Discuss about the Mathematics Learning and Teaching for Reflective Folio.
Recently, I came across an article in the journals that discussed the usefulness of mathematics in daily life. It was surprising to learn that most people feel that they wasted time learning math in school because they do not use the skills practically. I tried to look at the study areas for useful classroom and out of class maths that I could apply. I made entries that connected to mathematical content areas, concepts from the curriculum and knowledge. Mathematics is a science subject taught across different levels. It uses different models and guidelines to become effective. Used in everyday life, Math concepts represent the relationship between the social life and the pedagogical. I often wondered why mathematics tasks became more complex with the advancement of the learning levels. I came across theoretical explanations of this explanation and its development over the years (Feathestone & Knaus, 2015). Mathematical reasoning provides insight into the subject knowledge in different dimensions. Inspired by Math Reasoning, I made the contents as follows. I closed my eyes and tried to visualize numbers and their use in everyday life.
Connecting to my experience as a student, I could attest that the key ideas in Mathematics content are Mathematical Reasoning, which captures insight and skills. Models and measures in practical Math applications incorporate the key concepts (Wray, Bay-Williams, Karp, & Van de W, 2017). This gives teachers an understanding of the content area shaping the decisions made by teachers when preparing content.
As I started thinking about mathematics concepts, I came across Van de Walle, Karp, & Bay-Williams, (2017, p. 191) which talked about how to develop meaning in operations. In chapter 9, it talks about types of number problems and its use on distribution, modeling and computational equation. From this, I recalled some of the business news that I encounter every day in the dailies. I thought about the use of Math in digital communication and codes used in international communication with reference to the development of mathematical concepts in early years (Knaus, 2013). Online news links display Math as useful for shopping, creating menus, counting drugs in a pharmacy and in business matters among other areas. That is why academic content incorporates a variety of lessons such as measurement, pattern, and probability as well as reasoning. Learners start learning math concepts as early as the toddler age. Reasoning covers all types of content including the meaning of concepts.
I have always wondered when we have to use multiplication and division in real life. This is more complex when they are dealing with measuring units. From Van de Walle, Karp, & Bay-Williams (2017, pp. 203-217). For example, I cannot fully comprehend how measuring one litter of milk is an equivalent to one kilogram of stones. In a math class, students use models in order to measure concepts. My teacher often explained that in order to grasp the ideas, it was necessary to understand the mind behind the reasoning. I have taken to study famous mathematicians like Michael Faraday and Isaac Newton and the best way I could understand their ideas was through reasoning and direct comparison (Joseph, 2014). Although mathematics content and concepts feature ideas and ways in which learners can perform tasks mathematically, there are specific content areas. In my opinion, a perfect example is in the ICT sector where computer programming using algorithmic and coding systems has brought numerous changes (Knaus, 2013). The content knowledge, in this case, includes specialized content knowledge. Authentic learning practices based on thinking tactics encourage problem-solving skills. For example, probability lessons encourage learners to adopt different methods of making predictions to bring out skills in statistics.
After analysing content as a critical aspect of Math, I was curious to understand why teachers are keen on using specific content at a particular time. When laying the foundation for mathematics students, teachers incorporate “Everyday” concepts as the best way to describe math experiences (Feathestone & Knaus, 2015, p. 17). This reminded me of simple techniques like shapes used in road signs and symbols. These are strategic because people are quick to remember shapes even though these were lessons covered in preschool. For example, I took a driving lesson but it never crossed my mind that the signs and symbols came from mathematical shapes and patterns learned in preschool.
Knaus, (2013) discusses children’s experiences highlighting practical experiences. The human mind stores information for ages. In order to arouse the learner’s interests, course material design focuses on educational psychology techniques. The student-cantered approach to learning supports elementary and middle-level learning because learners at this level need problem-solving skilled and quality tasks. When developing strategies for additions and subtractions, creativity is necessary for enlarging content (Van de Walle, Karp, & Bay-Williams, 2017, pp. 291-299). This is why children learn maths with colourful blocks, rulers and measuring tools. Math advocates for the use of comparative techniques when teaching young learners. Learning activities include different tasks designed for their purpose. Modelling and arithmetic tests are some of the activities that support student participation. I recall how teachers used different instructions to explain the context and to move from one topic to another. The evaluation process was also essential because it marked the transition period when moving from one unit to another. It is important to consider questions such as effective learning within the math content (Lovin, Van de Wale, Bay-Williams, & Karp, 2014). This is applicable to case examples such as content diversity and mathematical application of tasks. I still remember when I was a learner at the intermediate level.
