Part 1: Maths Workbook: Observing maths

Complete Part 1 Observing maths in your Maths Workbook.

This part of the workbook is an assessed portfolio of work in which you are required to apply your learning from your study of Block 2 to observations of children working mathematically (in live activities in school and/or as shown in the Block 2 Practice-setting Maths audio/video materials).

Refer to the guidance and the example provided in the introduction to the Maths Workbook. Follow these to help you to complete the five sections for each of the four aspects of mathematics you select.

Your work should be clearly laid out for your tutor to read. Although there is no minimum or maximum word length for writing up this part of the workbook, please note the suggested length of around 500 words for each observation and follow the guidance in the Assessment Guide. If your contribution is excessively lengthy, this may have a negative effect on your mark.

PLEASE SEE BELOW (PLEASE follow this exact structure)

Introduction and instructions

Building on your Maths Audit, this Maths Workbook provides a structure for you to demonstrate how you have developed your knowledge and understanding of key mathematical ideas and their related vocabulary, as well as your wider understanding of mathematics as a subject within primary education.

Throughout the study weeks of Block 2, you should work towards completing this document, which you will then submit for TMA 02.

The Maths Workbook is in three parts:

1. Observing maths

2. Reflecting on your learning about mathematics and numeracy in Block 2

3. Academic language and learning checklist.

1. Observing maths

You are required to observe and write about, from the following aspects of mathematics covered in Block 2, four activities involving children working mathematically:

1 counting and understanding number

2 place value

3 using number words and/or symbols

4 fractions, decimals, percentages, ratio or proportion

5 properties of number operations

6 mental calculation strategies

7 written calculation methods

8 measurement

9 properties of shapes or transformation and symmetry

10 handling data.

The mathematical aspects set out above are arranged into four sections, A, B, C and D, as shown in the table below. Specific details of what you are required to write for your four chosen activities are set out below. You must choose one aspect to observe and write about from each section.

Aspects

A 1, 2, 3

B 4, 8

C 5, 6, 7

D 9, 10

In planning to complete the Observing maths part of your Maths Workbook, we strongly encourage you to try to carry out as many of your four observations as possible in your school setting. This will enable you to draw on your knowledge of the context, in particular the childrens prior learning, and also to discuss the activity with the children and practitioners in school. This may provide you with a greater depth of insight than it is possible to obtain from watching a video.

Your in-school observations can be either activities that you are directly involved in yourself, or activities taught by somebody else. We encourage you to try to observe activities across a range of age groups. This is not a requirement, but will help you to develop your appreciation and understanding of childrens mathematical learning across the primary years as a whole.

You can make use of one or more of the practice-setting videos for your observations of any of the four sections if you are unable to arrange to observe a live activity in school. Your selection of activities will therefore comprise one of the following three possibilities:

four live observations in school

a combination of observations of live and video activities

four observations from the practice-setting videos.

For in-school activities, you may find it necessary to complete your observation in school before you carry out the relevant reading online and in the Maths Reader. This will be fine. You will be able to write down details of the school-based activity in this document, and then complete your analysis once you have done the necessary reading and online activities.

There are five sections to complete for each of your chosen aspects. Please read the guidance below, in Structure, for what to include in each section. We have also provided a completed example, which you should refer to as a guide to the level of detail required. We do not specify a minimum or maximum word length for writing up each observation because the Observing maths part of the Maths Workbook is in the form of a portfolio rather than an academic essay. We suggest that around 500 words per activity will enable you to fully meet the requirements for TMA 02. Please remember that your completed Observing maths section will form a part of your submission for TMA 02, for which you will be required to show the following:

how your own mathematical subject knowledge has developed

how this will impact on your work supporting children in school.

You need to include sufficient detail to demonstrate both of these. This means that when assessing what you have written about your observations, your tutors will be paying particular attention to the following sections:

Key mathematical ideas and vocabulary

Role of resources/mental imagery

Implications for childrens subsequent learning.

References: you should include in-text references as you would for an essay to make links to relevant reading, e.g. Haylock and Manning (2014); or NRICH (2016). This is important to show how your subject knowledge is developing.

At the end of the workbook, include a reference list that contains the source details for everything you have referred to in both Part 1 Observing maths and Part 2 Reflecting on your learning in Block 2.

Structure

Live activities in school may involve a group of children or an individual child. For ease of expression, guidance here refers generally to children. Each of the five practice context videos shows an activity with a group of children.

There are five sections to complete for each aspect; these are set out below.

Activity

State what the intended learning outcomes were for the activity. Individual schools may have their own term for learning outcomes for example, learning intention, we are learning to or learning objective). For live activities you will need to liaise with the class teacher to ascertain the learning outcomes for the activity, or produce appropriate learning outcomes if you plan the activities yourself.

Describe what the children were doing. You should include the age of the children, and describe the role of the teacher or other adult (who might be you) in the activity.

Childrens learning

Describe what you feel the children learned from the activity, or what they found difficult to grasp, if appropriate. Indicate the evidence that led you to form this conclusion. This might include what the children did, wrote or said.

