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Proposal: Using concept maps to support mathematical problem solving

Jennifer Piggott

Year of posting: 2006

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Abstract:

Question

Can concept mapping software act as a tool to mediate and support learners' independence in "stepping into" mathematical problems?

Resources

Access to concept mapping software available from the NRICH with the functionality to save and store maps to act as data.

Collaborative work on concept maps if possible

Access to partially structured and completely open concept maps to support problems.

Technical issues of saving and sharing concept maps for analysis will need to be addressed.

Methodology

Sample: group of approximately 30 students from a school who are familiar with concept mapping (and preferably have some experience of mathematical problem solving).

Identification of 6 problems for students to investigate over a period of two to three months.

Sample will be split into three groups each tackling the 8 problems in four different ways in rotation ensuring that each problem is tackled by all the groups but on a complementary cycle:

Group A: No concept map, Structured concept map available, Unstructured concept map, Given concept map containing hints, ...

Group B: Stuctured concept map available, Unstructured concept map, Given concept map containing hints, No concept map, ...

Group C: Unstructured concept map, Given concept map containing hints, No concept map, Structured concept map available, ...

Alternate model would include three groups, but instead of having one of the three scenarios being based on "no concept map" the focus would be on collaborative concept map development - sharing and moving on.

This will be followed up by a questionnaire aimed at elucidating students' views of the value of the concept maps in aiding them in "thinking about" and stepping into" the problems.

Possible subsidiary questions

Do hints represented in concept maps support learners in stepping into problems?

Do structure maps have advantages for some/all pupils?

Do the nature of the problems affect the potential value of concept maps?

Is there value in collaboratie concept map creation in supporting problem solving?

 

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Keywords:

problem solving, concept maps, on-line, NRICH

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Study

A mathematical problem is dependent both on its content but also on the individual solver. A problem is only a problem if, for the solver, the solution is not immediately obvious and for progress to be made some starting point has to be established. Problem solving involves a range of strategies, some of which are designed to help the solver "step into" the problem and make the first tentative steps on a journey, for example "have I seen something like this before" , considering what I know and what I need to know, working backwards and so on.

The aim of this exploratory study is to evaluate the ability of concept mapping software to mediate and support solvers in stepping into problems delivered remotely and moving students from a state of "not kowing" to "investigating and exploring".

The NRICH website (www.nrich.maths.org) publishes a range of mathematical problems every month to a target audeince of students aged from 5+. Problems include hints (to support students in stepping into problems) and notes (for teachers). No solutions are offered until the end of each month when solutions sent in by students are edited and published.

The study would identify an initial sample of problems and ask a groups of students to use concept mapping to support them in moving into a problem. This support would be at four, increasingly open scenarios:

1. A concept map containing structured question specific hints
2. A semi-structued map with some suggested questions ("have I seen something like this before? What?" ) but not question specific
3. A content free concept mapping tool
4. No concept map.

Issues/potential outcomes:

Identifying the potential strengths and limitations of concept mapping software in supporting mathematical problem solving

Existing familiarity with concept mapping

Existing experience of mathematical problem solving

Roles of concept mapping in the problem solving process

 

 

 

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