Analysis of curriculum of mathematics at elementary level

Analysis Of The Curriculum Of Mathematics at Elementary Level.

Mathematics

Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined.

Importance of

Mathematics

The study of mathematics equips students with knowledge, skills and habits of mind that are essential for winning and satisfying participation in such a society. The more the technology is developed the greater the level of mathematical skill is required.

Mathematical structures, operations and processes provide students with a framework and tools for reasoning, justifying conclusions and expressing ideas clearly. As students identify relationships between mathematical concepts and everyday situations and make connections between Mathematics and other subjects , they develop the ability to use Mathematics to broaden and apply their knowledge in other fields.

The following themes fill the National Curriculum for Mathematics:

(1). The curriculum is designed to help students build the solid conceptual foundation in Mathematics that will enable them to apply their knowledge skillfully and promote their learning successfully. (2). The curriculum emphasizes on the geometrical concepts that enable the students to think logically, reason systematically and make assumptions sharply. (3). The curriculum stresses graphics that enable the students to visualize and understand mathematical expressions correctly rather to manipulate them ‘blindly’.

National Curriculum for Mathematics:

(4).The curriculum recognizes the benefits that current technologies can bring to the learning and doing mathematics. It, therefore, integrates the use of appropriate technologies to enhance learning in an ever increasingly information-rich world. (5). In the National Curriculum for Mathematics teachers’ role has been re-routed that shifts from ‘providing information’ to ‘planning investigative tasks , managing a cooperative learning environment and supporting students’. (6). To ensure that assessment and evaluation are based on curriculum expectations and the achievement levels outlined in the curriculum, specific strategies are suggested that lead to the improvement of student learning.

(7). Print materials, particularly the textbooks, have to play a key role towards providing quality education at all levels. Although there are many stakeholders that contribute towards the overall learning of the child yet the importance of textbook as a reservoir of information/knowledge cannot be ignored. (8). In addition to the textbook, teaching and learning resources include teacher’s handbook, workbook and electronic resources. The guidelines to develop these resources are elaborated.

Math standards

Standard1

Numbers and

Operations

Standard 3

Measurement and

geometry

Standard 4 and 5

Information handling, reasoning and logical

thinking

Standard 2 Algebra

According to National Curriculum Of Mathematics

Numbers And Operations

Analysis Of Curriculum Of Mathematics

Objectives Of Curriculum Of Mathematics From Grade I-VIII

Grade I-II

• Count, read and write numbers up to 999. • Write numbers up to 100 in words. • Identify the place value of each digit in a 3-digit number. • Add and subtract up to 3-digit numbers. • Multiply numbers within multiplication tables of 2, 3, 4, 5 and 10. • Divide numbers within multiplication tables of 2, 3, 4, 5 and 10 with remainder zero. • Recognize and represent unit fractions up to 1|12.

Grade III-V

• Read and write Roman numbers up to 20. • Read, write, compare, and identify place values of numbers up to 1 000. • Multiply and divide up to 6-digit numbers by 2- and 3- digit numbers. • Differentiate between factors and multiples. • Calculate HCF (LCM) of three (four) 2-digit numbers using prime factorization and division method.

• Use four basic operations on fractions. • Convert percentage to fraction and to decimal and vice versa. • Calculate unit rate, direct and inverse proportions. • Add and subtract measures of distance, time and temperature.

Grade VI-VIII

• Identify different types of set with notations. • Verify commutative, associative, distributive and De Morgan’s laws w.r.t. union and intersection of sets and illustrate them through Venn diagrams. • Identify and compare integers, rational and irrational numbers. • Find HCF and LCM of two or more numbers using division and prime factorization.

• Add, subtract and multiply numbers with base 2, 5 and 8. • Apply the laws of exponents to evaluate expressions. • Find square and square root, cube and cube root of a real number. • Solve problems on ratio, proportion, profit, loss, mark-up, leasing, zakat, ushr, taxes, insurance and money exchange.

ALGEBRASTANDARD-2

The students will be able to • analyze number patterns and interpret mathematical situations by manipulating algebraic expressions and relations, • model and solve contextualized problems, • interpret functions, calculate rate of change of functions, integrate analytically and numerically, solve non-linear equations numerically.

OBJECTIVES AT DIFFERENT LEVELS

GRADE I-II

• Analyze patterns and relationships with respect to size, number, color/shape and other properties.

GRADE III-V

GRADE VII-VIII

• Explain and analyze patterns, identify missing numerals and elements in a pattern or sequence and determine a rule for repeating and extending patterns. • Use symbolic notation to represent a statement of equality.

• Identify algebraic expressions and basic algebraic formulas. • Manipulate algebraic expressions using formulas. • Formulate linear equations in one and two variables. • Solve simultaneous linear equations using different techniques.

MEASUREMENT AND GEOMETRY

STANDARD-3

The students will be able to • identify measurable attributes of objects, construct angles and two dimensional figures, • analyze characteristics and properties of geometric shapes and develop arguments about their geometric relationships, • draw and interpret graphs of functions.

GRADE I-III

• Identify and apply measurable attributes of length, weight/ mass, capacity/ volume and time. • Identify square, rectangle, triangle, circle and oval.

GRADE I-V

• Add, subtract and convert standard units of length, weight/ mass, capacity/ volume, time and temperature. • Draw, label and classify lines, angles and triangles based on their properties. • Determine the perimeter and area of a square, rectangle and triangle using formulas.

