ASSESSMENT PRACTICES
6.2 Description of teacher educators' instruction
6.2.1 Description of Emily's instruction
Emily was handling Methods of Teaching Basic School Mathematics, a module for second-year pre-service teachers. All of the 48 students were female. Emily's lesson was interactive, using group presentations and whole-class discussions. Emily conducted each of the mathematics lessons that were observed in a different way.
138
In the first observed lesson, Emily was teaching the addition of integers. She began by exploring the existing knowledge of her students through questioning, as per the excerpt from the transcribed lesson below:
Emily: Who is owing someone money?
Student: Madam, I.
Emily: Whom are you owing?
Student: …… [name withheld]
Emily: How much do you owe her?
Student: Five Ghana cedis [Ghc 5.00]
Emily: How much were you having …. [name withheld] before she borrowed the Ghc 5.00?
Student: Ghc 10.00.
This teacher-student interaction set the stage for the introduction of the day's lesson. Emily sought the prior knowledge of her students and based on that she mentioned that the topic for the lesson is integers and followed up by sharing the learning goals with her students. After introducing the lesson, Emily wrote a sum (see Example 1) on the marker board, and explained that the signs in front of the numbers 1 and 4 are called directional signs, whereas the sign in between the two numbers (+1) and (+4) is called an operational sign.
Example 1:
She explained that the directional sign represents the position one needs to face when carrying out the activity. For example, a positive sign means to face the right direction or the positive direction, while a negative sign indicates facing the left direction. On the operational signs, Emily said a plus sign indicates forward movement, and a minus sign indicates a backward movement. With her guidance, students performed the activity. She then sketched a picture (see Figure 6.1) of the modelled number line on the board for the students.
( +𝟏) ± ( +𝟒 )
139
Figure 6.1: Emily's model number line of the sum (+1) + (+4).
The example was followed by an activity for her students to try their hand at. Emily asked her students to write an activity that they would use to teach a Grade 6 pupil (+3) + ( -2) using the number line model.
After reading out the question to her students, she gave them 5 minutes to work on the activity.
After this, she called a student to the board to record her solution for the entire class:
Emily: What was your answer?
Student: I had 1, madam.
Emily asks the class: Is she correct?
Students: Yes madam [answer in chorus].
Emily: Okay, write your solution on the board and explain how you arrived on 1.
Student: Madam, first, you assist learners in drawing a number line. Starting from 0, ask learners to turn in a positive direction and move 3 steps. Then let learners turn and face the negative direction and move 2 steps forward, landing on a positive 1.
Figure 6.2: Student model number line for adding (+3) + ( -2).
After engaging her students actively in the lesson through questions and answers, individual hands-on activity on the concept, she ended by summarizing the lesson through questions.
0
+3
1 2 3
-2 -1
-2
0 1 2 3 4 5
-2 -1
+ 4 + 1
140
Emily's second observed lesson took place as scheduled. The date and time were agreed upon after the first observed lecture. She was teaching Number Basis this time round. Before the start of the lesson, Emily informed her students of the intention of learning (learning goals) for the day's lesson. After highlighting the goals for the units for the section, she wrote a mathematical sum on the board and asked “Who can read 435 + 325?” One student said “Madam, 43 Base 5 plus 32 Base 5.” Another student said “She is wrong; I disagree with her,” then Emily asked “Why do you disagree with her answer?” Emily asked. The student replied “Madam, the numbers are written in Base 5, and so we cannot have 40 or 30 as an answer." Emily asked "So how should it be read?”
and the student said "I think 4-3 Base 5 plus 3-2 Base 5."
Emily explained further after the students had read further, and hinted that they should always be mindful of the Base of the question:
Ladies, since the question was given in Base 5, you have to be mindful of the numeral. So, for this question, the digits required are 0, 1, 2, 3, and 4. Numbers like 5 the Base you are working with, and above 5 should not be part of your result. So, you cannot have 30 or 40, as she said.
The lesson continued with Emily assisting her students in solving the question. She asked her students to bring out their materials. Students placed bundles of sticks, thread, and some loose sticks on their table. Because the question was on Base 5, Emily assisted her students in having some bundles of 5 sticks and tied them with the thread. After they were done, she guided the students in solving the sum 435 + 325:
Emily: Select four bundles of 5 bundle sticks and 3 loose sticks representing the first addend. What should be the next step?
Student response: Teacher will assist learners in picking three bundles of 5 sticks and 2 loose sticks to represent 322, the second addend.
Emily: What should the learners do next with the selected bundle of sticks and loose ones?
Another student: I think you ask learners to put the bundles of 5 sticks together and the loose ones also together.
141
The process continued until they arrived at the answer: one bundle of 5 bundles of 5 sticks and 3 bundles of 5 sticks. This was finally written mathematically as 1305. She followed it up with the following examples for the students to work out:
a) 234 + 114 b) 1012 + 1102 c) 278 + 158
Her third lesson was on the properties of operation and was presented by students via group presentations. Groups took turns to present aspects of the subject matter. The groups presented on the commutative property, associative property, and distributive property. Two groups presented on commutative property. One group presentation was on the commutative property of addition, while the other group's presentation was on the commutative property of multiplication. The same went for the associative property, while the last group presented on the distributive property. After each presentation, group members were questioned by other students. Emily was always the last person to comment on a presentation. After all the groups had finished presenting Emily said “This ends the lesson on properties of operation. I am not treating it again.” She concluded the lesson by asking students a few questions to highlight key concepts learned on the day.