##### Ralleia Experimental Primary Schools

Math Lessons with Operations:  Divide by two-digit divisors

Classes: D2

Teachers: Anagnostopoulou Konstantina

2. The division concept that was taught with the official course book examples was easy for me.

3. Some concepts in the book were very difficult for me.

4. The explanation of the division concept from the mah course by my teacher seemed understandable.

5. The course will be more interesting if it had more activities.

6. The course exercises were difficult for me.

7. It would be better if we had used digital devices in the course.

8. I felt anxiety when I tried to solve the course exercises.

9.  The taught course activities got my attention.

10. Ultimately the lesson was useful.

11. I liked the book's images from the course.

12. Studying the division process from the book seemed more understandable than what we learned in the class.

13. I'm pleased from the teaching process.

14. After course completion we feel much more familiar with division in maths.

It seemed difficult for students to understand the division example concept presented in the official math course book. Division calculation based on the creation of the  divisor factors table process seemed overwhelming. The students tried to repeat the process by creating their own tables for the same example, which are presented below.

In the picture above the student has created a numbers table, which contains in the odd rows, numbers starting from one and incremented by one in each advancing cell of the odd rows.

In the even rows of the table the student writes down in each corresponding cell the product of the number contained in the same cell of the previous odd row and the divisor. In the above example the divisor is the number 13 and the dividend is the number 197.

So the first cell of row 1 (odd row) contains number 1, the next cell contains 2 (previous cell number incremented by one) next advancing cell contains 3 and so on.

The first cell of row 2 (even row) contains number 13 which is the product of the number contained in the exact position cell of the previous row which is 1 and the divisor which is 13 (1x13=13). Next cell of row 2 contains 26 which is the product of the number contained in the exact position cell of the previous row which is 2 and the divisor which is 13 (2x13=26).  Next cell contains 39 (3x13=39) and so on. The process continues until the student calculates a product to write down in a cell that is greater than the dividend. In our example last cell is 196 (15x13=196) because next cell (16x13=208) is greater than the dividend, which is 197.

In order to help the students better understand the divisor factor table, aided division calculation process implemented as a scratch application was developed using the MIT scratch online platform.

The application displays a schoolteacher that asks for a dividend and a divisor as an input. After that by using automatic narration techniques, the teacher presents the divisor factor table creation process to the students and calculates the division outcome by using the calculated table data dynamically.

Questionnaire ( after scratch application usage)

After scratch application usage students seemed to better understand and accumulate the division concept of their classic math course.  It was also clear that they liked a lot to experiment using the scratch app in order to find the quotient and the remainder of difficult division examples.