using formative assessment rubrics in mathematics · web view1.1 – the student demonstrated they...

Using formative assessment rubrics in Mathematics

Early multiplicative thinking Levels 1 and 2

Authorised and published by the Victorian Curriculum and Assessment AuthorityLevel 7, 2 Lonsdale StreetMelbourne VIC 3000

© Victorian Curriculum and Assessment Authority 2019.

No part of this publication may be reproduced except as specified under the Copyright Act 1968 or by permission from the VCAA. Excepting third-party elements, schools may use this resource in accordance with the VCAA educational allowance. For more information go to: https://www.vcaa.vic.edu.au/Footer/Pages/Copyright.aspx.

The VCAA provides the only official, up-to-date versions of VCAA publications. Details of updates can be found on the VCAA website: www.vcaa.vic.edu.au.This publication may contain copyright material belonging to a third party. Every effort has been made to contact all copyright owners. If you believe that material in this publication is an infringement of your copyright, please email the Copyright Officer: [email protected]

Copyright in materials appearing at any sites linked to this document rests with the copyright owner/s of those materials, subject to the Copyright Act. The VCAA recommends you refer to copyright statements at linked sites before using such materials.

At the time of publication the hyperlinked URLs (website addresses) in this document were checked for accuracy and appropriateness of content; however, due to the transient nature of material placed on the web, their continuing accuracy cannot be verified.

The VCAA logo is a registered trademark of the Victorian Curriculum and Assessment Authority.

Using formative assessment rubrics in Mathematics – Early multiplicative thinking, Levels 1 and 2

ContentsWhat is formative assessment?.........................................................................................................5

Using formative assessment rubrics in schools..............................................................................5

The formative assessment rubric.......................................................................................................6

Links to the Victorian Curriculum F–10...........................................................................................6

The formative assessment task.........................................................................................................8

Description of the task (administration guidelines).........................................................................8

Interpreting evidence of student learning...........................................................................................9

Setting the scene............................................................................................................................9

Sample 1.......................................................................................................................................10

Sample 2...................................................................................................................................13

Sample 3...................................................................................................................................18

Sample 4...................................................................................................................................20

Using evidence to plan for future teaching and learning..................................................................23

Teacher reflections...........................................................................................................................23

Appendix 1 –....................................................................................................................................24

Skip counting patterns......................................................................................................................24

Appendix 2 –....................................................................................................................................25

Making groups..................................................................................................................................25

Appendix 3 – Arrays.........................................................................................................................26


What is formative assessment?Formative assessment is any assessment that is used to improve teaching and learning. Best-practice formative assessment uses a rigorous approach in which each step of the assessment process is carefully thought through.

Assessment is a three-step process by which evidence is collected, interpreted and used. By definition, the final step of formative assessment requires a use that improves teaching and learning.

For the best results, teachers can work together to interrogate the curriculum and use their professional expertise and knowledge of their students to outline a learning continuum including a rubric of measurable, user-friendly descriptions of skills and knowledge. Teachers can draw on this learning continuum and rubric to collect evidence of each student’s current learning in order to provide formative feedback and understand what they are ready to learn next.

The VCAA’s Guide to Formative Assessment Rubrics outlines how to develop a formative assessment rubric to collect, interpret and use evidence of student learning to plan teaching and learning. For more information about formative assessment and to access a copy of the guide, please go to the Formative Assessment section of the VCAA website.

Using formative assessment rubrics in schoolsThis document is based on the material developed by one group of teachers in the 2019 Formative Assessment Rubrics project. The VCAA acknowledges the valuable contribution to this resource of the following teachers: Damon Quah (Park Orchards Primary School), Amelia Perkins (Guthrie Street Primary School) and Jill Benham (Taylors Hill Primary School).The Victorian Curriculum and Assessment Authority partnered with the Assessment Research Centre, University of Melbourne, to provide professional learning for teachers interested in strengthening their understanding and use or formative assessment rubrics.

This resource includes a sample formative assessment rubric and task and describes how the teachers implemented the task in their schools and also includes representative student work samples.

Schools have flexibility in how they choose to use this resource, including as:

a model that they adapt to suit their own teaching and learning plans a resource to support them as they develop their own formative assessment rubrics and

tasks.

This resource is not an exemplar. Schools are advised to consider whether the sample formative assessment rubric and task meet the needs of their student cohort and is appropriate in the context of their whole-school teaching and learning plan. Additional support and advice on high-quality curriculum planning is available from the Curriculum Planning Resource.

© VCAA

https://www.vcaa.vic.edu.au/Footer/Pages/Copyright.aspx


The formative assessment rubricThe rubric in this document was developed by three Victorian teachers to help inform teaching and learning in Mathematics. It supports the explicit teaching of multiplication.

The rubric was designed to provide teachers with information about what students are currently demonstrating in relation to multiplicative thinking. It can be used in conjunction with a formative assessment task that that will give students the chance to show that they can:

skip count by 2s, 5s and 10s make groupings apply strategies.

