Effectiveness of teacher selected strategies on students’ academic performance in mathematics, A case of form three students.

Mathematics is a compulsory subject to all students. It is regarded as a career subject since anything students do after high school revolves around mathematics. Teachers of mathematics always strive to improve students’ performance in mathematics. They always make sure that they complete the syllabus to give students a chance to do better in mathematics. Despite the importance of mathematics, most students in many schools still fail mathematics Examinations. The performance over the years has been persistently very poor. The purpose of this study was to find out which of the strategies of learning mathematics improves students achievement in mathematics; individualization for Mastery approach (IMA) or completing the syllabus (CSA).This entailed the use of the two approaches in the learning of Vectors 11; a form three mathematics topic. This study investigated the relationship between the achievement of students where teachers of mathematics used Individualization for Mastery approach (IMA) and those ones where the teachers worked hard to complete the syllabus. The theoretical framework which guided this study was social constructivism theory. The study adopted a pre-test post-test non-equivalent group design. The target population for this study was all the form three students in 39 secondary schools in Mumias sub-county. Stratified random sampling was used to select schools that took part in the study. The strata were Boys’ schools, Girls’ schools and co-educational schools. From girls’ and co- education schools, the researcher randomly selected three schools from each out of 10 and 26 schools respectively, while from boys’ schools; two schools were selected using saturation sampling giving a total of eight (8) schools that participated in the study. One stream selected randomly from each sampled school took party in the study. Experimental group had a total of 126 students while the Control group had 130 students. The Control group used completing the syllabus approach (CSA) while the Experimental group used Individualization for Mastery (IMA) approach. Each group (CSA and IMA) comprised of four schools selected randomly from the eight schools. The students’ Achievement test was used to collect data. The instrument was developed basing on the objectives and given to the experts in Mathematics Education to validate. To determine the reliability of the instrument, Split half technique was employed since it involves only one testing session and it eliminates chance error. Data was analyzed using both descriptive and inferential statistics. Results indicate that there is a significant difference in achievement between students who used Individualization for Mastery (IMA) approach and those who used completing the syllabus (CSA) strategy in favor of the (IMA) group.

Cause and effect: The epidemiological approach

Cause and effect understanding is the highest form of scientific knowledge. In epidemiology, demonstrating causality is difficult because of the long and complex natural history of many human diseases and because of ethical restraints. Epidemiologists should: hold the attitude that all judgements of cause and effect are tentative; understand that causal thinking demands a judgement; be alert for the play of chance, error, and bias; always consider reverse causality and confounding, utilize the power of causal models that broaden causal perspectives; apply guidelines for causality as an aid to thinking and not as a checklist; and look for corroboration of causality from other scientific frameworks for assessment of cause and effect. The ultimate aim of epidemiology is to use knowledge of cause and effect to break links between disease and its causes and to improve health. The application of erroneous knowledge has serious repercussions.

Why internal and external validity of experimental studies are relevant for clinical practice?

In randomised controlled trials (RCTs) there are two types of validity: internal validity and external validity. Internal validity refers to the extent to which the observed difference between groups can be correctly attributed to the intervention under investigation. In other words, it is the extent to which the design and conduct of the trial eliminate error. Internal validity might be threatened by two types of errors: systematic error (also called bias) and chance error (also called random error or statistical error) (Keirse & Hanssens, 2000. Systematic error, or bias, may be the consequence of erroneous ways of collecting, analysing and interpreting data. This may produce differences between treatments that are not real, with an overestimation or an underestimation of the true beneficial or harmful effect of an intervention (Juni et al., 2001). In RCTs there are four types of bias: selection bias (when the groups differ in baseline characteristics because of the way participants are selected), performance bias (when the care provided to the trial participants differs systematically between the experimental and control group), detection bias (when there are systematic differences in outcome assessment), and attrition bias (when the loss of participants from the study systematically differs between the experimental and control group). By contrast, chance error, or statistical error, is due to outcome variability that may arise by chance alone. Studies with small sample sizes are more likely to incur in this type of error than studies with large sample sizes. Thus, the risk of random error may be minimised by recruiting sufficiently large samples of patients.

Testing the Agreement/Tense Omission Model using an elicited imitation paradigm

The present study used an elicited imitation paradigm to test the prediction of Schutze & Wexler's (1996) AGREEMENT/TENSE OMISSION MODEL (ATOM) that the rate of non-nominative subjects with agreement-marked verb forms will be sufficiently low that such errors can reasonably be disregarded as noise in the data. A screening procedure identified five children who produced non-nominative subject errors (all her for she) who were then asked to repeat 24 sentences with 3sg feminine pronoun subjects (she) and agreeing main verbs or auxiliaries. All five children produced at least one non-nominative subject (her) with an agreement-marked verb form, and for none of these five children was the non-NOM+AGR rate significantly different to the rate that would be expected by chance, given the independent frequencies of non-nominative subjects and agreement-marked verb forms in their data. The three children for whom this expected (by chance) error rate was significantly greater than 10% (representing an acceptable level of noise in the data) produced non-NOM+AGR errors at a rate significantly greater than 10%, counter to the prediction of the ATOM. These results replicate and extend the naturalistic-data findings of Pine et al. using a different method. They also provide support for the use of elicited imitation as a methodology for assessing children's early grammatical knowledge.