Implementing Stage Three: Main Study-Kenya

This stage marked actualising increased pupil interaction, involvement and engagement when learning mathematics, following reports by Brown et al (2008) and Nardi and Steward

(2003). According to Australian DEAG (2013), quality learning environments can improve learning outcomes based on three principles:

 There is a direct relationship between how pupils learn and what they learn;

 Making it possible for every pupil to learn by developing personalised learning;

These principles added to calls for shifting responsibility for learning to pupils discussed by several researchers for example Lee and Johnston-Wilder (2013), Gresalfi et al (2009) and Boaler and Greeno (2000). I envisioned harnessing classroom ‘subculture’ to mediate Grid Algebra use and distribute responsibility and accountability in learning. The timing of Stage Three coincided with the term during which Form 1 pupils learn ‘Algebraic Expressions’ according to the secondary mathematics curriculum (see Section 1.2.3); every class has six 40 minute time-tabled mathematics lessons per week. It was agreed in a meeting with the

Principal and HOD-Mathematics, following Stage Two findings, to allocate one lesson per week per participating class, hence 40 lessons, to ICT-enhanced algebra learning. One largely underused computer laboratory with 25 pristine computers was dedicated to this project. On the premise of ethical arguments in Section 3.1.2, the entire cohort of 270 had access to Grid Algebra software. I group-administered the MRBQ to 270 pupils whose responses I discuss in Chapter 4 in light of pupils’ strategies in the ‘Baseline’ (see Appendix 10). I perceived data in Table 4.2 crucial in informing about pupil cognition as ‘met-befores’ (Tall, 2004) instead of relying on teacher assessment of pupil learning. It revealed difficulties pupils had with writing mathematics.

Each class had a total of 8 ICT-enhanced mathematics lessons. Pupils invested greater lesson time learning collaboratively on 8 of the 26 software-generated tasks discussed in Section 1.5.3. However, this study highlighted the plight of pupils who lacked basic computing skills. The pupil questionnaire collected quantitative data shown in Table 3.2. The SPSS output displays descriptive information on the pupils’ primary schooling and computing

background.

Class of respondent Total

1 3 4 5 2

Did you have any computer lessons before you were admitted to this school?

Yes 32 35 40 37 38 182

No 22 18 14 17 17 88

Total 54 53 54 54 55 270

Table 3.2: Distribution of the pupils’ prior computing experience per class

Approximately 67% of Stage Three pupils had prior experience with computers upon joining secondary school as shown in Table 3.2. Between 30 and 40% of pupils in a particular class had to acquire extra computing skills whilst grappling with learning algebra. Their initial low

computer confidence caused by a lack of ‘click-and-drag’ skills threatened the pupils’ active or full participation in ICT-enhanced learning. They faced being excluded from experiencing positive feelings engendered by computer-based activities that have been found to influence pupil engagement in mathematical learning. By offering ‘extra’ sessions (see Section 3.1.5.4), I supported in full the plan to provide 270 pupils with access to uniform learning experiences. Pupils subsequently encountered related written tasks based on Grid Algebra and textbooks. Two Bank (Public) holidays, Sports’ Day, Speech/Prize-giving Day, five-day half-term, and an impromptu school inspection disrupted some sessions. I arranged make-up sessions with affected pupils outside time-tabled hours in these instances. I agreed to lead ICT-enhanced sessions for the first few weeks. I introduced Grid Algebra to the participants whilst teachers observed. This plan was intended to build teacher confidence to take over and allow me to resume participant observer role. My assuming the lead in ICT-enhanced sessions provided ‘lead-in’ time and the support (Crisan et al, 2007) the participants required to use ICT in practical ways.

The weekly sessions adopted a similar pattern to the one I describe shortly. Following Pimm (1987), in the first session with each class, I explained my expectations of the why, how,

when, where then what of the ‘ground rules’ to facilitate productive working in ICT-enhanced activity. Each subsequent session usually began with brief whole-class revision of written work focusing on areas of difficulty followed by introducing new tasks, after which pupils worked collaboratively on a software-generated task in much of lesson time such that:

1. Groups of at most three pupils formed per computer;

2. Pupils took turns to speak and listen respectfully to each other; 3. The contributor operated software whilst explaining their reasoning; 4. Other pupils offered justification for alternative views.

When a class entered the computer laboratory, Grid Algebra was already lit up on the screens of working desktops on tables for pupils’ use. The software beamed from my laptop onto the whiteboard ready for use in whole-class demonstration. Pupils complied with instructions by gathering in groups of at most three around desktops. Two pupils stood on either side of one seated peer in order for each to have clear vantage point of the screen and whiteboard in front of them. Each had their marked ‘Baseline’ script for reference. With pupils’ eyes fixed on the projected grid, they became quiet and waited for the why that shaped the learning experience.

Having studied strategies pupils readily used in the ‘Baseline’ (see Table 4.2), I initiated ICT- enhanced sessions by introducing the main software features (see Section 1.5.1). A whole- class discussion ensued. By using question-and-answer technique to revise ‘Baseline’

questions 5, 8 and 9, I aimed to consolidate pupils’ understanding of Grid Algebra. I intended the pupils to see formal notation for themselves: that addition and subtraction signs were preserved whereas multiplication and division signs ‘disappeared’, and replaced by brackets and line notation respectively. This activity served to link the why to when and where.

To consolidate the how of learning, I selected a software-generated task for projection. Pupils collectively read the accompanying instructions made as explicit as possible. I hoped to ensure every pupil understood what was expected of them. Upon selecting the lowest level of difficulty, I invited the whole class to answer the projected puzzle. Low murmurs erupted; pupils solved the question, some individually while others discussed softly. The pupils raised hands to indicate their willingness to contribute. The ‘ground rules’ governing the activity required that we all listen to one contribution at a time. A randomly selected pupil offered their response which I entered into the program. Everyone else listened to the speaker whilst considering the software feedback. When an answer was deemed to be ‘wrong’, a ‘No Entry’ sign and a bin at the right-hand corner appeared on the screen. I paused to request the

contributor to explain how they obtained their answer. The rest of the class listened, assessing the reasoning behind the solution. A whole-class discussion ensued; I invited the other pupils to point out the flaw in reasoning, and possibly correct it. In this way, why, when, where, and

how of learning fed into each other. The class worked together through a level of difficulty in order to make pupils aware of what to expect at the end of each level. The regular teacher and I watched and listened closely. Many pupils seemed to revel in this learning experience; they interacted freely and participated in debates about why solutions worked or not.

I then asked pupils to turn to their desktops, and work as expected through a selected task: the

what. The software provided immediate feedback on solutions. As instructed, the pupils took turns working through puzzles whilst operating computers: each talked through their answers. Pupils seemed more confident in their comprehension of what was expected of them as they explored, negotiated and discussed their answers. The regular teacher and I offered assistance when and where it was asked for. We at times drew whole-class attention to the salient points in summaries. Some related written tasks were then administered and done individually.

I held retrospective discussions with regular teachers, and later with some pupils, as detailed in Section 3.1.5.4. Through the discussions, I learned that pupils apparently transported ‘new’ learning behaviour into non-ICT mathematics lessons. Surprisingly high levels of pupil interest, involvement and engagement were reported by participants in interviews and questionnaires.