Links to the Victorian Curriculum F–10

Curriculum area: Mathematics

Levels: Levels 1 and 2

Achievement standards extracts:

Level 1 – Students describe number sequences resulting from skip counting by 2s, 5s and 10s.

Level 2 – Students represent multiplication and division by grouping into sets and divide collections and shapes into halves, quarters and eighths. They recognise increasing and decreasing number sequences involving 2s, 3s, 5s and 10s ...

Content descriptions:

Level 1 –

Investigate and describe number patterns formed by skip counting and patterns with objects ( VCMNA093 )

Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero ( VCMNA086 )

Level 2 –

Recognise and represent multiplication as repeated addition, groups and arrays ( VCMNA108 )

Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences ( VCMNA103 )

© VCAA


https://victoriancurriculum.vcaa.vic.edu.au/Curriculum/ContentDescription/VCMNA103





Learning continuum MathematicsLevels 1 and 2Number and Algebra

Phase 1 Phase 2 Phase 3 Phase 4

Student skip counts by 2s, 5s and 10s. Student uses skip counting and repeated addition to count collections.

Student recognises and represents multiplication as groups and arrays.

Student uses efficient strategies to solve more complex problems.

Organising element

Action Insufficient evidence

Early multiplicative thinking

1 Skip count 1.0 Insufficient evidence

1.1 Recites skip counting patterns of 2s, 5s and 10s

1.2 Uses the skip count strategy to count objects

2 Grouping 2.0 Insufficient evidence

2.1 Makes equal groups of objects 2.2. Can make equal groups and find the total by skip counting

2.3 Uses an array to group objects in 2s, 5s and 10s

3 Application of strategies

3.0 Insufficient evidence

3.1 Solves problems counting by 1s 3.2 Solves problems using any skip counting to match the objects being counted

3.3 Writes or models the strategy used to solve the problem

3.4 Justifies any efficient strategy to solve problems beyond skip counting, such as multiplication facts, doubling, additive facts (e.g. 10 + 10 = 20)

© VCAA



The formative assessment taskThe following formative assessment task was developed to elicit evidence of each student’s current learning and what they are ready to learn next.

Description of the task (administration guidelines)

Part 1: Skip counting patterns

Students are given the skip counting patterns worksheet (Appendix 1) to complete. This can be administered verbally if required, for example for those students who cannot

access the literacy component of the activity. Counting patterns include 2s, 5s and 10s.

Part 2: Making groups

Students are required to use counters/Unifix to make different groupings of 2, 5 and 10. They will then need to record (write or draw) what they made on a worksheet (Appendix

2) or show it visually with counters. They will need to find the total number of items for each set of groupings. They will need to explain their thinking or method in regards to finding the total.

Part 3: Arrays

Students are given an array and asked to show different ways they could group or represent it (Appendix 3).

Further instructions:

Students complete these activities within a 50- or 60-minute session.* The teacher should familiarise themselves with the rubric and the teacher guidelines. The teacher collects work samples. The teacher maps students’ work against the rubric.

Evidence collected from this task student work samples (completed worksheets) teacher observation checklist based on rubric

*See Teacher reflections in this document about increasing this time for Year 1 students.

© VCAA



Interpreting evidence of student learning Evidence collected from each student was mapped against the rubric:

The quality criteria that were achieved was shaded in blue. The phase that the student is ready to learn next was shaded in green.

Please note, the following annotated student work samples are representative examples only.

Setting the sceneThis formative assessment task was implemented in one regional and two outer metropolitan Primary schools.

The task was presented to Years 1 and 2 and delivered at the very beginning of a multiplication unit in a one-hour Mathematics lesson.

The task was given verbally to those students who had trouble reading.

Students were allowed to show or speak answers rather than record (write or draw) them.

Sample 1

© VCAA




Sample 1: Evidence of student learning

Annotations 1.1 – The student demonstrated they could skip count by 2s to 24, 5s to 60, and 10s to

120.

Insufficient evidence:

2.0 – The student could make and draw 5 groups of 2 and work out how many altogether. She could also explain her thinking; however, she could do this only for 5 groups of 2. Her representations of 3 groups of 5 and 4 groups of 10 were incomplete.

3.0 – The student did not represent the groups accurately so was not able to demonstrate how she solved the problem.

What is the student ready to learn next?The student was assessed as ready to learn Phase 1 next. She could accurately and confidently skip count by 2s, 5s and 10s but when applying this information to the second part of the task, she encountered some challenges. She didn’t have the same confidence in her approach to using concrete materials. She was on the right track with her thinking in making the initial group; however, she had difficulty making and drawing groups beyond this.

It is important to ensure that the next phase of learning is based on using skip counting and repeated addition to count collections.

