A dynamic understanding of mathematics is transformative. It is problem driven, and

A dynamic understanding of mathematics is transformative. It is problem driven, and

continually expanding [it] can be surprising, relative, doubtful, and aesthetic (Raymond,

1997, p.557). It doesnt work in absolutes, but instead believes that mathematics is not bound

by truth and can in fact be proven wrong (Yazlik et al., 2022). It is seen as an exploratory

and creative practice that is alive and a way of interpreting the world rather than simply

categorising it (Boaler, 2008, p.25). The learner must be an active participant in being

curious, posing questions and problem solving (Raymond, 1997). This view has taken on

many different names such as fallibilism (Cooke, 2003), platonist (Grigutsch & Trner,

1998), deep (Crawford et al., 1994) and even abstract/creative (Johnson, 2020). Whilst they

all have slightly different terminology, they all share these dynamic characteristics.

With computers able to perform the static functions of mathematics, number, fact-focused,

making calculations, the need for people to have a dynamic understanding of mathematics

becomes ever more important (Gravemeijer et al., 2017). Whilst studies throw around

different statistics as to the number of jobs that are likely to be replaced by artificial

intelligence, one fact they all agree on is that they can certainly perform these static functions.

Burghes & Hunter, 2021; Gravemeijer et al., 2017). This is reinforced by the idea that

mathematics is really four steps, and only one of them can be performed by computers, and

its the majority of what we teach in schools (TED, 2010). So what mathematics do we teach

when computers do all mathematics? (Tupouniua, personal communication (lecture notes),

2023).

Johnson (2020) emphasised that a focus on group worthy tasks that are open, relevant, and

allow for productive struggle (p. 91) is the most effective way to transform students

mindsets from static to dynamic. Burghes and Hunter (2021) stress the need for critical

thinking, collaboration, inquiry-based learning and authentic contexts are needed if students

are to not only meet the demand of the future workforce, but to use mathematical knowledge

to face social injustices and offer solutions head on. Mental arithmetic, the ability to

calculate or estimate calculations in your head, is still important, but should not be the whole

focus (TED, 2010). TED (2010) argues that mathematics needs to be more practical and

more conceptual simultaneously. Getting students to develop their own questions about theirown problems and constructing their own ways of getting there is crucial to their sense of

understanding what mathematics truly is (Boaler, 2008; Gravemeijer et al., 2017; Johnson,

2020).