Kingston Numeracy Network

Early Years Assessment

Nadia Walker

2 June 2010

A quick task …

Lucky dip!

Choose two numbers from

the lucky dip box and tell

your partner the

difference between

them.

How many ways can you

record your thinking?

37 16

44 11

59 9

66 33

• How could this be used as assessment?

• What information can I get out of this task?

• What misconceptions might be uncovered in this task?

• How could I make this easier/ harder? How could I differentiate this assessment?

Discussion points:

Overview of workshop …

• Maths Online Interview

• Common Misunderstandings

• Informal assessment tasks

Discussion point:What does it mean to have “high

expectations of all learners”?

How can I exceed people’s

expectations, if nobody ever

expects anything of me?

Learner at the centre

… within an online environment …

Maths Online Interview Maths Developmental Continuum

Scaffolding Numeracyin the Middle Years

Fractions and Decimals Online Interview

Common Misunderstandings

Other Maths domain page

resources

http://www.education.vic.gov.au/studentlearning/assessment/preptoyear10/assessadvice/default.htm

Assessment for learning helps teachers place the learner at the centre

Assessment for learning

What is the Maths Online Interview?

• One-on-one interview away from the regular classroom

• Mainly hands-on tasks incorporating concrete materials

• Focus is on mental computation• Responses focus on strategies that the students

use … not only the correct answer• 61 questions and sub-questions• Questions ranging from Level 1 – 4 (VELS)• Should take 20 - 30 minutes

2009 data: Schools using the Maths Online

Interview• No. of schools: 865 schools

67% approx. of all Vic Gov. Primary schools

• No. of students interviewed in 2009: 166 469

• Spread of student enrolments: P - 10

Areas assessed by the Interview• Counting• Place value• Strategies for addition & subtraction• Strategies for multiplication & division• Time• Length• Mass• Properties of shape• Visualisation

Maths Online Interview links with the VELS

Who is the Interview appropriate for?

• Powerful for all students in Levels 1 – 3 (Prep – Year 4)

• The ‘high ceiling’ provides scope for questions up to Level 4 in some areas

• Potential for use with ‘at risk’ students in Year 5 and beyond.

Why use the Interview?

Assessment FOR learning

• Understand individual students’ needs • Find out how students ‘think’ and ‘feel’ while

doing Mathematical tasks • Insight into student thought process in action • Generate detailed profiles showing students’

achievement in relation to points of growth• Track student growth over time• Inform planning for focused teaching at the

point of need

Further resources…

• Mathematics Online Interview Booklet (PDF)

• Teaching strategies linked to the Mathematics Online Interview

• Mathematics Online Interview links with the Victorian Essential Learning Standards

• Starting Points• Observation Notes

Discussion points:

• What recommendations for grouping might you make based on these data?

• What recommendations for teaching might you make based on these data?

• What would be your next step?

Unpacking the Group Profile: Using samples for Counting & Place Value

Enables students to showcase their skills and understandings due to individualised

pathways through the Interview.

Discussion:

Why is the individual nature such a powerful feature of the Interview?

How will you communicate the strengths of this assessment tool to a teacher unfamiliar with it?

Assessment for Common Misunderstandings

• Multiplication makes larger, division makes smaller

• The larger the numerator or denominator, the larger the fraction

• When dividing you don’t need to record 0 as it means nothing (eg, 6540 divided by 5 = 138)

About the tools…

• they expose critical aspects of student thinking

• they provide targeted teaching responses to the ‘common misunderstandings’

• they are particularly useful in identifying the learning needs of students who teachers believe are ‘at risk’

• they have been designed to be administered

individually and generally take between 5 and 10 minutes

• The tools at each Level have been chosen to address key ideas at that Level which, if not understood, will seriously undermine students’ capacity to engage meaningfully with core aspects of the Number Strand in subsequent years.

• It is hoped that the tools will prove a useful resource in addressing the needs of all learners but particularly those that fall behind.

About the tools…

The key ideas addressed at each level are listed below

• LEVEL 1 – Trusting the Count, developing flexible mental objects for the numbers 0 to 10

• LEVEL 2 – Place-value, the importance of moving beyond counting by 1s, the structure of the base 10 system

• LEVEL 3 – Multiplicative thinking, the key to understanding rational number and developing efficient mental and written computation strategies in later years

• LEVEL 4 – Partitioning, the missing link in building common fraction and decimal knowledge and confidence

• LEVEL 5 – Proportional reasoning, extending what is known about multiplication and division beyond rule-based procedures to solve problems involving fractions, decimals, percent, ratio, rate and proportion

• LEVEL 6 – Generalising, skills and strategies to support equivalence, recognition of number properties and patterns, and the use of algebraic text without which it is impossible to engage with broader curricula expectations at this level

Level 1: Trusting the Count

• a failure to understand that counting is a strategy to determine ‘how many’ and/or that the last number counted says how many;

• a mismatch between the oral words and the objects counted (eg, matches objects to syllables, omits certain number names);

• a failure to organise the count to avoid counting objects already counted; and/or

• a superficial understanding of numbers 0 to 10 (ie, limited to simple counts and recognising, reading and writing number names and numerals).

Level 2: Place Value

• inadequate part-part-whole knowledge for the numbers 0 to 10 and/or an inability to trust the count (see Level 1);

• an inability to recognise 2, 5 and 10 as composite or countable units (often indicated by an inability to count large collections efficiently);

• little or no sense of numbers beyond 10 (eg, fourteen is 10 and 4 more); and/or

• a failure to recognise the structural basis for recording 2 digit numbers (eg, sees and reads 64 as “sixty-four”, but thinks of this as 60 and 4 without recognising the significance of the 6 as a count of tens, even though they may be able to say how many tens in the tens place)

Assessment for learning helps teachers place the learner at the centre

Summary

• Assessment communicates to students what is important

• Explicit feedback related directly to a task improves student achievement

• Assessment for learning helps teachers put the learner at the centre, meeting their collective and individual needs

• Teachers gain insight into students’ needs by carefully observing written work, listening, noticing, probing and questioning, and looking for patterns in student responses