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Mastering Place Value – The Adventures of Papa Titioning
Dave Godfrey
Papa Titioning is one of the many characters found in Number Fun. He is a lumberjack and he has been created to help children master aspects of Place Value and Calculation.
The Power of Story
Story is an extremely powerful tool for engaging children in deep mathematical learning and for developing their understanding.
Research into the use of storytelling in learning is extensive. Zazkis & Liljedahl (2009) state that, ‘Story can make mathematics more enjoyable, memorable, engaging and understandable.’ Research by Kieran Egan (1986) demonstrates that, ‘Children readily understand abstract concepts when they are organised in story form’.
When I wrote the first Number Fun songs in 1999, characters naturally appeared, like Farmer Pete, Chip the Chopper, Firefighter Esme, Number Bond (006/004) and the amazing Doubling Machine.
Based on a deep understanding of how children learn mathematics, Number Fun combines the powerful tools of song, visualisation, animation and humour – but at the heart of Number Fun is the use of story. Number Fun features an ensemble cast of fun-filled characters that live together on Number Fun Island.
Problem Posing
From Primary 1 (our Year 2) children in Singapore are encouraged to create their own mathematical stories - this activity is called Problem Posing. This activity helps children develop and demonstrate their understanding whilst enabling teachers to make assessments for learning (Singapore Ministry of Education, 2012). For children to become fluent in creating their own mathematical stories, they need to constantly be emersed in mathematical story.
Two ways Story Characters are used in Number Fun
Number Fun comprises over 600 video presentations (with supporting resources) that include a song, the song words and animated graphics to support the teaching and learning of a specific mathematical objective from across the domains of the national curriculum. The majority of these videos feature a story context and aim to help children in the following ways:
1: By placing mathematical concepts into a story context, as you might have in a word problem. Such problems typically combine words, a context, a mathematical idea (e.g. coin values) and a problem to solve. For example, if I offered you a 20% discount on a jacket worth £18, how much would you pay?
2: By embedding mathematical structures into a story context to help children grasp underlying mathematical structures. This may or may not be in the form of a problem, but the imagery reflects a formal mathematical arrangement, e.g. I might deliberately arranged 7 eggs into a 10s frame egg box to show the ‘5 and 2 more’ arrangement, which also reveals that 7 is ‘3 less than 10’ (see image above).
Papa Titioning’s Log Classification System
Papa T’s Log Classification System is an example of this second, extended use of a story context. His Log Classification System is designed to mirror the mathematical structure of our Base 10 system. The imagery for 1s, 10s, 100s and 1,000s mirrors the base 10 (Dienes) equipment used widely in schools. It also provides a pictorial representation for exploring place value from millions through to thousandths. Place value counters can be used as a concrete resource that span these values, but, unlike Base 10 equipment, they do not show the cardinality (size) of each number. Papa Titioning’s Log Classification provides children with a story context on which to hang their understanding and their use of concrete resources, and even create their own mathematical stories.
Papa Titioning, Partitioning and Mental Calculation
The Base 10 arrangement of Papa Titioning’s Logs has been utilised in a host of ways on Number Fun.
Papa Titioning first featured in a song cunningly entitled Papa Titioning(!) that explored different combinations of 10s and 1s to make up a 2-digit number. E.g. 74 is 7 tens and 4 ones, or 6 tens and 14 ones, or 5 tens and 24 ones etc. Papa Titioning now features in a series of videos exploring the use of partitioning as a mental strategy across all four operations (see links below).
Papa Titioning and Formal Methods of Calculation
For me, one of the most exciting uses of Papa Titioning has been in creating a set of videos that help children grasp formal column methods. Typically formal methods are taught without context, even when modelled using concrete resources. Utilising Papa T’s Classification System helps both teaching staff and children develop conceptual understanding of the formal methods.
For example, in Papa Titioning’s Division Song, the video puts the procedure into a log context and the animation reveals that sharing, rather than grouping, is the underlying structure for understanding. It also helps children visualise the concept of regrouping whilst maintaining the integrity of place value - something often lost in the formal procedure. It equips them to tell division stories of their own and use concrete resources effectively.
Check out the links below to explore how Papa Titioning helps children understand and engage creatively with formal methods found across all four operations.
Papa Titioning - a Story Character for Wider Place Value Understanding
The character of Papa Titioning is now being used to support a range of concepts. The Number Fun Portal includes videos such as Digit Zero (who helps children grasp the concept of zero as a place value holder) and One Tenth (which helps them embed decimal place value into a context).
Papa Titioning’s Playing Cards & Gattegno Charts
To support the use of Papa Titioning in the classroom, I’ve created a set of Papa Titioning resources. These include Papa Titioning Playing Cards and Gattegno Charts which are also downloadable on EuHu.
Papa Titioning - A Tool for Learning
Papa Titioning is one of many Number Fun characters. Number Fun brings story, song, visualisation, animation and humour together in powerful video presentations. These videos are designed to support classroom reasoning and help teachers convey clarity in mathematical understanding, structures and vocabulary, whilst engaging children in fun-filled learning across their primary school years.
Note: All thumbnails below are hyper-linked to their location on EuHu, a Number Fun subscription is required for access.
Place Value
The original KS1 song partitioning 2-digit numbers into combinations of tens and ones.
Papa Titioning’s Log Classification System Millions through to Thousandths
Digit Zero helps Alice understand how many logs Papa T. has. (LKS2 & UKS2 versions)
Exploring relationships between a whole, 10 tenths, 100 hundreds and 1000 thousandths.
Papa T. and Alice read large numbers at a Log Lumbering award ceremony!
Mental Calculation
Addition by Mental Partitioning
Versions for each Year Group
Subtraction by Mental Partitioning
Versions for each Year Group
Multiplication by Mental Partitioning
Versions for different Year Groups
Division by Mental Partitioning
Several graded versions
Formal Methods
Column Addition with Understanding.
7 different graded versions
Column Subtraction with Understanding.
7 different graded versions
Column Multiplication with Understanding.
4 different graded versions
Short Division with Understanding.
4 different graded versions
About EuHu
EuHu is Findel’s digital learning platform designed to support teachers with high-quality resources, CPD, and curriculum content. Our mission is to make teaching easier by providing practical tools and ideas that reflect the realities of the classroom.
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