Key mathematical ideas and vocabulary

Outline the key mathematical ideas involved in the activity, with reference to any relevant reading you have carried out. This may be your online reading for Block 2, the Maths Reader or include other online sources, books, resources in school, national curriculum or guidance documents. You may need to refer to chapters from the Reader beyond those you have been directed to read in the module activities. You must acknowledge the source of your reading.

Where appropriate, identify any links with other areas of mathematics. Identify key vocabulary. Acknowledge the source for any definitions you include.

Role of resources/mental imagery

Briefly discuss the role of resources and/or mental imagery in supporting childrens understanding. If there was no evidence of this, you should state that this was so and suggest how you feel resources or imagery might have helped, if appropriate. Again, you should refer to your relevant reading.

Implications for children’s subsequent learning

What mathematical ideas and vocabulary do you feel the children require further experience of?

What do you feel the children are ready to move on to next, if appropriate?

What do you feel went particularly well in the activity, and why do you think this was the case?

What (if anything) would you suggest might have been done differently, and why?

Example of a completed section

7. Properties of number operations

(This example is of an observation of an activity carried out by another adult. If you are writing about an activity you have taught yourself, please state this and write in the first person i.e. using I)

Activity

Maria (a teaching assistant not her real name) worked with a group of three eight-year-old children in representing multiplications (e.g. 5 x 3) as arrays.

The learning objectives were:

– to understand that multiplication can be carried out in any order

– to improve rapid recall of multiplication facts.

Marias role was to encourage the children to use a range of relevant vocabulary, and to assess their understanding that multiplication can be carried out in any order.

No resources were provided the children were asked to draw the arrays in their maths books.

Childrens learning

All three children were able to produce an appropriate diagram of an array from a multiplication presented in written form, e.g. for 5 x 3:

X X X X X

X X X X X

X X X X X

They could all explain this as five lots/sets/lines of three, although Jo used the term five rows of three. This was due to her confusion over the terms rows and column rather than misunderstanding of what 5 x 3 meant.

All three children knew that the order of the numbers could be changed to give the same total, and they could all draw an appropriate array to represent this:

X X X

X X X

X X X

X X X

X X X

Nayeem said, All times tables can be done the same both ways. The answers are the same.

The children agreed that the two arrays each had the same number of crosses: Its just like the crosses have been turned round (Jo).

Key mathematical ideas and vocabulary

1 Multiplication as repeated addition (see Study Guide, Week 8) this relates to the idea of lots of or sets of (Haylock and Manning, 2014, p. 135).

2 Image of multiplication as a rectangular array (Haylock and Manning, 2014, p. 138). The NRICH (2016) website explains some other useful contexts for arrays (e.g. helping children to learn multiplication facts, exploring factors/prime numbers).

3 Commutative law of multiplication i.e. that multiplication can be carried out in any order (Haylock and Manning, 2014, p. 148). I was interested in Haylock and Mannings learning and teaching point that although, technically 3 x 5 means 5 lots of 3, there is no need to make a fuss over how children say or represent it, as it is much more important that they understand that multiplication can be carried out in any order.

4 Key vocabulary: lots of, groups of, sets of, times, multiplied by.

5 Jos comment about the number of crosses staying the same demonstrates a grasp of conservation of number (Haylock and Manning, 2014, p. 32)

Role of resources/mental imagery

The image of the array itself is powerful, as it shows at a glance that, for example 3 x 5 is the same as 5 x 3. A peg board would be a good hands-on resource to allow children to explore factors e.g. How many ways can you find to make 24?.

Implications for childrens subsequent learning

Look for opportunities to develop the childrens understanding of rows and columns. This could be in data handling or through other subjects (e.g. science, ICT, geography).

Use the image of a multiplication square to encourage the children that, because of commutativity, they already know most of the difficult times-table facts (e.g. 7 and 8).

The children seemed to like producing a picture for their answer, and I think this definitely helped them to achieve the first objective.

2. Reflecting on your learning in Block 2

You should work on the second part of the Maths Workbook after you have completed all of the Block 2 readings and activities.

Reflect back on your learning during Block 2, and identify and discuss two mathematical concepts, techniques, procedures or approaches to maths teaching and learning for which you have developed your understanding.

The following bullet points illustrate the terms used in the previous paragraph, but are examples only you do not need to restrict your choices to these examples.

A mathematical concept might, for example be place value, the counting principles or equivalent fractions.

Techniques or procedures are more specific for example, a mental or written calculation strategy, classifying shapes by their properties.

Approaches to mathematics might, for example include creativity (as presented in Block 2), using visualisation and mental imagery. If you choose to write about this kind of more overarching approach, make sure you include specific examples to illustrate how your understanding has developed.

For each of your two choices, write about how your understanding has developed and what has contributed to this understanding. For example:

specific module readings and online activities

online discussion with fellow students and your tutor

your observations of childrens mathematical learning

discussion with teachers, other adults or children in school

reading beyond the module materials (e.g. websites, textbooks).

