ABSTRACT
The babble of humans communicating while collaborating is a wonderful sound; people living near schools would attest to the exuberant sound of children playing together at lunch as would those living near walking paths who often have streams of jaunty ramblers passing their house particularly during the summer. Messy problems provide opportunities for children to communicate thereby creating a babble of (working?) noise as they explore pathways towards solutions. They also enable children to be exposed to “activities out of which habits of mind might emerge” (Askew, 2015, p. 59), which means that the practices that children develop in mathematics are brought about by being involved in mathematical activity rather than learning a specific mental process. This approach can be challenging for teachers to prepare, because it means that the boundaries of generalities and definitions are extended (Askew, 2015) usually with children being engaged with others often of different abilities: reasoning becomes a collaborative mathematical activity. These problem-solving tasks can also be challenging for teachers because they require children to work in groups to produce one group artifact rather than children working together but with each creating an individual output. While the discussion of how to engage children to work cooperatively is not the focus of this text, the necessity of children being able to function productively in groups is key for many successful problem-solving activities. Humans don’t spontaneously collaborate, although some individuals seem to have more skill at team or group work than others. We would suggest that you develop children’s mental models of effective group work early in the year if they appear to be unproductive at producing group artifacts in lessons. Appendix 2 has an outline of an approach (4R Approach) we have used with different groups 76and, when used systematically and patiently, such a structure will enable all children to develop functional mental models of working in groups. So assuming that your class is at the ‘functional’ stage of collaborative group work, we have included this messy problem that engages children by enabling them to understand and interpret requirements of a task that is messy to start with but concludes with a ‘neat’ solution.
