| In the study of fractional multiplication,students tend to remember the rules and not understand the algorithm.Based on the importance and difficulty of fractional multiplication,This paper mainly studies the learning trajectory of fractional multiplication in the teaching materials,and the learning trajectory of fractional multiplication which researchers and S teacher designed,and how to improve and optimize the learning trajectory.We conducted an action research method in an ordinary primary school in Hangzhou.The research procedures are as follows: first of all,S teacher designed lesson plans in accordance with his own understanding of the teaching materials and students.Then,in order to understand the basis of students,we carry out pre-test in class A,then S teacher started teaching in class A,in order to understand the situation of students and the achievement of teaching objectives,we implement the post test after the class,And then the teache,the researchers and the teacher development mentor and so on together to discuss the just ended classroom teaching.S teacher introduced his teaching design intention,teaching implementation,problems and improvement ideas,the researcher and the instructor of the development of teachers analyzed the classroom teaching,and then put forward the suggestions for improvement,reach a consensus with S teacher of perfect learning path.Finally,S teacher designed the teaching once again,in the teaching and research process of a class of second class repeat to teach in class B,and epeat the teaching and research process of class A in class B.Get the optimized learning path as follows:(1)The learning path of a fraction multiplied by an integer.On the basis of multiplication of integer,guide students to explore the task:"Xiao ming,Mom and Dad together to eat a cake,every one eats 2/9,how much of the 3people eat?" Visual representation: guide the students to draw maps;and then to the abstract representation(explain in words or express with formula),this task explains the principles and rules of fractional multiplication,its meaning is the same as integer multiplication.Finally,guide the students to summarize the rule: a fraction multipliedby an integer,the product of molecular * integer as the molecular of the result,the denominator does not change;Finally,the rules are optimized,can to remove can to first remove and then calculate,the result is similar.(2)The learning path of an integer multiplied by a fraction.The learning path of an integer multiplied by a fraction serves as an important and difficulty progress.Design as follows:Task 1:"There are 3 pieces of mooncakes in a box;if you eat 3 boxes,how many pieces of mooncakes do you eat?(3×3);if you eat one box,how many pieces of moon cakes do you eat?(3×(1/3));Task 2:if you eat 1/3box,how many pieces of mooncakes do you eat?(3×(1/3));Task 3:if you eat 1/4box,how many pieces of mooncakes do you eat?(3×(1/4));Task 4:if you eat 2/7box,how many pieces of mooncakes do you eat?(3×(2/7)).Take 3×(1/4) as example,then give a brief description of the role of connecting link.The role of commitment lies in: the 1/4 box of mooncakes is the whole is divived into four parts averagely and then take one,lay out is 1/4+1/4+1/4,According to the meaning of fractional * integral can get 1/4+1/4+1/4-1/4×3,according to the meaning and algorithm of fractional * integer(including anschauung)can get that 1/4×3-(1×3)/4-3/4.This learning path says the algorithm of integer * fraction and the rule is "What is the fraction of a number,can use the multiplication to express"(it is different from the conclusion that given by the example 2 of the PEP textbook: "A number multiplied by a fraction represents that what is the fraction of the number"),Here,transformation(a fraction * an integer?an integer * a fraction)is the key factor.The role of opening up lies in: According to the meaning of integer * fraction can get: how much is 3 of 1/4 uses multiplication 3×1/4,according to the meaning of scores can get 3×(1/4)=1/4+1/4+1/4,still according to the meaning of a fraction * aninteger can get (1/4)+(1/4)+(1/4)=(1/4)×3,then 1/4×3=3×1/4(it is based on the operation principle of inheritance),here,the meaning of fraction is the key factor.Especially the intuitive understanding,it is the dominate the field.And it is different from the learning path that given by the example 2 of the PEP text book uses“unit quantity * number = total”:12×3,12×(1/2),12×(1/3).(3)The learning path of a fractional * a fractional.The learning path of a fractional * a fractional is desined as follows:According to the connecting role of an integer multiplied by a fraction,by using the area mode,we designed the task of a fraction * a fraction in this order: unit fraction * unit fraction(1/2×1/3 and 1/2×1/5)?unit fraction * non unit fraction(1/2×2/3)?it fraction * non unit fraction(2/3×2/5).Visual representation: guide the students to draw maps;and then to the abstract representation(explain in words or express with formula),will pull through fraction multiplication and get the law: "use the product of the denominator * denominator as the denominator of the result,use the product of the molecule * molecule as the molecule of the result".The students' understanding level is improved and the ideal teaching effect is achieved.Finally,the post test show that the learning path is reasonable and optimized.According to the results,we propose the main teaching suggestions following:(1)In the teachering of integer * fraction use the model of "mooncakes" as the task context rather than the model of "bucket",play the connecting role of this part,not only to get the algorithm of integer * fraction but also to pave the way for learning fraction * fraction and get "What is the fraction of a number,can use the multiplication to express".(2)In the teachering of fraction * fraction,add the task of non unit fraction * non unit fraction(2/3×2/5). |
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