Assessing Authentic Numeracy Tasks

Jennifer Brown & Bianca Chopra

Assessing Authentic Numeracy Tasks

Background: In the past two years A.P.PS has had a Numeracy focus on developing,

providing and resourcing stimulating hands on engaging student programs.

Quality individual, unit, team and whole school professional development with excellent numeracy consultants such as Michael Ymer has been undertaken.

Unit teachers have been supported in developing new term numeracy planners based on hands on authentic tasks.

This year two teachers attended the 3 day numeracy professional development sessions run by Charles Lovitt at the Huntingdale Golf Course, where authentic numeracy tasks were explored and the E5 Instructional Model touched upon.

Assessing Authentic Numeracy Tasks How has this shaped or influenced our AGQTP Action

Plan development?Through collegiate discussions we decided that we’d investigate further the

development of our Numeracy Planners to incorporate the storytelling element (which was such a strong focus of Charles Lovitt’s professional development sessions).

With the hands on nature of the activities and the problem solving elements at the core of these activities, we wondered how we could effectively assess our student’s learning outcomes in a manner that was informative and in context of the style of programming.

We agreed that we wanted Rich Assessment Tasks that would: Connect naturally with what has been taught Engage the learner Allow all learners to make a “Start” (various entry / exit points) Encourage students to disclose their understandings Provide an element of “choice” or “openness” Address a range of outcomes in the one task Was time efficient and manageable Use a range of methods or approaches Allow students to make connections between the concepts they have learnt Help teachers decide what help students may require in the content areaDot point ideas gained from “Mathematics Assessment For Learning: Rich Tasks & Work Samples

Assessing Authentic Numeracy Tasks How has this shaped or influenced our AGQTP

Action Plan development? We then looked at the assessment practices we currently use and explored

other more open-ended approaches, considering Assessment As Of and For.

Current Assessment Practices:

Open-ended, Rich Tasks allowing for multiple levels of thinking:(To be investigated)

*VELS based unit tests (Formal paper tests)*NAPLAN*UNSW*Early Years of Numeracy On-Line Interview*Teacher Anecdotal

*Reflective Comments*Thinkboards*Rubrics*Tell Me All You Know*DeBono’s 6 Thinking Hats*Open-ended questions and tasks

A New RockeT / ROBOT• Focus: SYMMETRY:

Introductory Story: Toys R Us has approached you to make a new toy Robot / Rocket…

• *Using a range of geo-shapes create a rocket / robot. Trace & colour.

• *What is your rocket made up of.. (Data: shapes & tallies)

• Final Story: ToysR Us has got back to you, it must be symmetrical..

• *Use of Maths Mirrors to explore & investigate symmetry of Geo Shapes

• *Test symmetry of Robot / Rocket using Maths Mirrors. Is it Symmetrical? Why /why not?

• *Can you alter your Robot / Rocket to make it symmetrical?

A New RockeT / ROBOT• Assessment: Children’s Reflective

Comments• I think this was a very effective

form of assessment as it complemented the activity.

• Through their answers I was able to gain insight into whether they understood the concept of symmetry.

• Their answers also revealed their knowledge of other mathematical concepts such as right / left and names of 2D shapes.

• Their answers as to how they could make their rocket / robots symmetrical also illustrated their Mathematical Reasoning skills.

How Do You Measure A Dinosaur?

Focus: MEASUREMENT:

Story: Big Book: “How DO You Measure A

Dinosaur?”

*Grid References- create a dinosaur*Measurement in metres (length)*Outside using chalk, class draws a m2 grid

(Quadrangle area)

*Each child (or pair) draws 1 of the squares to help create the class’ dinosaur

*Children get inside / lie/ sit next to etc the dinosaur whilst teacher goes inside & takes a photo from the upstairs (5 / 6 area)

window*Children paste a photo into their maths

books and write their reflective comments

Assessment: Children’s Reflective Comments The children in their comments drew

attention to grid references, measurement in metres,

the processes involved in taking a small drawing and enlarging it and their enjoyment in the activity.

Who’s Behind The Boat?

Focus : Problem Solving, Number,

Mathematical ThinkingSTORY: There are 20 legs dangling behind a boat. These legs could possibly belong to

turtles, octopus or snorkelers. How many of each were hiding behind the

boat? Draw the possible creatures. Can you write this as a number sentence?

Extension: How many other possible combinations of

these characters are there?

ASSESSMENT:Scoring Rubric

ASSESSMENT:Scoring Rubric

The Scoring Rubric clearly sets out features to look for when assessing children’s understandings.Caters for children at different developmental levels within the one assessment task.

Interactive Whiteboard was used for the introduction and evaluation stages of the assessment task.

Allows for multiple answers and mathematical reasoning to the task.

Caters to multiple entry and exit points for a group of children.

Music CardsA shop sells two

styles of music download cards, each allowing a different number of songs to be downloaded. Which card is better value for money?

Assessment- 5Whys & Rubric

Music Cards 5 Whys & Rubric5 Whys- I found many students were not very

articulate when expressing their thinking When answering the 5 Whys most students

did not draw on the information they had discovered while working out the problem

Some students used each ‘why’ as a dot point as to why their answer was correct rather than answering ‘why’ to the previous response they had given.

If this form of assessment were to be effective I would need to model its use many more times and much more explicitly. At this stage and for this task it was not a useful form of assessment.

Rubric- Students appear to be very honest and

accurate in the self assessment of their understanding using a rubric

I see rubrics (particularly the ones I used for this task) to be very valuable self assessment tools that would be relevant for many problem solving tasks. However, rubrics have their weakness in that they do not show the accuracy of a students answer/mathematical knowledge

Soft Drink CansHeather’s Summer

job was to stack soda cans into crates with 6 rows of 4. Can you help her to arrange 18 cans, ensuring all rows and columns had an even number of cans?

Assessment- De Bono’s Thinking Hats

Soft Drink CansDe Bono’s Thinking Hats Assessment De Bono’s Thinking

Hats Assessment I think this was a

reasonably effective form of assessment for this task because it gave a well rounded insight into the children’s thoughts and understandings.

Because the students had limited room to write answers, the reluctant writers were not put off by the written reflection.

Win at the FairEach class will be

running a fundraising venture at our school fair. Our class will use a game board with monetary prizes. Can you make the game board more profitable for the school?

Assessment-Tell Me Everything You Know

Win at the Fair Tell Me Everything You Know Tell Me Everything You

Know; some chose to do this in the form of a (KWL)

While I thought this assessment tool would be the most insightful, I have found again, that students are much more able to verbalise their reflective thoughts in a meaningful way, than write them down.

Speaking to the students individually and questioning them gave me a clearer, more extensive idea of what they understood and had learnt.

Assessing Authentic Numeracy Tasks

Our Findings: Our students were highly engaged on the authentic

numeracy tasks. They particularly liked the story starts to the problem solving tasks / learning experiences.

The children’s reflective comments were enlightening. This style of assessment was easy to administer and allowed for different levels of thinking within the one task. (Assessment OF learning)

Rubrics allowed for assessment of different stages of development, but required more pre-planning. (Assessment OF learning)

Work samples (Assessment OF, FOR learning) “Tell Me Everything You Know” and “Thinkboards”

(Assessment OF and FOR learning) Teacher observation of the task was by far the most

effective and informative. It allows for you to listen to children’s “self talk” and observe their willingness to trial

a variety of approaches. (Assessment OF, AS and FOR learning)

Where To Now? Inform the rest of the school staff of our project findings

and the positive elements that can be incorporated into others planning.

Continue to investigate a range of Rich Authentic Assessment Tasks in the area of Numeracy.