Newman’s Error AnalysisNewman’s Error Analysis

The Australian educator Anne Newman (1977) suggested five significant prompts to help

determine where errors may occur in student’s attempts to solve written problems.

From reading to processing: Using Newman’s 5 promptsFrom reading to processing: Using Newman’s 5 prompts

Western Sydney Region 2013

Making mistakesStudents 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.

The hurdlesThe hurdles

Newman identified that students may havedifficulty 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, • encoding the result of a procedure to answer the question.

READING

COMPREHENSION

TRANSFORMATION

PROCESS SKILLS

ENCODING

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.

Food for thought…

1. Reading• Can students read the words of the problem?

‘Read the question twice. Circle important information. If you don’t know a word leave it out or substitute another word.’

Newman’s Prompts Overview

2. Comprehension• Can students understand the meaning of what is read?

‘Tell me what the question is asking you to find out.’

3. Transformation• Can students determine a way to solve the problem?

‘What could you do to get the answer? Predict what the answer will look like. Do you need to draw a picture to help you understand?’

4. Process Skills• Can students engage in the mathematical process?

‘Try to answer the question and explain to me what you are thinking. Check your answer with another strategy.’

5. Encoding• Can students record and interpret their answer in relation to the problem?

‘Write down your answer. Does it make sense? Have you answered what was being asked?’

Newman’s Prompt 1 - Reading

Mr Left had 8 apples. His wife was given 3 apples. How many apples did Mr Left have?

Many students responded by doing 8 – 3 = 5 or 8 + 3 = 13 Why?

Some students do not have effective problem solving strategies and guess or

focus on a key word, e.g. ‘left’

There are 26 sheep and 10 goats on a ship. How old is the captain?

76 out of 97 students did one of the following:

26 + 10 = 3626 – 10 = 1626 x 10 = 26026 ÷ 10 = 2·6

Research Bernard Tola, CLIC DEC

We need to read for meaning.

1 Please read the question to me. If you don’t know the word leave it out. ( highlight any word you do not know)

The problem• Many students cannot read the words correctly.• Students may not understand the meaning of words.Teaching strategies• Students can work with a reading partner.• A team approach to reading may help students overcome this difficulty.• Have mathematics word charts displayed in the classroom.

Newman’s Prompt 2 - Comprehension• Ensure the students

understand the vocabulary

• Familiarise students with the text features

• Teach students how to identify and use key mathematical language

• Use known literacy strategies such as:

literal (here) “reading ON the lines”

interpretive (hidden) “reading BETWEEN the lines”

inferential (head) “reading BEYOND the lines”Henry the octopus has 6 spots

on each of his legs, how many spots has Henry?

• What was the most/least popular food?• How many children bought fruit?

• How many more children chose a salad sandwich over a cheese sandwich?• How many children are represented in the graph?• If there are 100 children in the school how many did not choose a food lunch?

• What season do you think this survey was taken in? • Explain why you think this.

2. Tell me what the question is asking you to do.

• Most students can find and underline the question.

• This does not mean that they understand the question.

Comprehension - Super Six StrategiesComprehension strategies are the cognitive and metacognitive strategies readers use to accomplish the goal of comprehension.Comprehension strategies are interrelated and will rarely be used in isolation.The six key strategies are:•Making connections•Predicting•Questioning•Monitoring•Visualising•Summarising

Six metacognitive comprehension strategies

Making ConnectionsLearners make personal connections from the text with:• something in their own life (text to self)• another text (text to text)• something occurring in the world (text to world).

•What do I already know about the problem?•Have I done similar problems before?

Six metacognitive comprehension strategies

Predicting Learners use information from graphics, text and experiences to anticipate what will be read/viewed/heard and to actively adjust comprehension while reading/viewing/listening.

•What operation is the problem asking me to do?•Will my answer be bigger or smaller than the numbers in the problem? Why/ why not?•What words or visuals do I expect to see in this problem?•Were my predictions accurate? Why/ why not?

Six metacognitive comprehension strategies

QuestioningLearners pose and answer questions that clarify meaning andpromote deeper understanding of the text. Questions can begenerated by the learner, a peer or the teacher.

•What information in the problem helps me know what to do?•When you read the problem did it remind you of anything you know about or have done before?

Six metacognitive comprehension strategies

MonitoringLearners stop and think about the text and know what to do when

meaning is disrupted.•Is the problem making sense?•Do I need to re-read/view/listen to the problem?•What can help me fill in the missing information?

Six metacognitive comprehension strategies

Visualising Learners create a mental image from a text read/viewed/heard.Visualising brings the text to life, engages the imagination and usesall of the senses.

