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21st Century Skills and Modern Mathematics Curriculum

Sarah@outnumber.app, Research Editor, 11 June 2020
Number Sense, Contextual Learning, International Reach

Over the last two decades, digital innovation has inevitably changed the landscape of the workplace. The skills required of our future workforce reflect the changing demands of a technologically advancing world.

Whilst it’s down to education systems to effectively prepare learners, mathematics, in particular, is responsible for ensuring students have the numerical & problem-solving prowess that’s so highly sought after by employers - not only to fulfil emerging job roles but to fuel further innovation.

The question remains: are current mathematical curriculums effectively equipping students with the skills required to thrive in the 21st century? In this article we unpack ideas from some leading thinkers in mathematics education as well as the 2021 mathematics framework proposed by OECD Programme for International Student Assessment.

What are 21st Century Mathematical Skills?

Skills widely regarded as essential for the 21st century are creativity, communication, critical thinking & collaboration¹. Also known as the 4C’s, these overarch the OECD’s list of mathematical modern-day skills:

✓ critical thinking;
✓ creativity;
✓ research and inquiry;
✓ self-direction, initiative and persistence;
✓ information use;
✓ systems thinking;
✓ communication; and
✓ reflection².

Basic numerical skills are another important consideration; both as a foundation to build upon mathematically and as a fundamental requirement for the workplace. Mathematician Keith Devlin describes this skill as ‘number sense’, viewing it as vital for the 21st century³.

Number sense can be defined as ‘a child’s fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons⁴.’

Traditionally, mathematics has been viewed linearly. However, the ‘number sense’ concept promotes that even basic calculations can be approached in many different ways. Learners should be encouraged to be creative, flexible and inquisitive - skills that were not developed with the old method of algorithmic thinking or reasoning. Instead, following a creative mathematically founded reasoning (CMR) pathway (or a mathematical freedom model) can lay the foundation for true mathematical understanding.

When we compare the two approaches to teaching mathematics, we are better able to see how CMR pathway is a more effective model for instilling the discussed 21st-century skills:

Number Sense, Contextual Learning, International Reach

Unfortunately, many curriculums are not utilising the mathematical freedom approach and therefore, many children are not being adequately prepared for their future. How can we effectively teach the skills required to accommodate the demands of the modern age?

How to Teach 21st Century Skills

Preparing learners for the modern-day world and workplace means ensuring the aforementioned skills are addressed in a progressive mathematics curriculum. PISA has identified four focal content areas as a framework for 21st-century mathematics education²:

1. Change & Relationships

This proposed focal point develops flexible thinking, harnessing creativity by encouraging students to explore and consider ever-changing and evolving interactions in the world.

In life, there are variable degrees of ebbs and flows. It’s why PISA have highlighted ‘growth phenomena’ as a particularly important sub-category. Growth and decay can’t always be predicted in a linear, or even exponential, fashion as an algorithmic approach suggests. Change and relationships consider traditional skills but apply them in a way that showcases their real-life complexities².

2. Space & Shape

PISA appreciates that whilst a grounding in the basics of the shape and space domain is essential, this focal point extends beyond shapes, graphs & geometry. It’s both a tangible and intangible concept that requires creativity and strong visualisation skills to apply learnt knowledge in a broader context.

Formulaic ways of looking at space and shape fail to acknowledge that patterns and symmetry are not always seen in real-life contexts. Current curriculums tend to consider shapes as fixed, whereas the reality is that dimensions and positions are subject to change. PISA places additional focus on ‘geometric approximation’ to instil in learners that flexibility of thought is required to find approaches to complex real-life space & shape problems².

3. Quantity

Quantification plays a huge role in both mathematics and many everyday situations. By considering quantity learners are better able to grasp magnitude and scale, using this to reason and develop number sense.

Although quantity can help with interpretation, large data sets often require the implementation of tools. PISA acknowledges the role of ‘computer simulations’ to assist in the data handling and problem-solving process, leaving space for student creativity².

4. Uncertainty & Data

Whilst modelling solutions & interpreting data can be useful, there are many scenarios in life which are more complex and unpredictable than the traditional teachings of probability and statistics. Economic predictions, poll results and weather forecasts are all examples put forward by PISA of real-life data sets that come with their fair share of uncertainty.

PISA highlights ‘conditional decision making’ as a key topic within this focal point, to ensure learners recognise variance and how conclusions are drawn from assumptions and relationships, which when altered themselves, can change outcomes. By understanding that mathematical conclusions are not always definitive, students become more aware of the uncertainty in all aspects of life, building resilience and the ability to think critically².

Mathematics has been described as ‘inescapable’ in the workplace⁸, but current classroom mathematics is rarely being used or applied in the same way as the maths found in work environments⁹. By looking through a lens of real-world application, PISA’s proposed framework zones in on important and relevant concepts & ideas, however, there’s a need for them to be delivered with relevant contextual richness.

So, how do we teach 21st-century skills using context?

Being able to apply these 21st-century skills in a real-life setting can be described by the term ‘mathematical literacy’, defined by PISA as ‘an individual’s capacity to reason mathematically and to formulate, employ, and interpret mathematics to solve problems in a variety of real-world contexts².’ By teaching maths through context-rich problems, learners are better able to see the relevance of their mathematical knowledge.

