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The Quality of Learning and Teaching in Developing Countries: Assessing Literacy and Numeracy in Malawi and Sri Lanka - Education Research Paper No. 41, 2000, 90 p. [Previous Page] [Table of Contents] [Next Page] Chapter 5 - Results
Part 1 - Teaching and Assessment Part 1 - Teaching and AssessmentOne aim of the study was to identify what kinds of teacher activities and what assessment practices existed in both countries. During the research period, a large number of observations was carried out and teachers were interviewed. The research was particularly concerned with finding out how literacy and mathematics were taught and assessed in the two countries. In Malawi the classroom activities observed showed that there was very little teaching of reading. Where reading activity was observed, teachers read to the whole class from text books. Listening to individual children read from fiction and non-fiction readers occurred in a small percentage of the lessons observed, although in most of the occasions observed, teachers were engaged in another activity, usually, marking exercise books, while children were called to the front to read. The rest of the class was asked to follow the text in their books. Only in a very few of the lessons observed did the teachers take a active role in reading. They tended to read with children and helped them when they encountered difficult words. Even here though, the teacher was more concerned with correcting reading errors, rather than helping the child enjoy the book by drawing attention to characters, pictures, print and so on. No records were kept on childrens abilities as readers. Teaching support for the development of writing was minimal. There was little evidence that teachers were engaging in activities designed to enhance and enrich the creative and factual writing abilities of their students. In only a small number of the lessons observed did teachers provide students with a variety of tools for writing. In some of the lessons observed, teachers provided resources for writing. This consisted of teachers recycling paper to make books for students to write in. This was particularly encouraging as in most cases, teachers pointed to the lack of resources for writing as a reason for limited writing activity. Even more encouraging was where teachers helped students to identify different audiences for their writing. In about a third of observed English lessons, teachers emphasised for example the differences between writing a friendly letter and a formal letter. Very few teachers viewed writing as a process where they encouraged students to produce more than one draft. This however, was not the norm in Malawi. The assessment of writing was focused on formal accuracy - grammar, spelling and punctuation - and a mark, usually out of 20, was awarded. Very few records were kept. In mathematics, teacher concentrated mainly on addition, subtraction, multiplication and number work of different kinds. Very few, if any, observations were made of children investigating or solving problems through group discussion. The assessment of mathematics consisted of marking answers right or wrong and very few records of childrens progress were kept. In Sri Lanka it was clear that the context of learning and teaching was very different to that in Malawi. Schools were far better resourced and teachers were engaged in numerous activities to support both literacy and mathematics. Most encouraging to observe was established practice of recording student progress. Numerous innovative teacher made systems for recording childrens progress in literacy and mathematics were visible in all the research schools. One of the researchers on the team made the following remark: In classrooms, I came across recording systems used by teachers to record pupil progress -achievement on several criteria judged at four levels, each half term. Progress over the year is monitored, in some cases, publicly displayed and, in one school, analysed and available in the Principals study. For one teacher, her record led to the short-listing of pupils who needed special help and these were monitored more closely with a more detailed set of criteria. In mathematics, I saw reports, or heard about, several more substantial surveys of what pupils can do at various stages in the primary school.These findings are consistent with the view taken by Little (1991). According to her, continuous assessment was introduced as an alternative procedure to formal testing during the 1972 reforms in primary education, mainly to reduce the anxiety of sitting tests and to ensure that corrective measures could be taken quickly as soon as teachers realised the particular competencies each child failed to master. The use of assessment for formative, rather than summative, purposes was expected to help improve the competence level of pupils gradually. Teachers, however, need much training and commitment as records need to be kept carefully and regularly. Currently, continuous assessment is expected to be used in Years 1-3 while end-of-term formal