The Melbourne Declaration of Educational Goals for Young Australians (MCEETYA 2008) recognises that numeracy is an essential skill for students in becoming successful learners at school and life beyond school, and in preparing them for their future roles as family, community and workforce members. More broadly, a highly numerate population is critical in ensuring the nation’s ongoing prosperity, productivity and workforce participation.
Individuals who are numerate are better prepared to participate and engage in a world that is increasingly focused upon creativity, innovation and which focuses upon knowledge creation and sharing.
This blog post is based upon the research of Professor Merrilyn Goos and many of the ideas here have been inspired by the great work of Tom Barrett. He is a tremendous inspiration for all teachers, not just in the work he does with Ewan McIntosh for NoTosh, but also in his tremendous crowd-sourced series, Interesting Ways. I would encourage you to follow him on Twitter (
@tombarrett), as a regular source of great ideas and resources.
21st Century Numeracy
Professor Merrilyn Goos has developed an excellent model for 21st Century numeracy:
A model for 21st century numeracy by Merrilyn Goos
Click on the thumbnail for a larger version, or read about the model in more detail in the following Keynote Presentation: http://www.nlnw.sa.edu.au/files/links/Goos_SAkeynote.ppt
Explaining the model:
You still need mathematical knowledge to be numerate! This includes concepts, skills, and problem solving strategies, as well as the ability to use sensible estimations. A numerate person also has positive dispositions – a willingness and confidence to engage with tasks – independently and in collaboration with others – and apply their mathematical knowledge in flexible and adaptable ways.
Numerate practice often involves using tools. These include:
1. Representational tools like ready reckoners and charts and tables that might be used in a manufacturing context, and of course
2. physical tools like mathematical drawing instruments and the work related tools of a trade or profession
3.digital tools – technology.
A numerate person can organise their personal finances, for example in relation to credit card spending and mobile phone use. They manage their personal health by making decisions about their eating and exercise habits. They engage in leisure activities that require numeracy knowledge, such as travel, sport, perhaps gambling.
All kinds of occupations require numeracy. Many examples of work-related numeracy are very specific to the particular work context, and often the mathematics used is either invisible to the user or is used in very different ways from how mathematics is taught at school.
Informed and critical citizens are numerate citizens. Almost every public issue depends on data, projections, and the kind of systematic thinking that’s at the heart of numeracy.
Numeracy – A General Capability
In the Australian Curriculum students become numerate as they develop the capacity to recognise and understand the role of mathematics in the world around them and the confidence, willingness and ability to apply mathematics to their lives in ways that are constructive and meaningful.
As they become numerate, students develop and use mathematical skills related to:
- Calculation and number
- Patterns and relationships
- Proportional reasoning
- Spatial reasoning
- Statistical literacy
With this in mind, below are four examples of different ways technology can be used creatively to enhance students’ numeracy skills. These ideas do not focus specifically on maths, but rather on broader strategies that require the application of a number of the mathematical skills numerate students demonstrate.
1. Wolfram Alpha –
creating interesting calculation and number problems with real information
Wolfram Alpha is a computational search engine. Although it works at extremely complex levels, there are many challenges that can be set using Wolfram Alpha as inspiration and to check results against.
Write down everything you know about the number 28. http://www.wolframalpha.com/input/?i=28
1) Is 10 001 a prime number? http://www.wolframalpha.com/input/?i=Is+10001+prime%3F
Or create engaging calculations using information that is nominated by the students. For example:
1) Which Harry Potter movie is the longest, and by how much (students need to compare numbers, order them and then subtract second longest from longest) http://www.wolframalpha.com/input/?i=Harry+Potter+and+the+Philosopher%27s+Stone&a=*C.Harry+Potter+and+the+Philosopher%27s+Stone-_*Movie-
2) How much closer is Brisbane to the South Pole as the North Pole? http://www.wolframalpha.com/input/?i=Brisbane+to+North+Pole
3) Are there more men or women living in Australia, and by how much? http://www.wolframalpha.com/input/?i=how+many+men+in+australia
2. Proportional Reasoning using Scootle
There are fantastic learning objects available on Scootle that allow students to see and interact with fractions and the understandings required to develop proportional reasoning.
Explore this learning path of examples of some of the quality learning objects:
http://www.scootle.edu.au/ec/pin/EDWHQM?userid=20960 – Pin number is EDWHWM
Help a park ranger to arrange fencing in a wildlife sanctuary. Divide common geometric shapes into equal-sized sections for keeping cassowaries. Group the enclosures to form a quarantine zone, then express divisions of the enclosures as fractions. Work through facts about the life of cassowaries: physical characteristics; diet; habitat; life cycles; and locations. Interact with graphs to see how people can help to save cassowaries. This learning object is a combination of two objects in the same series
Help a town planner to design two site plans for a school. Assign regions on a 10×10 grid for different uses such as a playground, canteen, car park or lawn. Calculate the percentage of the total site used for each region. Use a number line to display fractions and equivalent fractions. This learning object is a combination of two objects in the same series.
Measures: scaling down
Compare the areas of squares, rectangles and triangles before and after being scaled down (reduced). Notice that ‘similar shapes’ in the mathematical sense have the same shape but different areas. Explore the relationship between side-length reduction and area reduction when scaling down shapes. This learning object is the third in a series of eight objects that progressively increase in difficulty.
Spatial Reasoning using Resources from Flickr
A great deal of Maths is visible in the everyday. Having students identify where they see Maths can be an engaging way to relate the concepts being taught to real life examples.
Using Flickr students can:
- search for specific examples of spatial concepts in real life
- students upload their own photos and share explanations for their choices – use the ‘notes’ feature on photos in flickr to add explanations, as seen in this example:
Developing Statistical Literacy using Google Docs
Using Google Docs allows students to create forms that are automatically linked to spreadsheets for analysis of data.
The difference between using a program such as Excel and Google Docs is that with Google Docs you can provide a web link or embed the form on a class blog or website to provide more open access. Also, multiple students can access the form/spreadsheet at the same time, making it possible to set group tasks or even homework (e.g. survey parents etc).
An example is here:
Google Forms can be as simple or as complex as required, and provide the option to view responses in a summary format also:
Google Spreadsheets allow data to be visualised also:
Developing Measurement Skills using Google Maps
Google maps allow you to zoom in on many different areas of interest. If you have a Google Account, you can create maps with pins that have associated maths challenges.
As part of the Maps Labs, you can tick an option to have a distance measurement tool function that students can then use to measure different distances – not only the distance between different points, but the area and perimeter of swimming pools and other large constructions and locations. To access this tool, you need to be logged in – why not create a generic Google account for students so that they can use this and other features.
Have you used a contemporary tool in an innovative way to develop numeracy skills?
Share your ideas or experiences in the comments – we’d love to hear of more ways to engage students in this vital area!