PISA puts forth 4 different contexts in which mathematics should be presented to pupils to highlight the variety of its applications. By doing so, students can become more empowered and engaged with the subject, recognising how it resonates with them, their life and their future needs. These contexts are:

❑ Personal
❑ Occupational
❑ Societal
❑ Scientific²

Aside from contemplating the contexts in which children will encounter maths in their adult life, we also need to consider the tools they’ll use to aid them with the problem-solving process, particularly technology.

How Technology Can be Used to Teach 21st Century Skills

The rise of technology in the workplace has questioned the underuse of it in mathematics education. This is a concern shared by founder of Computer-Based Maths Conrad Wolfram, who believes the key difference between maths in the real-world and maths in the classroom is computers¹⁰.

“In real-world maths, computers do almost all the calculating; in educational maths, people do almost all the calculating¹⁰” - Conrad Wolfram

It’s because of this that Conrad puts forward another core skill: computational thinking. A method of problem-solving, computational thinking can be broken down as a 4-step process:

1. Define questions
2. Abstract or translate to maths
3. Compute answers
4. Interpret results¹¹

Conrad notes that mathematics education currently focuses on manually completing step 3, mostly disregarding the other steps. However, computing answers can be done much more efficiently, and at a larger scale, with digital tools¹⁰, freeing up time to focus on steps 1,2 & 4 of the computational thinking process - steps that we know are vital for mathematical literacy.

Utilising technology in mathematics education is crucial for bringing modern-day relevance to the classroom. As Conrad states: ‘If you remove the computer from maths education, you remove the context¹⁰.’ Many learners are already surrounded by technology and will continue to use it into adulthood, arguably in more sophisticated ways in the workplace.

Computational thinking also complements the 4 focal point PISA framework¹¹. Its four-step process maximises 21st-century skills and appreciates that mathematical skills don’t exist independently of one another. Rather, problem-solving is an amalgamation of thoughts, processes, ideas, mathematical concepts and creativity. The next step is ensuring the fluidity of mathematics is portrayed in classrooms, transforming current teaching practices to instil essential 21st-century skills.

Implementing a 21st Century Mathematics Curriculum

Implementing change at this scale isn’t without its challenges. As summarised by Gravemeijer et al., ‘All In all, we may conclude that successful educational change aiming at 21st century skills will require a fundamental change in curricula, tests, and instructional practices, which we (with Wagner, 2014) believe is only possible with a broad support of policy makers and the society as a whole⁹.’

Accessibility to the tools and technology that aid contextual learning is an issue in many areas of the world. However, these problems further highlight the need to bring together an international curriculum. One that is based on leading national curricula, PISA’s proposed framework, computational thinking and the demands of today’s digital age.

The aim should be to create an empowering educational experience for pupils by teaching skills that hold clear relevance in modern society. An international curriculum, that is not constrained by current obstacles, has the power to provide opportunities for all learners worldwide. It would ensure pupils are both mathematically and technologically literate, to continue fueling workplace evolution and innovation across the globe.

Whilst contextual learning is a large part of creating a 21st-century relevant curriculum, it’s also important to consider how pupils best learn, maximising mathematical understanding and engagement. In the next article, we’ll explore how cognitive science can be applied to learning mathematics.

References:

1. Kivunja, C. (2015). Exploring the Pedagogical Meaning and Implications of the 4Cs “Super Skills” for the 21st Century through Bruner’s 5E Lenses of Knowledge Construction to Improve Pedagogies of the New Learning Paradigm. Creative Education, 6, 224-239.

2. OECD, 2018. PISA 2021 MATHEMATICS FRAMEWORK (DRAFT). [online] OECD. Available at: <https://pisa2021-maths.oecd.org/#Overview> [Accessed 6 April 2020].

3. Devlin, K. (2019). How technology has changed what it means to think mathematically, in Danesi. M (Ed), Interdisciplinary Perspectives on Mathematical Cognition, New York, NY: Springer, 2019

4. Gersten, R. & Chard, D (1999), Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities, Journal of Special Education, Vol 33, No 1, pp.18-28.

5. What is number sense?. 2016. [video] Directed by J. Boaler. Stanford University: YouCubed.

6. Jonsson, B., Norqvist, M., Liljekvist, Y. and Lithner, J., 2014. Learning mathematics through algorithmic and creative reasoning. The Journal of Mathematical Behavior, 36, pp.20-32.

7. Boaler, J., 2019. Creative, Flexible Mathematics.

8. Henry-Nickie, M., 2018. The 21st Century Digital Workplace Makes Mathematics Inescapable. [online] Brookings. Available at: <https://www.brookings.edu/blog/techtank/2018/09/11/the-21st-century-digital-workplace-makes-mathematics-inescapable/> [Accessed 8 April 2020].

9. Gravemeijer, K., Stephan, M., Julie, C., Lin, F. and Ohtani, M., 2017. What Mathematics Education May Prepare Students for the Society of the Future?. International Journal of Science and Mathematics Education, 15(S1), pp.105-123.

10. Fundamentally Fixing Math(s) Education. 2020. [video] Directed by C. Wolfram. Youcubed Data Science Summit: YouCubed.

11. Computerbasedmath.org. n.d. Computer-Based Maths And PISA 2021: Exceeding The Requirements. [online] Available at: <https://www.computerbasedmath.org/pisa/> [Accessed 8 April 2020].

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