Mathematics: guidance MUST be adhered too:

50% of the module assignment

Please choose a small aspect of one area of mathematics to discuss. This might be an area you observed in school or one which we have covered in the module so far. The area of mathematics MUST RELATE TO NUMBER (select one from the list below).

For example you might consider a small part of:

Counting – say counting to ten

Place value –say exchanging ten ones for a ten, or ten tens for a hundred, or ten tenths for a one

Properties of number – say odd and even, or prime

Addition and subtraction – say the structures of addition, or subtraction, or the commutative law, or addition and subtraction to ten, or the column method or the link between addition and subtraction

Multiplication and division – say the structures of multiplication and division, or the commutative law for multiplication

Fractions – say equivalent fractions, or changing mixed numbers to improper fractions

It is important to choose a SMALL area to discuss IN DEPTH.

Once you have chosen your area, you must read widely around it. There are plenty of readings for you:

  • the subject knowledge books listed on your tracker
  • the readings scanned for you on the Curriculum and Pedagogy blackboard under Learning resources, mathematics

ESSENTIAL READINGN LISTED

Fair Education Alliance report on the attainment gap in Maths – https://www.faireducation.org.uk/news/2017/2/23/closing-the-numeracy-attainment-gap

The effects of date of birth, gender and school type on primary maths attainment – https://www.teachingtimes.com/age-gap-early_101218/ 

Multiplication Tables Check: NAHT report – https://www.naht.org.uk/news-and-opinion/news/curriculum-and-assessment-news/multiple-concerns-naht-members-response-to-the-multiplications-tables-check-pilot/

EEF reports – https://educationendowmentfoundation.org.uk/tools/guidance-reports/maths-ks-2-3/

http://www.acme-uk.org/media/33228/beginningteachingbestinclass2015.pdf

Sturman, L., Burge, B., Cook, R. and Weaving, H. (2012). TIMSS 2011: Mathematics and Science Achievement in England. Slough: NFER – https://www.nfer.ac.uk/media/2212/tmez01.pdf

AMCE (2012) Raising the Bar: Developing able mathematicians –

http://www.acme-uk.org/media/10498/20121212_acme_raising_the_bar.pdf.pdf

Ofsted 2012 Made to Measure

Pisa survey 2013

http://www.acme-uk.org/media/7627/acme_theme_b_final.pdf

https://www.ucl.ac.uk/ioe/  

Additional readings to be used:

https://www.cambridgemaths.org/espresso/

https://educationendowmentfoundation.org.uk/school-themes/mathematics/

https://educationendowmentfoundation.org.uk/school-themes/mathematics/

http://www.ibe.unesco.org/fileadmin/user_upload/Publications/Educational_Practices/EdPractices_19.pdf

https://www.vlebooks.com/Vleweb/Product/Index/2018017?page=0

MUST engage with the research summaries on:

https://www.cambridgemaths.org/espresso/

MUST engage with readings on mastery from the Primary Maths blackboard under the Mastery button, and from the NCETM:

https://www.ncetm.org.uk/resources/47230

Please engage with the reading available for you on the Primary Maths Blackboard, under Additional Readings, ‘Readings which are particularly useful for assignments.’

Key readings there are:

Skemp, R. (1976) ‘Relational understanding and instrumental understanding‘, in Mathematics Teaching, vol 77, pp.20-26.
Harris, A. (2000) ‘Some Theories of Learning and Their Application to Mathematics’. University of Cumbria. Unpublished.

 

  • There are multiple copies of key books in the library, and many of these are available as e books. Use the reading list to help you. You will find this on the Curriculum and Pedagogy Blackboard under Learning resources, mathematics.

You must read about the actual area of mathematics you have chosen to discuss. For example, if you have chosen to discuss place value, you must refer to chapters on place value.

In your essay please follow this format:

  • Introduce the area you have chosen and what you hope to cover in the essay
  • Reflect on the key mathematical ideas that children will learn in this area in the Early Years or the primary curriculum. Refer briefly here to the EYFS framework or the National Curriculum, and in detail to your reading related to this area.
  • Reflect on how you want the children to understand these ideas. For example you might refer to the aims of the National Curriculum. When you discuss conceptual understanding you may refer to the theory of Skemp (which is on the primary maths blackboard under additional readings, readings for assignments). When you discuss fluency you may refer to the paper by Russell (which is on the primary maths blackboard under additional readings, readings on fluency.)
  • Identify the manipulatives and images which are used to represent these key ideas. If you wish, you can paste in pictures of these manipulatives and images. In this section refer to readings on manipulatives on the Primary Maths blackboard under additional readings.
  • Discuss the way in which you can use conceptual and procedural variation to draw the children’s attention to the key ideas in this area of mathematics. Refer to some of the readings on variation on the Primary Maths blackboard under the Mastery button. For example, you might want to paste in a picture of a series of examples to show how you might use procedural variation in your teaching.
  • Consider how to promote learning of this area of mathematics in another curriculum subject or area of learning.
  • Please conclude by reflecting on how the essay has helped to you develop your understanding and your progress against the Teachers’ Standards.

Throughout please ensure you are providing a critical reflection. You should refer to reading throughout your essay. REFLECT on ideas rather than just reporting them. BRING the ideas of more than one writer together to compare views and explore complexities. For example, what are the subtle differences between the ideas of Liebeck, Bruner, and Haylock and Cockburn on the use of manipulatives?