An Investigation Of Pupils’ Rectangular Area Learning From The Perspective Of Learning Progression

"Learning progression" refers to the description of thinking in which learners’ understanding of a certain learning topic gradually deepens and tends to be complex in a long period of time.Rectangular area is an important content of the third grade mathematics,is the beginning of learning area knowledge for primary school students,but also the basis of learning other graphic area.However,since the concept of area is more abstract for primary school students,there will always be many difficulties in the first learning.There are many researches on rectangular area learning,but few from the perspective of learning progression.The research focuses on the following four questions:(1)How to construct the rectangular area learning progression framework for primary school students?(2)Pupils rectangular area learning progression level distribution?(3)What are the characteristics of rectangular area learning of pupils at different levels?(4)What are the enlightenments to teaching from the current situation of pupils’ rectangular area learning progression?In order to solve the above four problems,firstly,literature related to learning progression and rectangular area content was studied.At the same time,teachers were interviewed in order to further understand students’ cognition of rectangular area.According to the interview results and combined with the analysis of the textbook and curriculum standard of rectangular area unit,a preliminary framework of rectangular area learning progression is constructed.Then,according to the framework,the paper develops the elementary school students’ learning progression prediction of rectangular area.Predicted and found the problems existing in the advanced test paper and the preliminary framework of learning progress,and modified it under the guidance of front-line teachers and tutors to form the rectangular area of elementary school students’ learning progress test paper.118 students in Grade 3 of a primary school in X City were tested,and 118 valid papers were recovered.The test found that the rectangular area had the largest proportion of students studying at level 3,and the proportion of students from level 0 to level 3 showed an increasing trend,while the proportion of students from level 3 to level 5 showed a decreasing trend.It is found that the main problems in the rectangular area learning of students are: misunderstanding the concept of rectangular area;Rectangle circumference and area formula are confused;Incorrect use of length unit and area unit;Do not understand the meaning of the problem,practical problems into mathematical problems ability;A calculation error;Can not skillfully use rectangle circumference and area formula inverse operation;The conversion method between rectangle circumference and area is not mastered.Less use of the idea of combining numbers and shapes.In order to solve these problems,the teaching suggestions are pointed out from the following three aspects:(1)Apply learning progression to mathematics teaching;(2)Promote students’ knowledge understanding of rectangular area;(3)Improve students’ ability to apply knowledge of rectangular area.