Learners' personal experience of the context also influenced the way they interpreted and responded to the task. I compare this journey she took me to my experience of the Comrades Marathon.
OVERVIEW
FOCUS AND PURPOSE OF STUDY
Today, students are expected to engage in a context with minimal input from the teacher, who is seen as a mediator in the learning process. Little research has been done into the way students learn in the changed circumstances and into the strategies they use.
DETAILS OF STUDY
It is hoped that examining students' thinking strategies will help teachers understand how students think through mathematical contexts and add to knowledge about the considerations that ML students make when answering assessment tasks. It will also motivate teachers to become aware of their own learning and teaching styles in mathematics and will advise task designers on aspects to consider in selecting contexts and designing valid assessment tasks.
REVIEW OF RELATED LITERATURE
- Background to Mathematical Literacy in South Africa
- Recent Literature about Teaching and Learning Mathematical Literacy in South Africa
- The Role of Contexts in Teaching Mathematical Literacy
- Design of Assessment Tasks in Mathematical Literacy
Mathematical Literacy provides learners with an awareness and understanding of the role that mathematics plays in the modern world. Thirdly, Cleo's experience of the context of a holiday (staying at home) differed from that used in the tasks (holiday to Kruger National Park).
THEORETICAL FRAMEWORK FOR THE STUDY
First, the written context is a textual representation of a real-life context, and cannot capture all the details of the context. Third, the language used in the assessment tool affects the ways in which students respond to the items.
SUMMARY
The theoretical framework underlying this study is closely related to the idea of constructivism. Previous knowledge and encounters with the contexts will influence students' perceptions and understanding of the contexts.
- RESEARCH PURPOSE
- RESEARCH PARADIGM
- CONTEXT OF THE STUDY
- SELECTION OF THE SAMPLE
- DATA COLLECTION AND ANALYSIS
- Document Analysis
- Statistical Analysis of Students Responses
- Interviews
- VALIDITY AND TRUSTWORTHINESS
- ANALYSIS OF DATA
- ETHICAL ISSUES OF THE STUDY
- LIMITATIONS OF STUDY
- CHAPTER SUMMARY
A document analysis of the 2009 Preparatory Examination as well as the learner's written solutions was undertaken. A document analysis of the Preparatory Examination was undertaken to assign categories to the variety of contexts in the paper.
- RE-MARKING OF LEARNERS SCRIPTS AND RECORDING OF MARKS
- MARKS OBTAINED PER QUESTION
- DOCUMENT ANALYSIS OF THE 2009 GRADE 12 TRIAL EXAMINATION PAPER TWO IN
- CHAPTER SUMMARY
An analysis was also made of the percentage of learners who achieved full marks, partial marks and no marks for each question. In question 1.2.1(a) the dimension of the nut was given in the question and learners simply had to replace it and get the answer. The difference in performance on these questions based on the same context can be attributed to the cognitive level of the questions with question 3.1.1 assuming the basic level of 'know' and question 3.1.3 characterized by the cognitive level of 'applying routine' procedures in a familiar context'.
Detailed labeling of students' scripts shows that students performed best when questions were not embedded in context. An independent samples t-test was conducted to compare the performance of English first language speakers (Indian) and second language speakers (African).
Role of Diagrams
It is pertinent to note that 23 students read the height of the socket as 3.5, which is the height of the round hole in Figure C. However, the student said that the diagram of the socket in the paper was very confusing and didn't look like what he thought was an electrical outlet. P10 also said that the diagram was not helpful in finding the circumference of the sleeve as the diameter was given in question 1.2.1(a), but he had to refer to the diagram to find the height of the sleeve.
P6 felt that she did not need the diagram to calculate the circumference of the nut as the diameter and formula were given. Despite knowing what a socket looked like, she was still unable to extract the height of the socket from the diagram to calculate the surface area of the socket.
Errors or inconsistencies in the paper or marking memorandum
Some students (10) took the difference between the highest and lowest value in the graph 'boys from the 50th century' and the graph 'boys from the 87th century' (5 students). Others (9) noted the difference between the birth weights in these two graphs, which is understandable as these were the only two graphs dealing with boys' weight. There were 13 students who, like the examiner, considered the difference between the values in the graphs of the first (87th centile boys) and the third (third centile girls).
This was due to a line on the graph being obscured by the number "5 kg", with the respondent thinking the line ended at 5 kg; therefore, she chose 5 kg as the maximum value instead of 4.5 kg, where the line actually ends. However, the 9.5kg answer seems to have been read from the graph labeled 3rd centile girls (yes, the same graph used in V4.1.2 to calculate the mass range of boys).
LEARNERS’ RESPONSES
- Some constraints to learners’ success in the examination tasks
- Some strategies utilised by learners when answering the examination questions
None of the students used the explanation about mortality in the first part of question 4 to answer the question. This indicates that the respondent does not know how to calculate the ratios and therefore resorts to a number grabbing technique from the previous question. This question asked for two benefits of the Student Achiever Account, based on the information in the table.
However, the respondent calculated the volume of the bucket using the formula for the cylinder despite knowing that the bucket and the cylinder are not the same shape. P2 believed that the shape of the bucket and the cylinder were the same, although he drew a bucket that was wider at the top than at the bottom compared to his straight sided cylinder.
