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Question: cut words to 660 at the moment around 760 problem...

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Cut words to 660 at the moment around  760 


Problem solving is an essential component of the learning process for students, and it is one that facilitates their relational understanding of mathematical skills and content. 


Learning through problem solving enables students to understand a step-by-step process of the question. Learning can show their thinking and understanding of the mathematical question that requires problem solving techniques. This can be using visual stimulation such as learning resources, integrated technology, verbal mathematical terminology, separating mathematical questions into their current answer to gain a deeper insight to why their answer is correct or incorrect (Kilpatrick et.al, 2001). In using visual stimulation it provides for additional information to ensure for developing a learners ability to question the answer and ensure the necessary changes are made through discussion of their working out strategies. To illustrate this, when a student completes a fractions activity hands on through showing different fractions they are able to understand how these fractions are formed rather than just get an answer. With which hands problem solving techniques, enables students to develop their relational understanding through visually and verbally connecting the stages involved in working out a mathematical problem. In turning emphasising for how hands on learning through trial and error and use of real word examples allowing for  developing mathematical knowledge through motivation, engagement and participation.

In learning mathematical skills and content through problem solving it enables for developing relational understanding by problem posing to discern for challenging, comprehending, connecting and critically thinking.  Cheng.P.L 2013 provides for insight into when a teacher uses physical learning to complete a problem solving activity, the student not only gains a stronger understanding of the problem solving process, but they can then use learning resources to explain their understanding and way of thinking. This is more beneficial in contrast to a simple verbal discussion because it allows for the student to understand how they reached their answer and improve their understanding.


A positive approach to problem solving can be to use a combination of differentiation strategies that connect students’ different learning levels, outcomes and needs through verbal and visual examples. In implementation of problem solving strategies in various contexts such as individually, small groups and whole class activities it reinforces for using a diverse range of mathematical learning resources. These resources could take form in coloured dices, large numbered cards and board games which allow for altering the mathematical problem solving activity and embedding for transformed learning opportunities. (Department of Education and Training, 2020). In transforming the learning opportunity it transpires for supporting for relational thinking through  understanding for and learning new mathematical skills and concepts easier, in retaining previous knowledge and deviate from the  typical mathematical rules of practice through ensuring for enabling to make connection. In which blending the mathematical process of problem solving questioning becoming integral to segmenting for differentiation amongst representing mathematical questions through numeric and sentences requiring for different problem solving techniques to be implemented.

Consequently, Problem solving enables a learner to see the complete picture of their mathematical learning experience. The most important achievement with using problem solving strategies is to enable a teacher to use assessment tools to identify a student’s level of understanding and thinking about a question. The teacher is then able to better understand the student’s needs and weaknesses to be able to work with them to strengthen their ability. In incorporation of problem solving it fosters for supporting relational thinking of the direction of variation for diverse learners, design rich mathematical tasks and thinking strategically. (Stephens, 2006). In example problem solving strategies enable the learner to utilise all aspects of their thinking process to strengthen and identify their level of understanding. Additionally enabling a learner to use the strategies of applying answers to their mathematical questions in the form of why, when, where, who, what and when situations. In using problem solving techniques in a mathematical classroom it prompts relational thinking through ignoring a response to the task hand before becoming submerged into the task. This is achieved through elimination of student learning differences as the learners will be focusing on completing the mathematical challenge using creative learning resources. Which can be especially beneficial if the mathematical rotation activities are to be completed within a set time frame, as the learners will have a deadline to meet. 

Essentially, it is essential that learning is made through problem solving in order to support the development of relational understanding of mathematical skills and content for it enabling for better grasping, developing and challenging understanding.


challenging understanding. .

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