newman's problem solving steps

Little Learner Hub

Empowering Educators to Ignite Curiosity in Little Learners – Welcome to the Little Learner Hub!

Using Newman’s Prompts in Lower Primary

Young children are natural problem solvers: that is how they learn.

I was first introduced to Newman’s Error Analysis by a numeracy consultant many years ago and it has been the basis of my problem solving teaching ever since. Problem solving is an important way of learning, because it motivates children to connect previous knowledge with new situations and to develop flexibility and creativity in the process.

By consistently using Newman’s Prompts to explicitly scaffold the problem solving process , student’s quickly develop confidence and a range of problem solving strategies.

So what is Newman’s Error Analysis?

Newman’s error analysis came from research into language issues in maths in the 1970s. As a result of these studies Anne Newman identified five basic steps students typically work through to solve written word problems:

2. Comprehension

3. transformation, 4. process skills, 5. encoding, newman’s prompts.

Newman suggested  five prompts  to determine where errors may occur in students’ attempts to solve written problems.

Reading 1. Please read the question to me.

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

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

Processing Skills 4. Show me what to do to get the answer.

Encoding 5. Now, write down your answer.

Using Newman’s Prompts in Lower Primary

I introduce Newman’s Prompts to solve mathematical word problems as soon as my students are able to read basic sentences. Giving students problems with words that they can decode helps to build both their reading and math confidence.

I teach my students the steps with these Newman’s Prompts posters and then they each have a bookmark to remind them.

Here is an example of how I structure the lesson:

THE PROBLEM

I created a freebie that you can use to teach your students using Newman’s Prompts. You can grab it with the link below:

FREEBIE – Newman’s Error Analysis Problem Solving Worksheet

To save yourself a tonne of time… Buy my other Newman’s Prompt resources here:

Newman’s Error Analysis Problem Solving Booklet – Numbers to 20

Newman’s Error Analysis Posters and Bookmarks

Visit Little Learner Hub to find more great teaching resources!

SUBSCRIBE FOR UPDATES AND FREEBIES IN YOUR INBOX!

Enter your email address

Share this:

Leave a reply cancel reply, discover more from little learner hub.

Subscribe now to keep reading and get access to the full archive.

Type your email…

Continue reading

• Sales & Support
• +61 2 4225 9698
• [email protected]

Book Week – Top 10 Renaissance Book Titles

5 Reasons we Love myON

Incorporating literacy in mathematics using newman’s prompts.

By: Anita McMahon

Just like oil and vinegar, it has been believed that mathematics and literacy do not mix. The use of mathematical word problems in the classroom has long attracted a range of opinions, with some teachers believing that such word problems are designed to ‘trick’ students [1]. There is also evidence that suggests students struggle with the literacy demands of mathematical word problems [2]. But what if I told you, that if you did mix the two – you will a) get a great salad dressing, and b) greatly enhance students’ critical thinking skills.

In fact, the relationship between mathematics and literacy is bidirectional, each providing tools for the acquisition of knowledge in the other [3]. Mathematics itself, presents students with countless opportunities to develop a range of literacy skills in reading, comprehension, and interpretation. Therefore, literacy strategies such as Newman’s Prompts can be implemented to assist in the systematic and explicit teaching of Mathematics.

What are Newman’s Prompts?

Newman’s prompts were developed by an Australian language educator, Anne Newman during the mid-1970’s. They were designed as an error analysis tool to provide teachers with a framework to consider the underlying reasons why students are answering worded questions incorrectly [2].

According to Newman, there is a hierarchy of five skills that must be applied when answering worded mathematical questions [2]. Each of the following skills has an associated prompt:

• Reading (Decoding) – Read the question out loud, and if you don’t know a word, leave it out.

A reading error occurs when the student cannot read the key words or symbols in the question, preventing them from proceeding further to answer the question [4].

• Comprehension – What is the question asking you to do?

A comprehension error occurs at this stage if the student cannot understand the meaning of the words in order to solve the problem [4].

• Transformation (or Mathematising) – How are you going to find the answer?

This refers to the student’s ability to manipulate the words of a question into an appropriate mathematical equation. A transformation error occurs when a student is unable to identify the correct operations or process required to solve the problem [4].

• Process Skills – Show me what to do to get the answer. Talk aloud as you do it, so that I can understand how you are thinking.

This allows teachers to understand the students process. Errors are highlighted when the student is unable to complete the set of operations necessary to answer the questions correctly (although they were able to identify the operations needed) [4].

• Encoding – Write down your answer to the question.

The final prompt asks the student to write down the answer in an acceptable written form. Errors can still occur at this stage, and this is evident when the student is unable to express their solution in an acceptable form, despite being able to correctly solve the problem [4]. Failure at any level of the sequence will prevent students from obtaining the correct answer. It is possible for a student to make careless errors along the sequence or provide an incorrect response because of lack of motivation. This obviously isn’t indicative of the student’s true ability and such an error is categorised as “Careless” [5].

How Can Newman’s Prompts be used in the classroom?

Newman’s prompts can be implemented in the mathematics classroom as a pedagogical tool, creating a scaffold for students as they answer worded problems. As students work through the five prompts, they will develop a systemic approach to problem solving that can also be applied to several other subjects. Examples of how to implement this strategy in the classroom include:

• Visually displaying a poster outlining the 5 prompts in the classroom.
• Printing out a table with a summary of the 5 prompts which can be pasted into the student’s workbooks and used as a scaffold when necessary.
• Having students work collaboratively in groups and read the prompts out loud to one another as they work through the problem together.
• Having students highlight the literacy features as they rearrange a deconstructed problem in the correct sequence.