testing is used in years 4 and 5. Although a format has been prepared, and guidance on filling it out has been provided, widespread use of these procedures is not evident (Little 1991). By contrast, end-of-term formal testing is evident in most schools, even for Year 1. It is clear from the above account that there is a considerable variety of assessment practices in use in schools in the two countries studied. This ranges from, at one extreme, teachers who are faced with such an overwhelming combination of huge class sizes and lack of even the basic resources that they are unable to employ any sort of systematic classroom assessment practice at all. At the other extreme are teachers whose professional skill and commitment has led them to develop their own procedures for maintaining pupils progress in order to support individual learning most effectively. Clearly, it would not be possible to devise a system that could meet this range of needs. However, these observations do underline the value of teachers routinely being provided with suitable assessment tools which would enable the majority to develop and operate much more useful systems for monitoring individual pupil achievement and for providing classroom-level feedback on the profile of student learning. Part 2 - Assessing Literacy LearningGeneral principles Literacy learning was assessed in Malawi and Sri Lanka. In both countries, both English and other national languages were assessed. In the case of Malawi, assessments were made of childrens oral and written language and of reading in English and Chichewa. Similarly, in Sri Lanka, assessments were made of childrens oral, written work and their reading in English, Sinhahla and Tamil. In each case, standard tasks, designed by the researchers and participating teachers were used to assess achievements. Tasks to assess literacy learning in Malawi and Sri Lanka The tasks were designed to assess childrens abilities to communicate in different communicative contexts. In assessing Oracy and Reading, teachers were asked to select six to ten children in their classes on the basis of whom they thought were good, average and weak communicators. Once they had made their selection, they were to write the names of these children on Record Sheets which were provided. For the assessment of writing teachers were able to select all the children in their classes. Over the course of the research, the communicative competencies of the selected samples of children were assessed. Teachers recorded the results on the record sheets, and in the case of writing, collected corpora of texts from their students. Because of the diversity of the student samples, on these scores of children aged nine to 10 years (junior primary in Malawi and year 4 in Sri Lanka are reported here). Developing a framework for the assessment of literacy learning As described in chapter 3, teachers met in groups on several occasions to discuss the samples of childrens work. Each teacher brought to these meetings, samples of childrens records (oral language was recorded verbatim on the teacher record sheet), their own assessment of the level these samples had achieved and the teachers written comments of the work, justifying the level awarded. Teachers were encouraged to bring samples of those childrens work who they had rated as doing well, average performance and experiencing difficulties. At the meetings teachers worked in small groups in which they exchanged the samples of students work. The went about the task of studying these samples in order to determine what it is that children do when confronted by the given tasks. They looked at the comments written by the class teacher and the levels awarded to each sample. On this basis, teachers began to draft statements describing each level. Once the descriptions for each level had been decided, a second sample of records was selected. Each teacher was provided with a scoring sheet and rated each record. The level of agreement was high amongst teachers when these records were subjected to a statistical reliability procedure (Cohens Kappa). This exercise allowed teachers to refine the level descriptions they had agreed on earlier to accommodate a wider variety of student work. The level descriptions differ between countries, but not markedly, and also between English and national languages within each country. The level descriptions for English in both cases were lower that the expectations expressed in formal curriculum documents of what students could achieve in the national languages at each level. The literacy scale below is an example for the assessments conducted in English in Malawi. The Literacy Scale and Level Descriptors Oracy Level 1 The child shows awareness of the context and can name things in the illustration. The child is capable of making short sentences or statements about things in the illustration. Level 2 The child shows an awareness of the context and can describe individual things or events in the illustration in simple terms. There is some evidence of the use of conjunctions. Level 3 The child understands the context