•How can I represent this problem visually?•Can I describe the visual I have made for the problem?•How did the visuals help me understand the problem?

Six metacognitive comprehension strategies

SummarisingLearners identify and accumulate the most important ideas and

restate them in their own words.•What are the main ideas and significant details in the problem?•If you were to tell another person how you solved the problem, what would you tell them?•What information will help you solve the problem?

Newman’s Prompt 3 - TransformationTo overcome this hurdle children need to:• Construct a simple visual representation of the problem eg. teach them to draw a Tape Diagram as a thinking tool

• Have the problem modelled several ways, as good comprehension of mathematical texts aids transformation

• Write own problems – builds familiarity of features of word problems• Have distractors in problems so they are forced to explore a range of

problem solving strategies• Have text altered for different operations and have students identify key

words and clues that help select operations• Explicitly discuss the visual clues within the tape diagram

3. Tell me how you are going to find the answer.

• At this point the function of understanding takes over from the function of reading.

• The link between comprehension and transformation is very strong and may require the student to go through several cycles of asking the question and trying to find ways to find the answer.

The problem• The density of mathematical language. There is a lot packed into a small number of words.Teaching strategies• Read the first sentence. What does it mean? What do you know?• Make mindmaps or charts to assist students develop the language of mathematics.

What’s the problem with word problems?

• What we want students to think about is how the numbers in a problem relate to each other.

• To achieve this we often encourage students to draw a diagram.

• Tape diagrams can be used to provide a common framework in using diagrams as thinking tools.

• A tape diagram offers students a thinking tool to visually represent a mathematical problem and transform the words into an appropriate numerical operation.

To get to work, I travelled on the train for 14 minutes, then I caught a bus which took half an hour. Finally I walked for 9 minutes. How long did it take me to get to work?

Teaching Transformation – Tape Diagrams

14 minutes Half an hour 9 minutes

53 minutes

Using tape diagrams

There were some oranges in a box.Because we bought 14 more oranges,there are 21 oranges in the box altogether.How many oranges were in the box at first?

Number of oranges at first

14 more oranges were bought

21 oranges altogether

+ 14 = 21

= 21 – 14

or

Newman’s Prompt 4 - Processing• Count Me In Too Resources• DENS Books• Counting On• Sample Units of Work• Talking about Patterns and Algebra• Red Dragonfly Maths• Fractions Pikelets and Lamingtons• Programming support website• Reciprocal Numeracy

These programs and strategies help us teach processes with a focus on mental computation and problem solving.

4. Show me what to do to get the answer. Tell me what you are doing as you work.

The problem• Students can sometimes find or guess the correct answer

without understanding the problem. They can also use an incorrect or incomplete procedure.

Teaching strategies• Ask “What do you need to know to be able to work out

the answer?”• Make lists or diagrams linking words that are associated

with a process.

Newman’s Prompt 5 - Encoding

• Does it make sense?

• Does it answer what the question is asking?

• Think of ways of recording the answer.

• Have you used the correct units?

5. Now write down the answer to the question

The problem• Students often forget the question, especially

in measurement questions and do not answer all of the question or answer using an incorrect unit.

Teaching strategies• Have students reread the question and

compare it with their answers.

The 5 questions - RECAP

1. Read the question to me.2. What is the question asking you to

find out?3. What method did (could) you use?4. Try doing it and as you are doing it tell

me what you are thinking.5. Now write down your answer.

These can be used to diagnose where the problem lies

NEWMAN’S ERROR ANALYSISSTAGE 2 ASSESSMENTS

Kate has 96 pencils. Each box of pencils holds 10 pencils.

How many full boxes of pencils can Kate make?

If pencils come in boxes of 15, how many pencils are in 20

boxes?

1 READING

2 COMPREHENSION

3 TRANSFORMATION

4 PROCESS

5 ENCODING

6 No Problems

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?

Natalie paddled 402 km of the Murray River in her canoe over 6 days. She paddled the same distance each day. How far did Natalie paddle each day?

STAGE 3 ASSESSMENTS

SNAP 2006 36 % and 14 % ATSI correct

Teaching Transformation with Newman’s Prompts – another example using a Tape Diagram

JamesJames

Newman’s in the classroomNewman’s in the classroomWhere do you think James had problems?

ReadingComprehensionTransformationProcess SkillsEncoding

Ricky-AnnRicky-Ann

Newman’s in the classroomNewman’s in the classroomWhere do you think Ricky-Ann had problems?

ReadingComprehensionTransformationProcess SkillsEncoding

Newman’s method in the classroomNewman’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.

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

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