Learning outcomes in Mathematics

Introduction

Various educational surveys and achievement data over the years show that learning achievements of children in various subjects--especially Mathematics– are not up to the expected levels despite all the efforts made by States/ UTs. It is a fact that many a time, teachers complete the syllabus as per the textbook, but they do not have a clear idea about the kind of learning they expect from children in various subjects including Mathematics.

‘Curricular expectations’ define what a child should know and be able to do as well as the dispositions that should be acquired over a period of time. The learning outcomes derived from the curricular expectations and the syllabus may help all the stakeholders in understanding the goals to be achieved. The learning outcomes are generally treated as assessment standards or benchmarks for assessment.

Highlighting the end product of the learning process generally leads to it being achieved through rote memorisation without understanding. However, the highlighting of the end product in mathematics learning, lays emphasis on remembering the facts and using algorithms without understanding. Further, it develops a handicap in children about use and applications of mathematical ideas in daily life. The integration of the environmental component with mathematics has been taken up. The teachers are excepted to provide learning opportunities while transacting different concepts of mathematics to help children explore and connect with their immediate surroundings, (self, family, school etc). The suggested pedagogical processes include examples for the same.

Learning is a continuous process. The learning outcomes are impacted by the learning /pedagogical processes used to develop competencies. The learners are expected to realise and use mathematics as an important tool that they can talk about, use and explore as well as understand its structure. Therefore, this document lists the learning outcomes in Mathematics for Classes I to VIII along with some suggested pedagogical processes which may be undertaken to achieve the outcomes. These pedagogical processes are not exhaustive. Also, they are suggestive in nature, and may vary according to the learners’ context. An innovative and creative teacher may be able to achieve the learning outcomes through these and many more different pedagogical processes.

Primary stage - Curricular Expectations

Children are expected to 

• Develop a connection between daily life contexts and mathematical thinking.
• Understand shapes and articulate their observable properties as similarities and differences among them.
• Develop own methods of performing operations on numbers in daily life (addition, subtraction, multiplication and division).
• Develop language and symbolic notations with standard algorithms of performing number operations. 
• Estimate outcome of operations on two or more numbers and use it in daily life activities.
• Learn to represent the part of a whole as a fraction and order simple fractions.
• Collect , represent and interpret simple data from her/his contexts and use it in everyday life.
• Identify and extend simple patterns in shapes and numbers.

Upper primary stage - curricular expectations

Children are expected to:

• move from concrete ideas of numbers to number sense
• sees relationships between numbers and looks for patterns in relationship
• understand and applies concept related to variables, expressions, equations, identities, etc.
• use arithmetic and algebra to solve real life problems and pose meaningful problems
• develop aesthetic sense by discovering symmetries in shapes like triangles, circles and quadrilaterals
• identifies space as region enclosed within boundaries of a shape
• develop spatial understandings in terms of perimeter, area and volume and uses them to solve day to-day life problems
• learn to provide reasoning and convincing arguments to justify her/his own conclusions in mathematical context
• collect, represent (graphically and in tables) and interpret data/information from her/his life experiences.

For Children with Special Needs (Mathematics)

To overcome difficulties of access with respect to learning mathematics, some pupils may require tactile, and others specialised, equipment for work related to shape, geometry, calculations, etc. Some may require simpler language or more pictures. Others may need help in interpreting data in graphs, tables, or bar charts. There may be children who may need help in interpreting oral directions or while making mental calculations. Use of ICT may be required to overcome difficulties in quantitative and abstract thinking.

Some specific needs of children with different disabilities are given below which may be taken care of to help them learn with their peers and accomplish the desired learning outcomes.

Learning Outcomes at the Elementary Stage- For Visually Impaired Children

• Development of spatial concepts (concepts related to space) and understanding the relationships between spatial concepts
• Understanding three-dimensional objects transformed into two-dimensional forms
• Understanding special characters (symbols) used in Mathematics
• Difficulty in audio recording of mathematical text, for example, equations etc.
• Difficulty in transcribing and reading mathematical text in Braille because of spatial arrangement and colour codes 
• Learning of Nemeth or any other Mathematical Braille Code.

 Learning Outcomes at the Elementary Stage - For Hearing Impaired children

• Delay in linguistic growth, leading to lack of general vocabulary and technical vocabulary of Mathematics (words like reciprocal, linear etc.)
• Understanding the wordiness (use of a number of words to explain meaning or making a point) of mathematical problems
• Distinguishing words with multiple meanings like interest , table, credit, angle, rate, volume, power, point
• Distinguishing mathematical words while student is lip/ speech reading (tens and tenths, sixty and sixteen)
• Limited use of cognitive strategies to select the relevant information and approaches necessary for solving problems.
• For Children with Cognitive Impairments, Intellectual Disability
• Sequencing, step-wise problem solving and difficulty in place value
• Mathematical calculations (computations), number reversals, copying problems etc Confusion in operational symbols, such as + for ×, and difficulty in recalling sequence of operations
• Identifying different shapes in geometry and directionality
• Abstract concepts like in Algebra and integers, etc.
• Comprehension of word problems.

To access class-wise Suggested Pedagogical Processes and Learning Outcomes, click here.

Source : NCERT