Assignment Coversheet

Student Name Rachel Dunne

Student ID number U3o44572

Unit name Mathematics Education 2

Unit number 6897

Name of lecturer/tutor Greg Taylor

Assignment name Programming

Due date 19th April 2013 5.30pm

Student declaration:

I certify that:

the submitted assignment is my own work and no part of this work has been written for me by any other person;

all material drawn from another source that has been referenced in APA style.

Signature of student: Rachel Dunne

Date: 19.4.13

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MATHEMATICS EDUCATION 2: ASSESSMENT 2 – PROGRAMMING CONTENTS

Rationale…………………………………………………………………………………………………..2Data Analysis from pretest…………................................................................4Length across curriculum concept map…………………………………………………….5Planning placemat…………………………………………………………………………………….6TPACK model…………………………………………………………………………………………….7Length Overview……………………………………………………………………………………….8Week 1 programme………………………………………………………………………………….9Week 2 programme………………………………………………………………………………….11Appendices

Appendix 1 – KWL Chart…………………………………………………………….13 2 – Measurement recording tally sheet …………………….14

3 – Question Cards……………………………………………………..15 4 – Rich Task Scenario…………………………………………………16 5 – Planning Sheet………………………………………………………17 6 – Marking checklist………………………………………………….18 Mathematics assessment criteria…………………………19 7 – Evaluation Sheet……………………………………………………20

References ………………………………………………………………………………………………21

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RATIONALE

This programme is designed to develop and extend students mathematical understanding, knowledge, thinking and language through the incorporation of a dynamic inquiry based authentic mathematics curriculum. The lessons are designed to be less transmittal than traditional pedagogy, developing students communication and reasoning skills (Maths 300, 2010).

The programme looks to incorporate Muir’s (2008a as cited Siemon, Beswick, Brady, Clark, Faragher & Warren 2011) 6 principles of effective mathematics teaching. Those being; making connections, challenge all students, teach for conceptual understanding, purposeful discussion, focus on mathematics and positive attitudes. This has been incorporated through the challenging rich task, the in depth focus on length as a foundational concept for students to build from, importance placed on group and class discussion and the teachers’ and students engagement and enjoyment in the task and challenges.

These principles relate directly to the Pedagogical Content Knowledge (PCK) and Technology Pedagogy and Content Knowledge (TPACK) models. The pedagogical knowledge is demonstrated within the approaches to teaching, the differentiation and the varied assessment strategies. The Knowledge of students is evident within differentiation, meeting student’s individual needs, including students with misconceptions as identified through their errors in the pretest (page 3) and all students other students within the class. This also incorporates background knowledge of students, cultural understanding, knowledge of preferred learning style, ability to work in a group and student’s language and communication skills. Content knowledge and more specifically the knowledge quartet (Rowland et al., 2009 as cited by Turner, 2013 p.78) involves

Foundation- teachers subject knowledge and beliefs about mathematics. Transformation – How trainees are able to transform what they know and make it accessible to children Connections – decisions about progressions, sequencing in learning, conceptual connectivity within the lesson, including the relationship to previous lessons and prior knowledge. Contingency – The ability to respond to the unexpected such as child’s questions and responses.

Whilst content knowledge cannot be planned for within this programme, it is evident within the planning of the programme, the sequencing of lessons, the depth given to length as a foundational concept of measurement. The scaffolding of students, the use of questions and the connections to previous lessons all involve content knowledge. The teacher’s beliefs and attitudes to mathematics relate not only to the teacher and how they teach mathematics but also by extension the students and their positive attitude or lack thereof (Potari & Georgiadou-Kabouridis, 2009). This link between content knowledge and pedagogical belief underlie the programme. This programme has attempted to incorporate technology through the use of manipulatives, resources and tools to assist students through their development phases of learning and support the pedagogical style of the teacher (page75).

