Course Contents

Real and complex number theory, Matrix, Types of Matrix Define •a matrix with real entries and identify row matrix, column matrix, rectangular matrix, square matrix, zero/null matrix, identity matrix, scalar matrix, diagonal matrix, transpose of a matrix, symmetric and skew-symmetric matrices Multiplicative Inverse of a Matrix Define the determinant of a square matrix. ii).Evaluate determinant of a matrix. iii).Define singular and non-singular matrices. iv). Define ad joint of a matrix. v). Find multiplicative inverse of a non-singular matrix A and verify that AAIAA11−−where I is the identity matrix. vi) Use ad joint method to calculate inverse of a non-singular matrix Solution of Simultaneous Linear Equations Solve a system of two linear equations and related real life problems in two unknowns using •Matrix inversion method, •Cramer’s rule Permutations (i)Rules of permutation (ii) Use of permutations to solve real life problems. Combinations i) Rules of combination (ii) Use of combination to solve real life problems. Circle i) Demonstrate a point lying in the interior and exterior of a circle. ii) Describe the terms; sector, secant and chord of a circle, concyclic points, tangent to a circle and concentric circles. Sequence and series ________ Define sequence and series (ii) finite and infinite series Presentations Increasing and decreasing Sequence Monotone increasing or decreasing sequences ii. Solve numerical problems Binomial theorem (i)Define binomial theorem (ii) Define binomial distribution. (iii)Mathematical induction Linear Equations (i). Define linear equations (ii).Solution of linear equations (iii). linear equation in two variables Quadratic Equations (i). Define linear and quadratic equations (ii). Solution of quadratic equations Trigonometry Define trigonometry. ii) Define trigonometric ratios of complementary angles. iii) Solve right angled triangles using trigonometric ratios. iv) Solve real life problems to find heights (avoid naming angle of elevation). Trigonometric Ratios of Acute Angles i)Define trigonometric ratios of an acute angle. ii) Find trigonometric ratios of acute angles (30, 60 and 45 degrees). Trigonometric Identities Prove the trigonometric identities and apply them to show different trigonometric relations Review

Course Synopsis

Mathematics is the mother of all subjects Mathematics learning can inculcate problem-solving, logical-thinking, and reasoning skills in students only when they are taught in such a way that they learn conceptually instead of by drill and practice. In previous semesters, we have focused on mathematics content, but this course intends to extend Student Teachers’ understanding of pedagogy as well as build their understanding of the nature of mathematics, teacher beliefs and perceptions, and mathematics teaching and learning. This will enable Student Teachers to develop students’ problem solving, logical-thinking, and reasoning skills. This course will help in creating awareness of the history of mathematics as well as its scope and significance. Also Student Teachers will be able to design plans for integrating Information and Communications Technology (ICT) to develop students’ mathematical learning. The importance of designing effective assessment items to facilitate students’ learning is also considered. The following main ideas are discussed in this course: • The nature and scope of mathematics • The attitude of teachers towards mathematics learning and their perception of it • Research in mathematical processes • Planning for assessment and teaching.

Course Learning Outcomes

After completing this unit, Student Teachers will be able to: l discuss how teachers’ beliefs, perceptions, and attitudes influence their teaching practice. List the common misconceptions about teaching and learning mathematics. Critically review their own beliefs and attitudes towards teaching and learning mathematics and discuss how to develop students’ conceptual understanding, develop teaching activities from their own context for teaching mathematical concepts use the developed teaching activities for the progression of mathematical concepts. Explore different schools of thought, such as absolutist, fallibility, constructivist, and social constructivist identify possible connections between and influences of perspectives on the nature of mathematics and its teaching and learning, relate the importance of mathematics in daily life, explain the relationship of mathematics to other subjects, critically analyses mathematics content and students’ learning outcomes in light of the mathematics philosophy proposed in the National Curriculum for Mathematic.