21st Century Skills and Modern Mathematics Curriculum
We consider how we cannot predict the mathematical problems of the future. That’s why context and numerical reasoning are vital skills The Outnumber Project helps to develop, ensuring flexible, adaptable minds.
PISA (Programme for International Student Assessment-OECD) measures 15-year-olds’ ability to use their reading, mathematics and science knowledge and skills to meet real-life challenges. See PISA mathematics rankings here. open_in_new
PISA Mathematics Framework: A Curriculum Bridge to the Digital Age
PISA’s framework considers the essential mathematical skills of a 21st-century prepared mathematician. Mapping existing skills to this framework serves as a starting point to upgrade mathematics education to better prepare students for the demands they will face in the future.
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 creativity.
Change and 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. 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 complexities.
Uncertainty and 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. Mathematical conclusions are not always definitive. 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.
Space and Shape
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 problems. It’s both a tangible and intangible concept that requires creativity and strong visualisation skills to apply learnt knowledge in a broader context.
21st Century Skills
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. PISA’s list of mathematical modern-day skills: ✓ critical thinking; ✓ creativity; ✓ research and inquiry; ✓ self-direction, initiative and persistence; ✓ information use; ✓ systems thinking; ✓ communication; and ✓ reflection.
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: ❑ Personal ❑ Occupational ❑ Societal ❑ Scientific² Being able to apply 21st-century skills in a real-life setting is true ‘mathematical literacy’ as ‘an individual’s capacity to reason mathematically and to formulate, employ, and interpret mathematics to solve problems in a variety of real-world contexts.’
Outnumber Primary Module : Expected First Release Q1, 2021
Our primary module is based on a superset of leading national curricula contents adapted to PISA concepts of 21st century skills and context-rich learning. With an innovative approach we aim to support all national curricula within an internationally competitive framework.
Content Knowledge Matrix: Primary Completion at Age 11+
UK(England🏴), New Zealand🇳🇿 & Hong Kong🇭🇰: Year 6; USA🇺🇸, Canada🇨🇦, Australia🇦🇺, Ireland🇮🇪, Singapore🇸🇬: Grade 5
✔︎ Whole numbers, fractions, mixed numbers decimals, percentages and ratios ✔︎ An understanding of place value for both whole numbers as well as fractions and decimals. ✔︎ Prime numbers, composite numbers, square, cube and triangular numbers ✔︎ Using number sense, rounding & estimation to find accurate and approximate solutions, which can include decimals ✔︎ Making connections between equivalent fractions, decimals and percentages ✔︎ Relationship between fractions and ratios; simplifying & equivalent ratios, using ratio notation & dividing into a given ratio ✔︎ Recognise units, using correct notation and symbols
Change and Relationships
✔︎ Arithmetic four operations with whole numbers, fractions, mixed numbers and decimals with an understanding of the role of brackets. ✔︎ Understanding percentage increase/decrease; factors and multiples ✔︎ Exploring relationships between distance, time and speed; changing speed ✔︎ Expressing relationships using variables and simple equations; finding unknowns by solving simple linear equations and using substitution to further evaluate ✔︎ Recognise the relationships between numbers and fractions in a sequence; compare & order numbers; understand and use the inverse of operations to check solutions ✔︎ An understanding of rate in contextual situations & calculating rate
Data and Uncertainty
✔︎ Data Collection, Display and Interpretation: identify and carry out data collection methods; compare and interpret data using bar charts, pie charts, area charts and line graphs, including interpreting different scales on axes ✔︎ Data Analysis: explore the concept of variability in a dataset and how that relates to concepts of mean, median and range ✔︎ Chance: Describe probabilities using fractions, decimals and percentages and recognise mutually exclusive & non-mutually exclusive scenarios. ✔︎ Chance: Explore chance experiments with both small and large numbers of trials and compare observed frequencies with expected frequencies.
Space and Shape
✔︎ 2D Shapes and Patterns: areas, perimeters and other properties of triangles, rectangles, different quadrilaterals and 2D shapes (including circles & composite shapes) ✔︎ 3D Shapes and Patterns: understanding shape properties, finding volume of a cube/cuboid; building different solids from unit cubes and finding volume ✔︎ Length, Volume, Weight: measuring, comparing and converting to different units using decimals ✔︎ Space, Position and Direction: translations, enlargements, reflections and rotations of two-dimensional shapes; line and rotational symmetries; angles; four-quadrant coordinate-grid; simple map interpretation ✔︎ Identify, compare & measure angles; use basic angle properties to find unknown angles; use understanding of angles to recognise regular and irregular polygons ✔︎ Recognise perpendicular and parallel lines