Problem Statement and Scope
With regards to the identified literature sources for this activity, children are oriented to mathematical thinking long before they even begin going to school. The orientation is because they undergo a process of tremendous growth in their numeracy skills just before they join preschool. The attainment of informal knowledge for number is known as ‘number sense’. There are many situations in everyday life that children portray their number sense. Mostly, the situations involve measurements and numbers. Children are able to define when or who has more things than the other, come up with means and strategies for enabling equal shares, then use numbers and ability to count to reason out with others. Such skills are built when children interact with their guardians and peers, after which they are encouraged to create their own understanding in situations of play.
This paper is generally a literature review activity that tries to assess the outlined mathematical numbers and algebra frameworks according to the Australian curriculum for children in foundation grade to year three. In this case, we have identified six literature sources (and other supporting references) that demonstrate how educators as well as the Australian Curriculum encourage central arithmetic development particularly in algebra and numbers and they include:
- (2018) Mathematics Challenge for Young Australians (MCYA). Australian Mathematics Trust. Retrieved 28 Aug 2018, from https://www.amt.edu.au/mathematics/mcya/
- Learning Hub. (2018) MATHS IS EVERYWHERE. Early Childhood Australia. Retrieved 28 Aug 2018, from https://learninghub.earlychildhoodaustralia.org.au/elearning/maths-is-everywhere/
- Perry, B. (2016). Early Childhood Numeracy.University of Western Sydney, 45(4), 2-42.
- Reid, K. (2016) Preschoolers and numeracy development. Teacher Insight. Retrieved 28 Aug 2018, from https://www.teachermagazine.com.au/articles/preschoolers-and-numeracy-development
- Sansome, J., E. (2016) Building teachers’ pedagogy practices in reasoning, to improve students’ dispositions towards mathematics. Office for Education Research Faculty of Education Queensland University of Technology, 32(5), 4-195.
- National Curriculum Board (2009) Shape of the Australian Curriculum: Mathematics. Attorney-General’s Department, 2(3), 3-13
The paper, therefore, intends to use a multi-disciplinary research format to review the identified principles and practices all of which support the designed mathematical frameworks for the betterment of children in foundation up to the grade of three.
The Topics’ Key Aspects
All the identified articles talk about the structure of the Mathematics Curriculum and teaching methodologies to ensure that the desired academic outcomes are achieved by the children. Most definitely, the articles highlight on:
Though this activity mainly focuses on algebra and numbers, the curriculum is organized on the basis of proficiency and content strands; all of which closely interact as put by Acara (2018). The content strands with regards to the mathematics curriculum include:
- Algebra and Numbers
- Geometry and Measurement
Algebra and Numbers: According to the study sources, Reid (2016) in particular, early years assessment requires the educators to focus on numbers. However, as the compulsory years approach, a lot of emphasis will be put in algebra. On the contrary, AMC (2018) asserts that there is a connection between algebra and numbers. The combination of the two learning points brings about logics and functions.
Geometry and Measurement: The two aspects have connections that are limited and thus, won’t be the basis of our review in this activity. However, general description involves the study of spaces and locations as covered in mathematical concepts. Mostly, location aspects including scales, maps, and bearings align with measurement. Geometry on the contrary, describes the study of things to do with properties of shapes as well as giving logical and prominent justification and definitions.
The Topics’ Key Aspects
Probability and Statistics: This aspect deals with data, statistics, and chance for the description study activities and goals. For instance, through the study of statistics and probability, we learn that it is mathematically insufficient to summarize or construct data. Data should not be summarized but interpreted, represented, and analyze such data. Probability in itself helps in determining the chance by which something happens or not.
Identifiably, the named content strands represent mathematics sub-disciplines that are substantial and are also a reflection of the purpose of the mathematics curriculum. As Identified by Learning Hub (2018), the reduction of the content strands to three by the curriculum developers ensures that there is a greater coherence within strands. It also ensures that a connection is created between topics that relate throughout the strands.
