Designing "Problem Posing" Tasks In Elementary School Mathematics Textbooks In The Context Of Deep Learning

Innovation begins with the formulation of problems."problem posing" is an effective entry point for the development of innovation and problem-solving."However,the phenomenon of " high evaluation but low application " is widespread.Problem posing" is highly expected in "planned curricula" of various disciplines in different countries.the quality of the questions from students is often poor,and they tend to ask non-mathematical,irrelevant,and closed questions,which revealed the inefficient questioning practices under shallow learning and limiting the development of students’ thinking.Deep learning is a need to transform the superficiality of learning in the context of quality education.In this case,the concept of deep learning provides new ideas to improve the shallow problem of "question posing".In terms of the process of curriculum operation,textbooks are the first level of transformation of "problem posing" from policy text to curriculum teaching,and the kind of "problem posing" tasks presented in textbooks is directly related to the deep learning effect.This study focuses on three editions of elementary school mathematics textbooks and analyzes the "problem posing" tasks quantitatively and qualitatively to provide deep learning opportunities.While filling in the gaps in the existing research,it provides useful references for curriculum standard revision,textbook writing and teaching practice.The core question of this study is "How to design ’problem posing’ tasks in elementary school mathematics textbooks to facilitate deep learning ",and the following three questions are examined.(1)Do current elementary mathematics textbooks provide“problem posing” tasks to facilitate deep learning(2)Do current elementary mathematics textbook “problem posing” tasks facilitate deep learning to occur?(3)How to design“problem-posing”tasks in elementary mathematics textbooks in order to promote deep learning.This paper uses the literature research method to construct a theoretical framework for the design of "problem posing" tasks in primary school mathematics textbooks that point to deep learning.This theoretical framework is based on the core point that "deep learning is the goal of ’problem posing’ and ’problem posing’ facilitates deep learning".The main elements include the overall setting of the problem-posing task,the problem context,the problem-posing process and the cognitive types of the problem-posing task."Each problem-posing task in a mathematics textbook provides students with a potential opportunity for deeper learning." Textbooks need to provide sufficient ’problem posing’tasks,otherwise teachers will not have time to develop the higher-order skills required for deep learning and their transferable application."Depth" is the key word for deep learning.The problem situation,the "problem posing" process and the cognitive type of "problem posing" themselves imply a requirement for depth,and from these three dimensions A number of sub-dimensions have been identified to provide insight into how the "problem posing" tasks in primary school mathematics textbooks contribute to deep learning.Firstly,the statistical results of the overall setting of "problem posing" tasks in textbooks were used to answer the question of whether existing primary school mathematics textbooks provide "problem posing" tasks to facilitate in-depth learning.In this study,the number of "problem posing" tasks in textbooks is classified according to four dimensions: overall number,grade distribution,knowledge domain distribution,and purpose of use distribution,and their quantitative characteristics in different dimensions are analysed.The study shows that "problem posing" is not only a form of mathematics,but also a form of mathematics.The study shows that the proportion of problem posing in current primary mathematics textbooks is very low,and that there is an imbalance in the distribution of knowledge areas,grade levels and purposes of use.In general,current primary mathematics textbooks are designed with a small and uneven number of ’problem-solving’ tasks,providing few opportunities for in-depth learning.Secondly,three aspects of problem situations,problem posing processes,and cognitive types of problem posing were identified to determine whether the problem posing tasks in current primary mathematics textbooks promote deep learning.Learning occurs.The study revealed that the problem contexts were mostly represented by pictures that were of interest to students,with fewer diagrammatic representations that were inquisitive in nature,and that the problem contexts were staged in a way that was predominantly good problem contexts and poorly constructed problem contexts.In terms of the process of "problem formulation",the textbook presents five sequences of"problem posing" tasks,with a variety of sequences but an imbalance in their proportion,focusing on the development of reflective consciousness,with some sequences distributed in stages,and with a variety of guidance but with vague and unspecific instructions.The textbook has a variety of cognitive types for the ’questioning’ tasks,but the proportion is skewed."The ’reproducible’ tasks are distributed in stages,but the’linking’ and ’transferable’ tasks are arranged in a disorderly manner.In general,the problem-setting tasks in the current three editions of primary school mathematics textbooks do not provide sufficient opportunities for in-depth learning,and are difficult to sustain and stimulate.Thirdly,the principles and recommendations for how to design ’problem posing’ in primary mathematics textbooks to facilitate deep learning.The design of problem-posing tasks in primary school mathematics textbooks in the context of deep learning should follow four basic principles: staging,appropriateness,guidance and inquiry.The first two focus on the overall layout of the textbook ’problem-posing’ tasks,while the second two focus on the specific design of the ’problem-posing’ tasks in primary school mathematics textbooks for deeper learning.Specific design suggestions are as follows:(1)Adjust the arrangement of textbook ’problem-solving’ tasks to point to students’ deeper learning.Specifically,the proportion of "problem posing" tasks should be increased and the distribution of "problem posing" tasks should be expanded to provide opportunities for deeper learning;the design of problem contexts should be optimised to sustain motivation for deeper learning;and the sequence of "problem posing" tasks should be balanced to ensure that students can learn more deeply.The sequence of "problem-posing" tasks is balanced to ensure a high level of student participation in the in-depth learning process;the distribution of cognitive types of "problem-posing" tasks is coordinated to facilitate a high level of achievement of students’ in-depth learning objectives.(2)Enhancing the practicality of the textbook’s "problem-posing" tasks to guide students’ deep cognitive processing.Specifically,the textbook should include prompts that are relevant to the quality of the questions asked and guide deeper thinking;focus on the detailed design of the strategy guide and design the "problem-posing" process in depth;develop the "problem-posing" section of the textbook to point to deeper learning objectives;and present thematic "problem-posing" textbook examples.(3)Pay attention to the textbook "problem-posing" section,pointing to in-depth learning objectives;presenting thematic "problem-posing" textbook examples to enhance the hierarchy of in-depth learning.(3)Pay attention to the high quality of the textbook "problem-posing" tasks to promote in-depth learning.Specifically,on the one hand,realistic problem situations are created to stimulate deep learning,and on the other hand,problem strings are selected to drive the deep learning process.