Any feedback given

The student was encouraged to focus on making the groups with counters or Unifix – represent the problem first and then draw it. This will help the student to work out how many counters there are altogether. Thinking about how this problem was solved is really important for future learning.

© VCAA



Sample 2

© VCAA


2.2. Can make equal groups and find the total by skip counting





Annotations 1.2 – Student demonstrated ability to skip count various amounts. 2.2 – Student can make equal groups and count the totals by skip counting. 3.3 – Student demonstrated the ability to model and write the strategy they used to

solve the problem.

The student is beginning to think about other ways to group objects and justify their thinking; however, there was insufficient evidence to show that this was beyond skip counting or grouping by 1s.

It may be that the student does not have the necessary skills yet to construct an array or use a strategy beyond skip counting.

What is the student ready to learn next?The student was assessed as ready to learn Phase 3 next. The student is able to write and model the skip counting strategy they used to solve a problem. The next step for this student is learn about arrays and how to represent groups and multiplication as an array. She also needs to learn efficient strategies beyond skip counting to solve problems.

Any feedback givenFeedback was given to the student about the next step in their learning. It was explained to the student that they do an excellent job at skip counting and using that strategy to make equal groups and find the totals. The next step is to learn about arrays and other strategies that they could use to solve problems such as doubling, using repeated addition and multiplication facts.

© VCAA



Sample 3

© VCAA







Annotations 1.2 – Despite encountering some difficulties completing the skip counting pattern

activity, the student demonstrated skip counting by various amounts (2s, 5s and 10s) when making and totalling different groupings. The student has clearly achieved this criteria despite possible literacy issues affecting the previous section.

2.2 – Student made equal groups and skip counted by the amount within each group. 3.3 – Student was able to clearly identify how they skip counted and modelled this with

written sentences.

What is the student ready to learn next?The student was assessed as ready to learn Phase 3 next. The student needs to demonstrate they can use arrays to group objects.

Any feedback given

When recording skip counting patterns it is important to match this to oral skip counting. If the student can skip count orally the next step is to record this thinking. Using a range of efficient strategies to solve problems is our next focus.

© VCAA



© VCAA

3.4 Justifies any efficient strategy to solve problems beyond skip counting, such as multiplication facts, doubling, additive facts





Annotations 1.2 – Student demonstrated skip counting by various amounts. 2.2 – Student made equal groups and skip counted by the amount within each group. 3.4 – Student showed multiple ways to employ repeated addition, implying that they have

at the very least a basic understanding of the multiplication process as an efficient strategy. Further teacher judgment and discretion will be required in assessing and confirming this, most likely by asking the student to verbally explain or justify how their repeated addition number sentences were determined.

What is the student ready to learn next?Further data is needed to make an on-balance judgment about the phase at which the student has demonstrated achievement.

No arrays were drawn or described (criterion 2.3); instead discrete groupings of items were used. It must be considered that the student may or may not have this skill, as the task did not explicitly require the use of arrays.

The student is ready for the conventions and language of multiplication, as displayed by their confidence grouping various collections by applying different skip counts for solving (2s, 5s, 10s) as well as representing repeated addition. The next step is to arrange groupings into rectangular arrays to explore a greater range of efficient strategies (doubling, splitting arrays, etc.)

Any feedback given

The use of skip counting was an efficient strategy that was applied correctly and groups were made equally. Repeated addition is an effective way to group and this should continue to be used and encouraged as new multiplication learnings are introduced. One of the next steps is to use an array to group objects.

© VCAA



Using evidence to plan for future teaching and learningThe data gathered when implementing the task showed how well students connected skip counting to objects and groups and the recording of skip counting patterns provided an insight into the disconnect between skip counting verbally and continuing the pattern.

The data provided opportunities to focus on differentiation and to target future teaching.

Teacher reflectionsThe task really provided a snap shot in time of what the students can and can’t do.

For Year 1 students it took longer to complete Parts 1 and 2, with only a handful of students attempting Part 3. We would recommend more time for these students or provide another opportunity to attempt Part 3.

Part 3 proved difficult to understand for some students. We would recommend additional teacher instruction and providing extra materials.

When using the rubric again it would be up to the discretion of the teacher as to how and when they use Part 3 or if they use it as an extension task only.

Teachers could use these tasks for Years 1 and 2 but also for high-achieving Prep students. Part 3 could be used for Year 3 students.

© VCAA



Appendix 1 – Skip counting patternsContinue these number patterns.

0, 2, 4, 6, _____, _____, 12, 14, _____, _____, _____, 22, _____

0, 5, 10, 15, ____, _____, 30, 35, _____, _____, 50, _____, 60

0, 10, 20, _____, 40, _____, 60, 70, _____, 90, _____, 110, _____

© VCAA



Appendix 2 – Making groups

Make Draw it How many altogether? How did you work it out?

5 groups of 2

3 groups of 5

4 groups of 10

© VCAA


using formative assessment rubrics in mathematics · web view1.1 – the student demonstrated they...

Documents