Incorporated within PCK is the belief and attitudes towards language as a critical component of mathematics (Hawkins, 2012, Siemon et., al. 2011 & Turner 2013). The strong emphasis placed on language development is evident throughout each lesson. For conceptual understanding to take place students need to be given the opportunity to explore, investigate, explain, elaborate and identify links, relationships, ideas and patterns. This cannot occur in isolation but rather within a meaningful and social context. The programme is designed to encourage this,

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the teacher being the facilitator of learning, by providing students with opportunities and situations that are within their zone of proximal development. This is done through the scaffolding of students into these challenging tasks and providing them with the skills and strategies necessary to relate the concepts to real world applications – transferability.

This transferability relates to how mathematical concepts are used within other curriculum areas (page 5). By acknowledging the links in all areas of the curriculum students begin to identify how and where mathematics fits within everyday life. For some students this is an innate idea for others they need to be encouraged to make these links in order to appreciate WHY mathematics is important and useful. The ongoing discussion throughout the lessons focus on real world context these discussions are to encourage this beyond the classroom thinking.

Throughout all lessons differentiation has been planned in formal ways but will often be carried out informally in addition to this. The formal differentiation acknowledges the students misconceptions as identified through the pretest (page 4) and scaffolds and supports them to meet the outcomes of the lesson. In addition to this informal differentiation will occur through the use of questioning. The incorporation of starter questions, questions to stimulate mathematical thinking, assessment questions and final questions (White,Way, Perry & Southwell. 2006) promotes higher order thinking. Through changing the verb in the question all students can be working on the same task at their level of operation (can you identify/classify/demonstrate/examine/design or appraise). This form of differentiation also allows students to demonstrate their understanding without limitations, allowing for a more qualitative assessment strategy.

The range of assessment strategies incorporated are to reflect the varied forms of assessment, the purpose of the assessment, the content being assessed and the varied learning styles of the students. The formative assessment is designed to be ongoing and allow for the teacher to make timely, specific and constructive feedback to the student in addition to informing the teacher of the students understanding and prior knowledge and the effectiveness of the teaching strategy employed. The assessments as learning tasks are designed to encourage metacognition, to promote students critical thinking in regards to their own ideas, strategies and understanding. The assessment of learning is designed to allow the students to demonstrate through authentic application, the knowledge, understanding, processes and skills. Feedback should be given to students in regards to all areas of assessment, enhancing students learning and reducing the gaps in their knowledge and understanding (Hattie & Timperley, 2007).

The design of the programme is sequential and the format is in a day by day structure. It is acknowledged that whilst all lessons are planned to be 60 minutes long (including warm up and closure) that some of these lessons may roll into each other. The nature of the student lead approach adopted within this programme sees value in letting students continue to explore concepts as necessary rather than moving into the next lesson in the sequence due to time. Obviously this timing would be negotiated by the teacher through observation of the students and their engagement in addition to other timing factors.

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DATA ANALYSIS FROM THE PRETEST 2 WATSON

Measurement An

toni

Bren

da

Brig

id

Cath

Chris

Chris

tine

Henr

y

Jack

Jean

nie

Jess

ica

Jodi

Joe

John

ny

Katie

Kier

an

Leo

Lilli

meg

an

Mel

anin

e

Mel

issa

Mic

hael

Paul

Scott

Tim

Consistently align objects correctly when comparing length 13Consistently fills measuring cup when measuring capacity

  10

Consistent 1 to 1 correspondence

  5

Consistently records o'clock times on an analogue clock

  11

Correctly Identifies the hands on a clock

  9

Accurately positions hands on an analogue clock for half past the hour

 

14Correctly orders the months of the year

  6

Can name the months of the year

  3

Accurately match events to appropriate duration

  6

Demonstrated Not evident

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Key:

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Length integrated across curriculum areas

Curriculum links

Curriculum links

Curriculum linksCurriculum links

How and where length will be used

How and where length will be used

How and where length will be used

How and where length will be used

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PLANNING PLACEMAT

Experiencing Applying

KNOWN

Drawing on learner prior knowledge and experience, personal interests, life worlds, the everyday and the familiar, and making connections to self. Warm-up activities and establishing baseline knowledge.

