The term, "fluency" as applied to mathematics is often misunderstood (Bay-Williams & SanGiovanni, 2021). Procedural fluency, as defined by the National Research Council and the National Council of Teachers of Mathematics, involves these three components: efficiency, flexibility, and accuracy (Kilpatrick et al., 2001; NCTM, 2014). These elements are interrelated and collectively define what true mathematical fluency looks like in practice. Computational fluency refers to computation within the four operations (Bay-Williams & SanGiovanni, 2021).
The misunderstanding often comes from equating fluency solely with the ability to recall basic facts quickly (Bay-Williams & SanGiovanni, 2021). Research indicates that developing automaticity, or the quick recall of answers without conscious calculation, is crucial for long-term success in math education (Stickney et al., 2012; Cumming & Elkins, 1999; Woodward, 2006). While basic fact fluency is important, it is not the entirety of mathematical fluency. Procedural fluency encompasses a broader range of skills beyond basic fact recall, including operations like comparing fractions, solving proportions, and simplifying expressions (Bay-Williams & SanGiovanni, 2021).
In educational practice, it's crucial to communicate the broader definition of fluency to families and other stakeholders, emphasizing that fluency involves more than learning basic facts. This broader understanding helps in appreciating the complexity and depth of mathematical proficiency (Bay-Williams & SanGiovanni, 2021). Read more about the importance of how we define and discuss math fluency here.
Consequences of Lacking Math Fluency
Children who do not develop fluency may experience several negative outcomes (Miller et al., 2011):
Loss of Confidence: Struggling with basic math can lead to a lack of confidence in their abilities. When children repeatedly face difficulty with foundational skills, they may start to view themselves as "bad at math," leading to a fixed mindset that hinders their overall academic growth (Miller et al., 2011).
Math Anxiety: Persistent struggles and failures in math can lead to math anxiety, a condition characterized by intense feelings of fear and apprehension when dealing with math. This anxiety can create a cycle of avoidance and further difficulties, as children shy away from math-related activities and learning opportunities (Szucs & Toffalini, 2023).
Doubt and Mistrust: Parents play a crucial role in supporting their children's education and forming perceptions about the effectiveness of the educational approach (Hiles, 2018). If parents see their children struggling with math fluency in a Montessori setting, it may lead to concerns about the adequacy of the Montessori method in teaching fundamental skills. Parents may begin to doubt the Montessori approach if they perceive that their child is not keeping up with peers in traditional education settings. This doubt can lead to mistrust in the school's ability to provide a comprehensive education (EuroSchool & EuroSchool, 2024).
Pressure on Teachers and Schools: Concerns about math fluency can result in increased pressure on Montessori teachers and schools to demonstrate the effectiveness of their methods. Schools may need to provide additional support and resources to address parents' concerns and ensure that children develop the necessary fluency skills.
Decision to Switch Educational Paths: In extreme cases, parents may decide to switch their children to traditional schools if they believe their child’s basic skills are not being adequately addressed in a Montessori setting. This can impact the child's continuity of education and adjustment to different teaching methods (EuroSchool & EuroSchool, 2024).
Source: Sagasti Escalona, María. (2020).
Graphicacy: represent, record and communicate mathematical facts from an early age to avoid mathematical anxiety.