## Mathematics - Introduction

Mathematics 1-8

Introduction

OVERVIEW and INTRODUCTION:

Mathematics plays an essential role in every aspect of our daily life, in hidden ways and in everyday usage all around us: whether it is time tracking, driving, cooking, computers, airplanes, body scanners, software, coding or jobs such as accounting, finance, banking, engineering, and software. These functions require a strong mathematical background. It is excellent for our brains and develops neural pathways that not only deepens knowledge of the field but improves the brain power as well. While solving mathematical problems, data are collected, disassembled, and then interconnected to solve them. This develops analytical and problem solving skills for a child which he/she then transfers to resolve any issues in their daily lives.

Mathematics is the “universal language” as it is universally understood across cultures, countries and languages. The simple arithmetic equation of 2+2=4 is understood all across the world and remains the same all around the world. It would not be incorrect to say that mathematics is the pillar of organised life for the present day. Without numbers and mathematical evidence, we cannot resolve any issues in our daily lives.

The Single National Mathematics Curriculum 2020 has been designed from the perspective of modern trends in Mathematics and emerging requirements of society in terms of National Integrity and Social Cohesion. The Single National Curriculum (SNC) of Mathematics for grade I-VIII aims to ensure that learners become proficient in doing Mathematics, develop mathematical literacy, induce logical thinking and are able to apply mathematical reasoning in real life and problem-solving.

This document helps teachers to design, implement, and analyze instructions, and assessment methods to accomplish the overall goal of the curriculum. The entire curriculum is divided into four strands, Numbers and Operations, Algebra, Geometry and Measurements and Statistics and Probability, all underpinned in Reasoning and Logical thinking which serves as a cross-cutting strand.

This Curriculum comprises standards, curriculum templates and a progression grid to show the progression of Mathematical concepts across the grades. The curriculum templates identify the student learning outcomes given in the progression grid into two essential aspects: knowledge and skill for the teacher. It also provides a sample of activities that match the Student learning outcomes and the content. Another essential feature of the curriculum template is the sample assessment questions and means for both formative and summative measures.

The learning outcomes emphasize the development of knowledge and conceptual understanding through application and reasoning skills. This curriculum emphasizes values to promote students' spiritual, moral, social, and cultural development through mathematics.

The learning approach that is encouraged for the teaching of mathematics throughout this curriculum is the Concrete-Pictorial- Abstract (i.e. CPA) approach. The Concrete-Pictorial-Abstract (CPA) approach is an approach in learning Mathematics which is done in stages. Each stage is built on the previous stage and must therefore be taught sequentially. The CPA approach consists of three stages of learning namely learning through physical manipulation of concrete objects, followed by learning through pictorial representations of manipulation of concrete objects, and ends with solving problems using abstract notation (Witzell, 2005). Several research support the effectiveness of this approach, including enhancement of problem solving skills, analytical, reasoning skills, fewer procedural errors incur by students using this approach in algebraic variables compared to students learning through conventional learning.  As students manipulate objects, visualize, create or design objects, and find solutions to a mathematical problem by imagining objects or their numbers proportionally, it develops their spatial sense abilities, problem solving abilities.

AIMS OF MATHEMATICS CURRICULUM

The basic aims of the mathematics curriculum from grade I-V are as follow:

• instill Mathematical skills for everyday use.
• strengthen basic mathematical skills to set the foundation for higher-level mathematics.
• develop the ability to think logically to analyze diverse situations.
• develop a sense of appreciation and enjoyment while learning mathematics.
• develop a deep and sustainable understanding through the Concrete, Pictorial and Abstract (CPA) approach by Jerome Bruner.
• Engage in investigations and inquiries to develop skills in mathematical reasoning, processing information, making connections to real-life situations and making judgments.

The SNC Mathematics is based on standards that provide a set of progressive and detailed learning outcomes for each topic and grade. The grade-wise learning development is shown through a progression grid/matrix.

The Student’s Learning Outcomes (SLOs) for each grade are further categorized as knowledge and skill, which will help teachers to plan their lessons and administrators to monitor the effective learning process. This curriculum document includes details of pedagogical approaches designed to help mathematics teachers achieve the overall aims of this curriculum. For example, among others, real life situations are used to achieve this curriculum's aims. It helps engage students in analyzing situations and applying mathematical knowledge to solve related real-life situations. Moreover, students get opportunities to construct similar situations to engage intellectually with mathematical content.

Mental Mathematics and the inquiry approach, equally important strategies are also used especially for developing number sense, forming predictions, justifying arguments with evidence and drawing conclusions. Thus, this curriculum focuses on principles, patterns and systems so that students can apply their growing mathematical knowledge and develop a holistic understanding of the subject.

This document also includes assessment guidelines to ensure meaningful relationship and alignment between curriculum learning outcomes, instructional design and assessment methods. Specific formative assessment strategies are suggested that lead to improvement of students learning. An effective learning-outcomes-oriented quality assurance system, which is based on constant monitoring and an effective feedback loop, is recommended.

Mathematics teachers are therefore expected to:

• Shift from dispensing information to plan investigative tasks.
• Encourage mastery of concepts instead of accelerating learning to complete syllabus.
• Encourage students to realise the inter concept and intra concept connections.
• Create a cooperative and collaborative learning environment.
• Draw valid inferences about students.
• Use this information to improve their teaching practices

MATHEMATICS CURRICULUM CONTENT STRANDS AND STANDARDS

The curriculum for Mathematics is comprised of the following five strands. The strands are intentionally kept broad to allow flexibility to the teachers to adapt their teaching styles by their students. These strands include Numbers and Operations, Algebra, Geometry and Measurement, Statistics & Probability.