- Importance of the Curriculum Structure
According to Acara (2018), the structure of the Australian Curriculum ensures that educator mold successful, creative, and confident individuals out of young timid boys. The article also holds that the curriculum ensures that after their learning processes, such individuals are molded into informed and active young people that are ready to give everything to the society.
The curriculum also sets goals for things that need to be taught in early learning processes. The curriculum has eight areas of learning. Such areas are intended to help learn, coexist and work in this current society.
Most importantly, the National Curriculum Board (2009,5), states that the mathematics curriculum is built on the draft of National Declaration against Young Australians’ Educational Goals to have children educated on how to be active, interpret and think mathematically. Mathematics should be the basis of all formed decisions and predictions when it comes to financial and personal priorities.
Three articles have majorly tackled this topic. The articles, as identified, are written by Perry (2016), Learning Hub, and Australian Curriculum (2018ab).
In relation to the objectives of algebra and numbers as a content strand, Perry (2016), argues that assessment is one of the important parts of achieving the desired study outcomes. Numeracy learning requires teachers to be responsible for the validation and assessment of study outcomes. Early childhood learning via assessment must highlight:
- Comprehensive accounting of the knowledge gained by the students. Assessment, in this case, is considered as a tool used towards the attaining of curriculum goals.
- The continual progression of students including the concepts they have gained and how they apply such concepts in their leaning processes.
- The provision of feedback regarding the mathematical development of a student and how teachers help in achieving the same.
Learning Hub (2018) then uses the same line of assessment proclaimed by Perry (2016) to determine how the module helps educators to support and grow the numeracy and math concepts of children. The article outlines that the module supports day-to-day learning practice, outdoor programs, and play. According to the article, it is important to focus on child-led learning as well as intentional teachings then demonstrating the vitality of having teachers model the way young children between foundation and year 3 grades mathematically talk and think. Learn Hub (2018) also agree with Perry (2016) by accepting the fact that assessment is important for educators and students because the same concept is applied in every stage of such individuals’ professional development.
Learning Progression
According to the Australian Curriculum (2018), the module helps young learners with the ability to understand:
- How to employ numeracy and maths concepts in all kinds of daily practices as well as prepare them for mathematical leaning
- The role of young learners when it comes to planning programs associated with learning numeracy and maths.
Sansome (2016) suggests four major proficiencies including fluency, understanding, reasoning, and problem solving as a clear framework for mathematical teaching and learning processes. She claims that such proficiencies can help teachers in the assessment of learning processes. The framework would ensure that focus is not only put on fluency alone but other aspects as named herein. She believes that the proposition of the Education Board regarding the national mathematics curriculum containing the use the four proficiencies is a step forward towards ensuring that success is achieved in such learning processes.
The four proficiencies define the nature and range of actions that are expected against the described curriculum content. According to the Australian Curriculum, mathematics ought to be a description of the proficiencies through which students are engaged. However, Acara (2018) proposes that the content of the curriculum needs to be arranged in terms of the three strands named earlier on and four proficiencies added to bring in a new learning dimension.
On the same idea, Victoria State Government (2018) highlights that the intention of the Australian Mathematics Curriculum should include having the proficiencies applying to all the aspects of algebraic and numbers learning. The article challenges educators to search for means through which a balance can be incorporated when teaching young and older students such proficiencies.
- How the topic is addressed
The Australian Mathematics Curriculum requires that every content strand outlines its achievement standards to ensure that young learners are provided with quality learning processes. The articles discussed herein, have identified that such achievement standards include the understanding depth, knowledge extent, and skills sophistication. The standards are measures whether a student is on the right track to begin his or her learning process or move to the next level of education having attained the required achievement level.
The standards, as discussed herein, and determined by the Australian Curriculum, apply to learners between Foundation and year here grades. The same standards are applied according to the Algebra and numbers’ achievement standards (we don’t necessarily consider other content strands though they are important).