portrayed in the illustration and is able to describe events and items in the illustration in a simple and more complex sentences. The child is also begins to interpret the illustration and to reason or question beyond what is visible. Level 4 The child understand the context portrayed in the illustration and is able to talk fluently about the events and items using a wide range of vocabulary and sentences in which meaning is embedded in complex ways. The child is able to interpret the illustration and reason and question what is not visible Administering Oral Language Tasks in Malawi The tasks comprised of an illustration, taken from language books for ten year olds children in both countries (see example on the next page). The selected students were to look at the illustration and talk about it. Teachers were provided with Record Sheets and recorded what children said verbatim, as far as was possible. An illustration of the task is shown overleaf, and the instructions to teachers and teacher record forms are contained in the appendices. The Samples In Malawi, 270 samples of childrens use of English language were collected and the same children were assessed again in Chichewa. The age range was nine to ten year olds. In Sri Lanka, 60 samples of childrens oral use of English language were collected; 20 samples of childrens oral use of Tamil; and 80 samples of their use of Sinhala were collected. Interpreting the Literacy Profiles The following literacy profiles were constructed through an analysis of all samples of childrens work in relation to the literacy levels developed in each country. The results are not intended to be compared between countries nor between languages. The profiles show however what children are achieving in each language, in each country, in relation to the expected standards set by teachers. Even though level statements are different for each country and within each country in relation to languages, teachers set an arbitrary standard, level 3 in each case, as the desired norm to be achieved by at least 50% of children. This gives us a basis for interpreting the results of each country in terms of childrens achievements in relation to the benchmarks set for each learning area. Assessing Oracy: Malawi The illustration on the following page shows the task used to assess the use of oral language in Malawi. The profiles of achievement are shown below. ENGLISH - JUNIOR PRIMARY ILLUSTRATION FOR ORAL TASKS - WORKSHEET 1 Illustration of the Language Task - Assessing Oracy in Malawi
Profiles of Achievement Figure 1: Profile of Oral Competence - English Figure 1 shows that 22 percent of children achieved Level 1. 38.8 percent of children achieved Level 2 while 27.7 percent achieved Level 3. Only 11.1 percent of children achieved Level 4. Figure 2: Profile of Oral Competence (Chichewa) Figure 2 shows that 12.2 percent of children achieved level 1. 32.9 percent of children achieved level 2 while 40.7 percent achieved level 3. Only 14.4% of children achieved level 4. EXAMPLES OF INDIVIDUAL CHILDRENS PERFORMANCES FOR EACH LEVEL The following examples drawn from oral samples in Malawi gives an illustration of the kinds of work considered to be at levels 1-4. In these examples, the verbatim records as written by the teachers are illustrated in the boxes below and the teachers comments, justifying their decisions to award a particular level, are also reproduced. Level 1 Box 1 - Example of verbatim record of oral language
In this example, the child simply names items in the illustration. An attempt is made to construct the events illustrated in the picture but the child fails to follow through completely in English and completes the description in Chichewa. The teacher has this to say about the childs performance. Box 2 - Teacher comments and reasons for awarding level
Level 2 Box 3 - Example of verbatim record of oral language
In this example, the child names items in the illustration but there is an attempt to construct simple sentences. The child also is clearly able to construct the events illustrated in the picture but like the child above, fails to follow through completely in English and completes the description in Chichewa. The teacher has this to say about the childs performance. Box 4 - Teacher comments and reasons for awarding level
Level 3 Box 5 - Example of verbatim record of oral language
In this example, there is evidence of an attempt to construct simple sentences. The child is also able to construct and interpret the events illustrated in the picture even where the actions arent themselves illustrated. For example the child say take the tube from the tyre then put it in the basin of water to find where the puncture is. The child also lapses in to Chichewa to complete the description. The teacher has this to say about the childs performance. Box 6 - Teacher comments and reasons for awarding level
Level 4 Box 7 - Example of verbatim record of oral language
