Investigations
Mathematical Investigations
are a great way to involve all students to their level of understanding.
An investigation should be relevant to the students, and have an easy starting point.
As students progress they should ideally be asked (or ask themselves, with more experience)
some open questions like:
What if … I used different numbers….
I change the starting point….
I use a larger model….
An example of an investigation:
Take students to a set of steps and ‘act it out’
There are four ways of walking up three steps:
one step at a time:
one big step of three:
a step of one followed by a step of two:
and a step of two followed by a step of one.
How many ways are there (using this pattern) to walk up four steps…
six steps … ten steps …
Try to find a pattern so that you can predict for any number of steps,
how many different ways there are.
Recording
Giving blank paper and no prescribed method of recording often encourages a wide variety of recording, from steps drawn with arrows to number combinations.
A different pattern
What if… you can walk up only one or two steps at a time?
( a famous set of numbers will emerge.)
A Good investigational task has several characteristics:
- Everyone can get started
- There are multiple pathways
- Recording methods are chosen by each person/group
It is important to:
- Provide a variety of hands-on material
- Allow some choice by providing several options
- Value all outcomes by making time to share individual discoveries
(simplest first is best).
- Allow time for discussion on all aspects of the activity
ie. how well the group worked, and who provided insights, as well as the
pathways and outcomes.
Several investigations are on the QSA website
as part of the Support Materials (link to links page)
http:/www.qsa.qld.edu.au, and follow the prompts to 1-10 and Mathematics.