5.3 Grade 2: Classroom observation
5.3.2 Lesson 2: Mathematics lesson Duration: 2 hours
The final learner was Asanda. He was seated in the front of the class, next to Ms Miya’s desk.
He had not begun the exercises, seeming unsure as to what to do and seemed to have persistent difficulty with the logical reasoning and critical thinking process of repeat addition, grouping and multiplication. He was extremely shy, lacked confidence and had low self-esteem. Ms Miya sat next to him and quietly worked with him.
Ms Miya demonstrated to Asanda, one-on-one, the concept of 3 groups of four by drawing the circles in his exercise book. She showed him how to group the circles into 3 groups of four, which would then represent 4+4+4=12 or 3 x 4=12. She then had him add all the circles in the groups asking him how many there were. He answered with 12. She went on to say to Asanda:
Ms Miya: Remember this is times, asking you to repeat something. Now show me this with 5 rows of 6.
Asanda: He slowly started drawing the circles in the 5 groups with 6 counters in each group with the assistance of Ms Miya. He was very hesitant and kept looking up and checking with Ms Miya.
Ms Miya did not use the counters with Asanda, but used only the semi-concrete drawings of the group of circles.
While Ms Miya was working with these learners on an individual basis, some of the learners had completed their exercises and approached her to have their work marked. They interrupted her when assisting struggling learners. The noise level in the class also began to increase and Ms Miya responded by saying:
Ms Miya: Once you are done with your Maths, get a book from the corner (classroom library). (Some of the learners went across and selected a book to read).
Using the library meant the learners could practise their reading and it would keep them occupied as well. The lesson ended at 09h50 with Ms Miya’s instructing the learners to line up to go and get their hot meal.
5.3.2 Lesson 2: Mathematics lesson
backwards requires more concentration and does not come as easily as does counting forwards.
Asanda used his fingers when counting down from the 10 to the 1 between 200 to 190, 190 to 180 and 180 to 170, visibly seeing how many fingers were left when counting down. Ms Miya commenced the lesson by asking a question.
Ms Miya: Now I want to know what I mean when I speak of a half. What do you have to do when you cut in half?
Learner: Take an orange and cut it in half.
Learner: Fractions.
Ms Miya: There is a half in fractions. I am talking about let’s say 10 sweets and somebody says share them in half.
Learner: Each child will get 5.
Ms Miya: How many children will there be?
Learners: 2
Ms Miya: 2. Okay, what else do you know about halves? Vusi is trying to have a conversation, please listen.
Vusi: Sharing an apple into 2.
Ms Miya: Sharing an apple for 2 children is also a half. (She drew the apple cut in half on the board shared between 2 stick figures). Each child must get the same amount, almost the same size, so equal sharing.
Ms Miya illustrated halving by using an example of cutting an apple in half and sharing it between two people. She drew two half apples on the board with two stick figures underneath them, demonstrating that each stick figure received half an apple.
Ms Miya then used another example of halving by getting a group of 8 learners on the one side of the classroom to come up to the front of the class.
Ms Miya: So, if we are sharing, where would we share in the last row?
The learners in the front of the class conversed amongst themselves and then split into 2 groups of 4 each. Some of the other learners in the class shouted out 4 on each side.
Ms Miya continued by instructing one of the learners to sit down and asked where would we share in half? There were 7 learners, so she responded by saying we have 3 and 3 and we will cut the one learner in half. She continued by having one learner sit down each time, until the last two learners were left and they were halved, 1 and 1 on each side. All the learners were engaged with this example, visibly seeing the process of halving. Ms Miya had made the lesson more interesting for the learners by involving them in an activity that demonstrated the significance of halving.
Ms Miya: Always equal sharing and two parts.
Ms Miya went on to present examples of sharing 24 cupcakes and 30 bananas in half and various learners answered with 12 and 15 respectively. She then asked the learners to take out their Mathematics workbooks, to write the date and “Halving” as the heading. She wrote some exercises on the board for the learners to attempt (see figure 5.4 below).
Figure 5.4: Halving exercises
The learners started working in their Mathematics workbooks, while Ms Miya walked around the classroom checking the learners’ work and helping individual learners who were having difficulties with the concept of halving. She spent a full 20 minutes assisting Asanda with the understanding and logical reasoning of the concept of halving.
To help Asanda with the concept Ms Miya used concrete objects. She handed Asanda a container of red beads. The sum on the board was to halve 30 triangles (see illustration Figure 5.5 above).
Ms Miya: Count the beads first. There are 30 beads. (The beads represented the 30 triangles to be halved).
Asanda: He slowly counted out 30 beads.
Ms Miya: Share them in half. (She drew a line on the page in his exercise book and showed him the process of sharing and halving by placing one bead on either side of the line).
Asanda: He continued to place one bead at a time on either side of the line.
Ms Miya: Now count the beads on one side of the line.
Asanda: He slowly counted the beads, struggling to get to the correct amount of 15.
Asanda had difficulties holding and counting the beads. This could have been due to his fine motor ability or the difficulty of counting correctly.
Ms Miya decided to get out her container of the larger colourful counters. This was easier for Asanda to manipulate as they were flat and larger in size. She had Asanda count out 30 counters and to once again place them on either side of the line. She then asked him to count the number
of counters on the one side of the line. This time he found it easier to count out the correct amount of 15 counters on each side of the line. She then asked him to attempt the next sum of 28 squares.
Ms Miya had visually and kinaesthetically shown Asanda a technique of halving a set number of counters by placing them, one at a time, on either side of the line. He was sharing the counters between the two sides. She was extremely patient and encouraged Asanda by gently prompting him through the process.
Some of the learners followed the way Ms Miya had demonstrated with an example on the board, and drew the number of objects to be halved in their text books, such as 10 diamonds, then drawing a line half way between these drawn objects (after 5 diamonds), representing halving them. They used semi-concrete drawings to help them visualise the halving of the objects.
The lesson ended with Ms Miya’s asking the learners to line up to get their hot meal of the day. Asanda and a few other learners had not yet completed their work.