In design and development study, a need analysis needs to be carried out to ensure that the learning module for retention of conceptual and procedural knowledge to be developed can meet the needs of the study target. A need analysis has been conducted to identify the Form 1 topics that students find difficult, moderate difficult and most difficult to learn, examine students’ perceptions on the difficulties they encounter in learning Mathematics and examine students’ perceptions on the characteristics of module that they want into retaining conceptual and procedural knowledge of Form 1 Mathematics topics learnt. The respondents of this study consisted of 150 Form 1 students and 150 Form 2 students. Data collection was done using questionnaire form. The results of descriptive statistics analysis showed Linear Equation as the most difficult topic, Algebraic Expressions as moderate difficult topic and Linear Inequality as difficult topic to be learnt in Form 1 Mathematics. As for the difficulties students encounter in learning Mathematics, the results of descriptive analysis found that students faced difficulties in terms of procedural and conceptual knowledge mastery, remembering and recalling. In addition, characteristics of module that students want into retaining conceptual and procedural knowledge of Form 1 Mathematics topics learnt indicated that the respondents’ consent level were Very High for most of the proposed module features. The implication of this study informed the researcher on what to consider when developing a learning module to retain conceptual and procedural knowledge of Form 1 Mathematics topics.
Abstract. The generalized presentation of a Bieberbach group with cyclic point group of order two can be obtained from the fact that any Bieberbach group of dimension n is a direct product of the group of the smallest dimension with a free abelian group. In this paper, by using the group presentation, the homological functor of a Bieberbach group a with cyclic point group of order two of dimension n is found.
A torsion free crystallographic group, which is also known as a Bieberbach group is a generalization of free abelian groups. It is an extension of a lattice group by a finite point group. The study of n-dimensional crystallographic group had been done by many researchers over a hundred years ago. A Bieberbach group has been characterized as a fundamental group of compact, connected, flat Riemannian manifolds. In this paper, we characterize Bieberbach groups with trivial center as exactly those with finite abelianizations. The abelianization of a Bieberbach group is shown to be finite if the center of the group is trivial.
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