Finding out why students make mistakes
The Australian educator Anne Newman (1977) suggested five significant prompts to help determine where errors may occur in students attempts to solve written problems. She asked students the following questions as they attempted problems.
1. Please read the question to me. If you don't know a word, leave it out.
2. Tell me what the question is asking you to do.
3. Tell me how you are going to find the answer.
4. Show me what to do to get the answer. "Talk aloud" as you do it, so that I can understand how you are thinking.
5. Now, write down your answer to the question.
These five questions can be used to determine why students make mistakes with written mathematics questions.
A student wishing to solve a written mathematics problem typically has to work through five basic steps:
1.Reading the problem
2. Comprehending what is read
3. Carrying out a transformation from the words of the problem to the selection of an appropriate mathematical strategy
4. Applying the process skills demanded by the selected strategy
5. Encoding the answer in an acceptable written form
The five questions the teacher asks clearly link to the five processes involved in solving a written mathematics problem.
If when reworking a question using the Newman analysis the student is able to correctly answer the question, the original error is classified as a careless error.
Research using Newman's error analysis has shown that over 50% of errors occur before students get to use their process skills. Yet many attempts at remediation in mathematics have in the past over-emphasised the revision of standard algorithms and basic facts.
Read more about Newman’s error analysis
If you would like to read more about Newman’s error analysis, download this article by Dr Allan White from
How can teachers assist their students
Teaching ideas for addressing the first three hurdles: