Teaching and Learning Mathematics through Problem Solving

Task 1

Here are your first tasks together with a short background article; please read through the attached files and then complete the questions (that should not take too long and please be honest - there are no right answers so just say what you think). Complete them in the given Word file and save so that you will already have some information and data towards your write up for assessment.

There are also questionnaires for you and your students. These have been designed for Key Stage 3 students so please adapt and modify as you think fit (they are in a Word file for easy changing). For those teaching in Years 1-4, you will probably need to get someone to discuss the questions with your class in order to get their feedback (you could for example use a 1-5 scale using fingers on their hand to get precise data); it is though important that they respond honestly rather than thinking what you want to see; hence having someone else to undertake this would be an effective way forward.

Finally, after discussion with colleagues, you are asked what you think makes for "great instruction" in mathematics teaching. Again be honest; say what you think even if this will be later challenged.

Let me stress again that you are free to adapt and modify what we are suggesting to fit with your interests and expertise.

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Task 2

Here are a number of interesting articles for you to look at and for you to choose at least three or four to focus on.

I suggest that you make some summary notes and relate these to the context of your current teaching; it would be helpful to focus on problem solving but you can replace these suggested readings by any others that seem relevant to your interests and to possible innovations you might like to make in the classroom.

I have also attached a copy of an article that my colleague Derek Robinson and myself wrote for the introduction of problem solving through the new Core Maths courses for post-16 Education. This might also be of interest to you, whatever age groups you might be teaching.

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Task3

We now move on to consider the part that problem solving could have in great instruction, encouraging your learners to think for themselves and to develop new skills to solve problems.

This is the main focus of Task 3. In Task3, part 2, we will be giving a set of “open” problems to use with your learners.

Part 1

Before this though, in Task 3, part 1, we want to make you aware of the potential of lesson study to enhance this innovation and indeed to help sustain you and colleagues in seeking models of great instruction in mathematics teaching and learning.

Many of you may well be aware of how lesson study can be used to enhance practice but for those of you less familiar with this, I have attached:

1. PowerPoint presentation that gives the procedures for implementing lesson study;

2. Document that summarises the main aspects of lesson study.

You might also consider looking at a more detailed account for enhancing mathematics teaching through lesson study, available at: https://www.cfbt.com/en-GB/Research/Research-library/2010/r-lesson-study-mathematics-2010

These documents give an outline of lesson study - you might well have to modify them for your specific situation.

Hopefully there will be colleagues in your school or college you can work with and it may be that you develop with them just one “research lesson” for review and evaluation in this way.

Please make sure that you keep full documentation for this process as this will form part of your assignment.

If there is no one that you can easily work with in this innovation, please contact me so that we can (through email) provide some of the collaboration necessary for lesson study.

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Part 2

Here is the file (in two formats) of open problem solving tasks.

We hope that you will innovate with one to two of these problems with your class.

I have given a recommended strategy for implementation in the classroom on the first page of the file.

Please let me know if you need any further guidance

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Task 4

For those of you who have already undertaken the classroom based innovation, I am sending a number of files to help you with your write up.

1. The final submission should be between 4000 - 5000 words and I have attached details of a suggested writing up framework, with notes, and also presentation guidelines (together with a file on the Harvard system for references).

2. For a full masters degree at Plymouth, we use what is called "deep criteria" - these are criteria that should underpin your work; I have attached the details but do not get too concerned about this document as you will be using some of these criteria in your work if you have followed our schedule of tasks.

3. We also use “assessment modes” for our Plymouth masters degree and I have attached these; again if you are continuing onto more modules, then one or more of these need to be explicitly used but given the tasks we have set you, you will be using the “Critical Reflection on Practice” mode so I have also attached more details about this. I suggest that you read this document before you start on your write up, not to change what you have done but to help you focus on your writing up.

This all seems rather burdensome in terms of reading but the key document is the “Writing up framework” file; this is not meant though to be a straightjacket on you but just to be a helpful framework to incorporate work from your early tasks and provide a focus for your assignment.

Finally, we encourage you to provide an early draft of your work for comment; this does not have to be the final version, indeed it should not be, but we can comment on an early draft or outline. Please sent this directly to me by email and I will endeavour to get comments back within a week.

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