Mathematical Understandings Profile of The Child Education and Teaching Mathematics Case Study

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Education- numeracy skills in primary school (year 2) according to Australia's curriculum

Need to get a High Distinction for this paper. I can be contacted at all times if you have any queries. To do the assignment you will need to watch all videos first as it is part of the assignment( I will send you link to dropbox or via filehosting), you will also need to refer to Australia's school curriculum. I also attached the mathematics online interview booklet and the other materials mentioned in the question. I will continually work closely with you with regards to more relevant resources. The rubric is attached and the academic writing should be tailored for a High distinction essay! Thank you!

Assessment 1 Details from the Unit Outline

1. Case Study 50%

Examine and analyse a video assessment involving a child in an early year’s classroom. From the video and annotations, interpret the mathematical ideas and teacher comments to develop a mathematical understandings profile of the child being assessed. Provide detailed information on how the data was analysed (such as links to the relevant curriculum documents) to justify the findings. Create mathematically-focused feedback that could be shared with the child and create a report that would be suitable for parents including suggestions for future learning needs based in the classroom and play based family activities that will assist the child’s future mathematical understanding.

Additional Details

The aim of this assessment is for you to determine what a child’s mathematical understandings are based on the use of the Online Interview Booklet (Victorian Department of Education, Employment and Training [VDEET], 2001). The full Online Interview Booklet is available from the Reading List under Topic 1. Read through the Online Interview Booklet so that you develop an understanding of the interview process and the Online Interview Record Sheet. Note that not all of the Australian Curriculum: Mathematics is addressed by the Online Interview Booklet and that only a sub-set of the sections will be considered for this assessment. Videos of an educator completing specific sections of the Online Interview Booklet and the completed Online Interview Record Sheet for those sections are to be analysed to develop a mathematical understandings profile of the child.

The sections focused on will address the strand Number and Algebra (though note not all of the Strand is addressed). The Online Interview videos are available from the Maths Video menu item, specifically (attached):

Section A Counting
Detour
Section B Place Value
Section C Strategies for Addition and Subtraction
Section D Strategies for Multiplication and Division
The completed interview schedule for these videos is available from here Completed_Interview_Record_Sheet_Sections_A_to_D.pdf (note that the Detour is within Section A Counting, after Question 1 and before Question 2, as indicated by the purples lines and text).

Mathematical Understanding Profile

Identify what mathematics the child understands and what mathematics the child could not do (that is, may not understand). Base this on the evidence from the Online Interview videos and the completed Online Interview record sheet. Connect the evidence from the Online Interview video and completed interview record sheet (for example, question/s) to specific content descriptors from the Australian Curriculum: Mathematics. Justify points being made by referring to academic literature (for example, what is provided in the Reading List). Remember that not everything is addressed in the interview, so ensure assumptions are not made – evidence must be used. This should be written in third person.

Mathematically-focused feedback for the child

Craft what you would say to this child regarding the mathematical understandings they have identified. Again, this must be based on evidence from the Online Interview video and completed interview record sheet. Use terminology the child can understand. Consider both the mathematical understandings and the mathematical disposition the child demonstrates during the Online Interview video (for example, did they look confident, hesitant, concerned, worried). Make sure that feedback addresses both what the child could do and what they could not do, maintaining a presentation that enables the child to build a positive mathematical self-efficacy (that is, that they are able to do maths) and disposition towards mathematics (that is, they are willing to engage and persevere). This should be written in second person (ie., using ‘You’ when writing).

Report for the parents, including suggestions for future learning needs based in the classroom and play based family activities that will assist the child’s future mathematical understanding

Identify what the child could do and what the child needs to work on. Link this to specific mathematical terminology from the Australian Curriculum: Mathematics (such as you would find in the content descriptors and elaborations). Link what the child could do to activities to maintain and/or strengthen further and what the child needs to work on to activities that would develop these understandings. Emphasise the importance of the child’s mathematical self-efficacy and mathematical disposition. Support your explanations with references to academic literature (for example, what is provided in the Reading List). Use reputable sources for activities that are suggested [Note that a formal learning experience plan is not required for this assessment, just a range of targeted activities] such as the following resources made available under Topic 1 in the Reading List:

The First Steps in Maths series of books;
AAMT website links to sources such as maths3000, reSolve, and top draw teachers;
NCTM Illuminations website;
NCETM website.
This should be written in a mixture of first, second, and third person (for example, third person when considering what was found, first person when sharing your interpretation of what was found, and second person when providing suggestions for what the parents could do).


