**By Sara Leman & Amy Russo with Katy Pike**

*Mathseeds* is an innovative teaching and learning programme
that focuses on the needs of pupils learning mathematics in
reception to year 2. The programme has been carefully
structured to support individual learning by combining pedagogical
research on number sense, child development, technology,
motivation, and key curriculum initiatives. Taking into consideration
the needs, learning styles, and future direction of learners in the
21st century, *Mathseeds* combines a highly motivational play-based
online context with structured, sequential mathematical lessons. At
the core it is a teaching and learning sequence consisting of more than 150
lessons where key concepts in mathematics are taught, explored,
practised and assessed. Alongside the core lessons are fluency
and assessment components, as well as rewards and a range of
teacher resources to guide pupils toward their most successful
mathematical future. It seamlessly connects learning between
school and home across a range of computer devices. Teachers
are able to monitor and report on both whole class and individual
pupil progress, and provide useful feedback to pupils,
parents, and other key stakeholders in schools.
*Mathseeds* is carefully designed to motivate and maximise pupil
learning to provide the strongest foundation to achieve lifelong
mathematical success.

Recent studies conclude that numeracy skills in the United Kingdom have
deteriorated between 2003 and 2011, sparking renewed debate on the importance
of numeracy skills for future social and economic success (National Numeracy
for everyone, for life, 2016). Teachers of mathematics have a responsibility
to foster interest in mathematics to “open up the possibility of mathematics
being something that they *want* to pursue beyond what they are *required*
to do” (Askew, 2016, p. 1).

*Mathseeds* offers teachers an engaging, well-structured programme designed to
motivate pupils to want to learn mathematics. By positioning mathematics as a highly
interactive tool for problem solving and reasoning, mathematics becomes part of how
pupils think and experience success.

The *Mathseeds* programme demands a high achievement in mathematics learning in-line
with the government’s determination to make mathematics a priority in schools. This begins
in the early years of learning. From the first national curriculum in 1989, the government
committed to helping children to “delight and wonder” at mathematics (p. A3) and in the 2016
*Educational Excellence Everywhere* (2016) paper they re-affirmed this commitment for all pupils.

To teach a more challenging curriculum in the primary years, research supports evidence-based teaching alongside developing mastery (Department of Education, 2015, p89). This involves building a solid foundation in maths and quantitative skills. Research demonstrates these skills can be transformational for future generations in their social, cultural and educational settings (National Numeracy for everyone, for life, 2016).

“Number sense … shapes children’s mathematical futures and potentially their life chances, from their earliest engagement with mathematical learning.”

Rebecca Turvill, Brunel University, 2016

Children develop their mathematical abilities following natural learning progressions with number sense being a formative platform for numeracy success (Clements & Sarama, 2009; Klibanoff, Levine, Huttenlocher, Vasilyeva & Hedges, 2006). Broadly, number sense is the "understanding of number needed by children if they are to succeed in mathematics" (Howell & Kemp, 2006). It encapsulates counting abilities, number patterns, estimation; sequencing, connecting counting to cardinality, and number manipulation.

In their research, Cain, Doggett, Faulkner & Hale (2007) outline seven key elements that are core to number sense. Figure 1 shows these components: quantity/magnitude, numeration, equality, base ten, form of a number, proportional reasoning, and algebraic and geometric thinking. Faulkner (2009) asserts that ultimately these components of number sense operate as a useful framework in visualising the interconnectedness of the principles of mathematics. It is important to view this not as a progressive model but rather to see that each component is connected and integral to each lesson.

**Figure 1:** Cain and colleagues (2007) identified seven core components of number sense.

Strong number sense has been shown as a precursor of future mathematical success (Jordan, Kaplan, Locuniak & Ramineni, 2007, Back, Sayers & Andrews, 2013) with the suggestion it may prove to be to mathematics what phonemic awareness is to reading (Gersten & Chard, 1999). To help nurture the natural learning progress of number sense, pupils need to explore numbers and engage with them using multiple presentations and a wide variety of different activity types.

*Mathseeds* recognises the importance of number sense and the strong
developmental role it has for setting the most successful trajectory in
mathematics. It situates number sense activities in scenarios that are familiar,
such as playgrounds, kitchens for cooking, and shopping adventures. In doing
this *Mathseeds* provides a playful environment to explore and interpret the
quantitative concepts of number sense. This playful format also allows for number
sense concepts to be presented and explored by pupils in a variety of ways.
The sequence of lessons in *Mathseeds* supports children by continually revisiting
concepts and building on earlier skills in a way that deepens their understanding.
This provides a strong foundation for more complex mathematical processes to
come.

