more time on mathematics or algebra than science. Is this time well spent? Time spent and spent conscientiously correlates well with both learning (understanding and mastery) and enjoyment for science students but only with enjoyment for mathematics students. Thus it seems that that the time spent on homework by mathematics students has less value for learning. Help from the teacher with homework helps science students master material but only leads to increased enjoyment of the material for mathematics students. Thus the fourth result is that mathema75

tics students spend more time on homework than science students but it appears that the time spent may have less value for learning than for science students.

Summary and implications • Homework seems to be an invisible part of teaching plans. Even so almost all teachers expect students to spend around two hours a week on homework and many students spend at least this amount of time. Certainly if any changes are to be made in homework practices and if its potential for learning is to be realised, then teachers and researchers must first accept that it is as much a part of normal teaching plans as lectures, class exercises and laboratory work and as such should be an integral part of their plans and not just something to keep students busy. Homework practices also deserves more attention in teacher training and by researchers. • Learning as achievement in mathema tics and in science results from different types of homework, with science lear ningdemanding more reading ahead than mathematics, and some science teachers teaching science as if it were only calculations. The sample of teachers has taught and does teach a wide range of science and mathematics courses in the secondary schools, and there was essentially no difference between those teachers who described a science course and those who described a mathematics course. Are teachers fully aware of the types of homework which seem to correlate with student learning? Have they learnt to exploit these differences to the full, especially in tne science courses, where very many teachers concentrate on the exercise type of homework, turning chemistry and physics into applied mathematics courses rather than courses in which students can achieve a deeper un76

derstanding of some of the important methods and concepts of science? • Feedback and evaluation are very important to student learning but in different ways for science students and mathematics students. The science students want teachers' comments in order to check understanding and the mathematics group want the motivation of a grade as a reward for effort. Could it be that in the courses which have been described it may take longer for science concepts to "fall into place"? Thus do some students not want to be graded for work which is part of a process of understanding rather than proof of understanding which "correct" mathematics homework might be? For teachers this result means that it would be wrong to have only one approach to going over homework. Courses which require the falling into place of a number of concepts in order to understand a (new) concept should not rely too heavily on graded homework. Courses which require mastery of techniques and unrelated concepts could include graded homework as an incentive to students. • Time spent on homework seems from this survey to be more valuable for science students than mathematics students. Could this last observation reinforce the earlier comment that in the courses described mathematics students know when a method or concept has been mastered and thus time spent on homework after this point or conversely without understanding is simply wasted time? For mathematics teachers this would mean when teaching for mastery of a method or concept then the homework should be frequent and consist of only a few problems at a time, so that students can return to the classroom and gain the necessary help without spending too much time without reward. Since many physics and cheNämnaren 100

mistry courses are taught as if they were applied mathematics courses, this recommendation applies not only to mathematics teachers but also to some science teachers. • Differences in learning science and lear ning mathematics indicate that teachers should have a flexible and variable ap proach to the way in which they use homework in their courses. Instead of simply saying every day, "For tomorrow, do problems 4, 5, 6 and 8" or at thebeginning of every term that "Home work grades will be 25% of the final grade", teachers must think carefully about the content of each course and decide on the type of homework which might suit each topic in the courses, whether it should be graded or commented on and how much time should be spent on it. Furthermore, it would be nice to see teachers using more creative or unusual types of homework, requiring more readlng ahead, more writing in the form of explanations, summaries of investigations and questions which have arisen, and lastly more working together in groups so that there is more emphasis on cooperative than competitive learning. Our first observation was that homework was an invisible part of teaching plans. The visible part, the les-

sons described, seemed depressingly uniform. Using a wider variety of homework would also require teachers to start using a wider variety of teaching and learning methods in the classroom itself!

Acknowledgements Holar Agricultural College provided the funds for this research. Tumi Tomasson assisted with the translation into Icelandic of the questionnaires and was available for many discussions of the data collected. The teaching staff of the Holar Agricultural College tested and discussed a trial version of the teacher questionnaire. One class of students completed a trial version of the pupil questionnaire. The staff of the library of the Icelandic Teachers' University College obtained many materials through its interlibrary loan service and copied many others. I gratefully acknowledge the assistance of all these parties.

References Norusis, M.J. (1986) SPSS/PC+ for the IBM PC/XT/ AT. Chicago: SPSS inc. Paschal, R.A., Weinstein, T. & Walberg, H.J. (1984) The effects of homework on learning: a quantitative synthesis. Journal of educational research 78(2): pp 97 - 104. Tamir, P. (1985) Homework and science learning in secondary schools. Science education, 69(5): pp 605-618.

Ny bok om Problemlösning Detta är en antologi på 190 sidor och tredje boken i en ny serie som tagits fram i samarbete mellan Göteborgs Universitet, Studentlitteratur och Utbildningsradion. Författarna redogör för hur elevers tänkande och färdigheter i problemlösning kan utvecklas och vilken undervisning som kan hjälpa eleverna att bli goda problemlösare i och utanför skolan. De första böckerna i serien Tal och räkning 1 och 2 har sin tyngdpunkt i elevers grundläggande taluppfattning och aritmetikkunskaper och vilken undervisning som kan hjälpa eleverna till allsidiga räknefärdigheter med och utan hjälpmedel. (Bokserien och de första böckerna anmäldes i nr 2, årgång 18, s 4). Böckerna ingår i en serie i matematikdidaktik och är avsedda för fortbildning, grundutbildning och påbyggnadsutbildning av lärare i matematik. Författare är matematikdidaktiker verksamma som lärare, lärarutbildare, forskare eller läroboksförfattare. Redaktion: Göran Emanuelsson, Bengt Johansson och Ronnie Ryding Författare: Ann Ahlberg, Lars Owe Dahlgren, Göran Emanuelsson, Rolf Eriksson, Lena Fritzén, Barbro Grevholm, Bengt Johansson, Håkan Johansson, Jan Thompson, Bo Sjöström, Lennart Strandberg, Lennart Skoogh, Bengt Ulin, Margareta Wallebäck, Inger Wistedt, och Jan Wyndhamn Nästa bok i serien är Geometri och statistik. Böckerna ges ut på Studentlitteratur och kan beställas direkt därifrån. Nämnaren 100

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