Newman's Prompts as a Problem Solving Process

I have been aware of Newman's prompts and had them filed in my 'to be investigated'pile for a long time.  They were developed by an Australian educator, Anne Newman (1977).  From what I understand they were designed as an error analysis to help teachers determine why students make mistakes with written mathematics problems.


The prompts are:



1.  Read the question. If you don't know a word, leave it out.
2.  What the question is asking you to do?
3.  How you are going to find the answer?
4.  Do it!  Use your maths skills to solve the problem -  "Talk aloud" as you do it, so that others can understand how you are thinking.
5.   Now, write down your answer to the question.


So a student solving a problem follows a five step process:


1.  Reading.
2.  Comprehending.
3.  Transformation. (selecting an appropriate strategy)
4.  Process skills.
5.  Encoding.

With a renewed focus on problem solving across our school and subsequent to a discussion at my last University intensive, I have experimented in using the prompts as a scaffold - that is a step by step process for students to follow when solving a problem.  I printed each of the prompts onto a poster and have strongly encouraged (over and over!) students to make sure they consciously acknowledge each step - even when they think a problem, or part of a problem is easy.  

Results have been fantastic!  What I had long noticed was that students were fantastic at Newman's Stage 4 - the process - what they (and probably their teachers) regard as mathematics.  So often I have seen a student give a great answer - to a different question!  Newman making the other stages of the problem solving explicit has been a really effective solution to the difficulties that our school had identified in our students' problem solving skills - that often our students new the mathematics involved in a problem, but were getting tripped up by the literacy aspects of the problem.

My biggest buzz in the classroom at them moment is listening to students prompt each other - "what is this question asking us to do?" "how are you going to find the answer?" and especially the smiles and sense of satisfaction at the encoding stage - "the answer to this problem is...." 

Newman's Prompts as a Scaffold from Jason Fisher on Vimeo.

Glogster

Principles for the Design of Teaching - Reading Notes.

This post is my reflection on a journal article read as part of my Masters course.  I am treating it as an opportunity to think about its content while I type - and it saves my notes in a place where I can find them.

Bell, A. (1993a). Principles for the design of teaching. Educational Studies in Mathematics. 24, 5-34.

The general tenet of the article is that to design a learning activity a teacher needs to choose the situations and contexts which embodies the mathematics to be learned, then design tasks for students to work on that deeply involve the relevant concepts and relations. 

The underlying psychological principles put forward by Bell for good lesson design are:

1. Connectedness.  If what students are learning can be connected to students' existing knowledge they are more likely to retain it.  In this light the beginning of a lesson is crucial - start with a task that allows students to use their existing knowledge.
2. Structure and Content.  Structural knowledge is tied to the context in which it is learned.  Maths teachers should not assume just because a student is successful in one context that they will be able to apply it in an unfamiliar context.  So the best approach is to explore extensively the structural relations in one context and then repeat in another context making the links explicit.  
3. Feedback.  Learners should know immediately when they have correctly solved a problem.
4. Reflection and Review (of ) the process of performing the task and the new knowledge gained - labelling the new knowledge in one's memory so that it is accessible in the future.
5. Intensity  Intensive insight demanding tasks (not just memorisation!) produce long term gains.

My challenge is to translate these into practice when designing maths lessons.  The article contains a range of lessons that will be worth investigating and adapting to an appropriate level for my class.

Scribble Maps in the Classroom

With our city camp coming up I introduced the class to Scribble Maps this morning.  I had previously used Google Maps with them so they were aware of how the maps worked.  Most immediately began to investigate the functionality of the site - their task was to plot some of the places we are going to visit on the camp.

The wireless network had a bit of trouble coping with demand - few students lost some work at various stages but overall it was a success.  Distraction factor was high with the number of choices they had for markers.  At this stage no student was really up for looking at plotting routes on the map.  Something for the future.  Also need to investigate the saving and publishing options available.

A Start

The words of Will Richardson are still ringing in my ears.  Of all the things I've heard, read and learned about over the last couple of months it was Will's statement last week that as teachers we need to be expert learners that is banging around in my head most loudly.  As I have reflected on this I've come to the point where I think if I'm not at least trying to be an expert learner then I'm faking it trying to be a better teacher.

I've been tinkering with Web 2.0 in the classroom for three or more years - yet my my use of it personally is sporadic and fleeting.  Need to change.

I exhort my students to read.  I read mountains of stuff for work and study but my 'personal' reading habit is reflected by the novels gathering dust on my bedside table that haven't been touched for weeks.  Need to change.

I expect my students to write in a variety of genres.  I haven't written creatively for a very long time.  Need to change.

So a beginning.  I'm not sure to what end, but I do know it is time to start.  To engage.