This theme surrounds the change in perceptions of learning mathematics that the pupils associated with their use of Grid Algebra in mathematics lessons. Some pupils considered their non-ICT mathematics lessons in regular classrooms to be ‘boring’; many described being quite disengaged with learning, a common report by their teachers.
P205: It offers better understanding of concepts in algebra from the normal class lessons as one can actually see how the sums come about. They offer mathematical gain from the usual boring class lessons.
G019: It encourages me that maths is enjoyable and can be worked even on computers, and also makes me attentive in class since I can’t doze off yet there is some fun programme in front of me.
As Figure 4.3 indicates, several pupils noted changes in themselves. Some positive emotions (curiosity, enthusiasm, and interest shown in activity) are considered an indication of pupils’ high self-efficacy and engagement with their learning. The ICT-enhanced activity seemed to engender raised levels of engagement and concentration in learning.
Figure 4.3: Distribution of some affective aspects in pupils’ views of ICT-enhanced learning I explained the need for every group to select software-generated tasks at lower difficulty levels and gradually work their way to higher levels. The majority of pupils complied with this advice to build self-confidence; they worked, tentatively at first in animated discussions, then with increasing concentration as they received, reflected on and responded to feedback.
K115: It is more fun and easier to understand. It has improved my concentration level a great deal.
G054: I get to be alert every time a question is runned (sic) on the computer.
One teacher described many pupils’ evident positive disposition to learning.
T4: I have never seen these pupils so absorbed in the work they are doing like they were today! The fact that the Grid Algebra was marking as the pupils worked and even giving them
words of encouragement such as ‘Excellent!’ was really giving the pupils the impetus to do more and more work! That was great! It has ensured good classroom management. I have especially liked the way the software encouraged, motivated them to try more work.
Other pupils (11%; 31) stated fresh perspectives in their approach to mathematics attributed to the weekly ICT-enhanced sessions.
P187: With Grid Algebra, I understand algebra a bit more than before. It is also fun to work with a computer while doing maths. Most of the time I do not ‘anticipate’ to learn maths. With Grid Algebra, I usually ‘anticipate’; it made me understand maths especially algebra.
K122: It helped me to like algebra because I never used to like it. But now I do like it and understand it. It made mathematics very fun and a lesson to look forward to every time.
A marked change in pupils’ attitude to learning was attributed to the new learning resource.
K129: In the past, I never used to get algebra so I had a negative attitude towards it but it changed when I started doing Grid Algebra and I understood algebra more.
R251: It makes mathematics fun thus helps to develop a positive attitude towards mathematics.
U070: This is because working with the computer changed my attitude in maths and made me see maths as easy and enjoyable.
R242: It makes algebraic equations seem easier and makes one develop a positive attitude towards it. Using Grid Algebra is much more fun and exciting, helps one learn computer as well as mathematics, and it is much faster.
Some pupils reported shifting relations to mathematics as a subject and algebra as a topic due to intrinsic values. The pupils signalled changes in their identity as ‘mathematicians’.
P194: It’s because it makes you feel assured of yourself and believe you can do algebra questions given confidently.
U059: This shows us that mathematics is not only about books and mathematics is something you can enjoy doing.
P198: It creates an attitude toward math and especially algebra since it is seen as a difficult topic. It opens up minds to show that there is always a way out of what seems to be difficult
questions. Algebra could not have been well understood without using grid algebra. We know and understand, while in normal learning we try even if knowing is impossible.
P178: Learning has really become interesting. The lessons give one encouragement to learn more and more about maths.
The pupils showed increased confidence and competence in their ability as mathematical learners. The introduction of Grid Algebra was reported by the regular teachers to have raised pupil interest in their learning in other non-ICT mathematics lessons.
T1: Very good participation in class now because, everybody is striving to answer the teacher! You find them enjoying, and the interest is high now.
T3: NowI go to class with pieces of chalk, and they work on the board!Substitution, they are doing it very well! And when you have Integers like -2, the bracket comes in automatically.
These teachers’ remarks showed awareness of pupils applying what they learned in ICT- enhanced sessions. Some pupils claimed that software use may have resulted in increased progress.
G015: It was beneficial to me because it helped me improve in algebra by making mathematics (algebra in specific) more interesting.
R267: Using Grid Algebra changed learning in maths lessons because it is more interesting. It has helped me improve in mathematics and I did enjoy it.
P209: It became more interesting learning while using the computer so it gives me (psyche) to continue.
The pupils’ increased motivation to learn algebra was associated with the overall contribution of ICT-enhanced activity. As shown in Figure 4.3, this led to the raised levels of interest, self- concept, and changed attitudes to learning. It appeared to have influenced the pupils’ progress in mathematics, such that it warrants discussion.Measurement of the impact of Grid
Algebra’s use on overall pupil attainment in mathematics was beyond the scope of my study. Nevertheless, both teachers and pupils drew my attention to pupils’ progress in three
examinations taken in the course of the school term. These examinations were set at a departmental level and marked by the respective subject teachers. Pupil performance is as
shown in Figure 4.4; it includes results for the last examination taken prior to this research. The percentage mean scores per class in a given examination are indicated.
Figure 4.4:Pupil performance in mathematics examinations (Percentage means per class)
Questions on algebra featured in the end-of-term 2 examinations that were underway as I left the field (see Appendix 14). ‘Surprising’ feedback revealed pupils’ handling of questions. Stage Three pupils demonstrated a firmer grasp of algebraic concepts compared with previous years. The mathematics teachers attributed this change to pupils’ engagement with
Grid Algebra. Their reports amplified a comparison of two cohorts taught by the same teacher.
T3: When I check their (entry) marks, unless something ‘fluky’, they are able; they are able! I cannot compare them to Form Three class (who would) brainstorm you, but these ones…
This teacher observed that, although the Form 1 2010 pupils were considerably a more ‘able’ cohort (based on their end-of-primary education scores) compared to Form 1 2012 cohort, the latter handled ‘difficult’ algebraic concepts better. The mathematics attainment for these two cohorts is as shown in Figure 4.5.
Figure 4.5: Performance of Form 1 2010 and Form 1 2012 (mathematics-with-ICT) in examinations These results indicate that the 2012 cohort registered a higher improvement in mathematics than the 2010 cohort without the ICT-enhanced collaborative learning over the same academic period. Their teacher remarked on the notable differences in conceptual understanding.
T3: When we tell them and ask them, ‘What is that?’ They say, ‘It is the same!’ They can see as… (Speech is barely audible), and that way, they are able to factorise, because it is in both terms. They know terms which I have to teach the Form Three now since it seems they have not gotten the concept. Sometimes when you write , they write , which means the concept of a term is not there! I am very grateful because the (Form 1s) have gotten it.
Teacher T3 attributed the difference, discussed in Section 2.2.4, to the class’ interaction with
Grid Algebra defining the pupils’ learning.
T3: You have removed us from a stupor! What came out was, so mathematics can also be this interesting!
In summary, the comparison data in Figure 4.5 helped me to make sense of the participants’ appreciation of the intervention. The results in Figures 4.4 and 4.5 seemed to corroborate all participants’ attributing increased pupil attainment in mathematics to the changes introduced in the learning context. Albeit pleasing, the impact of learning gains revealed in the
mathematics examinations was incidental to my overall research aim: transformative learning processes.