GRADE VI-VII

• Draw and subdivide a line segment and an angle. • Construct triangle parallelogram and segments of a circle. • Apply appropriate formulas to calculate perimeter and area of quadrilateral, triangular and circular regions. • Determine surface area and volume of cube, cuboids, sphere, cylinder and cone.

INFORMATION HANDLINGSTANDARD-4

The students will be able to collect, organize, analyze,

display and interpret data/ information.

OBJECTIVES AT DIFFERENT LEVELS

GRADE III-V

• Compare data and interpret quantities represented on charts, tables and different types of graphs and make predictions based on the information.

GRADE VI-VII

• Read, display and interpret bar and pie graphs. • Collect and organize data, construct frequency tables and to display data. • Find measure of central tendency (mean, median and mode).

Measurement and geometry

STANDARD-3

The students will be able to • identify measurable attributes of objects, construct angles and two dimensional figures, • analyze characteristics and properties of geometric shapes and develop arguments about their geometric relationships, • recognize trigonometric identities, analyze conic sections, draw and interpret graphs of functions.

Grade I-V• Add, subtract and convert standard units of length, weight/ mass, capacity/ volume, time and temperature. • Draw, label and classify lines, angles, quadrilaterals and triangles based on their properties

Grade VI-VII• Draw and subdivide a line segment and an angle. • Construct triangle (given SSS, SAS, ASA, and RHS), parallelogram and segments of a circle. • Apply properties of lines, angles and triangles to develop arguments about their geometric relationships.

Information Heading

STANDARD-4

The students will be able to collect, organize, analyze, display and interpret data/ informationGrade III-V• Compare data and interpret quantities represented on charts, tables and different types of graphs (pictogram and bar) and make predictions based on the information.Grade VI-VII• Read, display and interpret bar and pie graphs. • Collect and organize data, construct frequency tables and histograms to display data.

REASONING AND LOGICAL THINKING

STANDARD-5

Students will be able to• use patterns, known facts, properties and relationships to analyze mathematical situations• examine real life situations by identifying, mathematically valid arguments and drawing Conclusion to enhance their mathematical thinking.

Grade I-III• Sort, classify and compare familiar shapes. • Apply analytical reasoning to explain features of a shape.Grades III-V• Communicate reasoning about patterns and geometric figures. • Explain method and reasoning when solving problems involving numbers and data.Grades VI-VIII• Find different ways of approaching a problem to develop logical thinking and explain their reasoning. • Solve problems using mathematical relationships and present results in an organized way.

Teaching Strategies

In Mathematics students memorize rules without understanding their rationale. There is no doubt that the timely reward to this way is more immediate and more apparent but this instrumental learning does not bring desired result subsequently

Kilpatrick et in 2001 present notion of Mathematical proficiency that is composed of following five steps:

• Conceptual understanding– comprehension of mathematical concepts, operations and relations.• Procedural fluency– skill in carrying out procedures flexibly, accurately, efficiently and appropriately.• Strategic competence– ability to formulate, represent and solve mathematical problems.

• Adaptive reasoning– capacity for logical thought, reflection, explanation and justification.• Productive disposition– habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy

Research indicates that teachers who have a good background in Mathematics also add richness to their lessons, involve students extensively in mathematical dialogue and capitalize on students’ questions/discussions to weave/extend mathematical relationships. They do not list only the definitions and step-by-step procedures for students to memorize without understanding their meaning and function.

Teaching Mathematics – Role of a Teacher (Part 1)

EFFECTIVE TEACHING STRATEGIES

• Students learn things in many different ways.

• They do not always learn best by sitting and listening to the teacher.

• Students particularly of the primary level can learn by presentation and explanation by the teacher, consolidation and practice, games, practical work, problems and puzzles, and investigating Mathematics.

INVESTIGATING MATHEMATICS

• Teachers may set students a challenge, matched to their ability, which leads them to discover and practice some new Mathematics for themselves.

• The key point about investigations is that students are encouraged to make their own decisions about:

PROBLEM SOLVING • A problem is a statement or

proposition requiring an algebraic, geometric, or other mathematical solution.

• ‘learning to solve problems is the principal reason for studying Mathematics’.

• A problem exists when there is a situation a learner wants to resolve but no solution is readily apparent

TIME DISTRIBUTION

• Teaching schedules are among the integral parts of Mathematics classrooms.

• They help school management to run and monitor the teaching of a particular subject.

• The following tables, indicating unit-wise time distribution, will be supportive to the teachers and education planners

Assessment

Assessment is the process of documenting, usually in measurable terms, knowledge, skills, attitudes and beliefs.

Assessment has two specific purposes:

1. To support and provide feedback to learners and improve their

ongoing learning2. To report on what they have

already achieved

Rowntree (1990)

Criteria for Assessing

•Was the student's use of mathematics effective in helping him or her solve the problem?•Did the student choose appropriate strategies for solving the problem?•Does the student show flexibility in his or her use of strategies?•Is the student's work accurate?

Assessment must include by focusing on a student’s ability to:

• communicate mathematically. • reason and analyze, and to think and act in positive ways.

• integrate and to make sense of mathematical concept and procedure. • examine real life situations by reasoning mathematically.