Exploring the Evolution of Mathematics Education

Introduction

There has been a long history of education and learning. These two events have been around since the start of civilization, but their purpose, appropriateness, and relevance have evolved over the years. In rich and developing countries alike, teachers and students are actively engaged in the teaching and learning process (Ormond, 2021). The fundamental goal of education is learning, and teaching is how it can be achieved. If the teacher is good, the student will learn well; if the teache ris bad, the student will not (Ormond, 2021). One of the subjects taught in school is mathematics. Teaching mathematics is the act of passing on mathematical knowledge, methods, calculations, and computations to another. Teaching can be official or casual. Mathematical knowledge is also crucial to understanding other subjects in the classroom, including science, social studies, and even music and the arts. In today's setting, mathematics education encompasses the teaching and learning of mathematics and the intellectual research that accompanies it. Mathematical education academics are generally interested in the tools, methods, and approaches that more efficiently perform practice or practice analysis (Ormond, 2021). Acquiring and analyzing correct insights for research via standard and confirmed techniques is an essential aspect of the study's data gathering. The Australian lower secondary mathematics curriculum guides mathematics in Australia. Three content and four proficiency strands are intertwined in mathematics. The three content strands are number and algebra, and statistics and probability and measurement and geometry (Sullivan & Davidson, 2014). They give an overview of what students can expect to learn. Therefore, this study will analyze the lower secondary mathematics curriculum's teaching and learning approach.

The Teaching and Learning Approach

Mathematics is concerned with the procedures that connect blocks and promote learning. Math is broken down into three topic strands and four proficiency strands in the Australian Curriculum, all interconnected. For example, an algebraic equation is expressed in the learning video, "So what does four cubed mean?” (TIMSSVideo 00:03:11). All these strands give an overview of what students can expect to learn. Australian Curriculum students are considered numerate when they can apply their knowledge and skills to other topics in the classroom and their daily lives. When it comes to arithmetic, numeracy encompasses a wide range of skills, information, and attitudes that children must possess to succeed (Ormond, 2021). Understanding the role of mathematics in the real world and students' attitudes and capacities for effectively using their mathematical knowledge and skills. Additionally, the curriculum and evaluation will allow teachers to use suitable classroom technologies to help students learn and teach math. As part of the curriculum, standards and expectations will be laid out for students who prefer to perform arithmetic cognitively, as well as for those who choose to use technology when appropriate. Most high school graduates should have the mental math skills to appropriately estimate 15% of an amount by multiplying or dividing by tens and hundreds or calculating a 10% gratuity (Norton, 2017). Computer algebra systems and dynamic geometry are taught properly in high school courses today.

The national mathematics curriculum includes three core strands: measurement and geometry, number and algebra and statistics and probability. It is possible to add meaning to algebra by integrating number and algebraic representations, such as relationships. An algebraic perspective can also improve numbers teaching in middle and later primary grades. Functions, sets, logic, and patterns or structures are all part of this combination. For example, in the video, the speaker says, "Four X all cubed simplified. Four cubed is?” (TIMSSVideo 00:02:26). Other issues, such as networks, are growing in both fields, but geometry and measurement have little in common in those respects, except a few characteristics. Different curricula use the term "space" to describe form and placement mathematical notions. Aside from the fact that many aspects of location are based on measurement, geometries focus on shape features and logical definitions and justifications (Sullivan & Davidson, 2014). Statistic and probabilistic language are more appropriate for defining the nature of learning objectives and student behavior than data or chance. Students need more than simply constructing or summarizing data. One needs to represent, comprehend, and evaluate it as well. Similarly, the term "probability" implies that the results of this investigation are more than just a remote possibility.

Modern teaching and learning rely heavily on the use of information technology. One of the most important aspects of integrating digital technology into the curriculum is ensuring that it is not optional. With the help of digital technology, students can learn arithmetic in new and innovative ways while also helping them connect representations and therefore improve their understanding. In math, logarithm tables and slide rules have had a profound effect. Increasingly powerful, accessible, and ubiquitous digital technologies have emerged in recent years. Modern mathematical technologies provide various functions, including numerical, statistical, graphical, symbolic, geometric, and textual (handheld devices or computer software). Using them separately or together is up to you. Using these techniques, many aspects of a function's or relation's behavior can be studied numerically, graphically, geometrically, and algebraically. It is easier to focus on meaning, transfer, linkages, and applications with these techniques. By using real-world data and examples, digital technology can make previously inaccessible mathematics more accessible to all learners.

The Lower Secondary Mathematics Curriculum

As stated, the Australian Curriculum divides mathematics into three topic areas and four skill areas. The three curricular streams are Number and Algebra, Statistics and Probability and Measurement and Geometry. They provide the groundwork for what students should be exposed to in the classroom. The four competency strands are fluency, understanding, reasoning and problem solving (Norton, 2017). Mathematical concepts are explained in terms of how they are studied or developed. Content strand descriptions have been updated to include vocabulary for describing the developmental aspects of mathematics learning. As a result of using this strategy, pupils' mathematical proficiency has grown, and their mathematical skills have improved. Problem solving and reasoning are just two of the many facets of math success (Ormond, 2021). Understanding includes making connections between representations of numbers, splitting and combining numbers flexibly, communicating time with appropriate language, and explaining aspects of symmetrical shapes. Fluency includes remembering multiplication tables, communicating fraction sequences, correctly measuring with instruments, forming patterns with transformations, and collecting and documenting data. Modeling and recording real-world scenarios such as processes with large numbers of time comparisons and numerical properties to continue patterns are all part of the process of addressing problems (Ormond, 2021). Finally, thinking comprises generalizing from numerical properties and calculating outcomes, inventing ways for unknown multiplication and division jobs, comparing angles, and judging the appropriateness of various display methods.

