Newman’s error analysis There is a view of learning that sees student errors as a problem that needs to be corrected. The correction often takes the form of more drill and practice. NEA is a tool that takes a positive view of student errors. The strategy of more drill and practice has been replaced by regarding errors as valuable sources of information about student thinking Our focus needs to be on analysing student responses Teachers need a tool to analyse where it is in the problem solving process that students are having difficulties Bernard Tola

Making mistakes Students can make mistakes in answering numeracy questions for different reasons. Newman’s research elaborated the different hurdles in answering a contextual word problem that can cause students to stumble. Perhaps the two hurdles currently best known by teachers are reading and comprehension. Newman’s Error Analysis is a simple tool that allows us to determine exactly what kind of other difficulties a student might be experiencing? Teachers need to be able to do this to address the students’ needs in the classroom.

The hurdles Newman identified that students may have difficulty in • reading the words, • understanding what they have read, • transforming what they have read so as to be able to form a course of action, • following through on procedures, or • encoding the result of a procedure to answer the question. As well as experiencing difficulties with reading, a student may well encounter other difficulties in dealing with a task Go through slide Newman identified two other possible categories of error: Careless errors, which can occur at any stage in the process Lack of motivation – this is an altogether different issue, that is very real and that schools may need to address

The 5 steps Read the question to me. What is the question asking you to find out? What method did (could) you use? Try doing it and as you are doing it tell me what you are thinking. Now write down your answer. In order to identify at which points in this process a student is experiencing difficulty, the teacher takes the student through five steps

The purpose Reading Comprehension Transformation Process skills Read the question to me. What is the question asking you to find out? What method could you use to get the answer? Try doing it and as you are doing it tell me what you are thinking. Now write down your answer. Reading Comprehension Transformation Process skills The aim of these is to provide teachers with the necessary information to analyse the difficulties that students are experiencing. Research carried out in Australia and Southeast Asia suggests that about 60% of students’ errors in responding to written numeracy questions occur before students reach the process skills level. In contrast, most remediation programs focus solely on the process skills. It may well be that students need assistance with process skills but this by itself will not assist a student to solve a problem if he or she is having difficulty at the Comprehension step, say. Encoding

An example One of the items on SNAP 2006 with a marked difference in performance was Q43 (State 36%, Aboriginal 14% responses correct). School may conclude that since this is a division problem, what needs to be done is to focus on the teaching of division and learning of tables. Yet this by itself may have no impact at all on children’s ability to work through this task. More practice with SNAP/BST/NAPLAN papers is not likely to solve many of the difficulties that students experience This item was chosen because of the poor performance of Aboriginal students, compared to the State average Note that the State average is not a great achievement either Observe the following student working through this task Identify where the first point of difficulty occurs

James NOTE: The movies that are part of this presentation have been removed. They can be accessed within the following two CD resources produced by Curriculum K-12 Directorate, that have been distributed to all regions: Newman’s Error Analysis 2006 Newman’s Error Analysis 2007 Most of the students who have contributed to this presentation were in Year 6 in a school in the South Western suburbs. Some of the students in this presentation are Aboriginal. All of the students made a significant effort to help us to understand the steps involved in solving some of the questions from the 2006 Secondary Numeracy Assessment.

Newman’s method in the classroom Reading Comprehension Transformation Process skills Did James have difficulty reading the task? MOSTLY OK. The question is, ‘Were the student’s reading difficulties serious enough to prevent comprehension?’ Did he have difficulty understanding it? YES Transforming it into a mathematical operation or sequence of operations? YES Was he able to carry out these operations accurately? Was he able to express the solution in an acceptable written form? Encoding Which hurdle caused this student the most problems?

Newman’s method in the classroom In using Newman’s error analysis in the classroom, it is recommended that you always go at least one step past where the first error occurs. Doing this allows you to see whether the student is able to continue with the problem unassisted.

Eugenia

Newman’s method in the classroom Reading Comprehension Transformation Process skills Did Eugenia have difficulty reading the task? NO Did she have difficulty understanding it? NO Transforming it into a mathematical operation or sequence of operations? YES Was she able to carry out these operations accurately? Was she able to express the solution in an acceptable written form? After the interview, I felt quite sure that if Eugenia had been asked to work out the algorithm 402  6, she would have been able to do this, but she was not able to identify that division was required and use it in a problem solving context. Encoding Which hurdle caused this student the most problems?