I could never dispute the importance of technology in teaching maths today. What was once a complex subject-is one of the most interesting today. This is because of the audio-visual techniques used for complex topics like geometry (Van de Walle, Karp, & Bay-Williams, 2017, pp. 533-549). My analysis of language identity approach is that it facilitates for the creation of comparisons and activities within the tasks given. Some tasks questioned the suitability of learning materials. I took a study of the early childhood level and the use of videos in order to shape pedagogical knowledge. Practical activities feature problem-solving as well as reasoning skills (Lee-Hammond, Knaus, & Hesterman, 2015). In Chapter 6 of her book, Marianne Knaus (2013) uses geometry to discuss spatial awareness and shape. Technology supports the use of mathematical for global solutions. Children can research on videos on the relationship between money and economic problems through simplified presentations.
The Australian Curriculum provides the specification for Mathematics content for all children across the years including Foundation Year through to Year 10. It shows their learning levels, generals capabilities, and cross-curriculum priorities. The acquisition of general capabilities calls for the development of numeracy, ICT, and problem-solving (Australian Curriculum, 2018). Equipping learners with practical skills involves a combination of skills and resources.
The curriculum shapes the skill acquisition by guiding learners and teaching activities. When I looked at the Australian Curriculum design, I noticed that the Mathematics section encourages teachers to take a record of accomplishment of the students work as evidence of their achievement (Victorian Curriculum Foundation-10, 2018). An effective system supports the application of skills through an elaborate system. For example, I looked at the purpose statement for year 1 and realized that its aim was to align the curriculum with learning opportunities. Its aim also targets the development of a task-specific standard that supports its structures. A study on measurement comes to life through techniques like visual comparisons and counting (Van de Walle, Karp, & Bay-Williams, 2017, pp. 477-511: Knaus, 2013). It starts with the preschool levels and goes on to intermediate and consequently proficiency. Pedagogical learning strategies focus on this progressive development.
The fact that achievement standards support learning capabilities means that the Mathematics system needs a comprehensive approach to schooling. The incorporation of technology tools and devices as learning aids raises questions about their conformance and compliance with the national systems. The Victorian system may encourage a curriculum design with a focus on learning areas as well as the capabilities. However, the diversity of learners raise questions about cultural perspectives in learning. The multicultural environment has content and techniques from different regions of the world. Students have unlimited access to online videos. Since the internet is a global phenomenon, controlling what learner’s access is a major challenge. This further complicates the management of learning programs. Mathematics is a multidisciplinary subject that involves language, social, health, and other sectors. Therefore, an interdisciplinary approach tackles diverse challenges as much as it takes advantage of the opportunities.
In conclusion, reasoning is an important part of Math lesson because it connects the academic theories to practical applications giving Mathematics a rational factor. My journey as a Maths student has fruits because I now recognize the application of its critical concepts and methodologies in every area of my life. I now understand why it is a critical subject in the educational systems.
References
Australian Curriculum. (2018). Understand how Mathematics Works. Retrieved from AC: https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/
Joseph, J. (2014, October 25). Building measurement tools to build understanding. Retrieved April 29, 2018, from https://commoncore.tcoe.org/docs/default-source/Math-docs/2014-10-25-cmc-south-measurement—jj.pdf?sfvrsn=0
Knaus, M., & Feathestone, S. (2015). Maths is All Around You. Bloomsbury Publishing PLC.
Lee-Hammond, L., Knaus, M., & Hesterman, S. (2015). What’s in your refrigerator? Children’s views on equality, work, money and access to food. ReasearchGate. Retrieved April 29, 2018, from https://www.researchgate.net/publication/281803298_What’s_in_Your_Refrigerator_Children’s_Views_on_Equality_Work_Money_and_Access_to_Food
Lovin, H. L., Van de Wale, J., Bay-Williams, J. M., & Karp, K. S. (2014). Teaching student-centered mathematics: Developmentally appropriate instructions for grade 6-8. Pearson.
Victorian Curriculum Foundation-10. (2018). Curriculum Design. Retrieved from Victorian Curriculum and Assessment Authority: https://victoriancurriculum.vcaa.vic.edu.au/overview/curriculum-design/standards-and-levels
Wray, J., Bay-Williams, J., Karp, K., & Van de W, J. A. (2017). Elementary and Middle School Mathematics: Global Edition. Pearson.
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