NEW

Introducing learners to a new experience by exposing them to new concepts and ideas, ensuring they can respond openly. Modelling, demonstrating and working with concrete materials.  Newman’s Prompts.

APPROPRIATELY

Applying independently what has been taught and providing assessment activities. It involves transformation, reinventing or revoicing the world in a new way and problem-solving.

CREATIVELY

Doing things in interesting ways by independently taking knowledge and capabilities from one setting and adapting them to a different setting. Problem-solving in unusual ways & creating problems to solve.

Diagnostic assessment

Concept map about measurement

Students KWL chart

Using checklist criteria to develop key conceptsMathematical languageQuestioning

Written responses

Measurement of objects

Approach to measuring height

Planning for the rich task

Conceptualising Analysing

NAMING

Identifying/defining new concepts/ideas/themes/, vocabulary, and number strategies. Focusing on

terminology, rules, definitions, and explaining processes and strategies. Modelling. Demonstrating.

THEORISING

Generalising and synthesising

concepts by linking and drawing them together. Practising to reinforce understanding & reflecting on how a strategy helps number solving. May include

‘what if’ scenarios.

FUNCTIONALLY

Examining structure and function in context. What is it for? What does it do? What are the effects? How does it work? Looking at the literacy of maths and mathematical grammar e.g. symbols, equations.

CRITICALLY

Interrogating purpose and audience, and individual, social, cultural and environmental effects. Who

gains, who loses with this mathematical knowledge?  What is its relevance?

Explicit teaching through Modelling, Sharing and Guiding

Measurement of objects

Recording of objects

Creating the ruler

Choosing appropriate units of measurement

Explaining the relationship between the size of the unit and the amount of units

Group discussions – language

Real world context for length

Rich task activityAppropriate units

Strategies used

Evaluation of strategies

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TPACK MODEL (Learning with Technology; retrieved from http://learnonline.canberra.edu.au/portfolio/view/artefact.php?artefact=17977&view=4915)

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TOPIC: Measurement (Geometric and spatial)

LEARNING OUTCOMES: Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037)

MATHEMATICAL LANGUAGE:

Measure, Size, Length, Longer, Shorter, Bigger, Smaller, Area, Volume, Capacity, Record, Compare, Attribute, Uniform, Mass, Distance, end, end-to-end, side-by-side, gap, overlap, measure, estimate, hand span, straight line, curved line, metre, centimeter, record, tally

RESOURCES: Butchers Paper, worksheets (appendices), Text the long red scarf, variety of strips of red crepe paper, paddle pop sticks, paperclips, sticks, skipping ropes, strips of card, chalk, string, paper, straws, jacket, white board, bluetac, markers, students pencils,

PRETEST ERRORS FOCUSED ON: Error 1: Did not consistently align objects correctly when comparing lengths. (Lessons 1, 2, 3, )

Error 3: Child miscounted frequently causing errors in the reporting of their measurements (All warm up activities and Lesson 3, 4)

ASSESSMENT:Assessment for learning

Type Lesson #Observations and anecdotal evidence Record on checklist. Student’s comments, language, strategies, contributions and engagement. All

Work samples Students’ written responses to questions, concept map, planning sheet and their ruler. 1, 2, 4, 5, 6, 8, 9 Assessment as learningWork sample KWL Chart, planning sheet, evaluation sheet 1, 8,9,10Observations Group discussions, questioning, open ended tasks AllAssessment of learningObservations and anecdotal evidence Record on checklist. Conceptual understanding, language, application of ideas and concepts. 7,8,9,10Presentations Summative presentation of planning, pattern and evaluation 10Interviews During the presentation interviewing questions and responses. 10Work sample Evaluation and planning sheet and created pattern. 10

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WEEK 1 MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY

Mathematical Content / Learning Intention

Identify types and uses of measurementIntroduce and explore mathematical language

Compare and order objects through direct comparison.Identify key concepts of measuring length.

