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. |