Numeracy teaching tips
Tip: Data analysis
By now schools should have downloaded their school and class reports from the QSA website. These reports contain information that can be used to analyse student performance on test questions. Queensland is the only state in Australia that provides teachers with both correct and incorrect responses students gave to multiple-choice and open-ended questions. We do this via the class reports.
While the correct responses on NAPLAN provide teachers with useful data, analysis of incorrect answers may highlight problem areas that teachers will find interesting to review. Such an analysis can sort the minor mistakes from the incorrect conceptual understandings. Access to student responses also provides a way of looking for
patterns of incorrect thinking and reasoning across groups of students.
SunLANDA is a test data analysis tool created for teachers by the QSA. Instructions for downloading the program and data can be found on the QSA website. Once schools upload their data from the CSV files supplied by the QSA, information about students and classes can be organised and viewed in various ways. For example, teachers will be able to easily see patterns in the incorrect responses, and to sort students based on similar needs. SunLANDA has links to an analysis of each test question, which includes a detailed description of the question, explanations of the answers given by students and teaching ideas to support the development of the
knowledge, skills and understandings required to answer the test question.
Tip: Error analysis
Many students find the problem-solving questions in the latter part of the test challenging. Teachers should provide students with opportunities to solve a variety of problems and discuss multiple ways of finding solutions. This can help them to build a bank of strategies, and fosters confidence in their ability to solve problems.
A quick and easy method for analysing the way students solve standard written problems is the Newman error analysis procedure, developed in the 1970s and used extensively around the world. It is based on the assumption that problem solvers need to be able to work through five stages: first, to read or decode the problem; second,
to comprehend what is being asked; third, to transform (or mathematise) the problem into some steps; fourth, to work through these steps; fifth, to express the answer in an acceptable form.
Through an interview approach, teachers analyse and sort errors into five categories, which allow teachers to pinpoint where they may need to focus their assistance and teaching. To begin, students are asked to attempt a problem that they have previously answered incorrectly. As they work through the problem the teacher uses the following types of prompts:
1. Please read the question to me. (reading error)
2. Tell me what the question is asking you to do. (comprehension error)
3. Which method do you use to get your answer? (transformational error)
4. Show me how you get your answer and tell me what you are thinking as you do it (process skills error)
5. Please show me your answer to the question. (encoding error)
If a student answers the problem correctly in this second attempt and the teacher believes that the original error was more a case of a careless error then it can be categorised as such.
It is also important that teachers resist the temptation to assist students in the process; it is important to analyse what they actually do on their own.
Many studies have used this method to research what students are thinking and reasoning when attempting problems. It also allows for careless errors or minor mistakes to be differentiated from more structural or conceptual difficulties. The Newman error analysis procedure is one way of delving into student’s errors. For further reading see the following references.
References
White, AL 2005, “Active Mathematics in Classrooms: Finding Out Why Children Make Mistakes — And Then Doing Something to Help Them”, Square One: Journal of the Primary Association for Mathematics, vol. 15, no. 4, Dec 2005, pp. 15–19
Further reading on Newman’s error analysis procedure:
Newman, MA 1977, “An analysis of sixth-grade pupil’s errors on written mathematical tasks”, Victorian Institute for Educational Research Bulletin, vol. 39, pp. 31-43
Newman, MA 1983, Strategies for diagnosis and remediation. Sydney, Harcourt Brace Jovanovich.
By now schools should have downloaded their school and class reports from the QSA website. These reports contain information that can be used to analyse student performance on test questions. Queensland is the only state in Australia that provides teachers with both correct and incorrect responses students gave to multiple-choice and open-ended questions. We do this via the class reports.
While the correct responses on NAPLAN provide teachers with useful data, analysis of incorrect answers may highlight problem areas that teachers will find interesting to review. Such an analysis can sort the minor mistakes from the incorrect conceptual understandings. Access to student responses also provides a way of looking for
patterns of incorrect thinking and reasoning across groups of students.
SunLANDA is a test data analysis tool created for teachers by the QSA. Instructions for downloading the program and data can be found on the QSA website. Once schools upload their data from the CSV files supplied by the QSA, information about students and classes can be organised and viewed in various ways. For example, teachers will be able to easily see patterns in the incorrect responses, and to sort students based on similar needs. SunLANDA has links to an analysis of each test question, which includes a detailed description of the question, explanations of the answers given by students and teaching ideas to support the development of the
knowledge, skills and understandings required to answer the test question.
Tip: Error analysis
Many students find the problem-solving questions in the latter part of the test challenging. Teachers should provide students with opportunities to solve a variety of problems and discuss multiple ways of finding solutions. This can help them to build a bank of strategies, and fosters confidence in their ability to solve problems.
A quick and easy method for analysing the way students solve standard written problems is the Newman error analysis procedure, developed in the 1970s and used extensively around the world. It is based on the assumption that problem solvers need to be able to work through five stages: first, to read or decode the problem; second,
to comprehend what is being asked; third, to transform (or mathematise) the problem into some steps; fourth, to work through these steps; fifth, to express the answer in an acceptable form.
Through an interview approach, teachers analyse and sort errors into five categories, which allow teachers to pinpoint where they may need to focus their assistance and teaching. To begin, students are asked to attempt a problem that they have previously answered incorrectly. As they work through the problem the teacher uses the following types of prompts:
1. Please read the question to me. (reading error)
2. Tell me what the question is asking you to do. (comprehension error)
3. Which method do you use to get your answer? (transformational error)
4. Show me how you get your answer and tell me what you are thinking as you do it (process skills error)
5. Please show me your answer to the question. (encoding error)
If a student answers the problem correctly in this second attempt and the teacher believes that the original error was more a case of a careless error then it can be categorised as such.
It is also important that teachers resist the temptation to assist students in the process; it is important to analyse what they actually do on their own.
Many studies have used this method to research what students are thinking and reasoning when attempting problems. It also allows for careless errors or minor mistakes to be differentiated from more structural or conceptual difficulties. The Newman error analysis procedure is one way of delving into student’s errors. For further reading see the following references.
References
White, AL 2005, “Active Mathematics in Classrooms: Finding Out Why Children Make Mistakes — And Then Doing Something to Help Them”, Square One: Journal of the Primary Association for Mathematics, vol. 15, no. 4, Dec 2005, pp. 15–19
Further reading on Newman’s error analysis procedure:
Newman, MA 1977, “An analysis of sixth-grade pupil’s errors on written mathematical tasks”, Victorian Institute for Educational Research Bulletin, vol. 39, pp. 31-43
Newman, MA 1983, Strategies for diagnosis and remediation. Sydney, Harcourt Brace Jovanovich.