Learning Trajectories for Primary Grades Mathematics

Maths
Education - Mathematics

Abstract:-
Presently changes in the education system leads towards the many challenges. This study is
related to the implication of authentic teaching, assessment, and learning. Development in the
learning task improves student learning and helps to achieve higher standards. In this study, we
will consider the implication in the activities and learning trajectories related to mathematical
activities.
Introduction:-
For development, natural learning progressions followed by the Children. For example,
children first learn very slowly, in a specific manner such as walking, running, jumping, and
skipping with increased ability and speed. Similarly, student follow the same procedure for the
progressions of natural development in math learning. Children learn mathematics skills and
ideas in according to their mental ability. An educator needs to understand these Sequence's
activities and developmental progressions for the children's development. Educators can develop
enriched learning environments for mathematics so that the development of children can be
effectively and appropriately (Stone, 2019).
One question is arising that on what basis Numeracy program is structured for
Mathematics? F–10 Australian Curriculum is essential for the development of the learner.
According to ‘The National Numeracy Learning Progression’, three elements are necessary for
the successful development of the learner. These elements comprise of Algebra and Number
Sense, Measurement and geometry, Probability, and Statistics (Curriculum, 2020). For the
numeracy capability it is essential aspects for the present developmental sequences, in which
each element contains the sub-elements. There are a total of nine sub-elements in the algebra and
Number system, two in the Probability and statistics, and four in Geometry and measurement
(Woodcock, Sisco, & Eady, 2015).
What is the relation of the numeracy progression and Australian Curriculum? In the
Australian Curriculum, Numeracy skill is a kind of explicit teaching for Mathematics. A learner
needs opportunities consistently to recognize the Mathematics at outside the classroom. So,
numerous peoples can apply for the general mathematical skills in unfamiliar and familiar

situations. In the Curriculum, using mathematical skills enriches the study in the learning area,
which helps to develop a deeper understanding of numeracy. Mathematical ideas are essential for
the students so that they can interact with their lives (Hammond, & Flook, 2019).
How can the progression of numeracy be used? The NNLP (National Numeracy Learning
Progression) can be used in a school, at the individual or team teacher level. This Numeracy
Progression provides the maximum benefits in the student learning. It also relates to the
collaboration and professional learning between teachers in a whole-school. This progression is
used to identify the individual student’s numeracy performance within the sub-elements. In
class, student abilities can be varied. Each student cannot be fit in a specific
progression level. Therefore, a logical sequence uniformly provides the progression.
Teacher judgments about the learner numeracy capability are based on the learning
experiences. Oral explanations, Number talks, and written or any task from any area of learning
can provide evidence of the learner's capability related to numeracy. Teachers use progressions,
which lead to the development of learners during learning and teaching programs. Students can
increase robust knowledge in a transferable and adaptable manner so that learners can develop
new ideas. They can connect new ideas with previous ideas and how they can represent their
thoughts differently. A learner can describe their thinking mathematically in an effective manner
(Lambdin, 2009).
The Curriculum of the Australian is designed to help all young Australians so that
children can become creative, confident, and successful learners. Foundation presented the
developmental Sequence of learning of year - 10, in which learning Curriculum of Australia
describes to the parents, teachers, students, and others in the community about what is to be
taught. The learning quality of young people can be expected as they progress in school
(Massie, 2019).
The Foundation 3-D designs - Year 10 of the Australian Curriculum identify the
importance of skills and disciplinary knowledge and understand the priorities of the cross-
curriculum. Understanding, skills, and Disciplinary knowledge are related to the Australian
Curriculum 8 learning areas such as Mathematics, English, Physical Education and Health,

Science, Social Sciences, and Humanities, The Technologies, Languages, and Arts. In each
learning subject or area, specific content describes the student what will learn. Achievement
standards describe the understanding of the depth and knowledge sophistication (Beams,
Manners, & Morgan, 2010).
Development of the child relates to the physical, language, cognitive development, math,
emotional-social, and learning characteristic. Traditionally precollege and vocational
mathematics separated in the schools. In the world of technology, the learner can connect
mathematics with real-life applications. Mathematics based on the workplace can be better
mathematics for everyone for every student. Trajectories learning consist of mainly three parts-1)
Goal of Mathematics 2) a path of development from which learners can reach the goal 3) set of
tasks or instruction activities. Each of these levels can help in the development of learners' higher
thinking.
The big idea of the mathematical learning trajectory is the make clusters of the skills and
concepts. This central idea relates to the thinking of the children, and there generates future
learning capability. This big idea comes from the several projects which are includes from the
National Math Panel and NCTM (National Council of Teachers of Mathematics) panels:
a) Establishment of the objective b) from where we have to start? C) Where we go next,
and how? D) How do we reach the goal?
Authentic learning is a type of learning design that connects with the students what they
taught in the school from the real word problems, issues, and applications. Learning experiences
in the real world also relates to the ambiguities and complexities of real life. Students learn
something new by' learning by doing approach.' Traditional forms of assessment, which includes
examinations and essays, have no particular application in the real world. The authentic
assessment helps the learner to investigate their learning skills(A, 2016).
The aim of any learning experience relates to the authenticity in every lesson, unit, and task
to ensure that students can develop the confidence and skills to solve the problem with its
learning abilities. Outside life, school life means to prepare the students in such a way that they