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The influence of context distance on sense making of per cent tasks : the case of Singapore pre-service secondary school mathematics teachers
Author
Teo, Soh Wah
Supervisor
Ng, Swee Fong
Cheng, Lu Pien
Abstract
This thesis investigated how "Mathematical Domain‟ (MD) and "Context Distance‟ (CD) influenced the sense-making of 231 pre-service teachers on per cent tasks. It required participants to identify the status of 21 concluding statements presented by hypothetical students in three areas of MD across tasks with three types of CD. Participants, as teachers, were expected to provide feedback to the students on these concluding statements, and their responses were evaluated.
The study used a “3 MD by 3 CD” matrix design to form a nine-item research instrument – Contextual Tasks – which consisted of three tasks with varying contexts. Each task had three items, one in each areas of MD. The quality of response was measured with three variables – the appropriateness that participants identified the status of the concluding statements (MI), the SOLO quality of justification to the correct concluding statements (MJ), and the SOLO quality of refutation to the erroneous concluding statements (MR). The analysis investigated the variations in the quality of responses with respect to the two constructs – MD and CD. Participants were “proficient” when they identified all statements appropriately, otherwise “less proficient”.
About two-thirds of competent participants, who could solve all the per cent problems in the three areas of MD in a Competency test, were „less proficient‟ in identifying all concluding statements appropriately. Findings showed that both the constructs affected the quality of response of all participants but affected less proficient participants more.
When participants made sense of all the concluding statements of an item without error, their quality of response was considered good. Among the 2079 responses (231 participants 9 items), there were only 786 (38%) good quality responses. The number of good quality responses was different in each MD. When CD increased, the number of good quality responses decreased in the hardest MD where participants scored the lowest in the Competency Test, increased in the easiest MD where they scored the highest in the Competency Test, and fluctuated with their best performance in the moderate CD in the MD which was neither having the lowest nor the highest scores in the Competency Test.
Studying the trends of the variations in the quality of response of each individual showed that CD affected the quality in three ways. Firstly, CD affected the quality of response differently in each MD. It affected the easiest MD the most, and the hardest MD, the least. Secondly, when individuals started with a task with moderate CD described as interesting by the interviewees, they took the shortest time to complete all nine items, yet were more likely to provide good quality responses. When they started with a task with far CD, they took the longest time to complete the same nine items, yet were less likely to provide good quality responses. Thirdly, when individuals experienced the task with far CD in their second task, they provided more good quality responses in their third task.
This study contributes to the widely-underestimated area of the influence of task context and how it affects one‟s performance.
The study used a “3 MD by 3 CD” matrix design to form a nine-item research instrument – Contextual Tasks – which consisted of three tasks with varying contexts. Each task had three items, one in each areas of MD. The quality of response was measured with three variables – the appropriateness that participants identified the status of the concluding statements (MI), the SOLO quality of justification to the correct concluding statements (MJ), and the SOLO quality of refutation to the erroneous concluding statements (MR). The analysis investigated the variations in the quality of responses with respect to the two constructs – MD and CD. Participants were “proficient” when they identified all statements appropriately, otherwise “less proficient”.
About two-thirds of competent participants, who could solve all the per cent problems in the three areas of MD in a Competency test, were „less proficient‟ in identifying all concluding statements appropriately. Findings showed that both the constructs affected the quality of response of all participants but affected less proficient participants more.
When participants made sense of all the concluding statements of an item without error, their quality of response was considered good. Among the 2079 responses (231 participants 9 items), there were only 786 (38%) good quality responses. The number of good quality responses was different in each MD. When CD increased, the number of good quality responses decreased in the hardest MD where participants scored the lowest in the Competency Test, increased in the easiest MD where they scored the highest in the Competency Test, and fluctuated with their best performance in the moderate CD in the MD which was neither having the lowest nor the highest scores in the Competency Test.
Studying the trends of the variations in the quality of response of each individual showed that CD affected the quality in three ways. Firstly, CD affected the quality of response differently in each MD. It affected the easiest MD the most, and the hardest MD, the least. Secondly, when individuals started with a task with moderate CD described as interesting by the interviewees, they took the shortest time to complete all nine items, yet were more likely to provide good quality responses. When they started with a task with far CD, they took the longest time to complete the same nine items, yet were less likely to provide good quality responses. Thirdly, when individuals experienced the task with far CD in their second task, they provided more good quality responses in their third task.
This study contributes to the widely-underestimated area of the influence of task context and how it affects one‟s performance.
Date Issued
2016
Call Number
QA117 Teo
Date Submitted
2016