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- PublicationRestricted16 to 18 year old students' errors and misconceptions in learning probability(1997)Chan, Wai SoenIn Singapore schools, many students study simple theoretical probability in Secondary 4, (15-16 year olds) and in the junior colleges (16-18 year olds). This present study aims to identify and explain the errors and misconceptions that junior college students have when they learn probability through formal instruction.
The Mathematics syllabi, based on the requirements of the Singapore-Cambridge General Certificate in Education Ordinary Level and Advanced Level for the secondary level and the junior college level respectively, stipulated certain requirements. A review of the past literature also indicated several misconceptions such as the use of judgemental heuristics and the assumption that random events were equally probable. The course requirements and the review of the literature resulted in four research questions. First, were junior college students able to reason with proportions and give examples of certain and impossible events? Second, were junior college students able to solve questions which required the skills and concepts taught in the Probability course in the secondary school and in the junior college and what errors would they commit? Third, what would be the main errors when second year students solve problems on conditional probability? Finally, do students use judgemental heuristics and exhibit the biases and fallacies reported in the literature?
Two minor areas were also investigated. One of them was the errors and misconceptions that occur when students use combinatorics. Another was students' verbal explanation of working. Data collection was divided into two parts. The first part consisted of written tests and a second consisted of interviews. The subjects consisted of 216 first year students (16-17 year olds) and 209 second year students (17-18 year olds). The focus of the study was on the second year students who had completed the Probability course in the junior college. The errors that surfaced would be used to improve the teaching programme. The first year students had received formal instruction on probability only at the secondary level. They would provide a convenient sample to which the second year students could be compared. The comparisons focused on the different types of errors and approaches for both groups.
This study found that both cohorts were able to reason with proportions although when considering a proportion of area, some students were affected by the physical appearances. There appeared to be a confusion between certain events and possible events and one reason was that an event was thought to consist of only one outcome.
Questions which concerned a conjunction of events were generally well done. However, when given empirical data, there was a tendency for students to compute a conjunction, assuming that the events were independent events when there was evidence to indicate that they were not.
The complementary rule was applied in questions where its use would make the solution easier. The main error was in defining a single complementary event.
Questions which involved a consideration of mutually exclusive but not equally likely cases brought out a few difficulties. One was the tendency to consider only one case out of several possibilities. This type of error was more prevalent amongst the second year students than the first year students. One reason for this error was that students did not consider the situation thoroughly and only arrived at a partial solution.
When the empirical probability of a union of 2 non-mutually exclusive events was required, students tended to assume that they were mutually exclusive although the evidence indicated otherwise. During the interviews, there was evidence to show that these students knew what "mutually exclusive" meant.
Conditional probability was difficult for many second year students especially when a backward conditioning event was given. Two main errors were the computation of a conjunction instead of a conditional probability and computing P(X) instead of P(X\Y) when event X preceded event Y.
Judgemental heuristics and biases existed amongst several students. This occurred to a greater extent amongst the first years. For the second year students, there was evidence that even though the probability of the event was correctly found, students did not use it to make a decision. The error of assuming that random events were equally likely was prevalent in both cohorts. For the second year students, one reason was because students thought it was only necessary to consider one outcome that satisfied the requirements.
Several second year students had difficulties with permutations and combinations when they used them to count the number of distinct outcomes. First year students who simply listed the cases fared better.
Students were generally uncomfortable with writing down explanations. During the interviews, students preferred to explain their working in terms of arithmetic operations, multiplication and addition, instead of formal terms like "intersection", "union" or "independent". There were subjects who did not associate terms like "and" and "or" with a conjunction or a union respectively. Instead, they associated them with the operations of multiplication and addition.
The study concluded with a discussion on implications for teaching and for further research.
