Question: please edit this the word limit is to be 600...
i need help making each paragraph flow... it is suppose to be a essay format but it seems like my paragraphs don't flow nicely into the next paragraphs..and that no paragraph starts with reference to a person
Rich and problematic mathematical tasks support developing concepts, skills and dispositions that are integral to supporting authentic differentiation creating engagement, participation rich learning experiences promoting, perseverance, pattern seeking and communication. Authentic differentiation creates opportunities, interest and readiness for mixed ability learners to master content, grasp content and mathematical understanding enriching learning through complexity and understanding.
Consequently, 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.
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.
In exploring problematic tasks through determining students readiness, interests and learning profile provides authentic learning opportunities connecting 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.
Sullivan et.al (2015) brings 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.
Ultimately rich and problematic mathematical tasks support authentic differentiation through practices of differentiated instruction with Weselby (2020) sharing that the Tomlinson model of differentiation requires for individualisation to learning styles and levels, development of readiness before designing a lesson plan. 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.