At your table

Newman’s method in the classroom Reading Comprehension Transformation Process skills Discuss and identify at your tables at which points in the procedure Ricky-Ann had difficulty Did Ricky-Ann have difficulty reading the task? NO Did she have difficulty understanding it? YES Transforming it into a mathematical operation or sequence of operations? NO Was she able to carry out these operations accurately? NO Was she able to express the solution in an acceptable written form? Encoding Where do you think this student had problems?

At your table

Newman’s method in the classroom Reading Comprehension Transformation Process skills Discuss and identify at your tables at which points in the procedure Becky had difficulty Did Becky have difficulty reading the task? NO Did she have difficulty understanding it? YES Transforming it into a mathematical operation or sequence of operations? NO but may have taken a guess Was she able to carry out these operations accurately? NO Was she able to express the solution in an acceptable written form? NO Encoding Where do you think this student had problems?

Using Newman’s in the classroom Suppose a student puts up his hand and says, “I can’t do this question!” Responding with a slight variation of Newman’s five questions can help to identify where the sticking point is. In the classroom, NEA enables teachers to quickly and accurately identify hurdles and enable students to move on. You would have noticed that NEA will be of most use in classrooms that are focused on students solving problems. If the focus in the classroom is upon working out algorithms, NEA is probably not very useful. NEA helps teachers make the connection between numeracy and literacy. Difficulties are occurring before students get to the point of carrying out operations accurately. Therefore, just improving mathematical knowledge will not necessarily improve the students’ ability to use mathematics

In the classroom Read the question quietly to yourself and let me know if you want help with any word. Can you tell me what the question is asking you to find out? What could you do to get the answer? Try doing it and as you are doing it tell me what you are thinking. Now write down your answer. When using Newman’s Error Analysis, it became evident early in the piece that another step would be of benefit: Step 1 Note Step 2: I originally was asking students, ‘Can you tell me what the question is asking you to do?’ This usually resulted in students leaping into providing me with a mathematical operation, possibly because they didn’t understand the problem or didn’t know what to do so they just took a guess Newman’s error analysis is not a Learning framework in the sense of being a progression of learning: students may, at any one time, encounter different hurdles with different problems it is not a description of conceptual understanding students do not necessarily advance through it as they progress through school. It gives us an overall understanding of where it is that a student is encountering difficulties when solving number word problems.

SNAP task The first international cricket team to tour England was an Aboriginal team. The team won 14 matches, drew 19 matches and lost 14 matches. How many matches were played? We will not be looking in detail during this workshop at following up NEA in the classroom. That is another workshop. I want to look briefly, however, at a strategy that doesn’t work well, yet is often suggested by teachers. This is a different SNAP item.

Cassy’s written response Cassy first added 14 and then subtracted it. To do this, she set out an algorithm, which led to a computation error. She does not appear to know that adding a number and then subtracting it leaves the result unchanged.

Cassy Teachers comment that they often teach their students a ‘key word’ strategy, such as altogether means addition, lost means subtraction, etc. Cassy shows us a possible result of doing this.

Newman’s method in the classroom Reading Comprehension Transformation Processing skills Did Cassy have difficulty reading the task? NO Did she have difficulty understanding it? YES Transforming it into a mathematical operation or sequence of operations? YES Was she able to carry out these operations accurately? NO Was she able to express the solution in an acceptable written form? NO Encoding Where do you think this student had problems?

SNAP 2006 A multiple choice item. The structure of the table is also not ideal for Newman’s Error Analysis We are still able to use NEA effectively Let’s watch how Julian manages this task

One to ponder Julian is working on the sit-ups problem. SNAP would show that she obtained the correct answer for this item! This is why we need to go beyond the data to analysing student thinking.

To find out more about NEA, access the two CDs that should be available in your office: 2006 (Numeracy) 2007 (also includes literacy) Quality Teaching: Mathematics in the Middle Years provides materials to introduce teachers to the use of tape diagrams to assist students to visualise word problems. These materials include: video of a lesson Lesson plan and materials PPT

Want to find out more about NEA? http://www.curriculumsupport.education.nsw.gov.au/primary/mathematics/numeracy/newman/index.htm http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/numeracy/newman/index.htm To find out more about using NEA in the classroom, requires another workshop. You can begin by looking in the Curriculum Support website, where strategies are provided to assist students who are identified using NEA as having difficulties with Reading, Comprehension or Transformation. You can also view there a student who works successfully through the five steps of NEA.