In deciding what to write about, you may wish to choose areas that you identified for development following the audit. These areas should provide you with plenty of scope to demonstrate and reflect on your learning. Alternatively, you may wish to consider other aspects of learning and teaching in mathematics that you had not considered in depth before, where your understanding has developed as a result of your study in Block 2. Such areas should provide equally rich focal points for evaluation.

Your writing should draw on the comments you made in your reflection after carrying out the Maths Audit in Block 1, and to your response after reviewing your audit answers within Block 2. The week 1 Study Guide What is subject knowledge section may be useful. You can also refer to the Block 2 readings, study activities and the Maths Audit commentaries.

Completing the Maths Workbook

For TMA 02 you will submit your completed workbook. To do this, save another copy of this document to work on. Your submitted workbook should only include:

a brief statement on ethical considerations (100 words)

four written observations for Part 1 (Observing maths)

your 1000 word reflection for Part 2

an Academic language and learning checklist for Part 3

a list of references.

Therefore, to prepare your workbook for submission you will need to delete the Introduction and instructions section of this document along with the sections for the aspects of mathematics that you will not be writing about.

Make sure you also follow the instructions in the TMA 02 document

on the Assessment page of the module website.

Maths Workbook Submission for TMA 02

Ethical statement

(In accordance with Section 6.2 of the Assessment Guide, include here a statement of no more than 100 words explaining how you have made appropriate ethical considerations in relation to undertaking educational observations and research in relation to Parts 1 and 2 of the Maths Workbook.)

Part 1. Observing maths

(Delete all uncompleted sections)

1. Counting and understanding number

(If you do not usually spend time working with or observing young children, for this aspect you may find it beneficial to arrange to observe children who are still developing their counting ability, either in school or in one of the practice-setting videos. However, as most mathematical activities involve some counting, you may choose to analyse the counting element of an activity undertaken by older children.)

Activity

Childrens learning

Key mathematical ideas and vocabulary

Role of resources/mental imagery

Implications for childrens subsequent learning

2. Place value

(Activities involving place value may involve whole numbers or decimals or both. Many mental and written calculation strategies require an understanding of place value.)

Activity

Childrens learning

Key mathematical ideas and vocabulary

Role of resources/mental imagery

Implications for childrens subsequent learning

3. Using number words and/or symbols

Activity

Childrens learning

Key mathematical ideas and vocabulary

Role of resources/mental imagery

Implications for childrens subsequent learning

4. Fractions, decimals, percentages, ratio or proportion

(For this aspect, you may find it beneficial to observe older children. However, very young children can also engage with ideas relating to fractions (e.g. equal sharing, half) and you may choose to analyse the relevant elements of an activity undertaken by younger children. The activity might focus on one of fractions, decimals, percentages, ratio or proportion, or involve making links between two or more of them.)

Activity

Childrens learning

Key mathematical ideas and vocabulary

Role of resources/mental imagery

Implications for childrens subsequent learning

5. Properties of number operations

(Although the activities in Week 8 focus on addition and subtraction, you may choose to focus on any, or all, of the four number operations for this observation.)

Activity

Childrens learning

Key mathematical ideas and vocabulary

Role of resources/mental imagery

Implications for childrens subsequent learning

6. Mental calculation strategies

(Although the activities in Week 8 focus on addition and subtraction, you may choose to focus on any, or all, of the four number operations for this observation.)

Activity

Childrens learning

Key mathematical ideas and vocabulary

Role of resources/mental imagery

Implications for childrens subsequent learning

7. Written calculation methods

(If you spend most of your time in school focusing on younger children, you may need to arrange to focus on older children if you choose to do this observation.)

Activity

Childrens learning

Key mathematical ideas and vocabulary

Role of resources/mental imagery

Implications for childrens subsequent learning

8. Measurement

Activity

Childrens learning

Key mathematical ideas and vocabulary

Role of resources/mental imagery

Implications for childrens subsequent learning

9. Properties of shapes or transformations and symmetry

Activity

Childrens learning

Key mathematical ideas and vocabulary

Role of resources/mental imagery

Implications for childrens subsequent learning

10. Handling data

(For students working with younger children, the following quote from the Maths Reader may be helpful: Learning to sort data according to given criteria is the foundation of data handling. Give younger children lots of experience of sorting, first using the actual objects themselves (Haylock and Manning, 2014, p. 402).

Activity

Childrens learning

Key mathematical ideas and vocabulary

Role of resources/mental imagery

Implications for childrens subsequent learning

PLEASE REFERENCE FROM: Mathematics explained for primary teachers, 5th edition by Derek Haylock with Ralph Manning.

Part 2: Reflecting on your learning in Block 2 (1000 words)

Identify and discuss two mathematical concepts, techniques, procedures or approaches to mathematics teaching and learning that you have developed your understanding of through your study during Block 2.

Write your answer in your Maths Workbook. For illustration of terms used above, suggestions to guide your choices and further details, see the introduction to Part 2 of the Maths Workbook.

PART 1- 500 WORDS FOR EACH OBSERVATION

PART 2- 1000 WORDS.

Many Thanks!

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