36 Assessing learning outcomes: exploring maths through questions
Language plays a critical role in mathematics and can often be overlooked in our approach to mathematical skills. Questions, conversations and interactions provide key opportunities for children to explore their play mathematically. The thinking that teachers catalyse through their interactions with children provide moments of extension, suggestions that support problem solving and reasoning all of which draws the child’s attention to the conceptual ideas that are present in the play.
How do teacher’s assess mathematics outcomes?
Asking mathematically rich questions
An essential role for a teacher as students explores, play with, and inquire about mathematical ideas, is to talk. Questions, particularly higher-order questions, and conversations that promote thinking critically and reflecting on the mathematical ideas and actions students are using, provide opportunities for assessment of and for learning, and encourage students to represent and think about their mathematical ideas in different ways.
As you look closely at the Questions starter interactive poster, click on the plus (+) icons below take note of the category of each question and the question starter. How do these questions support your practice?
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Asking mathematically rich questions – interactive image hotspots.
This interactive provide questions that promote thinking critically and reflecting on the mathematical ideas and actions for students undertaking different activities. As you click on the hotspots, consider the category of each question and the question starter. How do these questions support your practice?
The interactivity
The scene has six images with a clickable hotspot above each image that provide a category for each question and a question starter/s.
Hotspot one: Suggesting a line of inquiry (Child playing with colourful matchsticks)
What would happen if add another stick and make a new shape? What shape could you make?
Hotspot two: Focusing attention (Child playing with colourful blocks)
Why did you choose the red rectangle?
What did you notice about it when you were choosing it?
Hotspot three: Eliciting strategies (Two children playing with sand)
How did you get the wheel to turn using the sand?
What was the first thing you did, and what did you do next?
Hotspot four: Connecting (Child cutting paper with scissors)
What is the difference between cutting the wiggly lines and cutting straight?
Do you always end up with a curved shape if you cut wiggly lines?
Hotspot five: Clarifying (Two children playing a board game)
Can you describe what dice roll you will need to win? Can you show me many spaces you would move?
What would it look like if I had two dice and I need 7 to win?
Hotspot six: Comparison (Child putting blocks in a buckets)
How many blocks do you think you have in each bucket?
What could you use if you had to swap all the blocks in one bucket for something else that weighs the same?
Stepping into playful assessment – numeracy and mathematics
Strategies teachers can use, that lend themselves to play and inquiry contexts, include ways of sparking students’ dispositions for curiosity, pretence, sense of humour and playfulness (Gifford, 2005, as cited in DET, 2020b).
Research has found that statements made by the teacher, that engage these dispositions, provoke more discussion than questions, and statements can foster learning and provide opportunities for assessment.
In this interactive poster we would like you to consider the mathematical vocabulary that students use in their play. Click on the plus (+) icons below to explore playful mathematics from a “What do I see?” and “What do I hear?” perspective.
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Stepping into playful assessment: numeracy and mathematics – interactive image hotspots.
This interactive provide consider the mathematical vocabulary that students use in their play. As you click on the hotspots, consider how would approach each scenario from the perspectives of, “What do I see?” and “What do I hear?”
The interactivity
The scene has eight images with a clickable hotspot above each image. The eight images are evenly divided to sit underneath two categories:
Playful mathematics: What do I see?
- Sort familiar objects (Children playing with wooden colourful shapes)
- Shapes, position and pattern (Child drawing a picture with a house)
- Counting (Child counting on their fingers)
- Sorting (Child sorting beans into piles)
Playful mathematics: What do I hear?
- Child holding cards with objects
- Child playing with Play-Doh
- Child playing in cupboard box
- Child playing with toy gears
Hotspot one: Sort familiar objects (Children playing with wooden colourful shapes)
- Sort familiar two-dimensional objects in the environment
- Sort and classify familiar objects
- Create patterns with objects
Hotspot two: Shapes, position and pattern (Child drawing a picture with a house)
- Sort familiar two dimensional shapes
- Describe position
- Copy patterns with drawings
Hotspot three: Counting (Child counting on their fingers)
- Establish understanding of the processes of counting
Hotspot four: Sorting (Child sorting beans into piles)
- Sort familiar objects
Hotspot five: Listen – two aspects (Child holding cards with objects)
Listen for mathematical language when children use it in play. Don’t forget to listen for opportunities where you can use this language to enrich children’s play.
Examples of mathematical language:
- count, group, all, same, more, less, share, not enough, this many, put together, doubles, take away.
Hotspot six: Listen – two aspects (Child playing with Play-Doh)
Listen for mathematical language when children use it in play. Don’t forget to listen for opportunities where you can use this language to enrich children’s play.
Examples of mathematical language:
- big, small, full, empty, fit, cover, fill, empty, too much, holds more, holds less, around.
- thick, thin, long, short, longest, shortest, tall, heavy, light, heaviest, heavier.
Hotspot seven: Listen – two aspects (Child playing in cupboard box)
Listen for mathematical language when children use it in play. Don’t forget to listen for opportunities where you can use this language to enrich children’s play.
Examples of mathematical language:
- behind, top, bottom, over, under, inside, outside, beside, next to, up, down.
- straight, curved, pointy, wide, long, short, corner, fit, edge, side.
- turn, flip, slide, backwards, forwards, turn, left, right, this side, that side.
Hotspot eight: Listen – two aspects (Child playing with toy gears)
Listen for mathematical language when children use it in play. Don’t forget to listen for opportunities where you can use this language to enrich children’s play.
Examples of mathematical language:
- pattern, again, first, second, different, next, tomorrow, yesterday, today, beginning, end, middle, after, end.
Mathematics develops in socio-cultural contexts
Mathematics learning is a culturally embedded and socially mediated activity. Research has shown that children’s free and spontaneous play are also important in students’ development of mathematical graphics. Social play provides opportunities for students to draw from their cultural knowledge and create and use drawings, signs and representations to solve problems, and make and communicate mathematical meanings (Worthington, 2020). These informal mathematical representations can be used to gain insight into students’ mathematical thinking, knowledge and understanding and can be harnessed by teachers, to assess their current knowledge and to use that assessment to plan for ways to promote further mathematical thinking.
