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Edited by: Calvin S. Kalman, Concordia University, Canada

Reviewed by: Jennifer Szydlik, University of Wisconsin–Oshkosh, United States; Judith Elaine Hankes, University of Wisconsin System, United States

This article was submitted to Educational Psychology, a section of the journal Frontiers in Psychology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

For the last 10 years South American nations have finished in mid to bottom positions in the Programme for International Student Assessment (PISA) math test, significantly behind dozens of countries around the globe. Regrettably, the lack of improvement over the past decade does not depict an optimistic future for this region (OECD,

Research shows that multiple interrelated factors explain the poor performance of South American students in mathematics (Cerda et al.,

At this level, two principles could be incorporated into early math teaching. Both are supported by considerable evidence and could reduce the sometimes painful experience of learning math. The first principle states that a strong understanding of early mathematics can be built using children's intuitive mathematical ideas as a foundation. This principle mirrors Vygotsky's ideas concerning the bridge that should exist between formal and spontaneous concepts, as the former operates as a zone of proximal development (ZDP) for the latter (Vygotski,

Improving math education is important because it could promote the development of South American countries by strengthening their human capital. It is imperative to have more and better professionals in Science, Technology, Engineering, and Mathematics (STEM), who can tackle the challenges that countries face in an increasingly complex and fast-changing economy (Schwab,

Everyday mathematics refers to the use of intuitive mathematical notions in real-life contexts. In these situations, people are not directly concerned by specific mathematical principles, but instead use raw intuition to solve applied problems.

There are opposing perspectives on the role that everyday mathematics plays in formal learning. While some researchers see it as a foundation on which students can build meaningful understandings of concepts, others regard it as a source of interference (Carraher and Schliemann,

Since the 1980s, researchers have highlighted the role that intuitive mathematical knowledge can play in improving school mathematics, especially in generating more meaningful learning experiences for students (Carraher et al.,

Previous research has also shown the benefits of Cognitively Guided Instruction (CGI), a professional development program for teachers that underscores the role of children's intuitive ideas in early math education (Carpenter and Fennema,

Spatial skills play an important role in STEM disciplines. Longitudinal studies have shown that people with higher spatial skills tend to enjoy, choose, and succeed in STEM areas (Shea et al.,

For a long time, spatial abilities were seen as a stable and unmodifiable human trait (Newcombe,

Some studies have focused on the positive direct effects that spatial training can have on mathematical learning. For instance, Cheng and Mix (

Although we do not yet have a complete understanding of the mechanisms linking spatial abilities and mathematical performance, some studies have already provided hints. A study by Hegarty and Kozhevnikov (

The two aforementioned principles come together into a single pedagogical practice when diagrams are used to support math problem solving. This is by no means a new idea, as this methodology has been implemented in the educational systems of both Singapore (Ng and Lee,

Diagrams are visuospatial representations that depict significant information in a spatial display. Because diagrams are more abstract than objects/manipulatives but more concrete than mathematical symbols, they can provide a valuable bridge between initial and advanced learning stages. In their role as intermediate-level representations, they highlight relationships that could be difficult to spot in higher-level symbolic equations, particularly for novices (for an example, see

Diagrams showing part-whole models. Both figures are based on Kaur's ideas (Kaur,

Previous research shows that diagrams encourage the use of alternative, intuitive problem solving strategies. For instance, they can facilitate the application of children's intuitive mathematical ideas during early arithmetic lessons and more advanced algebra lessons (Edens and Potter,

The role of diagrams as visual-spatial representations that favor the use of intuitive problem solving strategies is stressed by concreteness fading, a theory of instruction based on the ideas of Bruner (

Similar ideas applied to learning geometry have been endorsed by Battista (

South American early math education could be improved through the adoption of these two central principles. The first principle indicates that learning formal concepts becomes more meaningful when teachers integrate what children already know. The second principle indicates that spatial abilities have a strong and positive effect on both the motivation to learn math and math performance itself. The evidence points out that spatial training at an early age can lead to improvements in the mathematical performance of students. While most early education programs consider the development of language and math skills, the development of spatial thinking has not received systematic attention.

Both principles are integrated into math problem solving through the use of diagrams. Diagrams, as intermediate representations between the concrete and the abstract, are highly effective in the development of mathematical learning. The attractiveness and simplicity of diagrams can make it easier for children to build meaning around mathematical activity. That is, students can link abstract concepts with elements of their own experience in a way that allows the appropriation of concepts.

Although the success of Singapore and Japan in mathematics is certainly the result of multiple features, evidence suggests that incorporating the methodical use of diagrams during math lessons could have played a role. These initiatives were possible due to the existence of public policies in education that encouraged new practices guided by scientific evidence. South American countries, in contrast, have a notable gap between public policies, scientific evidence, and educational practices. This is important because public education has a strong impact on a country's social and economic development, and there is no doubt that well-formed human capital tends to generate innovation, a crucial factor for competing in a globalized world.

All team members contributed to this project. FM-R, DV-B and AA-E wrote and reviewed the final manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors would like to thank the Vicerrectoría de Investigación, Desarrollo y Creación Artística (VIDCA) at the Universidad Austral de Chile for providing economic support in the publication of this article.