CHAPTER 5 : Conclusions

The analysis of the Year 4 sample for three independent written tasks revealed a range of strategy use. The Addition Examples were found to produce errors in renaming and in mixing the algorithms for addition and subtraction. The presentation of these examples in a vertical format was found to be problematic and may have cued children to use alternative calculation strategies. At Year 4 level, many children are still developing confidence with more that two addends or adding two or 3 digit numbers. Renaming was also a problematic aspect of the examples in the Speedo task with many children carrying the digit to the left hand place regardless. There were a significant number of no responses and incorrect answers indicating a high level of difficulty for this item due to the unfamiliar and contrived context and possibly some of the signifier terms used in the questions. The third written item was Money A that indicated difficulties with finding a fraction of a decimal, division of decimals and contextual difficulties posed by a task related to finding both discounts and a new discounted price.

The one-to-one task of 36 and 29 provided a rich source of verbal solutions. Children responded in many different ways and transcripts revealed a variety of solutions, of language, further detail about strategies, and opportunities for children to self-correct. This was an example of an assessment task where children could verbally express their thinking with the aid of an experienced other, the interviewer.

It is interesting to note that all four tasks are not included in the latest NEMP mathematics results (Flockton, Crooks, Smith and Smith, 2006). Some similar tasks appear such as subtraction and division algorithms rather than addition, place value questions are part of Number A (p. 14); and 36 and 29 is similar to the item Beans (p. 22), which is now a contextualized word problem. Money A has been transformed into an item called Super Sale (p. 39) where there are now two parts to the question, to find the savings and to find the new sale price. This new item is only for Year 8 children.

The research team also put together 'assessment profiles' for each of the eight children that they analysed. The profiles included the analysis of the four items plus the information from the survey data. Although these profiles have not been reported here, two issues arose that could lead to further investigation. Firstly, in our sample of 40, there were 4 children (10%) who consistently identified the strongly dislike category in most questions of the survey. Such strong reactions to mathematics at Year 4 concerned the researchers. In tracking through these four children's profiles, they found that the children had been assessed as incorrect or no response for most questions in each item. In the transcripts of the one-to-one tasks, 36 and 29, the children were found to use a counting strategy, counting on from larger (first addend), using fingers or equipment. Within the NEMP population, the data from the Year 4 children who identified a strong dislike of mathematics would be worthy of further investigation.

Secondly, the researchers returned to the children who were assessed as 'incorrect' or 'no response' for many of the questions in the task items, and included the four children identified above. These children (around 20%) appeared to have little success with questions in the written Items and would be an interesting group to study further. A more in-depth examination of the one-to-one tasks would provide information about their strategies and reasoning for a greater range of task items. Given current concern about the children who are underachieving in mathematics, a focus on the group of the least successful children at year 4 level could provide further detail about their mathematical activity.

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