Introduce indirect measurement through appropriate informal units

Develop understanding of indirect measurement and introduce appropriate units.

Develop and deepen understanding of indirect measurement and appropriate units.

Warm up activity Number card activity 0-11 Group activity – buzz Number card activity – one away

snapGroup activity – Buzz 2’s and 5’s

Number card activity (pairs) - Calling pairs to 10 whilst scrolling through the deck

Teaching strategies

Concept map of measurementPrompting questions: What is measurement?What do we measure? How do we measure?Why do we measure?

As a class start the brainstorm with what is measurement?In mixed ability groups to create a concept map for the other 3 questions. (2 groups could work on each question)Share as a class using a round robin strategy.

Ideas collected should include measurement in the forms of length, area, volume, time, calendar and seasons (Teachers prompts may be needed)

Ask students to create a KWL chart (appendix 1) on

Read text: The long red scarfAsk students how this text relates to their maths focus. (measurement / length)Group activity: students are given strips of red crepe paper of varied lengths as their ‘scarf’. Students then in their groups compare and order the ‘scarves’. As the groups are working challenge students perceptions through moving the paper, for example; changing the alignment, position the paper diagonally, curve the paper (conservation). Ask students why this changes? Why is that important?Students attach their strips in order (smallest – largest) to a sheet of butchers paper with bluetac.

Recap previous session and hand back butchers paper with scarves. Students discuss the techniques they used to compare the lengths of the scarves. Explain the new challenge ‘to compare and order the whole classes scarves’. The trick is that they can’t leave their desk!Brainstorm how this might be achieved. (Estimation & indirect comparison through an instrument).As students decide the need to use ‘something’ explain that for this activity they will be using paddle pop sticks (PPS). Before they start refer back to the previously developed criteria. Paying particular attention to starting points and alignment. Highlight the starting point for the first PPS (model laying PPS end-to-end as on top of the scarf on the board), ask students then where the second PPS would start from. Why? Challenge students perceptions (gaps and overlaps). Add newly

If possible leave the scarves from previous lessons up. Recap the closure from previous lesson. Would you get a different answer if paper clips were used? What about shoes? Sticks? Skipping ropes? Why?Have students complete the task from the previous lesson with different objects (paperclips, shoes, sticks, skipping ropes). Have the students record the number of objects used on a tally sheet (Appendix 2). As previously done have shoulder buddies check students measuring and counting.Have the whole class compare and order the scarves on the board. Are they able to compare and order the scarves in the same way? Are they correct? What

Recap previous lesson and the differences identified between accuracy when using different objects. Why is it important? How would being able to accurately measure something be useful outside the classroom? Do you think you will ever need to measure anything accurately? What? What will happen if you don’t measure accurately?In mixed ability groups have students answer questions based on the above from the question cards (appendix 3). Remind students that they will be presenting to the class.Have students present back to the whole class. Adding information to the measurement criteria as necessary.

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measurement. (students will have had previous exposure)

Use the concept map to construct a word wall for further mathematical language development in additional curriculum areas. Discuss words as they are added, students to share words they are familiar with.

Each group shares their findings. As students verbalise their strategies and ideas (child’s language) paraphrase using mathematical language to help reinforce and encourage students’ ownership of specific mathematical language.As a whole class start a checklist of criteria for accurate measurement – same starting point, consistent direction, straight lines v curve lines. Explain that this will be added to over the lessons and incorporated in literacy (procedural writing).

investigated information to the criteria. At desks students measure their scarf in PPS (as modeled). As students discover that the PPS don’t fit exactly introduce fractions (parts of). Have students count the number of PPS. When confident (no gaps or overlaps, correct number) have their partner check. As a whole class work through the comparison of all scarves. Start at 1, anyone have 1 PPS and continue (smallest number first). Attach them to the board as a visual. Was the class correct? How do you know? Would you get a different answer if paper clips were used? What about shoes? Sticks? Skipping ropes? Why?

differences do they notice? (Leading into appropriate units). Why would this be important?

