5.3 Grade 2: Classroom observation
5.3.1 Lesson 1: Mathematics Lesson
quietly until he had completed his writing. She accommodated this learner by allowing him extra time.
Ms Miya then counted in 3s asking the learners to count with her, pointing at each grouping in turn, 3, 6, 9. She also wrote on the board 3+3+3 = 9, thinking aloud as she did so. She then went on to ask:
Ms Miya: Tell me how many “four 4s” make? Let’s go for it.
Langa: 16 Anathi: 12 Mbulelo: 24
Ms Miya: Langa says 16, Anathi says 12 and Mbulelo says 24. Let’s see.
Ms Miya proceeded to draw 4 groups of 4 circles and wrote up 4+4+4+4.
Ms Miya: How many 4s. 4 of them. Let’s count them altogether.
The learners counted out loud together while Ms Miya pointed to the circles, and arrived at the answer 16.
Ms Miya: Let’s count in 4s. Let’s go for it.
Learners: 4, 8, 12, 16.
It could be seen that Ms Miya was attempting to demonstrate the concept of grouping and continuous adding by using various examples of semi-concrete drawings on the board. Leading up to the concept of multiplication, she then asked the following question:
Ms Miya: We worked out a sign we already know, “times”. (She drew the character “x”
on the board). So, times, what does it mean? You tell me, what do you have to do when you see that sign?
Learners: Times
Ms Miya: Let’s try it with a sum.
Ms Miya wrote up 5 x 2 on the board and asked the learners what this came to. Some learners replied with 10.
Ms Miya: How did you get to 10?
Learner: Double the 5
Ms Miya: What do you mean by doubled?
Learner: Put two 5s together.
Ms Miya: If we write it as a plus sum, how should we write it?
Ms Miya wrote 5 + 5 = 10 on the board.
Ms Miya: We come to the same number.
Ms Miya: Let’s go to another one.
Ms Miya wrote 6 x 3 on the board and asked Phumla (pseudonym) to come and do the sum on the board for the class. She was actively involving a learner.
Ms Miya: Come show us.
Phumla: She wrote 6+6+6 = 18
Ms Miya: Phumla did it as a plus sum and still got to the same answer. There are different ways of answering.
While observing the learners during the lesson conducted above, I saw that not all were engaged and following the processes being carried out on the board. One learner, Cebisa (pseudonym), seated at the front of the class, had her back to Ms Miya, turning around only a few times briefly to watch her. The learner opposite her, Fundiswa (pseudonym), was drawing in a book in front of her and only occasionally looked up at the board. Ms Miya did not ensure that all the learners were turned to face her and were focusing on the lesson and the concept being taught. The consequence was that she had to explain the process again at a later stage to these two learners (see below).
Ms Miya instructed the learners to get out their Mathematics exercise books and to open them at page 106 for mixed multiplication. She read out the instructions in the book and went through the first example given in the yellow box at the top of their exercise books on 5+5+5=15, 3 groups of 5 is 15 and 3 x 5 = 15 or 5 x 3 = 15. She asked the learners to look at the table below using the example in the yellow box to guide them. There was a further example given in the first row of the table which Ms Miya went through and then the learners were asked to complete the other three empty rows in the table. The learners began to work in their exercise books and Ms Miya walked around observing their work.
Ms Miya seemed unhappy with the learners’ understanding of what they had to do so, a few minutes later, explained with another example which she wrote on the board. This possibly illustrated that not all the learners had followed the previous examples, either because they were not focused and concentrating on the lesson or because they were unable to follow the logical reasoning of the process.
She drew 5 columns on the board, once again explaining to the learners that they needed to write in the numbers for skip counting (6, 12, 18), draw in the groups with small circles (000000, 000000, 000000), repeat addition (6+6+6), write “3 rows of 6” and finally write the times sum of 3 x 6 = 18 and 6 x 3=18 in each of the columns (see Figure 5.1 below).
Figure 5.1: Demonstration of mixed multiplication on the board
The learners began to do the exercises and Ms Miya walked around the class checking the learners as they worked. She spent extra time on an individual basis with three learners who were struggling with the exercises.
The first learner was Fundiswa, who had not paid attention during the lesson. Ms Miya rubbed out the work she had done so far and went through the first exercise again with her. Cebisa, the learner opposite Fundiswa, also listened to Ms Miya explaining the exercise to Fundiswa and was then able to continue with the exercises in her book. This would not have been necessary, possibly, if the two girls had been made to pay attention earlier in the lesson. Their being seated in front did not necessarily ensure that they were concentrating on the lesson.
The second learner, Bongani (pseudonym), was at the very back of the class. He had engaged with the lesson, as I saw him raise his hand on a few occasions. He, however, became confused with the conceptualisation of the number of groups and the amounts in each group. He was confused by the difference between the two exercises in the book, because the first exercise had 4 groups of 3 circles and the second exercise had 3 groups of 4 circles. Ms Miya took out a container of colourful discs or counters to help demonstrate the difference visually and physically. She had Bongani count out each group and the number of counters in each group.
He could then see the groups clearly. She had used counters as an aid to assist Bongani because he had struggled to understand the semi-concrete drawings of groups of circles in the textbook (see Figure 5.2 below).
Figure: 5.2: Grouping with counters
By observing the work done by a couple of learners next to Bongani, it was clear to me that they too had not understood the reasoning process of mixed multiplication and so were doing their exercises incorrectly. Ms Miya was busy with Bongani and, therefore, was unaware that these learners also were doing their work incorrectly and she was not able to assist them all at the same time (see Figure 5.3 below). I also noticed that a poor example was given in the exercise book, which may have added to the confusion of the learners; there were 4 groups of three circles shown under equal groups, and there were 3 rows of 4 crosses printed under the arrays (see Figure 5.3 below).
Figure 5.3: Incorrectly done worksheet
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