Module 3.6 Assessing numeracy and mathematics

Making sense of the world mathematically

“Assessment in mathematics and numeracy is more than forming judgements about a learner’s ability. It monitors the learner’s understanding of the mathematical language, concepts and skills and what they need to do to succeed.” (DET, 2020)

Assessing Mathematics through play

Mathematics has developed from our social activity and as a way of making sense of our world. Play-based and inquiry learning in its many forms involves students in mathematical experiences because mathematics is part of their world and everyday lives. This is why mathematics has practical or ‘real life’ applications that play-based and inquiry learning can reveal. It is also where we see students’ numeracy in action, as they draw on their mathematics skills and knowledge and use these purposefully in a range of situations.

Play promotes mathematics engagement

Mathematics learned through play and inquiry is holistic, and capitalises on students’ interests, intrinsic motivation, curiosity and ability to self-direct their learning. Due to this, play-based and inquiry learning that provides genuine choice for students, also provide opportunities for them to engage with a wide range of mathematical concepts, processes and explorations. Explore these concepts further within the Victorian Curriculum Learning in Mathematics.

These experiences are enhanced when students have teachers who can set curriculum goals that are facilitated through play, and who can support students to recognise, build, extend, reflect on and represent the mathematics that has emerged from their play. Play-based and inquiry learning therefore develops students’ capacities to play with mathematical ideas, and to inquire into and experiment with mathematical possibilities (Kinnear & Wittmann, 2018), making them ideal environments for noticing and assessing the mathematics learning they employ.

Mathematical ideas shared during meaningful conversations

Teachers can see students playing with mathematics even when they are not playing with objects. Mathematical ideas lend themselves to play. Teachers can observe in the conversations that takes place between each other and teacher and student.

Assessing mathematics in play

Perry & Dockett (2010) highlight that for teachers to assess students’ mathematical knowledge and understanding in play, they need “…mathematical knowledge; understanding the nature of students’ play, particularly the characteristics of play that promote mathematical learning and thinking and awareness of the role of adults in promoting both play and mathematical understanding.” (p. 715). The teacher’s openness to the opportunities play presents for mathematics assessment is also important. Let’s look more closely at these ideas.

To assess, we have to know what to look for, and what learning can come next, so an understanding of mathematics and mathematical learning trajectories is central to effective assessment. The Numeracy Learning Progressions supports teachers to understand how aspects of numeracy develop over time, and to use this knowledge to inform learning activities.

Ways of assessing mathematics

Although free play provides opportunities for mathematics learning, play that best supports mathematics learning, includes scaffolded dramatic and make-believe play (Clements, Sarama, Layzer, Unlu & Fesler, 2020), and is characterised as guided, where students experience choice and control in their play while the teacher brings the mathematics in the play into focus. In this role, the teacher uses questioning and discussion to guide explicit and extended exploration of the mathematics the students are engaging with and supports them to make connections between the mathematics and their play (Lee & Ginsburg, 2009).

Let's take a look at different ways of scaffolding and assessing students learning in mathematics.

‘Key thought’

“Assessment for learning and development is a continuous process of finding out what children know, understand, and can do in order to plan ‘what next’, build on previous learning and support new learning.” (DET, 2017, p. 7)

Making learning visible

We can make students’ learning visible through the actions we take and the data we collect about what students do and create.  Teachers need a range of strategies to gain access to students’ current and developing mathematical knowledge and thinking, beginning with what mathematics they notice students engaging with in their play and inquiry.

Play and mathematics learning

Play for mathematics learning develops students’ mathematical ideas through their language use, as the development of mathematical language enables students to reflect on their learning. Student language use, along with observation, is therefore a key indicator for assessing mathematical knowledge and mathematical thinking. An article by Caroline Cohrssen from the ECA Blog ‘The Spoke’ (2018) encourages teachers to think carefully about the role of questions and conversation when assessing play in mathematics.

High order questions

An essential role for a teacher as students explore, 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.

Mathematics develops in a context

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.

Asking mathematically rich questions

As you look closely at the Questions starter interactive poster, click on the + hotspot take note of the category of each question and the question starter. How do these questions support your practice?

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, pretense, sense of humour and playfulness (Gifford, 2005).

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.

For example, in a play scenario involving shop play, the following approaches and use of statements, could elicit students’ mathematical ideas and ways of thinking, where the students’ responses could be assessed against the Victorian Curriculum Mathematics Achievement Standards:

teacher wondering out loud: “I wonder where the boxes are that we need to build the shop shelves?” (VCMMG082 - Describe position and movement)

teacher making deliberate errors: Picking up a box priced “5” with five dots on the box to represent it and paying for it with four counters. (VCMNA072 - Compare, order and make correspondences between collections, initially to 20, and explain reasoning)

provocative statements: (in response to a small set of objects - “What a lot of bananas you’ve got! I think there’s 100!” (Achievement Standards - estimate the size of sets).

Putting the Illustrative Maps into practice

The VEYLDF Illustrative Maps emphasise the alignment between the VEYLDF and the Victorian Curriculum and support making connections between what we observe in play and curriculum when assessing.

For example, Outcome 4: Children are confident and involved learners in the VEYLDF is a rich basis for mathematics and numeracy assessment, because it engages many of the skills and processes where mathematics is used by students for problem solving, and in inquiry, experimentation and investigation.

Let’s apply Outcome 4

We can see assess mathematics and numeracy using Outcome 4 when we see, for example, students:

1. applying a wide variety of thinking strategies to engage with situations and solve problems,
2. creating and using representation to organise, record and communicate mathematical ideas and concepts, and
3. making predictions and generalisations about their daily activities…and communicating these using mathematical language and symbols.

Use the examples listed above to guide your observations of students engaged in play-based and inquiry learning in your classroom. Provide an example of the evidence you have gathered for either example I, 2 or 3 that you could use to assess a student in the Victorian Curriculum Mathematics.

Click on the + icon in the corner of the screen to make your contribution to the Padlet board.

Playful Mathematics

In this interactive presentation we would like you to consider the mathematical vocabulary that students use in their play. Click the hotspot +