Differentiation *Mixed ability enables students operating at different to share (peer learning and tutoring)*Concept map before the KWL chart enables all students to have some level of prior knowledge. *Students operating at a higher level will have much deeper replies particularly to what they want to learn.

*Manipulatives to assist visual and kinesthetic learners.*Challenging students perceptions & students verbalising responses will clarify measurement criteria & assist them in making connections (students Error 1) *Asking of questions; why is this important? Promotes deeper thinking (synthesis and evaluation level)

*Connection to previous lessons and checklist criteria to assist all learners with particular focus on error 1 students. *Use of ‘challenges and tricks’ to engage students and extend deeper thinking.*questioning and discussion to promote language and context to enable students to relate the content.*Intra personal, interpersonal, visual, kinesthetic learners catered for through group and individual work.

*Reflection on previous lesson to strengthen connection to prior learning.*Use of the same object being measured with varied units enables students to explore the units in a familiar context.*The questioning allows students to operate and answer at the level they are operating at.*Recording, counting and checking (students error3).

*Connection to real world context and background information. *Students have been scaffolded into the questions through previous lessons. *The questioning provides students with an opportunity to demonstrate their level of transferability.*Group discussions with peers promote mathematical language development.*Students struggling to respond will be supported and prompted by the teacher through redirection.

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WEEK 2 MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY

Mathematical Content / Learning Intention

Developing an understanding of structure of repeated units by making their own ruler based on paperclips or PPS (NSW DET 2009. p42.)

Apply understanding of structure of repeated units and indirect measurement to measuring the height of a student.

Indirect measurement of a student using uniform, informal units of measurement to make a jacket. (rich task)

Indirect measurement of a student using uniform, informal units of measurement to make a jacket. (rich task)

Presentation and evaluation of the jacket that the students made.

Warm up activity

Number bingo Heads and tails / odds and evens

Number card activity – one away snap

Group activity – Buzz 2’s and 5’s

I’m thinking of a number…

Teaching strategies

Revisit previous lesson. Discuss how, when & why we use different units to measure. (Appropriate units).Explain that the students will make their own ruler based on paperclips or PPS and then measure objects around the classroom. Students will align the paperclips or PPS end to end (no gaps or overlaps point out the criteria previously developed) on a strip of paper, marking each paperclip. Create a ruler that has 10 paperclips or PPS. Model this on the board, highlighting the alignment and marking of the units (where to write 1). Students to create their rulers individually or in pairs. As students measure objects & record measurements refer to

Revisit previous lesson, highlighting the concept of structure of repeated units.Explain that the task today is to measure and compare the height of all the students. “The challenge is that must use the ruler that you have made however you can’t use it on the student” (demonstrate using it directly to measure student’s height). Provide students with a range of resources including chalk, paper, string etc. Remind students to record their measurement and their strategy. Students to work in small groups or pairs using roles based on the primary connections model (director, manager, speaker which is familiar to students).

Recap all content covered on length.Particular focus on the previous day’s lesson when measuring height. Strategies used & how they worked.Introduce the rich task. Set the scenario (Appendix 4). You are a suit maker and you are going to make a jacket but first you need to make a paper pattern (show a paper pattern). Explain before you can make the pattern you need the measurements. Ask students what they would need to measure to make a jacket (have a jacket as a model for a visual prompt). Ask students what they think will be challenging to measure? What strategies might they use? Remind students that not all the measurements are straight lines. How would they measure them? Students will need to work with a partner to take the measurements

Discuss the rich task. How are students going? What challenges have they had? Strategies they have used?Remind students that they will be presenting their patterns and their planning to the class. And to think about that as they are working. What will they say etc. Continue with the individual work. (Although the work is individual students can still talk and discuss the task)

Students will complete an evaluation worksheet (appendix 7).Students present their planning, pattern and discuss their evaluation and reflection. Other students and the teacher can ask questions. Students complete the L in their KWL chart.In a circle time fashion share something from that L column of the KWL chart and a profession or job that you know would use measurement.