In this example, the child is aware of the context of events. She is able to identify what is happening in the illustration and describes these in clear sentences. The child has expanded on the events and has brought her imagination into play. She talks of events before those illustrated in the picture, thus widening the context. The teacher has this to say about the childs performance. Box 8 - Teacher comments and reasons for awarding level
Assessing Oracy: Sri Lanka Tasks to assess oral competencies in Sri Lanka As in Malawi, the tasks were designed to assess childrens abilities to communicate orally in different communicative contexts. Here too, teachers were asked to select six to ten children in their classes on the basis of whom they thought were good, average and weak communicators. Once they had made their selection, they were to write the names of these children on a Record Sheet which was provided. Over the course of the research, the communicative competencies of the selected sample of children were assessed. Administering The Task The task comprised of an illustration, taken from a reading book in for ten year old children in Sri Lanka - Lets Go to the Fair. The illustration is of a mother and her two children buying fruit from a fruit stall. The selected students were to look at the illustration and talk about it. The English task is shown overleaf. The tasks in Tamil and Sinhalese are contained in the appendices. The Sample 60 samples of childrens oral competence in English were collected. 20 samples of work were collected from Tamil speaking schools and 80 samples of work from Sinhalese speaking children. Example of task to assess oracy in Sri Lanka
Profiles of Achievement Figure 4: Profile of Oral Competence - Tamil Figure 4 shows that 50% of students are achieving levels 1 and 2 in oracy in Tamil. 20% are achieving Level 3 and 30% level 4. Figure 5: Profile of Oral Competence - Sinhala Figure 5 shows that 26.4 % of children are achieving Level 1, 43.3% Level 2, 20.7% Level 3 and 9.4% Level 4. Figure 6: Profile of Oral Competence - English Figure 6 shows that 27.7% of children achieved Level 1, 42.5% Level 2, 20.3 percent Level 3 and 9.2% Level 4. Figure 7: Profile of Oral Competence (Tamil, Sinhala and English) Figure 7 shows the profiles of achievement in oracy for all three Language groups. EXAMPLES OF INDIVIDUAL CHILDRENS PERFORMANCES FOR EACH LEVEL IN ENGLISH (SRI LANKA) The following examples drawn from oral samples in Sri Lanka gives an illustration of the kinds of work considered to be at levels 1-4. In these examples, the verbatim records as written by the teachers are illustrated in the boxes below and the teachers comments, justifying their decisions to award a particular level, are also reproduced. Level 1 Box 9 - Example of verbatim record of oral language
Teachers were asked to make a judgement of each childs writing proficiency and to complete notes on each child according to the following questions: 1. Does the child talk fluently? In this example, the child simply names items in the illustration. According to the teacher the child did not talk fluently, and hesitated very much. She also mispronounced many words. 2. Does the child describe the illustration in an imaginative way (describing imaginative events) or simply describe the objects in the picture? According to the teacher for the example given above, the child showed little imagination and simply tried to name the objects in the picture. 3. Is the information relevant to the illustration? In this example the child confined their description to what they could see in the illustration. The teacher completed the record as follows: Box 10 - Teacher comments and reasons for awarding level
Level 2 Box 11 - Example of verbatim record of oral language
1. Does the child talk fluently? According to the teacher the child spoke without any hesitation and her speaking was fluent. 2. Does the child describe the illustration in an imaginative way (describing imaginative events) or simply describe the objects in the picture? According to the teacher the child described the illustration in an imaginative way e.g. there are two boys. The boys are playing cricket. The ball is in the window. 3. Is the information relevant to the illustration? In this example all the information was confined to what was visible in the illustration and as such relevant. The teacher completed this part of the record as follows: Box 12 - Teacher comments and reasons for awarding level
Level 3 Box 13 - Example of verbatim record of oral language
1. Does the child talk fluently? According to the teacher the child spoke very fluently and her pronunciation was good. 2. Does the child describe the illustration in an imaginative way (describing imaginative events) or simply describe the objects in the picture? The child described the picture in an imaginative manner and the teacher points out that although the child described the situation in the picture she used her imagination on several occasions e.g. the boys are not happy. 3. Is the information relevant to the illustration? In this example all the information provide was relevant to the illustration. The teacher completed this part of the record as follows: Box 14 - Teacher comments and reasons for awarding level