- Suggested pedagogies’ connections
Sansome (2016), Acara, and Victoria State Government (2018ab) suggest four major proficiencies including fluency, understanding, reasoning, and problem solving as mentioned before. The proficiencies form a framework for mathematical teaching and learning processes supported by the Australian Curriculum (National Curriculum Board, 2009). The main idea behind Sansome’s work is that proficiency helps teachers in the assessment of learning processes. As put by Perry (2016), assessment is one of the important parts of achieving the desired study outcomes. Numeracy learning, therefore, would require teachers to be responsible for the validation and assessment of study outcomes. The entire proficiency framework, in this case, would ensure that focus is not only put on fluency alone but other aspects as named herein. Sansome then adds that the proposition of the Education Board regarding the national mathematics curriculum containing the use the four proficiencies is a step forward towards ensuring that success is achieved in such learning processes.
The four highlighted articles (written by Sansome, Perry (2016ab) Acara, and Victoria State Government (2018ab) agree on the point that proficiency defines the nature and range of actions that are expected against the described curriculum content. In line with the same thought, the Australian Curriculum mentions that mathematics needs to be a description of the proficiencies through which students are engaged (Victoria State Government, 2018). Finally, as Acara (2018) proposes that the content of the curriculum needs to be arranged in terms of the three strands named earlier on and four proficiencies (to bring in a new learning dimension), Victoria State Government (2018) highlights that the intention of the Australian Mathematics Curriculum should include employing the proficiencies to ensure that they apply to all the aspects of algebraic and numbers learning.
Conclusion
This literature review activity identified six main articles talking of the orientation of children to mathematical thinking. The identified articles also highlight a number of implications that the Australian Curriculum imposes towards molding young Australians into better students in later learning stages. The activity has identified ways through which the curriculum encourages skillful thinking through the study of algebra and numbers. However, this activity has also touched on other content strands in the field of mathematics. All the similarities and differences regarding the flow of ideas in the used articles have been discussed in relation to the concepts highlighted in the Australian Mathematics Curriculum.
Reference
Acara. (2018) THE AUSTRALIAN CURRICULUM – YEARS 1 AND 2. Australian Curriculum. Retrieved 28 Aug 2018, from https://docs.acara.edu.au/resources/Information_for_parents_years_1_-_2.pdf
AMC. (2018) Mathematics Challenge for Young Australians (MCYA). Australian Mathematics Trust. Retrieved 28 Aug 2018, from https://www.amt.edu.au/mathematics/mcya/
Australian Curriculum. (2018) Understand How Mathematics Works. Mathematics. Retrieved 28 Aug 2018, from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/?year=11751&year=11752&year=11753&year=11754&strand=Number+and+Algebra&strand=Measurement+and+Geometry&strand=Statistics+and+Probability&capability=ignore&capability=Literacy&capability=Numeracy&capability=Information+and+Communication+Technology+(ICT)+Capability&capability=Critical+and+Creative+Thinking&capability=Personal+and+Social+Capability&capability=Ethical+Understanding&capability=Intercultural+Understanding&priority=ignore&priority=Aboriginal+and+Torres+Strait+Islander+Histories+and+Cultures&priority=Asia+and+Australia%u2019s+Engagement+with+Asia&priority=Sustainability&elaborations=true&elaborations=false&scotterms=false&isFirstPageLoad=false&page=1
Learning Hub. (2018) MATHS IS EVERYWHERE. Early Childhood Australia. Retrieved 28 Aug 2018, from https://learninghub.earlychildhoodaustralia.org.au/elearning/maths-is-everywhere/
National Curriculum Board (2009) Shape of the Australian Curriculum: Mathematics. Attorney-General’s Department, 2(3), 3-13
Perry, B. (2016). Early Childhood Numeracy. University of Western Sydney, 45(4), 2-42.
Reid, K. (2016) Preschoolers and numeracy development. Teacher Insight. Retrieved 28 Aug 2018, from https://www.teachermagazine.com.au/articles/preschoolers-and-numeracy-development
Sansome, J., E. (2016) Building teachers’ pedagogy practices in reasoning, to improve students’ dispositions towards mathematics. Office for Education Research Faculty of Education Queensland University of Technology, 32(5), 4-195.
Victoria State Government. (2018). Number and Algebra. Mathematics. Retrieved 28 Aug 2018, from https://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/continuum/Pages/continnumber.aspx
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