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the measurement criteria again, highlighting the starting point as 0, record measurement correctly (15 paperclips), how to calculate the total length when the object is longer than the ruler.Report back to the class. Discuss the rulers, how they made them, any challenges, why a ruler is useful. Compare the length of an object when measured by the 2 different rulers.

Students to present back to the class. The strategy they used, what worked, what didn’t work?Write students names up in order from shortest to tallest in accordance with the recorded measurement. Teaching point – some students will be measured with PPS rulers and others with paperclip rulers. This may have been brought up early by perceptive students. This may be worked out by either having 2 separate comparisons or introducing how many paperclips to PPS.

but they will work individually for the rest of the task.Explain the planning sheet (appendix 5) as a way of recording their measurements and strategies. As students are working record observations on the checklist (appendix 6) paying particular attention to language used, synthesis of ideas and concepts, context of length within the task as a real world example in addition to attitude and engagement.

Differentiation*group, pair and individual work to support learners still struggling with concepts in addition to students learning styles. *creation of a ruler as a hands on application of previous understanding (no gaps or overlaps, starting points & alignment) and as a visual representation of repeated units to support students particularly error 1 students.

*Students have been scaffolded and supported into the activity through previous lessons.*Explicit criteria, high expectations and feedback will assist students to think deeply about the problem and begin to analyse and apply their new knowledge.*Open-ended problem solving activity will allow students to approach the question in a variety of ways depending on the learning style including prompting creative thinking.

*Scaffolding of students leading into the activity.* visual reference points – the measurement criteria, word wall, the red scarves on the wall, the scenario on the board, the jacket, the rulers. All help students to make connections to the learning from previous lessons.*Active listening and redirection, allowing the student to come to the answer themselves through thoughtful facilitation.*Opportunity to experiment, apply. Analyse, synthesis and discover will deepen all students understanding.

*Scaffolding of students leading into the activity.* visual reference points - help students to make connections to the learning from previous lessons.*The explicit connection to real world context to enable students to see the concept of length as relevant will assist some students.*The timeline, preempting any stress associated with presenting, providing them time and preparing students for that.

*Allowing students to plan, present and evaluate in style comfortable to them. It could include concept maps, think boards, lists, diagrams.*Students may feel more comfortable presenting their piece with their partner. *The questions asked by the teacher can vary depending n the verb used based on Bloom’s taxonomy – switching the focus from remember and understanding to synthesis and creating.

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Appendices: Appendix 1

KWL ChartK – What I know W – What I want to know L- What I learnt

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Object Unit of measurement

Estimation Tally Answer How close was the estimation?

Appendix 2

Measurement recording tally sheet

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Appendix 3

Question cards

Why is measurement important?

How would being able to measure something accurately be useful

outside the classroom?

Do you think you will ever need to measure anything accurately?

Why or why not?What would you need to

measure accurately? What would you

measure that doesn’t need to be precise?

What might happen if you can’t measure

something accurately?

How do you know which units of measurement to

use?

Appendix 4

Rich task scenario16

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You are a suit maker and an important customer named John comes into your shop. He wants to get a suit made that fits him perfectly; he will pay $300 for it if it fits. You don’t have any suits that fit him so you need to make a new paper pattern before you can make the suit. Your task is to create a paper pattern. You will need to work out: What measurements you need to make

How you will make the measurementsWhat units of measurement you will use

Then using butchers paper make the pattern.Appendix 5

Planning Sheet

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What do I measure?

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The unit of measurement I am using

is_______________________

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Appendix 6 Marking checklistSt

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AntoniBrendaBrigidCathChrisChristineHenryJackJeannieJessicaJodieJoeJohnnyKatie KieranLeoLilliMeganMelanieMelissaMichael PaulScottTimKey O = Observations, I-interview, WS = work sample, AE = Anecdotal evidence, P = Presentations, OET = ended task

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MATHEMATICS ASSESSMENT CRITERIA YEAR 2 (ACRAR, 2011)

students recognise increasing number sequences involving 2s, 3s and 5s.