Assessing reading in Malawi and Sri Lanka Reading Tasks The reading tasks were designed to gather evidence of children as independent readers. The task provides a broad assessment of childrens reading, allowing them to demonstrate their ability to read aloud from a text, show what they have understood and give a personal response. Reading books in Malawi and Sri Lanka used at the levels of education for the children involved in the study were selected and extracts were selected to serve as the reading task. A running record was developed, (a matrix containing a copy of the text to be read, with each word contained in a separate box in the matrix and with blank spaces beneath each word). Teachers would follow the reading and mark the record for each reader, indicating accuracy, self correcting strategies, words which are omitted and so on. An assessment record sheet was also provided for each reader. On this form, teachers would record comments on how the child read, what they understood from the text and their attitude towards the text itself. The Literacy Scale and Level Descriptors (Reading) The following levels and level descriptions were decided upon by teachers in Malawi. A similar set of descriptions for each level was decided upon by teachers in Sri Lanka. It is worth noting again that there were slight differences in what teachers expected reading levels should be in English and for national languages. Level 1 The child mis-reads most words and has no strategy for reading unfamiliar words. She does not show an awareness or an understanding of what she is reading. Level 2 The child recognises some words consistently and shows awareness of punctuation. The reader shows an appreciation of the text. Level 3 The child reads with accuracy and shows understanding of what he or she is reading through expression, volume and emphasis. She expresses opinions about the text. Level 4 The child reads with accuracy, shows understanding by reading through expression. She has the ability to express opinions about main events and ideas. Assessing Reading: Malawi The illustration on the following page is an example of a task used to assess the reading of 10 year olds in Malawi. Their achievements are profiled below. An example of the reading task - Malawi ENGLISH - JUNIOR PRIMARY READING TASK
Profiles of Achievement Figure 8: Profile of Reading (English) Figure 8 shows that 13% of children achieved Level 1, 37.6, Level 2, 32.4, Level 3 and 17% achieved Level 4. Figure 9: Profile of Reading (Chichewa) Figure 9 shows that in Reading Chichewa, 6.5% of children achieved Level 1, 30.5, Level 2, 39.2%, Level 3 and 23.8% achieved level 4. Figure 10: Profile of Reading (English and Chichewa) Figure 10 shows the profile of achievement for Reading in English and Chichewa. EXAMPLES OF INDIVIDUAL CHILDRENS PERFORMANCES The following examples of teacher comments based on evidence from both the running records and reading records of childrens reading in Malawi, provides an illustration of how decisions were made in awarding different levels. The example shown here is that of a child who was awarded Level 2. ENGLISH - JUNIOR PRIMARY READING RECORD
What to do 1. Complete the reading record as follows:
2. Comment on the childs reading performance. Use the set questions to help you. ENGLISH - JUNIOR PRIMARY Analysis continued... a) Does the child respond to what he or she is reading through expression?3. Ask the child to retell the story in his or her own words and to predict what might happen next (Ask the child some questions like: which aspects of the story did you enjoy or not enjoy?) Make a judgement about whether the child is able to re-tell the context of the passage, including, at least, two of the main points and whether she can make a sensible prediction about what might happen next.
4. Make a judgement about childrens abilities to talk in simple terms about the extent to which they find reading interesting or enjoyable. You could, for example, ask the child questions like: which aspects of the story did you enjoy/not enjoy?
Assessing Reading: Sri Lanka The illustration on the following page is an example of a task used to assess the reading of 10 year olds in Sri Lanka. Their achievements are profiled below. An example of the reading task - Sri Lanka
Profiles of Achievement Figure 11: Profile of Reading (English) Figure 11 shows that 17% of children achieved Level 1, 44.2% achieved Level 2, 30% achieved Level 3 and 8.8% achieved Level 4. Figure 12: Profile of Reading (Tamil) Figure 12 shows that 5.5% of children achieved Level 1, 31.5% achieved Level 2, 37.2% achieved Level 3 and 25.8% achieved Level 4. Figure 13: Profile of Reading (Sinhala) Figure 13 shows that 6.5% of children achieved Level 1, 35.5%, Level 2, 43%, Level 3 and 13% achieved Level 4. Figure 14: Profile of Reading (English, Tamil and Sinhala) Figure 14 shows the profile of achievement in Reading for English, Tamil and Sinhala Examples of Running Records and Teacher comments RESEARCH PROJECT ON ASSESSING THE QUALITY OF LEARNING AND TEACHING -1996 (NATIONAL INSTITUTE OF EDUCATION - SRI LANKA & BRISTOL UNIVERSITY - UNITED KINGDOM) ENGLISH ~ YEAR IV - READING RECORDS