- PublicationOpen AccessA 160 kJ dual plasma focus (DuPF) for fusion-relevant materials testing and nano-materials fabricationThis paper summarizes PF-160 Dual Plasma Focus (DuPF) numerical experiments using the Lee Model code and preliminary 3D design drawings using SolidWorks software. This DuPF consists of two interchangeable electrodes enabling it to be optimized for both Slow Pinch Mode (SFM) and Fast Pinch Mode (FFM); the latter using a speed factor (SF) of 90 kA cm-1 Torr-0.5 for FFM in deuterium [S Lee et al, IEEE Trans Plasma Science 24, 1101-1105 (1996)]; and the former with SF of less than half that value for SFM. Starting with available 6 x 450 μF capacitors rated at 11kV (10% reversal), numerical experiments indicate safe operation at 9 kV, 6 Torr deuterium with FFM anode of 5 cm radius; producing intense ion beam and streaming plasma pulses which would be useful for studies of potential fusion reactor wall materials. On the other hand operating at 5 kV, 10 Torr deuterium with SFM anode of 10 cm radius leads to long- duration, uniform large-area flow which could be more suitable for synthesis of nano-materials. The dual plasma focus design is illustrated here with two figures showing FFM and SFM electrodes.
- PublicationUnknownA 1D–3D interconnected δ-MnO2 nanowires network as high-performance and high energy efficiency cathode material for aqueous zinc-ion batteriesAqueous zinc‐ion batteries (AZIBs) have received significant research attention and widely investigated because of their high intrinsic safety and cost effectiveness. Manganese dioxide has been regarded as a promising cathode material for AZIBs, attributed to its friendliness, abundant resources, high theoretical capacity, and high working voltage. Herein, a unique one-dimensional–three-dimensional (1D–3D) hybrid network with interconnected δ-MnO2 nanowires was reported as a cathode material for AZIBs. A distinctive 3D nano network structure resulted in enhancement of electrolyte osmosis and significant increase in contact between electrode and electrolyte, and also provided more active sites and convenient rapid ion transport routes. Moreover, the fine nanowire structure and the optimum layer spacing resulted in easier insertion/deinsertion of ion in the active material. Taking advantage of this feature, the δ-MnO2 cathode provides high reversible capacity, fast rate capability and good longevity for cycling. Further kinetic experiments revealed that Zn/δ‐MnO2 system constitutes an electrochemical reaction regulated by the combination of ionic diffusion and pseudo-capacitance; and shows high energy efficiency during the charge/discharge states. This research may provide an advanced cathode material for AZIB development.
WOS© Citations 38 156 23Scopus© Citations 42
- PublicationUnknown20 years of research into L1 use in Malaysian ESL classrooms : a qualitative analysis(2019)Tan, Grace HuiminThis study examines research on the use of the first language (L1) in the Malaysian English as a Second Language (ESL) classroom through qualitative analysis. In particular, it aims to discover the themes which have dominated this field of research and to identify their key findings as well as issues found in the studies.
The data comprised of 16 studies that were conducted between 1998 and 2018 in Malaysian primary and secondary schools. These studies were subjected to several cycles of coding based on the constructivist grounded theory approach (Charmaz, 2006) which allowed for the dominant themes, key findings and issues to emerge from the data. From the qualitative analysis, three dominant themes were found in the data: (1) beliefs of L1 use in the Malaysian ESL classroom, (2) L1 use in the Malaysian ESL classroom, and (3) issues found in research on L1 use in Malaysian ESL classrooms. Key findings from the three themes revealed a mixture of negative and positive beliefs towards L1 use and classroom functions which the L1 was used for. The analysis also discovered effects of L1 use on teachers and students found by the studies. From the data, three types of contradictions became apparent. These were: (1) contradictions between beliefs and practices, (2) contradictions between beliefs and (3) contradictions between policies and practices. The analysis revealed issues regarding the lack of theory and evidence-based principles, the stigma of L1 use and the ambiguous stand of the Ministry of Education (MOE) regarding L1 use.
The findings of this study reveal a need for relevant parties in the Malaysian English language teaching (ELT) circle to reexamine their beliefs on L1 use in the ESL classroom and call for the MOE to clarify its position on L1 use in ELT. These findings also point at the need for more experimental research that would rigorously examine effects of L1 use in L2 learning. In sum, three key observations have surfaced from a critical understanding of this area:
1. The monolingual principle is problematic and impractical for the present-day Malaysian ESL context.
2. Teachers are unaware of literature and research legitimising strategic L1 use which could increase their knowledge and confidence in using the L1 to benefit L2 learning.
3. There is a purpose and place for the L1 in the Malaysian ESL classroom.