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Assessment 1 Details from the Unit Outline 1. Case Study 50% Examine and analyse a video assessment involving a child in an early year’s classroom. From the video and annotations, interpret the mathematical ideas and teacher comments to develop a mathematical understandings profile of the child being assessed. Provide detailed informati on on how the data was analysed (such as links to the relevant curriculum documents) to justi fy the findings. Create mathematicallyfocused feedback that could be shared with the child and create a report that would be suitabl e for parents including suggestions for future learning needs based in the classroom and play based family activities that will assist the child’s future mathematical understanding. Additional Details The aim of this assessment is for you to determine what a child’s mathematical understanding s are based on the use of the Online Interview Booklet (Victorian Department of Education, E mployment and Training [VDEET], 2001). The full Online Interview Booklet is available fro m the Reading List under Topic 1. Read through the Online Interview Booklet so that you de velop an understanding of the interview process and the Online Interview Record Sheet. Note that not all of the Australian Curriculum: Mathematics is addressed by the Online Interview Booklet and that only a subset of the sections will be considered for this assessment. Videos of an educator completing s pecific sections of the Online Interview Booklet and the completed Online Interview Record Sheet for those sections are to be analysed to develop a mathematical understandings profile of the child. The sections focused on will address the strand Number and Algebra (though note not all of t he Strand is addressed). The Online Interview videos are available from the Maths Video me nu item, specifically: • • • • • Section A Counting Detour Section B Place Value Section C Strategies for Addition and Subtraction Section D Strategies for Multiplication and Division The completed interview schedule for these videos is available from here Completed_Intervie w_Record_Sheet_Sections_A_to_D.pdf (note that the Detour is within Section A Counting, a fter Question 1 and before Question 2, as indicated by the purples lines and text). Mathematical Understanding Profile Identify what mathematics the child understands and what mathematics the child could not do (that is, may not understand). Base this on the evidence from the Online Interview videos an d the completed Online Interview record sheet. Connect the evidence from the Online Intervi ew video and completed interview record sheet (for example, question/s) to specific content d escriptors from the Australian Curriculum: Mathematics. Justify points being made by referri ng to academic literature (for example, what is provided in the Reading List). Remember that not everything is addressed in the interview, so ensure assumptions are not made – evidence must be used. This should be written in third person. Mathematically-focused feedback for the child Craft what you would say to this child regarding the mathematical understandings they have i dentified. Again, this must be based on evidence from the Online Interview video and comple ted interview record sheet. Use terminology the child can understand. Consider both the math ematical understandings and the mathematical disposition the child demonstrates during the Online Interview video (for example, did they look confident, hesitant, concerned, worried). Make sure that feedback addresses both what the child could do and what they could not do, maintaining a presentation that enables the child to build a positive mathematical selfefficacy (that is, that they are able to do maths) and disposition towards mathematics (that is, they are willing to engage and persevere). This should be written in second person (ie., using ‘You’ when writing). Report for the parents, including suggestions for future learning needs based in the clas sroom and play based family activities that will assist the child’s future mathematical u nderstanding Identify what the child could do and what the child needs to work on. Link this to specific ma thematical terminology from the Australian Curriculum: Mathematics (such as you would fin d in the content descriptors and elaborations). Link what the child could do to activities to ma intain and/or strengthen further and what the child needs to work on to activities that would d evelop these understandings. Emphasise the importance of the child’s mathematical selfefficacy and mathematical disposition. Support your explanations with references to academi c literature (for example, what is provided in the Reading List). Use reputable sources for acti vities that are suggested [Note that a formal learning experience plan is not required for this a ssessment, just a range of targeted activities] such as the following resources made available under Topic 1 in the Reading List: • • • • The First Steps in Maths series of books; AAMT website links to sources such as maths3000, reSolve, and top draw teachers; NCTM Illuminations website; NCETM website. This should be written in a mixture of first, second, and third person (for example, third perso n when considering what was found, first person when sharing your interpretation of what wa s found, and second person when providing suggestions for what the parents could do). What to submit: 1. 2. 3. 4. A brief introduction (recommended up to 150 words) Mathematical understandings profile of the child (recommended 1500 words) Mathematically-focused feedback for the child (recommended 200 words) Report for parents, including suggestions for future learnings and play based family a ctivities (recommended 1000 words). 