Authentic tasks are designed to help students see mathematics as worthwhile and important. When students understand the purpose of a given problem in mathematics, they are more likely to persist when challenged. Authentic tasks generally have an ‘open middle’ which means that students can use different representations and solutions to communicate their knowledge and reasoning.
These curated links provide MAV members with access to nine authentic tasks from some of our primary consultants’ favourite resources. The 11 criteria provide MAV members with a research-informed context to consider each task’s potential impact on student thinking, ways of working, attitudes towards mathematics, their knowledge and understanding.
The following criteria was used to select the tasks based on their potential:
| Criteria | Elaboration |
|---|---|
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Intriguing contexts capture the students’ interests and curiosities |
An opportunity for students to relate learning to their own lives and communities. High student motivation/enjoyment and sense of purpose can be anticipated or observed. |
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Problem solving is required to overcome obstacles |
Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. |
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Low entry/ high ceiling, and an open-middle encourages different strategies |
Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. |
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Opportunities for creative thinking and or visualising |
Students invent, discover and imagine new ways to solve a problem. Students make connections and see relationships by visualising the problem or representing solutions visually. |
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Encourages reasoning and critical thinking |
Logical, rational and critical thinking. eg: estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
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Opportunity to collaborate and see others working mathematically |
Students challenge each other, the computer, the teacher etc and observe how they work mathematically. Make decisions in groups to communicate findings, engage with different ideas, monitor and regulate each other's thinking. |
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Opportunities for students to develop fluency |
Estimating, collecting and interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. |
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Promotes feedback and metacognition. |
Self and peer reflection targeted at specific aspects of the work. eg: knowledge; how your thinking is changed as a result of lesson. Affective traits eg: problem solving attitude, collaborative skills. |
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Extends knowledge or applies knowledge in new contexts |
Provides students with access to forms of knowledge beyond what they can pick up in everyday life or via the Internet. |
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Promotes an understanding of the ‘why’ and ‘how’ of mathematics |
Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big Ideas) in different ways eg: developing number sense, place value. |
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Guides future learning |
Provides data on student growth to guide future direction. eg: identifies patterns or errors, level of progress towards goal. Makes suggestions for future learning. |
Used with permission © Martin Holt Educational Consultant 2017
If you would like to learn more about this approach to assessing or using tasks contact office@mav.vic.edu.au
Statistics and probability
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NRICH problem solving task: Three Block Towers |
Scootle lesson sequence: Dice Don't have Brains |
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Target Level: F - 2 |
Target Level: 1 - 6 |
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Why we love this task:
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Why we love this task:
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Measurement and geometry
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Wildmaths interactive game: Approaching Midnight |
Teach Engineering investigation: How Tall are we? |
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Target Level: 2-4 |
Target Level: F-2 |
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Why we love this task:
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Why we love this task:
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Number and algebra
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NZMaths lesson sequence: Six Circles |
MAV problem solving task: The 1,2,3,4 Problem |
ReSolve Maths by Inquiry lesson sequence: Bakery Challenge |
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Target Level: 5-6 |
Target Level: 1-6 |
Target Level: 5-6 |
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Why we love this task:
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Why we love this task:
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Why we love this task:
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These support pages were produced using Strategic Partnership Program funding from the Department of Education and Training.
