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# What Makes A Good Resource - Using Tarsia

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 08 September 2009 by ncetm_administrator
Updated on 03 September 2010 by ncetm_administrator

# Using Tarsia

Resource description:
Tarsia is a software program that enables relatively simple ‘jigsaws’ to be produced. There is one question for each internal edge in the puzzle (the other side of the edge is an answer). Outer edges are blank. Tarsia puzzles come in many shapes including squares and rectangles (made up of square pieces) and rhombuses, parallelograms and regular hexagons (made up of triangular pieces).

I produced a triangular Tarsia puzzle for my class on the topic of number sequences. The questions consisted of number sequences with two missing terms in. The answers were the two missing terms. Missing terms were not necessarily the final terms in the sequence. In some cases the missing terms were not consecutive. Most, but not all of the number sequences were linear.

Teacher comment:
Whenever a new teaching device comes along, I feel it is important to ask myself whether it brings anything new to the learning experience of the students or if it enables a clearer understanding of the topic that is being covered. Although Tarsia may not necessarily deepen a student’s understanding it does empower them to make decisions and it certainly encourages discussion provided the students work in pairs or groups.

It seems to me that one of the most useful features of Tarsia (over providing the same set of questions on a worksheet) is that students will automatically start to filter the relative difficulty of the questions as part of the process. Faced with the entire set of puzzle pieces, it quickly becomes apparent to students that in order to make good progress, they need to find the easier questions in order to get started. More traditional resources rarely provide this opportunity as they tend to be sequenced in questions of increasing difficulty. Because a Tarsia puzzle requires a selective approach by the students it is also advantageous that they have a meaningful, focussed and ongoing conversation. A definite end product encourages competition and often produces an air of excitement.

What I did:
I gave out the puzzle to the students with no input at all and was specific in not providing any initial assistance. Although some students were disconcerted at first, they soon settled to the task and quickly solved the puzzle.

However, I felt that once the puzzle had been completed, it may have been a wasted opportunity to put it away and go back to a more traditional mode of working – why not use the sequences on the puzzle to hang the development of the topic from?

I went on to introduce to the class the idea of an nth term and got them to generate the first 5 terms of a sequence and the 50th term of the sequence from the nth term. I then gave them a couple of sequences without the nth term and asked them to determine the nth terms using the information they had already produced.

Once students were happy to find the nth terms, I then asked them to find the nth terms for as many of the sequences in the puzzle as they could. I wanted them to realise that the approach they were using was only directly applicable when dealing with linear sequences. I refrained from telling the students that they could not find the nth terms for all the sequences and although some found the fact that some of the sequences could not be generalised in the manner they had just learned, I felt it was important that they realise for themselves that most mathematical processes are restricted by the context in which they are being used.

Reflection:
Whilst I was very happy with the way in which the Tarsia puzzle worked during the initial stage of the lesson, I probably would have felt dissatisfied with the exercise if I had then left it to move on to a relatively disconnected piece of work on number sequences (which was my original intention). I like it when a resource forms the basis of a more 'complete’ piece of work and it is surprising how often a rich resource like Tarsia offers the opportunity to do this provided there is sufficient thinking time invested on the part of the teacher. I felt that the students were happy to use the puzzle once they had built it (rather than dismantle it and move on to something else) and because of a conversation I had had with a student in the class, Tarsia subsequently went on to form the basis of much more substantial piece of investigative work for the class (see Tarsia Investigation).

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