5. A brief conclusion (recommended up to 150 words) 6. Reference list 7. Appendix (if needed) The word count is 3000 plus or minus 10%. This includes all text (headings, intext citations, captions, and direct quotes). It excludes the Reference List. Please note for this assessment your marker will stop reading when the word count is reached and only award ma rks on the material read. Opportunities to analyse Online Interview videos and completed interview recording sheets f or other areas of mathematics (one that won’t be the same as those for this assessment) will b e available during the Topics as activities and tasks. Your analysis of these can be discussed with peers, which will enable the skills for this assessment to be developed. These skills will be used every day in your role as an educator. Please ensure that you also view and consider the rubric as you complete your assessment – Assessment_1_Marking_Rubric.pdf Assessment 1 Marking Rubric This assessment represents 50% of the mark weighting of the Unit. Mathematical understandings profile of the child /18 Not met expectations “understanding not demonstrated” Met most expectations “understanding demonstrated” [Pass to Credit] Met or exceeded expectations “insight demonstrated” [Distinction to High Distinction] Minimal mathematical understandings identified. Not all mathematical strengths provided. Some mathematical ideas needing improvement missing. Unsuitable or inappropriate links to the curriculum. Mathematical disposition not considered. Lack of evidence to support claims. Limited or no use of academic literature to support points. Most mathematical understandings identified. Mathematical strengths and mathematical weaknesses provided. Appropriate links made to the curriculum but more were evident that were not included. Minimal consideration of mathematical disposition. Evidence used to support claims but more relevant evidence or more varied evidence needed. Use of academic literature to support points, though a Insight demonstrated when mathematical understandings identified. Judicious allocation of mathematical strengths and mathematical weaknesses. Discerning links made to the curriculum. Thoughtful consideration of mathematical disposition. Strong, frequent, and varied evidence used to support claims. Astute use of a range of suitable academic literature to support points. wider range or more frequent use needed. Mathematicallyfocused feedback for the child /10 Inappropriate or insufficient mathematics identified as areas of strength. Inappropriate or insufficient mathematics identified as areas needing work. Mathematics referred to that was not addressed in the Online Interview videos and completed interview record sheet. No consideration of child’s disposition towards mathematics. The child’s mathematical self- efficacy could be negatively impacted by the feedback as presented. Unsuitable or inappropriate language for the target audience (ie., the child). Suitable mathematics identified as areas of strength, although more were evident and could have been included. Relevant mathematics identified as areas needing work but there were more evident that should have been provided. Language suitable for the target audience (ie., the child). A range of both strengths and weaknesses provided that would help maintain the child’s mathematical self-efficacy. Consideration of child’s disposition towards mathematics provided. Perceptive identification of mathematics identified as strengths and mathematics identified as needing work. Highly appropriate and effective language for the target audience (ie., the child). Insightful presentation of strengths and weaknesses that would ensure the child’s mathematical self- efficacy is addressed. Thoughtful approach to ensuring the child’s disposition towards mathematics is supported. Report for parents, including suggestions for Incorrect mathematical understandings identified as strengths and/or Appropriate mathematical understandings identified as strengths and weaknesses, Pertinent range of relevant mathematical understandings identified as future learnings and play based family activities /16 weaknesses. Mathematics referred to that was not addressed in the Online Interview videos and completed interview record sheet. Inappropriate resources referred to. Activities not suitable or do not address the specified mathematical understanding. Mathematical activities do not address both maintaining and improving the child’s mathematical understandings. Inappropriate sources used for activities. Limited or no use of academic literature to support points. Unsuitable or inappropriate language for the target audience (ie., parents). Lack of consideration of the child’s mathematical self-efficacy and disposition towards mathematics. though more were evident and not included. Mostly suitable resources referred to. Activities are suitable to maintain and develop the specified mathematical understandings but a greater range would have been beneficial. Suitable sources used for the activities. Academic literature used to support points but this could have been more frequent or incorporated a wider range. Language suitable for the target audience (ie., parents). Demonstrates consideration of the child’s mathematical self- efficacy and disposition towards mathematics. strengths and weaknesses. A wide range of effective resources referred to. Judicious use of a selection of activities to maintain and develop the specified mathematical. Thoughtful and varied sources used for the activities. Discerning use of academic literature to support points. Highly appropriate and effective language for the target audience (ie., parents). Insightful consideration of the child’s mathematical self- efficacy and disposition towards mathematics. Academic writing /6 Poor presentation. Significant APA faults. Not within word or page limit. Deficient introduction and conclusion. Minor but distracting grammar and spelling errors. APA style attempted but not always successful. Introduction and conclusion are suitable. Total /50 Clear presentation. APA style used consistently. Succinct writing that clearly communicates ideas. Strong and insightful introduction and conclusion. Department of Education, Employment and Training 2001 Mathematics online interview booklet 0759401675 M a t hem a t i c s Online Interview Department of Education, Employment and Training 2001 Mathematics online interview booklet 0759401675 Early Numeracy Interview Booklet Published by the Communications Division, for the Office of School Education, Department of Education, Employment and Training, GPO Box 4367, Melbourne, Vic. 3001, Australia. © State of Victoria, August 2001 First published 2001 All rights reserved. Except under conditions described in the Copyright Act 1968 of Australia and subsequent amendments, no part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical and photocopying, recording or otherwise, without the prior permission of the copyright owner. Permission is hereby granted to the purchaser to reproduce appendices 1 and 2 from the book in quantities suitable for non-commercial use. National Library of Australia Cataloguing-in-Publication data Early numeracy: Bibliography ISBN 0 7594 0167 5 1. Numeracy — Study and teaching (Primary). I. Victoria. Dept. of Education, Employment and Training. 