Impact of a national professional development programme for out-of-field teachers of mathematics in Ireland

Figures & data

Figure 1. Teaching qualifications of respondents to Surveys 1 and 1R.

Table 1. Distribution of Fully Qualified and Out-of-Field Teachers of Mathematics by Year Level Taught, Survey 1 (2009).

Mathematics teaching qualification?	Year Level Taught
	First Year	Second Year	Third Year	Fourth Year	Fifth Year	Sixth Year
Yes (n = 168)	85 (51%)	100 (60%)	134 (80%)	95 (57%)	133 (79%)	131 (78%)
No (n=156)	81 (52%)	94 (60%)	79 (51%)	18 (12%)	45 (29%)	38 (24%)

Table 2. Distribution of Fully Qualified and Out-of-Field Teachers of Mathematics by Year Level Taught, Survey 1R (2018).

Mathematics teaching qualification?	Year Level Taught
	First Year	Second Year	Third Year	Fourth Year	Fifth Year	Sixth Year
Yes (n = 85)	48 (57%)	47 (55%)	57 (67%)	36 (42%)	50 (59%)	55 (65%)
No (n=29)	20 (69%)	19 (66%)	16 (55%)	5 (17%)	18 (62%)	16 (55%)

Table 3. Distribution of Fully Qualified and Out-of-Field Teachers of Mathematics by Year Level Taught, Higher Level Mathematics, Survey 1 (2009).

Mathematics teaching qualification?	Year Level Taught (Higher Level Mathematics)
	Second Year	Third Year	Fifth Year	Sixth Year
Yes (n = 168)	52 (31%)	71 (42%)	75 (45%)	68 (40%)
No (n=156)	7 (4.5%)	4 (3%)	0 (0%)	2 (1%)

Table 4. Distribution of Fully Qualified and Out-of-Field Teachers of Mathematics by Year Level Taught, Higher Level Mathematics, Survey 1R (2018).

Mathematics teaching qualification?	Year Level Taught (Higher Level Mathematics)
	Second Year	Third Year	Fifth Year	Sixth Year
Yes (n = 85)	25 (29%)	36 (42%)	27 (32%)	25 (29%)
No (n=29)	9 (31%)	8 (28%)	6 (21%)	5 (17%)

Table 5. Percentage Distribution of PDMT Graduates’ Responses to Belief Statements.

Belief Statement	SD	D	SWD	SWA	A	SA
Mathematics
1. Mathematics is computation (T)	4	14	15	45	20	2
2. Mathematics problems given to students should be quickly solvable in a few steps (T)	10	29	29	21	9	2
3. Mathematics is the dynamic searching for order and pattern in the learner’s environment (C)	2	5	8	48	30	7
4. Mathematics is no more sequential a subject than any other (C)	11	31	27	19	11	1
5. Mathematics is a beautiful, creative and useful human endeavour that is both a way of knowing and a way of thinking (C)	0	2	2	26	49	21
6. Right answers are much more important in mathematics than the ways in which you get them (T)	50	35	10	3	2	0
Mathematics Learning
7. Mathematics knowledge is the result of the learner interpreting and organising the information gained from experiences (C)	1	1	2	31	53	12
8. Students are rational decision makers capable of determining for themselves what is right and wrong (C)	1	11	22	38	24	4
9. Mathematics learning is being able to get the right answers quickly (T)	30	39	22	6	3	0
10. Periods of uncertainty, conflict, confusion, surprise are a significant part of the mathematics learning process (C)	1	2	6	28	47	16
11. Young students are capable of much higher levels of mathematical thought than has been suggested traditionally (C)	6	12	17	36	26	3
12. Being able to memorise facts is critical in mathematics learning (T)	4	19	20	35	18	4
13. Mathematics learning is enhanced by activities which build upon and respect students’ experiences (C)	0	1	3	21	55	20
14. Mathematics learning is enhanced by challenge within a supportive environment (C)	2	2	2	20	50	24
Mathematics Teaching
15. Teachers should provide instructional activities which result in problematic situations for learners (C)	1	3	6	29	47	14
16. Teachers or the textbook – not the student – are the authorities for what is right or wrong (T)	20	37	18	19	5	1
17. The role of the mathematics teacher is to transmit mathematical knowledge and to verify that learners have received this knowledge (T)	1	6	10	33	40	10
18. Teachers should recognise that what seem like errors and confusions from an adult point of view are students’ expressions of their current understanding (C)	2	2	7	33	44	12
19. Teachers should negotiate social norms with the students in order to develop a cooperative learning environment in which students can construct their knowledge (C)	1	4	7	32	47	9
20. It is unnecessary, even damaging, for teachers to tell students if their answers are correct or incorrect (C)	32	36	15	11	5	1

Table 6 Percentage Distribution of PDMT Graduates Who Engage in Various Classroom Practices.

Classroom Practice	Every/ almost every lesson	About half of lessons	Some lessons	Never
Relate the lesson to students’ daily lives	40	27	32	2
Ask students to explain their answers	58	25	16	<1
Ask students to complete challenging exercises that require them to go beyond the instruction	20	33	40	7
Encourage classroom discussion among students	36	32	30	3
Link new content to students’ prior knowledge	80	13	7	0
Ask students to decide their own problem solving procedures	23	29	45	3
Encourage students to express their ideas in class	59	23	17	2

Table 7. Percentage Distribution of PDMT Graduates’ Descriptions of Mathematics Teaching Approaches Before and After Completing Pedagogy Workshops.

Teaching Approach	Before PDMT	After PDMT
Transmission	56	5
Child-centred	23	51
Mixed	9	11
No change	9	26
Other	3	7