Open Case Study in Grade 4 Math Class: From Multiplication to Fraction

Open case study in Grade 4 math class: From multiplication to fraction

        In week one, when it was time to learn multiplication, I noticed one kid Tony, who was not good at math, felt great difficulty in doing multiplication. So I came to help him doing exercise. He was good at addition and subtraction, and what multiplication means. However, as he did 6*4, he was more willing to do 6+6+6+6.

        I understood that kid was always reluctant to do recitation. When I was a kid, my teacher had me memorize the facts table using a lot of strategies. However here now, memorizing facts table is no longer a norm in syllabus. As a result, teacher Susan didn’t force him to memorize the table, and the result is obvious, as he did multiplication exercise, he was slow and unwilling to continue.

        Remembering the facts table was hard for him, especially when he was not forced to do so. After a week as I returned to his class, I found that he was still not proficient enough to give out the answer quickly, but one thing I had to admit that he did improve a lot. Before a week, he didn’t even know 3*8, however now as I gave two numbers below 10 to do multiplication, mostly he will figure it out. He needs time. But, I am okay with it, as long as he can figure it out eventually.

        Next week was about division. Before I came, I thought Tony could not do division easily, and it turned out that I was right. He could do the division using long table. He knew when to put number above the table, and use subtraction, and divide the remaining part, and check remainder. But, it was slow. When he used long table to do division, he needed to check fact table to see the product and then did the subtraction. But anyway he solved it, so during this time, I thought fact table probably is not necessary to be memorized. But I did believe that a student memorized facts table will do the division faster than him.

        Things started to go wrong when it came to fraction. Adding and subtracting fraction were combinations of multiplication and division. Because Tony failed to calculate multiplication quickly, he didn’t know what to do with fractions with different denominators. He randomly added or multiplied the denominators together and came up with a new dominator as result.  I thought this really hindered his future learning. At the very beginning when he was learning new ways dealing with new situation, if he was not familiar with new ways, or for this new way, he could not solve the equation, he would abandon this correct way solving problems, although he maybe believed this way was actually correct. For example, he already learned from teacher that in order to add two fractions together, least common denominator needed to be found first. But since he didn’t master the multiplication, he tended to ignore this process, which I believe really hurt future learning.