LEARNERS’ PERCEPTIONS AND EXPERIENCES OF THE CONTEXTS
- Relevance of Context
- Reasons offered for the relevance of contexts
- Non- recognition of crucial information
- Personal experience of the context
- Complexity of contexts
For example, P3 said that he liked the scenario of taking care of animals (Q3) because it related to work and earning money; and for the CD player context (Q5), P4 explained that “the price is given to us. In question 2.2.3(a), the examiner wanted to know, using the FIFA scoring format, whether South Korea could overtake Spain, with each team having only one game remaining. In question 1.3.3 (a), the respondent estimated that a 10% reduction in a 9-hour day is 8 hours, which he used to calculate John's new working hours.
In question 2.2.3(b), the examiner wanted the candidate to suggest a result that would allow South Africa to qualify for the next round. I guess in the process of taking into account so many variables - the value of D from the previous question, analyzing the minimum number of points needed to advance to the next round, the fanatical scoring system, taking into account how many points South Africa already has, the goals needed to achieve the extra result, and on at the end it suggests a result from among the possible different results - the student has lost focus on what the question actually asks.
CHAPTER SUMMARY
ANSWERS TO RESEARCH QUESTION 2: HOW DID LEARNERS’ PERCEPTIONS AND
The context of the socket in question 1.2 was relevant for P4, P5 and P9, while P2, P3, P6 and P7 did not find the socket scenario relevant. There was not much difference in the performance of students who viewed the socket scenario as relevant or irrelevant; However, no conclusions can be drawn in terms of relevance as two of the three questions could have been answered. Many students found the context of the Football World Cup relevant, but also in terms of performance there was not much difference between those who found the context relevant and those who did not.
While learners may have heard of growth charts, they did not see them as relevant to them as scholars and therefore did not pay attention to how they were read. Those learners who mentioned the importance of the health chart to them as mothers could not answer the assessment questions very well, showing that their understanding of or familiarity with the chart did not help them answer the questions.
ANSWERS TO RESEARCH QUESTION 3: WHAT ARE SOME STRATEGIES UTILISED BY
- Number Grabbing
- Guessing without checking
- Making Simplifying Assumptions
- Scanning the Scenario without making sense
The number grabbing technique was used by participants in this study to devise solutions for the questions and/or the contexts they did not understand. P5 did not know how to calculate ratio and arrived at the ratio 10:1 by grabbing the number from the previous Question 3.1.2. This general response was more of a guess that could be made without reading the context.
Findings revealed that learners often scanned context information to identify crucial information without understanding the context. Although P7 admitted that he did not think the given cylinder formula could be used to find the capacity of the bucket, he “just used the formula” and “didn't really focus” on whether the formula was appropriate for the context. .
ANSWERS TO RESEARCH QUESTION 4: WHAT WERE SOME FACTORS THAT
- Design of Examination Task
- The actual contexts used
- Learner Constraints
The placement of text on the source document influenced students' success in the exam task. Students' own experience of the context and the real world influenced the way they interpreted and responded to the exam tasks. Due to the complexity of the information in the scenario, Participant 2 responded in the interview, “I'm not sure how they get points.”
In addition to issues related to task design and issues related to context, students. The lack of essential information due to the presentation of the exam task is not unique to this study.
LIMITATIONS
Many students complained that key information was too far from where it was requested. In their study, Ahmed and Pollitt (2000) found that students missed out on key information due to task setting and that this in turn affected their performance on the task. In this case, the boat context was used in the first parts of the question, followed by a general question about molecules in the second part.
Since the previous four sub-questions did not ask for any key information from the scenario, students feel that the scenario does not contain any key information to answer sub-question 2.1.5, which actually asked for key information about the time needed to complete the stadium. Khan (2008), analyzing students' experiences of the Common Assessment Task (CTA), found that students were missing 'key information'.
IMPLICATIONS OF THE STUDY
It may have been possible that ESL participants did not fully understand the questions posed during the interview, which may have influenced their responses to some questions. Furthermore, having to express their responses in English meant that L2 participants might not have been able to meaningfully express what they really wanted to say. Interventions to improve student performance should focus on knowledge, concepts, and skills learned in earlier grades and not just at the 12th grade level.
It is my opinion that it is extremely difficult to assess student performance in real life in an exam context, as there can be as many different solutions as there are students. The expected answer in the marking note considering the context would be 9 taxis because you cannot get a fraction of a taxi.
SUGGESTIONS FOR FURTHER RESEARCH
CHAPTER CONCLUSION
Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, Vol. Proceedings of the Eighteenth Annual Meeting of the Southern African Association for Research in Mathematics, Science and Technology Education. Social class differences in children's responses to national curriculum mathematics testing, in: The Editorial Board of the Sociological Review, UK: Blackwell Publishers.
Paper presented at the sixteenth annual conference of the Southern African Association for Research in Science, Mathematics and Technology Education. Proceedings of the 3rd International MES Conference, Copenhagen: Center for Research in Learning Mathematics, pp. Paper presented at the 13th Annual National Congress of the Association for Mathematics Education of South Africa (AMESA), Uplands College, Mpumalanga, South Africa, and Vol. .
Paper presented at the 24th Annual Conference of the Mathematics Education Research Group of Australasia.
