Academic journal article Australian Primary Mathematics Classroom

Early Mathematics Intervention-A Case Study: Helen Baldock and John Gough Describe Their Experiences in Trying to Help Embee, an 'At Risk' Child from Year 2

Academic journal article Australian Primary Mathematics Classroom

Early Mathematics Intervention-A Case Study: Helen Baldock and John Gough Describe Their Experiences in Trying to Help Embee, an 'At Risk' Child from Year 2

Article excerpt

At the start of the 2000 teaching year, Helen planned to carry out early intervention work with a small group of five children who had not performed as well as she had expected, according to the start of the year mathematics school-based assessments. The majority of Helen's class is Grade 2 with four children in Grade 1 who work at an 'average Grade 2' level. The majority of children are working at Mathematics CSF II Level 2, beginning and consolidating, with a minority of children working at CSF Level 3, beginning.

The students Helen planned to work with were judged to be at a low consolidating Level 2, according to the school-based assessment tasks on which they scored less than 65% overall on all strands. Considering the complexities of numeration and place-value involved at this initial stage of mathematics learning, Helen decided to work more closely with one child in particular rather than with the small group.

This child is repeating Grade 2. Helen was concerned and surprised about the misunderstandings she continued to have with important mathematics concepts. Embee (a pseudonym) was also considered to be 'at risk' in literacy at the end of last year, 1999, her first attempt at Grade 2. With her low level of achievement so far in mathematics and literacy, another consolidating year in Grade 2 had been recommended.

Helen's first step was to conduct a diagnostic interview with Embee using the items she had answered incorrectly on the school-based mathematics achievement test. The types of questions Embee had answered incorrectly were simple addition and subtraction. For example:

2 + 6 = 7, and -- and -- makes --

where a picture was provided of 6 white balloons and 3 black balloons so 6 and 3 makes 9.

In this latter case, Embee wrote 6 and 6 makes 9.

In particular, Helen was looking for examples in Embee's work that would relate mathematics, language and comprehension. Classification of Embee's mathematics task performance strategies, such as her 'comprehension' of the task and her 'ability to apply appropriate process skills' to solve the question would help identify appropriate remedial intervention.

However, the second attempt at the test showed that Embee was able to answer most items correctly. This led Helen to think that in a 'test' situation where the whole class is working on the test, Embee might have an attitudinal problem where she rushes to finish to be seen as one of the first to finish. By contrast, working with Helen avoided that type of pressure, and consequently the answers were correct. Another possibility for her correct results is that as a class the students have done many activities designed to improve learning outcomes about mental calculation strategies with numbers up to 20. This reviewing may have been eventually helping Embee catch up some of these early skills, by the time that she was being re-tested.

Helen concluded that the answers that were incorrect were 'careless errors' because after asking Embee to show her how she got those answers she worked on and corrected them.

Newman (1983) suggested that when a student makes an 'error', or 'miscue', in the first attempt at a task, but succeeds in getting a correct answer on a second or later attempt, and when there is no evidence from either attempt or fresh information that might explain why the initial error occurred, this is called a 'careless error'. Newman's research showed that around 30% of all errors were actually due to carelessness, failing to re-occur on subsequent attempts at the same task. While this is a high rate of 'inexplicability', teachers must always try to find explanations, as only these can lead to effective remedial intervention.

Prior to the diagnostic interview with Embee, it appeared that her initial errors were serious as they seemed to regularly surface in her work. However, given a second chance, she was able to perform accurately:

   If we look at the written responses from pupils
   we learn what they did. … 
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