Passage 3: The present
Uncle - Reading was nice. Rising and falling were in his reading; But in some places he dragged some words and stopped reading because he couldnt read the next word easily, example like present, and guess. His presentation was good.Overall presentation was good. All the students were active. They pronounced and expressed the ideas nicely. Assessing Writing in Malawi and Sri Lanka Writing Tasks The writing tasks were designed to gather evidence of children as independent writers The tasks were interested in assessing whether children could communicate meaning to a reader and whether they had an awareness of wide range of the functional aspects of language, including grammar, punctuation and the conventions of spelling and handwriting. The tasks took as their starting points, ideas related to passages from books, in some cases those related to the reading task (Sri Lanka) or in Malawi, to a text read in class. The Literacy Scale and Level Descriptors (Writing) The following levels and level descriptions were decided upon by teachers in Malawi. A similar set of descriptions for each level was decided upon by teachers in Sri Lanka. It is worth noting again that there were differences in what teachers emphasised as being important for each level depending on whether the assessments were in English or in the national languages. Level 1 The writing is organised in words and phrases. There is no evidence of use of punctuation or consistent orientation in shaping letters. Level 2 The writing communicates meaning in simple words and phrases. The is some awareness of the use of full stops. Letters have clear shapes and orientations. Level 3 The writing communicates meaning in narrative or non-narrative forms. Mainly simple sentences are used. Ideas are in some sequence. There is a clear awareness of the use of full stops, capitals and some with-in sentence punctuation. Level 4 The writing communicates meaning through the use of simple and complex sentences. There is an awareness of the reader. Ideas are expressed in a logical way. There is good use of both between sentence and within sentence punctuation. Letters are accurately formed and consistent in size. Assessing Writing: Malawi An example of a task to assess the writing of 10 year olds in Malawi is provided on the following page. Their achievements are profiled below. ENGLISH - JUNIOR PRIMARY
Profiles of Achievement Figure 15: Profile of Writing (English) Figure 15 shows that for writing a story in English 23.3% of children achieved Level 1, 30.2% achieved Level 2, 40.5% achieved Level 3 and 6% achieved Level 4. Figure 16: Profile of Writing (Chichewa) Figure 16 shows that for writing a story in Chichewa, 11.5% of children achieved Level 1, 35.5%, Level 2, 42.8%, Level 3, and 10.2% achieved Level 4. Figure 17: Profile of Writing (English and Chichewa) Figure 17 shows the profile of achievement for story writing in English and Chichewa. Examples of Story Writing - Malawi ENGLISH
AT THE HOSPITAL Dialogue At the hospital
Examples of Story Writing - Malawi AT THE HOSPITAL
Assessing Writing: Sri Lanka An example of a task to assess the writing of ten year olds in Sri Lanka is provided on the following page. Their achievements are profiled below. An example of the writing task - Sri Lanka RESEARCH PROJECT ON ASSESSING THE QUALITY OF LEARNING AND
TEACHING -1996
Profiles of Achievement Figure 18: Profile of Writing (English) Figure 18 shows that for story writing in English, 83.6% of the children in Sri Lanka achieved Level 1, 13.6%, Level 2 and 2.5% achieved Level 3. No students in the sample achieved Level 4. Figure 19: Profile of Writing (Tamil) Figure 19 shows that for story writing in Tamil, 18.5% of students achieved Level 1. 37.3% achieved Level 2, 38.7% achieved level 3 and 5.5% Level 4. Figure 20: Profile of Writing (Sinhala) Figure 20 shows that for the writing of stories in Sinhala, 15.3% of children achieved Level 1, 36.7% Level 2, 39% Level 3 and 9% achieved Level 4. Figure 21: Profile of Writing (English, Tamil and Sinhala) Figure 21 shows the profile of achievement for story writing in Sri Lanka. An example of the writing task - Sri Lanka RESEARCH PROJECT ON ASSESSING THE QUALITY OF LEARNING AND
TEACHING -1996 ENGLISH
Part 3 - Assessing Mathematics LearningGeneral Principles Learning Mathematics was assessed in Malawi and Sri Lanka. In the case of Malawi, assessments were made in English while in Sri Lanka, the tasks were locally translated so that assessments were made in Sinhala and Tamil as appropriate. In each case the assessment tasks emerged from the researcher working with local teachers and, in Sri Lanka, curriculum officers. Tasks to assess Mathematics Learning Two areas of the curriculum were selected, one for each of the two rounds of assessment. In the first round the focus was on number and operations on numbers. In the second, attention was given to measurement. Some tasks were designed to be undertaken by individual pupils who had to provide written answers. Other tasks invited pupils to work in small