These skills are covered in the standards curriculum includes identifying frequent comparable fractions in familiar situations, creating connections between fraction and decimal notations up to two decimal places, and solving simple purchase problems are all examples of effective procedures for multiplication and division calculations ad multiplication number patterns (Ormond, 2021). The speaker asks students to solve "Thirty-two divided by four" (TIMSSVideo 00:00:56). Other functions include finding unknown numbers in number statements, Comparing the regions of regular and irregular forms by using informal units, understanding the interdependence and independence of various events, resolving time-related issues, and learning to read maps using multiple data collection.

Also, the curriculum includes applying index laws to whole numbers to solve problems involving rates, ratios, and percentages rational and irrational numbers; and handling profit and loss concerns. Prism volume is a tool for addressing problems connecting algebraic formulas to real-world applications, finding the requirements for triangle congruence, deducing quadrilateral features, making sense of time (Norton, 2017). Using Venn diagrams and two-way tables to replicate real-world situations explaining events and studies with the correct language drawing attention to potential problems in collecting information and the influence of outliers on the distribution of the data using efficient mental and textual techniques to perform the four arithmetic operations with integers; simplifying a wide range of algebraic formulas. Solving linear equations and graphing linear relationships on the Cartesian plane calculation of parallelograms, rhombuses, and kites' perimeter and area giving names to and estimating the areas and circumferences of circles; identifying related occurrences and calculating the probability of each one occurring together (Joyce et al., 2017).

Inclusionary education and the abolition of streaming are two significant trends that have led to increased diversity in math classrooms. Including students with impairments in the educational process is a worldwide trend specified in international treaties and national legislation, including Australia (Joyce et al., 2017). Teachers in streamed classrooms may mistakenly believe that their job is done, and they may miss the opportunity to encourage and push their students. Inclusive mathematics education recognizes the diversity of the human race and aims to address the needs of all students in general mathematics programs. Examples of children's mathematical thinking and achievement serve as a resource for studying the wide range of ways children acquire mathematics and demonstrate associated skills. Students must have the ability to switch between groups as their needs change. Some schools divide their pupils into groups based on their mathematical talents, individual contributions, or different ways of thinking about mathematics (Joyce et al., 2017). As a result, rather than boosting fluency in processes and procedures, the groups focused on strengthening mathematical thinking—the AC reasoning M's and comprehension abilities; and mathematical challenge. Schools employed several grouping techniques to help students learn math. Even though many students were grouped according to their talents, social results were more important in other institutions. For an illustration of social grouping and the adjustments, educators made to accommodate pupils from various backgrounds (Joyce et al., 2017).

Australia's children's math scores have remained unchanged even after numerous treatments and policies. This indicates that the issue is multifaceted and suggests that there are still aspects that have yet to be studied. Mathematical education research has typically been influenced by educational psychology theories and frameworks, with emotional studies contributing to a better understanding of learning and instruction much later. Then there was the "social change" of the new millennium (Joyce et al., 2017). Student understanding of the interplay between logic and emotion in mathematics instruction and learning has recently expanded thanks to studies considering conative variables, including student motivation, mindsets, and values.

More than six hours of arithmetic instruction per week is associated with better maths achievement in Australia (Joyce et al., 2017). Students exposed to mathematics for a more extended period have a more accessible time learning. This demonstrates that excellent classroom discipline allows for more productive long instructional periods. Despite this, an increase in math instruction time has no statistically significant effect on test scores after accounting for the possibility that higher-achieving students may be assigned to better schools and grades. Pure mathematics is more strongly associated with more excellent performance in Australia. Higher-achieving students may attend schools with a greater emphasis on mathematics instruction, but exposure to pure mathematics is connected to better performance in Australia (Joyce et al., 2017). Also, applied mathematics experience is linked to higher performance at low exposure levels. In Australia, the performance difference between socioeconomically advantaged and disadvantaged students is attributed to a lack of familiarity with mathematical concepts among underprivileged students.

Conclusion

National curriculum implementation is certain to have an enormous impact on Australia's education system. Students learn math through three subject areas and four proficiency pathways. Three main topic strands make up the proposed curriculum's framework: (number and algebra, measurement and geometry, and statistics and probability). On the other hand, the proficiency strands form the core of the curriculum as it is now being used (understanding, fluency, problem-solving, and reasoning). Australia's children's math scores have remained unchanged even after numerous treatments and policies. This indicates that the issue is multifaceted and suggests that there are still aspects that have yet to be studied. Educational psychology theories and frameworks have typically influenced mathematical education research, with emotional studies contributing to a complete understanding of learning and instruction much later. Then there was the "social change" of the new millennium.

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References

Joyce, C., Hine, G. and Anderton, R., 2017. The association between secondary mathematics and first year university performance in health sciences. Issues in Educational Research, 27(4), pp.770-783.

Norton, S., 2017. Mathematics engagement in an Australian lower secondary school. Journal of Curriculum Studies, 49(2), pp.169-190.

Ormond, C.A., 2021. Teaching Classroom Mathematics: Linking Two Pedagogical Models for Promoting Student Engagement and Conceptual Connections. Australian Journal of Teacher Education, 46(4), p.3.

Sullivan, P. and Davidson, A., 2014. The Role of Challenging Mathematical Tasks in Creating Opportunities for Student Reasoning. Mathematics Education Research Group of Australasia.

TIMSSVideo. M-AU3 Data Collection and Representation (TIMSS Video). http://www.timssvideo.com/au3-data-collection-and-representation#.