Question: word limit is 600 i have 900 can you help...
Word limit is 600 I have 900 can you help cut it down and reword
A well-composed, rich mathematical problem in the classroom will enable all learners to be engaged, motivated, highly participative and challenged. Rich mathematical problem-solving strategies enable students to look beyond the obvious and simply state the correct answer but apply thinking and analytical skills to strengthen reasoning and understanding. In identifying the strengths and need to have rich mathematical problem-solving strategies in the classroom it supports authentic differentiation by interconnecting theoretical and practical factors.
Firstly, rich and problematic mathematical tasks support developing concepts, skills and dispositions that are integral to supporting authentic differentiation through creating engagement, participation rich in learning experiences and in promoting perseverance, pattern seeking and communication. Hsu et.al (2007) shares that simultaneous practice of teaching new and prior mathematical content through rich problematic mathematical tasks through enabling and extending prompts offering more complexity in mathematical situations. This transpires for authentic differentiation creating opportunities for exploring interests and readiness for mixed ability learners to ensure for mastering skills and content. In example students can use a range of learning resources to demonstrate their understanding and problem-solving techniques both visually, verbally and through technology based and real-world comparisons. Achieved through mathematical understanding that enriches learning through complexity and understanding.
Most importantly, rich and problematic mathematical tasks aim at grasping a maths concept through understanding, flexibly, reasoning and fluency through open ended approaches. Authentic differentiation stimulates higher order mathematical skills, knowledge, reasoning and thinking through trial and error, solution accuracy with creativity and applying prior knowledge. Differentiation achieves a more sophisticated approach to reinforcement and understanding through content, processes and product. Centralised content forms skills, knowledge, concepts and information as the process is central to the mathematical task developing a rich content.
Incorporating differentiation strategies in a mathematical classroom enables an inclusive learning environment to be achieved which encourages learning dynamics, motivation, creativity and engagement. According to researcher Guido (2016) offers insights into rich and problematic mathematical tasks supporting authentic differentiation through specific practices of inquiry, engagement and instructional strategies centralised in a classroom. Differentiation focuses on unique skills and concepts to foster alternative ways of learning and identifying students learning strategies. Mixed abilities groups interact and engage to help in categorising, development and in depth understanding allowing for extending learning opportunities.
The benefits of incorporating mathematical problematic tasks assist students readiness, interests and learning profile which strengthens authentic learning opportunities, physically and mentally needs through mathematical collaborative learning. McCarthy (2014) further emphasises the importance of rich and problematic tasks supporting authentic differentiation through differentiated instruction by meeting all students needs in an inclusive learning environment. Sharing an example of a lesson of fractions which can be altered through watching a video on fractions, physically moulding the fractions, discussing fractions or eating and cutting food to explore fractions. Exploring content outcomes enable learners to achieve rewarding learning experiences. Authentic differentiation captures a flexible, engaging, rich and rewarding problematic mathematical environment and interactions between students and teachers.
By creating differentiated mathematical problem solving lessons the learner's are able to achieve their individual learning needs through identical learning resources, teacher information and demonstration and learning outcomes. Differentiation will be incorporated into the lesson in an invisible process to the learner; a word, action, example, activity demonstration and question. According to theorist Sullivan et al. (2015) believe that mathematical problem-solving strategies (2015) bring to the attention the importance for structuring lessons through anticipating ways that different students might respond to the challenge or activity highlighting that enabling and extending prompt practice is crucial to understanding. Implying for that distinctiveness allows for a provision of enabling prompts that capture for involving and simplifying the rich and content mathematical tasks through reclarifying and altering the task at hand through reducing the number of steps, guiding students, using inquiry questions and varying the task through representation and modelling with explicitly intention and teaching. Subsequently, offering extending prompts encompass for the original tasks to be completed with more structure, complexity and that are consolidated and with inclusive learning environments.
The benefits of incorporating differentiation into the mathematical lesson ensures that every student's learning needs are identified, assessed, monitored and connected to a specific learning intention which explains how specific learning strategies will be applied to individual students' learning outcomes and process. Weselby (2020) sharee that the Tomlinson model of differentiation requires for individualisation to learning styles and levels, development of readiness before designing a lesson plan where differentiation means giving students multiple options for taking in information. This is achieved through mixed ability groups shared upon on interest, topic or abilities, in assessing students learning using formative assessment through observing students engagement in the task and in how students utilise prior knowledge and use of terminology, in managing the learning environment through creating collaborative opportunities and involvement with reinforcing continuous lesson altering being crucial to support and meet student’s needs, interests and abilities. This encompasses for underpinning and developing in-depth meaning and understanding through interpreting and investigating to communicate for conceptual understanding necessary to solve new problems or make connections between mathematical ideas, skills and concepts.
In conclusion, the world of mathematics is truly amazing. Rich mathematical problem-solving strategies can create an inclusive, challenging and rewarding learning environment. Differentiation strategies enable a simple mathematical question to increase a learner’s level of understanding, reasoning and thinking process by looking beyond what is visually presented in numbers and words but questioning the formation and connection.Z