Addition and Subtraction: A Learning Story

A while back I engaged with an assignment involving review and evaluation of a multiple tool approach to the use of IWBs in the numeracy hour. The PowerPoint learning story below, was how I chose to collect, collate and present the empirical data I used when discussing this in the assignment. This was finally submitted in two forms. one on paper, and the other as a navigable web page based structure.

The context of the story is a teacher designed, two week numeracy unit on written calculation methods. Drawing on framework plans as a structure, it began with the exploration, discussion and collation of the mental strategies students brought to the session as "available designs" from their previous encounters (Cope and Kolantzis 2000, Editors for the New London Group). All data presented here was collected initially during lessons using the Smart Notebook and whiteboard. It was not only used for research purposes in charting of the current lesson, and setting of new problems as we worked, but also provided feedback and feedforward from session to session. Following the classroom activities each day, the content of the notebooks was transferred to PowerPoint for evaluation and review.

Our intended learning outcome as a class was to learn how to use the standard written algorithms required to be taught within school, as ways of adding and subtracting two and three digit numbers. As an iterative process the students and I evaluated together the strategies we already knew and used, how they worked and shared them with each other as a community. We examined and reviewed our choices through discussion of their effectiveness in the calculation process. The students tested and compared outcomes of their using each other's methods, in paired activities on small dry wipe whiteboards. As the students worked I also photographed student outcomes and engagements for inclusion in our learning story, and for classroom display. Within the story I hope you can see how we began to unpick the methods we used, and to identify how apparently different and diverse methods could be reduced to common aproaches, such as partitioning and decomposition. In week two we began to transform these into the standard written algorithms the students are required to use. In effect the story shows how I helped the group intgrate their informal mental methods and jottings into a standard written form they could use and practice by the end of the unit of work.

This process was not only useful for the students but as an action research process was incredibly revealing for me. Until carrying out this task I don't think I had really given much thought to the complexity of the process involved in making links between the elements that are required to calculate using the standard written methods we ask of our learners. We often make assumptions, that since a progression of work has lead to this point in a child's development, that they recognise the processes for themselves. Exploring how students engage in calculation in this way has really helped inform the way I approach the planning and development of lessons, not only where ICT is used to mediate, assess and review learning. I try to begin units of work with initial explorations through discussion, of the mathematical strategies students themselves are bringing to sessions as a starting point, evaluating perceptions and where possible to use the tools students bring to the session to link my planned content with what is already known.

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