Teacher Follow-up on Learners’ Initial Response to Teacher Questions

Figures & data

Table 1. Teaching information

Participant	Number of years of experience in teaching	Learner race/social economic status	Years teaching mathematics in Grade 9 Class	Qualifications	Gender
Teacher A	16	Black/Low	11	Honours degree in teaching	Female
Teacher B	7	Black/Low	4	Tertiary diploma in teaching	Female
Teacher C	13	Black/Mid	8	Tertiary degree in teaching	Male

Table 2. Subcategories of follow-up

Insert	The teacher adds something in response to the learner’s contribution. She can elaborate on it, correct it, answer a question, suggest something, make a link, etc.
Elicit	While following up on a contribution, the teacher tries to get something from the learner. She elicits something else to work on the learner’s idea. Elicit moves can sometimes narrow the contributions in the same way as funnelling.
Press	The teacher pushes or probes the learner for more on their idea to clarify, justify or explain more clearly. The teacher does this by asking the learner to explain more, by asking why the learner thinks they are correct, or by asking a specific question that relates to the learner’s idea and pushes for something more.
Maintain	The teacher maintains the contribution in the public realm for further consideration. She can repeat the idea, ask others for comments, or merely indicate that the learner should continue talking.
Confirm	The teacher confirms that the learner has been heard correctly. There should be some evidence that the teacher is not sure what has been heard from the learner, otherwise, it could be press.

Adapted from Brodie (2010).

Table 3. Subtopics observed and class enrolment

Participant	Subtopics observed	Class	Number of learners
Teacher A	1. Factorisation of algebraic expressions 2. Factorisation of trinomials 3. Difference between two squares	9A	30
Teacher B	1. Properties and definitions of triangles 2. Classification of quadrilaterals based on their sides and angles 3. Properties of diagonals of quadrilaterals	9B	30
Teacher C	1. Flow diagrams 2. Describing the relationships in diagrams 3. Calculating the value of the independent variable when given the dependent variable	9C	30

Table 4. Teacher A follow-up moves

Teacher moves	Lesson 1	Lesson 2	Lesson 3	Total
Insert	1	1	2	4
Elicit	8	5	6	19
Press	5	6	4	15
Maintain	1	0	0	1
Confirm	2	1	0	3
Total	17	13	12	42

Table

4	T	Considering terms, what name do we give to this expression $x^2+5x+12$?	Elicit
5	L1	Trinomial
6	T	Why is it called a trinomial?	Press
7	L1	Eeeeh, because it has three terms and tri means three. Triangle for three angles (a round of applause from class).
8	T	Well explained. Let’s move on.	Confirm
9	T	Can someone give us the three terms? L2, are you able to do it for us?	Elicit
10	L2	Yes. Let me try. $x^2,5x\mathrm{and}12,$ so we have 1, 2, 3 terms.
11	T	Class, what else can we say about this trinomial?	Elicit
12	L3	It is called a quadratic expression.
13	T	Yes. Quadratic.	Maintain
14	T	What do you mean by quadratic? Explain to us.	Press
15	L3	Because of 2. I see 2 is placed on top of the first $x$.
16	T	On top of the first $x?$ Can you explain to us what you mean by on top?	Press
17	L3	Ummm, 2 is powering the first $x.$
18	T	Powering? What do you mean by this, L3?	Press
19	L4	x multiplied to $x$ double.
20	T	Double? Explain further.	Confirm
21	L4	Oh yes. I mean $x$ is multiplied by itself two times.
22	T	Is L4 correct, class?	Elicit
23	Ls	Yes. Twice (chorus).
24	T	Class, what other name is given to this powering number that L3 is talking about?	Elicit
25	Ls	Index, indices (chorus).

Table 5. Teacher B’s follow-up moves

Teacher moves	Lesson 1	Lesson 2	Lesson 3	Total
Insert	3	2	3	8
Elicit	5	5	4	14
Press	1	2	2	5
Maintain	1	1	1	3
Confirm	4	0	1	5
Total	14	10	11	35

Table

4	L1	360 degrees
5	T	Okay. What is the relationship between the sum of angles in a quadrilateral and the sum of angles in any triangle?	Elicit
6	Ls:	(Silence from learners)
7	T:	Oh, okay, guys. Let’s go back to triangles. What is the sum of the interior angles of a triangle?	Elicit
8	Ls	180 degrees (chorus).
9	T	We can divide a quadrilateral into two triangles. (Teacher draws a quadrilateral on the board and inserts one diagonal of the quad [from field notes].)	Insert
10	T	How many triangles do we have from this quad?	Elicit
11	Ls	Two (chorus).
12	T	Each triangle has how many degrees?	Elicit
13	L2	180
14	T	With all this in mind, guys, what then is the relationship between the sum of the angles in a quad and the sum of angles in a triangle?	Press
15	L3	I think the degrees in the quad are two times the degrees in the triangle
16	T	Is there anyone else who can say it differently?	Press
17	L4	The sum of angles in a triangle is half of the angles in a quad.
18	T	Yes. Triangle has 180 degrees so the quad has 180 times 2 we get 360. Do we all agree?	Confirm
19	Ls	Yes (chorus).

Table 6. Teacher C’s follow-up moves

Teacher moves	Lesson 1	Lesson 2	Lesson 3	Total
Insert	1	0	1	2
Elicit	5	5	4	14
Press	2	6	4	12
Maintain	1	1	2	4
Confirm	4	5	3	12
Total	13	17	14	44

Table

7	T	Once again, what name do we give to the $x$ value? Yes, L1.	Elicit
8	L1	It is called an independent variable.
9	T	Yes, independent variable.	Confirm
10	T	Okay. What about the $y$ value?	Elicit
11	L2	$\mathrm{Yy}$ is the dependent variable or output.
12	T	Good. It is called output.	Confirm
13	T	Considering the first given table, what is the relationship between the value of $x$ compared with the value of $y$? (Pointing to the table on the board.)	Elicit
14	Ls	(Learners busy working out [from field notes].)
15	T	Does anyone have a solution? Tell us what you think.	Press
16	L3	Yes. I got $y=2x$.
17	T	How did you arrive at that solution? Can you explain to us your idea, L3?	Press
18	L3	Eeeeh, $x$ value has been multiplied by 2 to get $y$ value, for example
$0\times 2=0,1\times 2=2,2\times 2=4$ and so on.
19	T	That’s a good observation. It is correct when you say $0\times 2=0,1\times 2=2?$	Confirm
20	T	Is there a different method or way of getting the relationship? Show by raising your hand. L4, I see your hand was up first. Let’s hear what L4 has for us.	Press
21	L4	The common difference of the $y$ values is 2 so the value of $y$ is obtained by multiplying $x$ by the common difference to get $2x$. This gives us $y=2x$, the relationship between the independent variable $x$ and the dependent variable, $y.$
22	T	Well explained, L4.	Confirm
23	T	Where else have we used this idea of common difference which L4 has just explained to us?	Elicit
24	Ls	Number patterns (chorus).
25	T	Yes, we have applied this concept in number patterns. I hope we have all obtained the same relationship from the values in the given table.	Maintain

Figure 1. Compound bar graph for teacher moves

Brodie, K. (2010). Working with learners’ mathematical thinking: Towards a language of description for changing pedagogy. Teaching and Teacher Education, 27(1), 174–186.

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