# Scaffolding Numeracy in the Middle Years: Authentic Tasks

The main point of an authentic task is to encourage students to find ways of solving rich mathematical tasks themselves. Different ways of solving a task reveal qualitatively different knowledge and skill sets, and these can be evaluated in terms of the Learning and Assessment Framework for Multiplicative Thinking (LAF)

## How the authentic tasks were developed

Authentic tasks in the Scaffolding Numeracy in the Middle Years (SNMY) project were developed at a school level by teachers and students.

Teachers and students researched possible problems, community issues or tasks that needed to be addressed and chose one of these to develop as an authentic task. The tasks chosen gave students opportunities to demonstrate many of the key ideas and strategies identified in the LAF.

## How to define an authentic task

In general, an authentic task is one which:

• is purposeful and engaging
• models how people solve real problems in work and/or communities
• puts knowledge to work
• potentially demonstrates what students know and can do
• supports multiple representations and solution strategies
• offers opportunities for meaningful learning and higher order cognitive thinking
• results in some product, presentation or outcome as a result of the deliberations of the group and/or individual.

Purposeful and engaging

Students, teachers and the community should see some real value in working on the task – that is, they want to solve it and see that it is worth the time spent on it.

Models how people solve real problems

The task should involve meetings or other activities that involve negotiation, planning, action, reporting, evaluating and exploring of alternatives.

Puts knowledge to work

The task should draw on a range of knowledge, skills and strategies from different areas of the mathematics and school curriculum more generally as well as what is known about the local environment.

Demonstrates what students know and can do

All learners should be enabled to make a start or contribute in some way. However the task should also challenge most learners at some level.

Supports multiple representations and solution strategies

For example, diagrams, stories, graphs, tables, symbolic expressions, written arguments, explanations and/or justifications can demonstrate multiple options.

Offers opportunities for meaningful learning and higher order cognitive thinking

For example, the task should allow for:

• ‘aha’ moments
• the development of an extended range of problem solving strategies and/or skills
• the construction and evaluation of conjectures, rules and/or generalisations.

Results in some product, presentation or outcome

Ultimately, there should be something tangible that can be ‘pointed to’ as a result of the deliberations of the group and/or individual.

## Guidelines for development

Teachers developing authentic tasks for their students should:

• research the problem
• discuss the ideas
• review and share
• document
• implement
• refine and modify.

Research the problem

At the school level, research possible problems, community issues and tasks. Involve students, parents and community leaders.

Discuss the ideas

Discuss task ideas, brainstorm possibilities for demonstrating the mathematics identified at your level of the framework. Specify and document how this knowledge might be demonstrated.

Review and share

Review task ideas and share possibilities. List the specific mathematical ideas and strategies that might be demonstrated at each zone of the Learning Assessment Framework in the process of doing the task. Decide what evidence of student learning will be collected.

Document

Document the task and consider scoring rubrics to support classroom implementation and the subsequent evaluation of students’ work.

Implement

Implement the task to evaluate the extent to which student numeracy learning has been impacted. During the implementation of the task, note as many observations as possible (yellow ‘stickies’ are a good way of doing this). Once the task has been completed collect evidence of student work.

Refine and modify

Once student work has been assessed, bring work samples and discuss. Brainstorm modifications to task and/or rubrics as necessary. Refine the task and/or rubrics on the basis of the discussion and feedback.

## General examples

The following descriptions are general examples of authentic tasks. Authentic tasks that specifically give students opportunities to demonstrate many of the key ideas and strategies identified in the LAF can be downloaded below.

Developing an Emergency Plan

What is the best emergency plan for the school and the local community and how do we know that this is the best plan? This might involve consideration of the issues and options involved (eg, deciding which is the best place to assemble and why), planning, communicating, evaluating if the plan works, and preparing a report with diagrams etc.

After School Care

A community wanted to determine the viability of setting up an after school care program. To attract a government subsidy to support the scheme, they needed to develop a business plan. Decide what is needed, consult with relevant people, collect and analyse relevant data and prepare a draft business plan.

Rubbish problem

A school identified both a health and a financial problem with the rubbish removal – too much rubbish was being generated, not all of it was placed in bins and sometimes it could not be collected because of weather conditions. They decided to reduce the amount of rubbish by recycling as much as they could. What sort of containers would be needed and would this initial expense be worth it in the longer-term?

Football trip

A community wanted to send a junior football team to compete in a regional competition for a week. What might this involve and how could it be supported? Devise a fund-raising plan to support this activity.

Council submission

A local developer wanted to build units on a vacant block of land next to the school. The block provided a safe passage for many of the native animals that travel regularly between the creek and the adjacent National Park. To convince the Council that the development should not go ahead, it has been suggested that the school needs to prepare an Environmental Impact Report.

School transport

The subsidy for school buses has been reduced. How can bus routes, timetables etc be organised to ensure that current service levels are maintained?