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Question: word limit 600 i have 750 please cut down to...

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Word limit 600 I have 750 please cut down to around 660


A well-composed, rich mathematical problem in the classroom will enable all learners to be engaged, motivated, highly participative and challenged as it enable students to look beyond simple concepts and apply analytical skills to strengthen their reasoning.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.Hsu et.al (2007) shares that simultaneous practice of teaching new and prior mathematical content through rich problematic mathematical tasks offers 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. For 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 mathematical 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. This enables an inclusive learning environment to be achieved which encourages learning dynamics, motivation, creativity and engagement. According to researcher Guido (2016) and Small (2017) offers insights into rich and problematic mathematical tasks supporting authentic differentiation through specific practices of inquiry, engagement and instructional strategies centralised in a classroom. Incorporating differentiation strategies in a mathematical classroom enables focusing on unique skills and concepts to foster alternative ways of learning and identifying students learning strategies. 


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 student's 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.

 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 through  a word and action, in example, activity demonstration and using questions. According to theorist Sullivan et al. (2015)  believe that mathematical problem-solving strategies 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 prompt practice is crucial to understanding and in distinctiveness for involving  clarifying and inquiry to ensure for explicit intentional teaching. Subsequently, offering for extending prompts that encompass for altering original tasks to be completed with more structure, complexity and that consolidate for 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. This enables us to explain  how specific learning strategies will be applied to individual student’s learning outcomes and processes. Weselby (2020) shares 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 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. That is achieved through groups based on mixed ability groups shared interests, in continuous assessment of students learning, observing students participation and ability to utilise prior knowledge and use terminology accurately. 

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.


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