Date Students count to and from 1000 Date

students recognise decreasing number sequences involving 2s, 3s and 5s.

They perform simple subtraction calculations using a range of strategies

They represent multiplication by grouping into sets They perform simple addition calculations using a range of strategiesThey represent division by grouping into sets They divide collections and shapes into halves, quarters and eighthsThey associate collections of Australian coins with their value Students order shapes and objects using informal units.Students identify the missing element in a number sequence They tell time to the quarter hour Students recognise the features of three-dimensional objects They use a calendar to identify the date and the months included in seasons.They interpret simple maps of familiar locations They draw two- dimensional shapesThey explain the effects of one-step transformations They describe outcomes for everyday eventsStudents make sense of collected information Students collect data from relevant questions to create lists, tables and

picture graphs.

Understanding Fluencyconnecting number calculations with counting sequences counting numbers in sequences readilypartitioning and combining numbers flexibly using informal units iteratively to compare measurementsidentifying and describing the relationship between addition and subtraction

using the language of chance to describe outcomes of familiar chance events

identifying and describing the relationship between multiplication and division

describing and comparing time durations

Problem solving Reasoning formulating problems from authentic situations known facts to derive strategies for unfamiliar calculationsmaking models and using number sentences that represent problem situations

comparing and contrasting related models of operations

matching transformations with their original shape creating and interpreting simple representations of data

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Appendix 7

Evaluation sheet

Making a pattern for a jacketWhat strategies did I use? ________________________________________________________________________ ________________________________________________________________________________________________What worked well? ______________________________________________________________________________What didn’t work?_______________________________________________________________________________Did I achieve what I wanted?_____________________________________________________________________What was the hardest part?______________________________________________________________________

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What would I change next time?__________________________________________________________________

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REFERENCES

ACT Department of education and training. (2007), Every chance to learn, Curriculum framework for ACT schools

Australian Curriculum Assessment and Reporting Authority (acara), 2009 The Australian Curriculum, Mathematics. Retrieved from: http://australiancurriculum.edu.au

Board of Studies: NSW. (2006) Sample Units of Work: Mathematics K-6. Board of Studies NSW; Sydney.

Hattie, J., & Timperley, H., (2007). The Power of Feedback. Review of Educational Research. March 2007, Vol.77, No.1. pp81-112. DOI: 10.3102/003465430298487. Retrieved from University of Canberra E-reserve.

Hilton, Nette (1987) The Long Red Scarf, Omnibus Books, Adelaide (in association with Penguin Books Australia Ltd), ISBN 0 949641 73 1. Illustrated by Margaret Power.

Maths 300 (2010). Education Service Australia. Retrieved from http://www.maths300.esa.edu.au

Reys R.E., Linquist M.M., Lambden D.V., and Smith N.L., 2009. Helping Children Learn Mathematics. 9th Edition,John Wiley & Sons, Inc.: New York.

Siemon, D., Beswick, K., Brady, K, Clark, J, Faragher, R. & Warren, E. (2011). Teaching Mathematics: Foundations to Middle Years, Oxford University Press: South Melbourne

Potari, D & Georgiadou-Kabouridis, B. (2008) A primary teacher’s mathematics teaching: the development of beliefs and practice in different ‘supportive’ contexts. Journal of Mathmatics Teacher Education. Issue February, 2009. Retrieved from: http://web.ebscohost.com.ezproxy1.canberra.edu.au/ehost/pdfviewer/pdfviewer?sid=8f60943d-50c1-4ab7-839a-cea063054a1e%40sessionmgr115&vid=2&hid=125

White, A., Way, J., Perry, B. & Southwell, B. (2006). Mathematical Attitudes, Beliefs and Achievement in Primary Pre Service Mathematics Teacher Education. Mathematical Teacher

Education and Development, 2005/2006, vol 7, 33-52. Retrieved from: http://search.informit.com.au.ezproxy1.canberra.edu.au/fullText;dn=165094;res=AEIPT

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