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Question: reword to reach essay limit 660...

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Reword to reach essay limit 660

A well-composed, rich mathematical problem in the classroom will enable all learners to be engaged, motivated, highly participative and challenged as it enables 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. 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. This transpires for authentic differentiation creating opportunities for exploring interests and readiness for mixed ability learners to ensure for mastering skills and content. 

Rich and problematic mathematical tasks aim at grasping a mathematical concept through understanding, flexibly, reasoning and fluency through open ended approaches. 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. Researcher Guido (2016) and Small (2017) offer insights into this 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 through inquiry based practice stimulating for higher order mathematical skills, knowledge, reasoning and thinking through trial and error, solution accuracy with creativity and applying prior knowledge.

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 on fractions that can be altered to suit individuals learning such as through watching a video on fractions, physically moulding the fractions, discussing fractions or visual representations. In exploring content outcomes it enables for 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. Where differentiation strategy is in incorporated into a practice through creating lessons that pose an invisible process to the learner through words, actions, demonstrations 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. With differentiation strategies enabling a simple mathematical question to increase for a learner's 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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