Research has indicated that several principles and critical factors underpin
the most effective mathematical pedagogy and instruction. These principles
include motivation and engagement, building on pupils' thinking, making
connections, structured lessons, tools and representations, feedback, and
assessment for learning (Anthony, & Walshaw, 2009; Jensen, 2005; Sullivan,
2011). *Mathseeds* combines each of these into an engaging environment for young
children. The programme focuses on pupil interaction and features a wide variety
of short instructional videos and highly motivating activities. Pupils
continually earn rewards which encourages active participation.

All *Mathseeds* lessons follow a similar structure. Each lesson focuses on a
particular mathematical competency, with instructional lessons being taught
by one of the five key characters. The programme offers pupils opportunities
to engage in practise and review activities, with up to 12 parts. Initial lessons
build on the pupils’ early mathematical experiences and focus on developing
number sense. Other lessons focus on operations and algebra, geometry, measurement,
and data.

*Mathseeds* Lesson 14 has 12 instructional parts and activities. The lesson
introduces the number eight. It has as a strong instructional focus on the early
skill of one-to-one correspondence which is an important prerequisite to rational
counting (Reys, Lindquist, Lambdin & Smith, 2012). Figure 2 shows this teaching
activity in action. Mango the monkey and Silky the spider help children identify
the number eight visually and by name. Various activities follow that reinforce
the number’s name and shape, and pupils identify number eight both in
isolation and when presented as one of three other numbers. Pupils count
one item at a time to reinforce the concept of cardinality. Figure 3 shows this
teaching activity in action.

**Figure 2:** *Lesson 14*, narrator is guiding pupil through one-to-one correspondence.

**Figure 3:** *Lesson 14*, narrator is guiding pupil through one-to-one correspondence.

After the initial lesson animations, Lesson 14 continues with a variety of
interactive activities that focus on number identification, number formation,
number name recognition, number lines, sorting, and counting. The final
learning activity is the ebook which recaps what has been learned and acts like
a plenary for each *Mathseeds* lesson to consolidate new concepts and skills.
The final part of each lesson is a pet-hatching animation. Each lesson ends
with the hatching of a unique pet that is added to the *Mathseeds* map. This is a
highly motivational element for children who look forward to seeing which animal
will be next. These hatching pets act as both a reward for lesson completion and
also encourage children to proceed to the next lesson in the programme.
In addition to the core lessons, the Driving Test area of the programme offers a
wide range of tests that assess skills and knowledge in number, operations,
patterns, measurement, geometry, and data. While the Number Facts area of the
programme focuses on building fluency with basic facts, this section brings mental
arithmetic to life, where pupils can engage in a huge range of fun activities
that develop number fact fluency.

“Mathematics is not only taught because it is useful. It should be a source of delight and wonder, offering pupils intellectual excitement and an appreciation of its essential creativity.”

National Curriculum, 1989

Research indicates that mathematical engagement occurs when pupils enjoy the subject of mathematics, value their mathematics learning, and see the relevance of it in their lives. The ability to make connections between the mathematics that is taught in class and the mathematics that is applied in the outside world is crucial (Attard, 2012; Roschelle, Pea, Hoadley, Gordin & Means, 2000). Similarly, Willis (2014) has stated that, "relevance increases engagement and reduces boredom when pupils recognise instruction as related to their interests…" (p.30). It is engagement, rather than memorisation tasks that activates more pleasure structures in the brain (Poldrack, Clark, Pare-Blagoev, Shohamy, Creso Moyano, Myers & Gluck, 2001).

In recognising the importance of this research, the lessons and Playroom activities encourage pupils to make connections between their experience of the real world and mathematical thinking. Anthony & Walshaw (2009) in their research commented how:

"Making connections across mathematical topics is important for developing conceptual understanding… When pupils find they can use mathematics as a tool for solving significant problems in their everyday lives, they begin to view the subject as relevant and interesting." (p.156)

New skills and concepts are taught in a context that is relevant, familiar, and of
interest to most young children. From choosing the correct bus as it drives by, to
feeding birds the correct number of worms in a bird café, to getting an astronaut
back to his rocket ship, the *Mathseeds* activities bring mathematical concepts
to life. And with more than 350 different activities, pupils are always
seeing content that is new and interesting. For pupils working through the
programme, the *Mathseeds* lessons and activities are all set in a nonthreatening
environment that supports risk taking and rewards perseverance.

