9 o'clock on a Wednesday morning in a central district of a very smoggy Beijing. We've been invited to join teacher researchers from the Beijing Institute of Education in a morning of mathematics with small children. The visit begins with the usual pleasantries and being shown around the three storey building which hosts 500 children from 6 to 8, in classes of 40. The walls are covered with the children's art work, notably some impressive examples of paper cutting for which the school is known and which every child learns from age 6. Various little people wave and say hello - although they are used to visitors, non-Chinese folk do attract curiosity and attention.
The first lesson is with the first grade. In our honour they have donned their uniform track suits over their regular clothes. The children sit at tables of four, chairs facing the front, and are remarkably quiet whilst the teacher sets up the two screens either side of the magnetic green chalk board.
Today's topic is about comparing two quantities. The lesson begins with a picture story about two cartoon characters in a competition to see who has the most fruit, the bear with 12 apples or the bear with 8 bananas. The children confirm that 12 is more and the magnetic fruit are arranged in one to one correspondence on the board. Each child then turns over their small magnetic board on which are grouped 12 red and 8 yellow counters and replicates the one to one correspondence. The teacher uses a couple of children's boards to retell the story and to record 12, 8 and 4 in the appropriate places on them, annotating in both Arabic and Chinese numerals. She also writes the calculation 12 - 8 = 4 and the children recite it.
Task two is a different competition between the snail pets of the bears. Which has left the longest trail, 15 or 9? Each child has pre-prepared strips of paper of yellow, 15 and blue, 9 units. The teacher models matching them up and marking 9 on the yellow strip. The children do the same and then get out their scissors and cut on the mark. They write 9,6 and 15 - 9 = 6, reciting together. And so the lesson ends.
The third graders arrive also in track suits but wearing their red neckerchiefs which they are awarded for good citizenship. Today's lesson is preparing for being able to multiply a 2-digit by a 2-digit number and the lesson begins with a photo of children in rows in the playground; 12 rows of 14 children. How many children? The link is made to a 12 by 14 array of dots. How many dots? The children get out their own paper versions and are told they have five minutes (timed on the board with a stopwatch) to find out the answer in any way they like. Each table of children are then asked to talk and listen to each other, to choose two methods they think are the best and be prepared to come and share them with the class. My Chinese wasn't up to understanding the nuances of the children's conversations, but they were very earnest!
Groups of four then came to the front. Using the visualiser and microphone they explained the way they had divided up the array and the calculations arising. They then very formally asked the class if they understood and if they had any questions, answering any that arose and defending their choices where necessary. In each case the teacher recorded the way in which the array had been divided up, pointing out where each number came from. Emphasis was given to the order, and the use of brackets, and the confirmation that this expression did indeed represent the diagram. Like expressions were collected together and the differences between the sets explained. Some were identified as being easy to calculate mentally, eg (12 x 10) + (12 x 4) others not eg. 12 x 2 x 7
The teacher then introduced 15 x 11 and asked how this might be broken down, then 71 x 13. She told them this was the springboard for the next lesson.
In the second part of this blog, I will discuss more about the observations and lessons learned.