groups which produced written outcomes of their work both as a group and individually. Teachers were encouraged to observe the working of such group activities and to note particularly the nature of the communication which took place. The tasks and instructions to teachers on how they should be administered are contained in the appendices. Examples and discussion of these follow. The Sample Teachers were asked to select all the students from their classes to participate in the research. About 300 students took part in the mathematics assessments (Junior Primary) in Malawi and about 150 students in the fourth primary class in Sri Lanka. Awarding Levels The use of Levels was attempted, to parallel that used in English. However the number of small items comprising the overall task made distinctions more difficult. A simple overall level grading was given following analysis based on the number of items pupils were successful in answering. Success in answering was not simply dependent on the final answer, but on evidence of working where this was appropriate. The tasks in Mathematics In each of the two rounds of testing there was an attempt to use both standard and less common type of test item on mathematical content in the mathematics syllabus at the relevant grade level. It was hoped that teachers would be encouraged to explore how their pupils responded to different types of question. (i) Number In the number items there were examples of · questions given orally and others which were written,Box II below gives an example of an activity for Infants in Malawi:
In the event with widespread participating teachers and schools, together with the only occasional contact between researchers and teachers, it became evident that the more subtle elements of feedback were being lost through problems of communication and the unfamiliarity teachers had in interpreting many of phenomena occurring in the learning of mathematics. A traditional expectation of items being right or wrong led to marking and summing of scores in spite of the analysis proposed. It proved too demanding to provide the security of the familiar, together with the challenge of that which was in form if not in mathematical content new to the mathematical experience of the teachers. Considerably more time would have been necessary with the teachers to support them in developing more usefully diagnostic testing with their pupils. In general pupils in both countries showed themselves relatively competent at the straight computation, were more troubled at problems which required the selection of the appropriate operation and often required considerable support and guidance in those problems which were of a more open and non standard type. In the end the most useful outcome was the variety of items developed with the teachers, giving evidence of ways in which the basic number skills can be applied in interesting and less closed situations. (ii) Measurement The selection of activities in this round of assessment was designed to provide data relating to skills and concepts but not the application of formulae which are often over emphasised in elementary work on measurement. Pupils had to find the length and area of shapes drawn on a grid but also to draw shapes according to given specifications.
They were also required to measure the size of a drawn rectangle and of the task sheet. On dotty paper we can draw triangles using a dot at each corner.
Use the dotty paper below to draw as many different triangles as you can on a nine dot grid. (Draw one triangle on each grid.)
Write a few sentences about what you have found. Finally there was a more investigatory task in drawing different triangles on a 3x3 grid. In the latter task teachers were again given guidance on some specific things to observe and several key questions were raised with teachers. However the research mechanisms did not provide for the effective collection and analysis of this data. It remains to be followed up in a situation where researcher and teachers can work more closely together over an extended period. The results from Sri Lankan schools in relation to measurement revealed some striking contrasts in the performance on particular items and sometimes between schools. Three examples may serve to illustrate: (i) Students were given an example of a snake drawn along the lines of a grid and shown how its length could be found. They were then asked:The measurement tasks therefore reveal some interesting aspects of performance which would be worth further exploration. The strongest impression is that pupil performance is highly developed over a limited range of skills but significant difficulties are revealed (especially in some institutions) when problems are even modestly less orthodox. This may reflect teachers perceptions of what is expected of them in general, or in particular examinations. However, if the mathematics being learned is to be useful to the pupils in the long term current practice could well benefit from review. Profiles of Achievement Mathematics Profile (Sri Lanka)
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