Quantitative Methods

Since receiving very detailed and verbose feedback from the team at Press Start, I have been beavering away and ‘learning’ – well, copying examples from webpages, books, software, etc – about statistics particular to student testing. I’ve been covering mean values, produced bar charts in Excel with box plots and error bars, I’ve been using independent and dependent paired-t tests. Time to append to my ongoing ‘Professional Update’ activities.

I am far from being an expert, but I at least have the materials and exemplars with which to work if I have the need to do so again.

I have also discovered an interesting programming language – R – suited to data analysis, or more wondrously titled ;data mining’. I plan to put it through its paces with my current S2 class which has just begun its Mars mission.  I am becoming more interested in the use of the pronouns, ‘I’ and ‘We’ in association with collaborative learning with or without the use of a digital game. I will, as always, use Cultural Historical Activity Theory (CHAT) as the analytic lens.

More to follow.



Triangulation.  A term I have encountered as part of my Educational Research Methods module at UWS, and relating to cross-examination of data assisted by a ‘critical friend’; a cross-examination by two or more individuals of data collected/collated by one or both parties.

Formative Assessment.  Peer assessment often involves two pupils marking each others work, providing each other with a positive comment and identifying at least one area for requires improvement.  This is mediated by the classroom teacher as each  learner demonstrates her/his understanding through the exemplification of skills and knowledge in teaching others.  But – and to my knowledge – this invariably involves pairs.

Is there a case for moving from pairs to triads?

Typically, this third role is undertaken by the classroom teacher.  But pupil ability is often spread – low, mid and upper – exhibiting what is suggested as Multiple Zones of Proxmial Development (Brown and Campione, 1994).

Each piece of work can generate discussion between three individuals, whereupon one individual is able to receive written feedback, feedback that has resulted in a discussion between two of his/her peers (and may include their own submissions).  This produces a ‘discourse’ about both strengths and the weaknesses of a piece of work, and the individual whose work is the point of focus has the opportunity to engage.

So: a lower-ability (Pupil A) can work on improvements with someone whose ability does not far exceed their competency (Pupil B), but whereupon (B) can work with a more advanced pupil (Pupil C) in assessing their own personal learning, but to use a mediation of the evaluation of ‘Pupil A’.

An able pupil (Pupil C) has the opportunity to assist two different pupils’ work, but also assumes a ‘mediation’ role in the ‘activity system’ that is created when he/she engages with ‘Pupil B’.  The triad approach provides the ‘mediation’ activity traditionally assumed by the classroom teacher.

The second presentation of (last year was a ‘test run’) a CfE ‘U-boat’ interdisciplinary task is underway, and already I have exceptional classroom engagement, and near-100% response for a piece of imaginative writing deliberately set between a non-contact day in order to allow pupils to undertake their own research on the actual U-96 crew member they had ‘drawn’.  (All of this after a single period of mediation, collaboration, a source text – and lots of freedom!)

The ‘triad’ approach to formative assessment is something I am currently employing, creating triads beyond the pupils’ physical working groups (4).  It also links with my research activities into the use of Activity Theory as a theoretical lens that allows me to analyse and evaluate classroom collaboration.


  • Pupils may already feel over-awed and have low self-esteem about their work without the additional burden of another ‘critical friend’


  • Discourse on learning is encouraged and made explicit
  • Facilitates a continuum approach to ability ranges
  • Cross-examination of a ‘third-party’ text may be undertaken more objectively
  • Multiple Zones of Proximal Development present a continuum of ability ; mediation includes highly-able pupil, but without the ‘ability gulf’ that could exist
  • More self-regulated learning, less teacher-intervention
  • Mid-ability are able to place themselves better, translating feedback from more able into personal targets, whilst  securing this understanding through the assistance of the lower-ability pupil
Much food for thought.  But with the grounding the UWS Chartered Teacher Programme has given me, I feel well-equipped and confident in the theory and practice, and the necessary teaching and research tools to begin an investigation…and to expect the unexpected!


Brown, A. L., & Campione, J. C. (1994). Guided Discovery in a Community of Learners.  In K. McGilly, Ed. Classroom Lessons: Integrating Cognitive Theory and Classroom Practice.  Cambridge, Mass.: MIT Press, pp. 229-270.