372.72044 Department of Education, Employment and Training 2001 Mathematics online interview booklet 0759401675 C ontents Section 1 2 Assessment Assessing early numeracy 3 Value of the one-to-one interview 3 Stages of mathematical growth 4 Links between points of growth and the Interview 4 Section 2 Introduction to the Mathematics Online Interview 7 • About the Interview 7 • Equipment 7 • Preparation 8 • Recording responses 9 • Before the first interview 10 • Administration Functions 10 • Determining starting points 11 • Conducting the interview 12 • Analysing the record sheet 15 • Student profiles 16 Section 3 Mathematics Online Interview Questions 21 Glossary 51 Bibliography 53 Section 4 Appendix 1 Equipment checklist and photocopiable support materials 57 Appendix 2 Interview record sheet 93 Appendix 3 growth 97 Department of Education, Employment and Training 2001 Mathematics online interview booklet 0759401675 SECTION 1 Assessment Department of Education, Employment and Training 2001 Mathematics online interview booklet 0759401675 A ssessing numeracy early The Early Numeracy Research Project (1999–2001) was commissioned by the Department of Education, Employment and Training and managed by the Early Years Branch. See Bibliography (p. 53) for references to research and related publications. As part of the Early Numeracy Research Project (ENRP), a need was identified for the development of a comprehensive assessment tool for early numeracy. Through the Early Numeracy Research Project a framework of growth in numeracy learning was created, informed by available research on young children’s mathematics learning. The framework provided a means of tracking students’ learning through significant growth points in number, measurement and space, organised into the domains of Counting, Place value, Strategies for addition and subtraction, Strategies for multiplication and division, Time, Length, Mass, Properties of shape, and Visualisation and orientation. The points of growth identified through the research project were used as the basis for the stages of mathematical growth in the Early Years Numeracy Program. This framework was then used to develop appropriate hands-on assessment tasks where students could demonstrate mathematical understanding and preferred strategies for solving increasingly complex tasks. These tasks have been presented to more than 11000 students during the research project in the form of a one-to-one interview. Value of the one-to-one interview The Mathematics Online Interview (Section 3) is a powerful tool for assessing students’ numeracy development during the first five years of schooling. Evidence of student learning gathered during the interview allows teachers to: • develop a profile of student numeracy development in the aspects of mathematics assessed in the interview • inform focused teaching of students. Time spent conducting the one-to-one interview is invaluable in enhancing teachers’ understandings of an individual student’s Interview booklet Anecdotal evidence and other data collected through ongoing monitoring and assessment of other mathematical areas can be used to support and expand the student profiles obtained through the interview.  Assessing Early Numeracy 1 Department of Education, Employment and Training 2001 Mathematics online interview booklet 0759401675 The teachers in the Early Numeracy Research Project trial schools have found that ‘the data from the interviews were revealing of student mathematical understanding and development in a way that would not be possible without that special opportunity for one-to-one interaction’. (Clarke 2000) mathematical understandings and the strategies they use. For this reason it is recommended that the classroom teacher administer the interview. Stages of mathematical growth Stages have been outlined to illustrate likely mathematical growth of students in the early years of schooling. These should not be viewed as discrete, sequential stages of mathematics development. At any time, students will demonstrate a range of skills and understandings related to the mathematics in which they are engaged. The stages of mathematical growth: • reflect the findings of relevant research in mathematics education from Australia and overseas • allow mathematical profiles of individuals and groups to be developed • form the basis of planning and focused teaching • support the identification and description of student improvement • enable the identification of students who may benefit from additional assistance in mathematics • have sufficient scope to describe the knowledge and understanding of most students in the first five years of schooling. Within each mathematical strand, stages are described by points of growth. Links between growth and points of growth and the interview the Interview Judgements based on one interview on a particular day need to be informed by ongoing assessment during mathematics sessions. ­ Tasks in the Interview are linked to points of mathematical growth. Student responses from the Interview can be tracked against these points of growth to develop a profile of mathematical skills and understandings in the sections of the Interview conducted. The student profile provides a guide in establishing a mathematical focus for teaching. Interview booklet Department of Education, Employment and Training 2001 Mathematics online interview booklet 0759401675 SECTION 2 Introduction to the Mathematics Online Interview Department of Education, Employment and Training 2001 Mathematics online interview booklet 0759401675 I ntroduction to the Mathematics Online Interview 3 About the Interview The Interview includes oral questions that invite students to respond verbally or to demonstrate their level of understanding using a variety of materials and equipment. An example is provided opposite. Early Numeracy Interview SECTION E: Time Equipment • children’s own hand-drawn clocks • moveable yellow clock • yellow June calendar card • digital clock showing 12:51 • excerpt from TV guide • blank digital and analogue clockfaces Prior to the interview, children need to be asked in class to simply ‘draw a clock’. If they choose to draw a digital clock, please ask them to then draw an analogue one. They then bring these clocks to the interview. 38 My Clock Equipment Depending upon the kinds of information shown in the child’s drawing of the clock, ask questions like the following: Tell me a...
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Explanation & Answer