It is important that literacy strategies such as Newman’s prompts are incorporated in the mathematics classroom because a student’s level of literacy will influence their ability to demonstrate understanding in numeracy. Furthermore, Newman’s prompts establish a simple, structured approach to problem solving that can be applied to all areas of mathematics.

So, go ahead and mix the two – literacy and numeracy that is, to create a wonderful and enriching mathematics lesson!

References: [1] Askew, M. (2003), Word problems: Cinderellas or wicked witches? In I. Thompson (Ed.), Enhancing primary mathematics teaching (pp. 78-85). Berkshire, England: Open University Press.

[2] White, A. L. (2009). Newman’s Error Analysis’ Impact upon Numeracy and Literacy. In  Third International Conference on Science and Mathematics Education Penang, Malaysia .

[3] Rhodes, H, Feder, M, & National Research Council, (2014), Literacy For Science: Exploring The Intersection Of The Next Generation Science Standards And Common Core For ELA Standards: A Workshop Summary , Washington, D.C.: National Academies Press.

[4] White, A.L. (2010). Numeracy, Literacy and Newman’s Error Analysis: Journal of Science and Mathematics Education in Southeast Asia , 33 (2), 129 – 148.

[5] Clements, M. A. & Ellerton, N. (1996). The Newman Procedure for Analysing Errors on Written Mathematical Tasks. Viewed 11 January 2021, <http://www.compasstech.com.au/ARNOLD/PAGES/newman.htm>

Related posts

Australian Teachers Lose 2.5 Hours of Curriculum Time Each Week Due to Reading Struggles

Australia Unveils New Curriculum Version 9: Embracing Innovation in Education

Back to Learning: 7 Essential Strategies for Post-Summer Success.

The use of Newman’s Error Analysis

Often when Mathematics is taught, the focus is on processing. For instance, we teach students how to multiply two digit numbers, or how to simplify a fraction.

To solve Mathematical Problems though, there is a lot more to it than just having processing skills. Students need to be able to read and understand the problem. They need to be able to think through what they know about Maths and pick out the appropriate strategies to solve a problem. They have to apply these strategies (processing) and finally check that they have answered the question properly.

Due to the fact that there is so much involved in solving problems, when a student gets an answer wrong, it is often difficult to know whether they have a problem with their processing, or whether they made a mistake at some other point.

In 1977, Anne Newman suggested a series of prompts to help teachers to determine where students are making mistakes in problem solving. In this blog, I will outline these prompts and discuss how I use them to diagnose student’s issues with problem solving. I will also point out the benefits of using these prompts to improve your students’ ability to use and understand mathematical language and strategic thinking.

The first prompt is “Please read the question to me. If you don’t know a word, leave it out.” I tend to say, “Read the question out loud. Are there any words you don’t understand?”

I find that if students stumble when reading the question out loud, it generally means that it doesn’t make sense to them.

One other thing I’ve found is that even when students say that they understand all of the words, what they think a word means and what it actually means are sometimes quite different. For this reason, it can be helpful at this stage to ask students what the key words mean.

The next prompt is, “Tell me what the question is asking you to do.” I tend to say, “Put the question into your own words.”

I find that students seem to struggle with this step when you first start using Newman’s prompts. Even students who are quite proficient problem solvers can struggle here. The prompt is, however, a great literacy exercise and students get better at this step the more they do it. This step is also critical, because it can make it really obvious when students have missed the whole point of the question.

The third prompt is, “Tell me how you are going to find the answer.” I tend to also ask, “What do you know that could help you to answer the question?”

As with the second prompt, students often struggle with this when they start using Newman’s prompts. That’s because many children do not pre-think their working and often use trial and error or whatever first pops into their head!

Apart from being a great tool for identifying students’ issues, this prompt is useful because it trains students to pre-plan their solution. It gets them to slow down a little, to use their reasoning. To consider that there are strategies involved in solving problems and that some will work more easily than others. By forcing students to explain and justify the strategy they’ve chosen, we’ve also given them an opportunity to use language to communicate mathematical ideas.

The fourth prompt is, “Show me what to do to get the answer. Talk aloud as you do it so that I can understand how you are thinking.”

Of course, by this stage you will already know whether students have a strategy to solve the problem. This is just the processing step, where we see whether they can actually do the Maths.

At this point, you may see ‘silly’ mistakes. You should also be able to gauge how quick or slow students are at their processing and see their mathematical confidence (or lack of).

As with the previous step, this prompt requires students to explain their thinking and gives them an opportunity to use mathematical language.

The final prompt is, “Now write the answer to your question.” I tend to say, “Re-read the question and check that you’ve answered it correctly”, or “Check that your answer makes sense.”

I don’t find this prompt to be all that necessary as a diagnostic tool, as it is fairly obvious to teachers when students have made a mistake at this point. This step is great for students though, as it forces them to look back and check what the question was asking them to do. Getting students to think about this step at the end of every problem alleviates the ultimate ‘silly’ mistake of using amazing strategies and reasoning but leaving out a small and vital piece of information right at the end!

In summary, Newman realised that when a student makes a mistake in problem solving, it is not necessarily because of flaws in their processing skills. Students could also have made an error in the reading or interpretation of the question, the identification of which strategies to employ, or in the final communication of their answer.

By using Newman’s prompts, you will be able to identify where your students are going wrong in their problem solving, so that you can accurately assess where they need extra assistance. The regular use of the prompts will also give your students a good framework for solving problems and will give them great opportunities to both understand and use mathematical language more effectively.  

Prompts used with permission from Anne Newman.