D.A.P. another view by Charlotte Wilkinson, New Zealand

This arrive in my inbox today and I felt it too was worth sharing.

What Counts as Meaningful Contexts for Learning Mathematics?
At the beginning of each level of achievement objectives our (NZ) curriculum states:

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically.
 
As educators we are constantly challenged to find ways of making mathematics interesting and meaningful to our students.

Discussion Question:
 
What is your perception of a meaningful context?
•Out of school contexts - sport, national or international events, places (e.g.supermarket), the home
•In school contexts - other curriculum areas, school events
•Use of mathematics in different occupations

Points to consider:
 
•What is everyday or real life for some may not be everyday or real life for all
•some adults are efficient mathematical problem solvers in their jobs but still view themselves as “no good” at maths.
Egan, K (1992) Imagination in Teaching and Learning challenges the assumption that to engage students in learning mathematics (or any subject matter) requires that they make connections with their everyday experiences.

Instead he suggests “the more distant and different something is from students everyday experiences and environments, the more imaginatively engaging it is likely to be”
 
Personal experiences, like developing the Maths Trails using story books, Flat Stanley and The Tiger who came to Tea certainly engaged students in mathematical learning - to the point where the students were requesting to be taught “stuff” they didn’t know.

Both of these books are available from the online store under the Sales section for just $20 for both books. (Limited number in stock) The Wilkie Way

The quality of a task need not be judged by its relation to real life but in relation to how it engages students’ to think about and do the mathematics featured in the task.

It has long been understood that students will often become engaged, sometimes to the point of obsession in topics outside their experience:

Dinosaurs, Spaceships & aliens, Fairies, Superheros to name a few.

In these days of personalised learning individuals often have areas of intense interest - real experience, real in terms of an interest, eg Aztecs and imaginary that will motivate them to engage in thinking. (I taught an 11 year old to read using motorbike magazines - intense motivation to learn)

Imaginative contexts, stemming from real or more imagined situations, can be important resources for mathematical engagement.

We should not disregard making connections to students real-life contexts but perhaps we should broaden our conception of what counts as real:

Brown S (2001) Reconstructing school mathematics: Problems with problems and the real world.
If we can speak of what is “real” in a more vibrant sense than what “exists” or what we can “touch” and “see” then we not only legitimize more interesting connections between mathematics and the real word but we also suppress the need to seek real world connections as a slave against an otherwise “unreal” world of mathematics.
 
Escape from reality and engage students‘ mathematical imaginations.