Please view explanation and answer below.

Running Header: CASE STUDY

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CASE STUDY
Student Name
School
Date

CASE STUDY
Outline


It has been seen that the teacher noted everything in the response book, and it was easy
for her to give feedback. Though the child's responses and activities have already been
discussed, the feedback is as follows.



According to the mathematically focused strategies, the child was good with counting.
The parents are fond of teaching their child at a young age, and counting was the basic
thing, so she was good at it. She understood the concept of placing the value. She was
good at it as well because she got what the teacher wanted to say.



When it comes to the backward pattern of counting, the child looked confused, and the
teacher had to guide her for it. In the case of addition and subtraction, she kept her
interest up, and it looked easy, but the subtraction and division were difficult, and it took
a lot of time for her to understand the different concepts.

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Running Header: CASE STUDY

1

CASE STUDY
Student Name
School
Date

CASE STUDY

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Introduction:
Mathematics is an important subject required for use in our daily lives to count, add and
subtract. These are the minor activities that are usually resolved with the help of mathematics.
Still, as we grow up and continue to study mathematics, we know that the application of
mathematics solves various complex functions. Australian Curriculum is used for the children to
ensure that they have sufficient knowledge of the subject and know basic techniques. It has been
seen that the children quickly learn about the techniques like counting, addition, and subtraction.
The project discusses a case study where a child and a teacher are sitting together, and it
seems the setting of informal education. The teacher is teaching the different techniques of
mathematics to the child. It has been seen that the child was two-year child, and she was sharp.
The teacher was teaching her addition and subtraction techniques, and she knew that the child
was interested in the lesson. It was seen that there are different videos where both the teacher and
child are seen learning mathematics strategies. The interview booklet is to be analyzed as well.
Mathematical understandings profile of the child:
The case study is based on the understanding of child of the mathematical concept. The
videos are available to see whether the child is learning the different strategies. It is necessary to
discuss the ways by which the child assessment can be done. It is necessary to know that what
factors play an important role in his learning and teaching. The teacher has been shown in an
informal setting where the child is given a specific education. Usually, the teacher teaches the
students in the class with a different audience, but the video has shown that there is only a
teacher and a student, and she is making her learn the different things (Leonard, 2018).

CASE STUDY

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The first factor that plays an important role in understanding the needs of a child is her
interest in the lessons and the strategies that the teacher is teaching. The videos show that the
child is taking an immense interest in the lessons as she listens to the teacher, gives attention to
the lessons, and responds to the techniques. It is easy for the teacher to teach her with this kind of
interest. It depends on the teacher how she makes her students comfortable and the strategies she
adopts to make things easier. It is seen that the student is taking an interest in the lesson because
of the environment that the teacher has created for her. She has created a friendly environment
and given her different blocks, toys, stickers, and shapes to understand and learn the techniques.
The teacher...


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