All of this content is underpinned by reasoning and logical thinking. All standards and students’ learning outcomes are built around these strands.

 Reasoning &  Logical Thinking
 Numbers & Operations
 Algebra
 Geometry and Measurement
 Statistics & Probability

ASSESSMENTS:

Assessment is a mandatory part of the teaching and learning process. It cannot be treated isolated from the teaching and learning process. It helps both teachers and learners to judge and evaluate their efforts and pace of learning.

In mathematics it becomes more essential, as mathematical concepts are linked with each other. Concepts grasped during one teaching session serve as a basis for the learning of upcoming concepts. Teachers use assessments for a number of purposes such as pre-assessing the learners’ need, providing relevant instruction, assessing the intended learning outcomes, placement of the learners in different groups, diagnosis of weaknesses and strengths of the learners, adjustment of teaching strategies / techniques and promotion of the learners to the next grade. Major functions of the assessment are instructional planning, feedback, making decision, and selection of appropriate resources and strategies to move forward.

In short the prime purpose of any assessment is to improve students' learning. Assessment, classified according to its purpose, and can be thought of as assessment for, as, and of learning.

The main forms are noted as:

• Assessment for learning (known as Formative assessment),
• Assessment as learning (known as Formative assessment).
• Assessment of learning (known as Summative assessment).

Formative Assessments:

Assessment for learning:

In this type of assessment, the teacher provides students with descriptive feedback and coaching for improvement. The purpose for teachers is to:

• gather evidence of student achievement consistently, fairly and conscientiously over short periods of learning time, optimally through informal methods;
• monitor students’ progress towards the defined learning goals;
• provide descriptive, detailed, clear and specific feedback and coaching to students to improve their learning;
• define teaching adjustments and next steps for teaching to help students reach their potential.

Note: The teacher would not use this data as assessment data for the evaluation of student learning.

The most common forms of assessment for learning (formative assessment) are:

Checklists, anecdotal notes, field notes, rubrics, exemplars/benchmarks, continuums, portfolios/ reflective journals, learning stories, reading running records, observation diaries, inquiry charts, CATs, observations of students non-verbal feedback, homework exercises, questioning (open and closed), quiz, projects, selected responses (may include MCQs, true: false, matching short answers, fill-in-the-blanks, etc), open-ended tasks, reflections, KWL, KWHL, performance assessments, process-focused assessments, conferences between student and the instructor, answering specific questions, students reflections, students feedback collected periodically self-assessments, portfolio, etc.

Assessment as Learning

The main purpose of assessment as learning is to provide evidence to the students of their learning. The purpose for students is to:

• Develop their ability to continuously and consistently self-assess themselves and know where they are in their learning and what they can do.
• Become independent and autonomous learners who are able to:
• set learning goals for themselves;
• monitor their own progress towards these learning goals;
• make adjustments in their learning approaches by determining and deciding next steps for developing their learning;
• reflect on their thinking and learning;
• guide and provide feedback to their peers to help improve their learning and achieve their learning goals.

Note: The teacher would not use this data as assessment data for the evaluation of student learning.

The most commonly used forms of assessment as learning (formative assessment) are:

In-class activities where students present their findings informally and provide feedback on peer assessments.

Summative Assessments

Assessment of Learning (Summative)

This assessment leads to the evaluation of student learning. It accurately summarizes and communicates to parents, individual students, teachers, other teachers, school leaders and policymakers what students know and can do concerning the overall curriculum expectations.

The teacher assesses a student’s summative work at the end of a learning period, to determine to what degree (at what level) the student has achieved the learning goal.

The purpose for teachers is to:

• Provide evidence of students’ achievement at strategic times during a specific class and often at the end of a learning unit.
• Summarize learning achieved by students at a given time, after a unit of learning;
• Provide assessment data for evaluation;
• Make judgments about the quality of students learning on the established curriculum expectations;
• Provide a value (pass/fail) to that quality of learning achieved by the students.
• Record and report student’s achievements to all stakeholders including parents, teachers, school and senior management as well as students themselves.

Note: The teacher would use this data as assessment data for the evaluation of student learning.

Commonly forms of assessment of learning (summative assessment) are:

class tests, end of unit tests, mid-year examinations, monthly tests, progress tests, standardized tests, unseen test/examination in controlled conditions, MCQs in controlled conditions, open book or take-away exam, Essay or Report in controlled conditions, portfolio, presentations (peer - or tutor – assessed in controlled environments), performance (musical or dramatic), oral examination etc.

References:

Growing Success- Assessment, Evaluation and Reporting in Ontario Schools (2013); and Assessment, Evaluation and Reporting Handbook (2013) retrieved from http://www.edu.gov.on.ca/eng/policyfunding/success.html]

Putri, H.E.; Rahayu, P.; Muqadas, I. and Wahyudy, M. A. (2019). The Effect of Concrete-Pictorial-Abstract (CPA) Approach on Improving Elementary School Students’ Spatial Sense Ability. Retrieved from: https://files.eric.ed.gov/fulltext/EJ1264986.pdf

Quddusi, M.A. (2018) Retrieved from: The Scientific World (2022) What is the importance of Mathematics in our daily lives. https://www.scientificworldinfo.com/2018/11/what-is-importance-of-mathematics-in.html