- ItemMathematical problem-solving processes of male and female secondary students in government and private schools on non-routine tasks(IMHOTEP Mathematical Proceedings, ) Opolot-Okurut, Charles; Bekolle, DavidThis paper reports a small study of secondary school students problem-solving practices in Uganda. A sample of 225 students (109 male and 116 female), in eight government and private secondary schools were used. Students problem-solving processes and strategies were assessed using three non-routine tasks. Solutions of students from government and private schools and differences by gender were categorised and rated as exceptional, proficient, satisfactory, limited, poor and blank. The solutions mean scores were also examined using t-tests of independent samples. The results of the t-tests for independent samples indicated no statisti- cally significant differences in students scores by gender. The results of the t-tests for independent samples indicated a statistically significant difference in students scores by school type. The results suggest that teachers in both government and private schools need to realise that when concepts and skills they teach make sense to students they learn faster, they remember better, and they are better able to use concepts and skills in subsequent problem-solving situations. This study needs replicating at different school levels and contexts using qualitative data collection techniques. Mathematics educators could benefit from knowledge of students problem-solving practices as students should be involved in solving problems rather than mastering skills and not applying them since "the ability to solve problems is at the heart of mathematics" (Cockcroft, 1982, p. 73).
- ItemConstruction of some new three associate class partially balanced incomplete block designs in two replicates(IMHOTEP Mathematical Proceedings, ) Kipkemoi, E. C.; Koske, J. k.; Mutiso, J. M.; Bekolle, DavidSearch for experimental designs which aid in research studies involving large number of treatments with minimal experimental units has been desired overtime. This paper constructs some new series of three associate Partially Balanced Incomplete Block (PBIB) designs having n(n - 2) /4 treatments with three associate classes in two replicates using the concept of triangular association scheme. The design is constructed from an even squared array of n rows and n columns (n _> 8) with its both diagonal entries bearing no treatment entries and that given the location of any treatment in the squared array, the other location of the same treatment in the array is predetermined. The design and association parameters for a general case of an even integer n >_8 are obtained with an illustrated case for n = 8. Efficiencies of the designs within the class of designs are obtained for a general case of even n >_8 with a listing of efficiencies of designs with blocks sizes in the interval [8,22]. The designs constructed have three associate classes and are irreducible to minimum number of associate classes.
- ItemOptimal compliance prediction models for estimating causal effects(IMHOTEP Mathematical Proceedings, ) Odondi, Lang'o; Bekolle, DavidUnderstanding the causal relationship between intervention and outcome is at the heart of most research in the health sciences, and a variety of statistical methods have been developed to address causality. However, noncompliance with treatment assignment is a key source of complication for causal inference. Estimation of causal effects is likely to be compounded by the presence of noncompliance in both treatment arms of clinical trials where the intention-to-treat (ITT) analysis produces a biased estimator for the true causal estimate even under homogeneous treatment effects assumption. Principal stratification method has been developed to address such posttreatment complications by stratifying the population into partially latent classes (principal strata) based on potential values observed after randomization (e.g. noncompliance) under each of the levels of randomized intervention. The present work combines the two strategies of model selection and principal stratification with a novel application to a real data from a trial conducted to ascertain whether or not unopposed oestrogen (hormone replacement therapy - HRT) reduced the risk of further cardiac events in postmenopausal women who survive a first myocardial infarction. The causal model links the resulting two marginal prediction models with a user-defined sensitivity parameter which is a function of the correlation between the two compliance behaviours. The method's key assumption of conditional prediction is verified for our data via sensitivity analysis comparing results of causal estimates using different sets of predictors of compliance. We adjust for noncompliance in both treatment arms under a Bayesian framework to produce causal risk ratio estimates for each principal stratum. The results suggested better efficacy for HRT among those who would comply with it compared to those who would comply with either HRT or placebo: compliance with HRT treatment only and with either treatment allocation would reduce the risk for death (reinfarction) by 47%(25%) and 13%(60%) respectively.
- ItemThe need for effective study skills under the 21st century: a case of USA and KENYA(IMHOTEP Mathematical Proceedings, ) T. Olszewski, Peter; Owiti, Dickson S. O.; Bekolle, DavidThe current world is operating in an economy that values creativity and innovation for scientific and technological development. Education gives people appropriate skills and knowledge they need to address their social problems. Mathematics and Science education is at the centre of this and needs to be at the forefront to connect the present to the future. The fact that a new generation of learners is in our classrooms requiring a paradigm shift in pedagogy is indisputable. Teaching in the same old way and emphasis on examinations, grades, certificates as well as lack of basic facilities have affected learning by generation Y students. As a result, Kenya like the United States of America faces a myriad of problems despite the fact that the youth is a reach reservoir for development. More than 50 per cent of the world's gold reserves, diamond, manganese, chromium, and cobalt are in Africa yet Africans live in the poorest situations imaginable. The United States, despite being the most powerful nation on the planet has, in general, have poor test scores in mathematics if results of international comparative studies are anything to go by. This paper argues in addition to poor teaching methods, strategies, and techniques, the assumption that stu- dents know how to study mathematics once in secondary school, college, and university and the failure to teach the same is partly to blame since year after year, students either drop out, receive poor grades, fail to attend classes and or don't take mathematics seri- ously. Millennials therefore need to be taught study skills in mathematics to ensure quality mathematics learning for creativity and innovativeness in the citizens. This will ensure education empowers Kenya, Africa, and the United States for global competitiveness. In particular, this paper intends to address the following current issues in Kenyan and Unites States schools: 1. Describe the Millennial Student, 2. Ramifications for Kenya and the United States, 3. Kenyan and United States curricula, 4. How to teach effective study skills, 5. What is needed of educators, and 6. What to do in the future.
- ItemGroups of units of commutative completely primary finite rings(IMHOTEP Mathematical Proceedings, ) J. Chikunji, Chiteng'a