“Over the past decade a suite of studies focused on the early bases of mathematical abstraction and generalisation has indicated that an awareness of mathematical pattern and structure is both critical and salient to mathematical development among young children.”

Joanne Mulligan, Associate Professor, Macquarie University

At the core of *Mathseeds* are the instructional movies and interactive activities
that make up the beginning of each lesson. Both the videos and activities
have been purposely designed to encourage active learning rather than
what Roschelle and his colleagues referred to as the "passive role of receiving
information" (2000, p.79). Evidence supports the belief that pupils learn best
when they are provided with short sessions, a quick instructional pace, and time
to process new information (Fuchs & Fuchs, 2001; Jensen, 2005). As shown
in Figure 4, Jensen (2005) recommends 5-8 minutes direct instruction for
early primary school pupils. The *Mathseeds* instructional video sequence
is interspersed with short, interactive activities that serve as practise and
consolidation, as well as a method for keeping pupils focused.

**Figure 4:** Jensen (2005) identified appropriate durations for direct instruction for children.

The *Mathseeds Playroom* contains several activities that have been designed
for young children. They are a combination of open-ended tasks, such as
stamping shapes to create a picture, or specific tasks such as popping balloons
on a 0–9 number line. Figures 5–8 show these learning activities in action.
The activities take into consideration the short concentration spans of young
children, but several activities loop for as long as the child wants to engage
and play.

**Figure 5:** *Playroom*, pupils continue simple patterns.

**Figure 6:** *Playroom*, pupils are playing with cardinality.

**Figure 7:** *Playroom*, pupils are exploring measurement.

**Figure 8:** *Playroom*, pupils are identifying numbers and colouring.

“Representations are key tools for mathematical learning, particularly the use of linked multiple representations. Often conceptual understanding comes through recognising representations and the connections between them.”

Anne Watson, Oxford University; Keith Jones, University of Southampton; Dave Pratt, Institute of Education; 2016

Interactive activities are by their nature, more compelling than paper and
pencil activities. A study by Moyer, Niezgoda & Stanley (2005) revealed the high level of creativity and complexity demonstrated by kindergarten pupils
using virtual manipulatives and software as opposed to concrete materials.
*Mathseeds* lessons use short and varied activities to maintain pupil interest
and regular rewards to g motivation. The activities are playful so that
pupils see them as an extension of how they play—and this means pupils
are more likely to be fully involved and immersed in the activity, which also
helps to build stronger connections and boost memory retention of new skills.
Many of the *Mathseeds* instructional movies end with a song. This acts as an
additional way for pupils to remember mathematical concepts in a fun and
engaging way (Hayes, 2009; Jensen 2005).

One important feature of the *Mathseeds* instructional format is that on
completion of every activity, the pupil receives immediate encouragement,
feedback, and error correction in a nonthreatening way. Feedback in the early
stages of learning is essential for keeping pupils on track and focused
(Garnett, 2005; Griffith & Burns, 2012; Jensen, 2005). Hattie and Timperley
(2007) reveal that "… the most effective forms of feedback provide cues or
reinforcement to learners… in the form of video-, audio-, or computer-assisted
instructional feedback…" (p.84). This view is shared by Roschelle et al. (2000),
who confirm that computer technology encourages rapid interaction and
feedback. Pupils who receive this type of prompt feedback are more likely to
be motivated to continue (Fuchs & Fuchs, 2001).

The interactive activities that follow each lesson give pupils vital
opportunities to review, revise, and repeat new skills (Jensen, 2005). They allow
pupils to build on their knowledge and see the links between mathematical
ideas, as evidenced as important by Anthony & Walshaw (2009). In keeping
with the concept of a spiral curriculum (Bruner, 1960), the *Mathseeds* programme
is structured so that ideas introduced in early lessons are later revisited at a
more advanced level. Mathematical vocabulary is introduced early in order to
prepare pupils for future, more complex learning (Anthony & Walshaw, 2009;
Jensen, 2005).

“Pluralisation achieves two important goals: when a topic is taught in multiple ways, one reaches more pupils. Additionally, the multiple modes of delivery convey what it means to understand something well. When one has a thorough understanding of a topic, one can typically think of it in several ways, thereby making use of one’s multiple intelligences.”

Howard Gardner, Developmental Psychologist, Harvard Professor

Much has been written regarding individual learning styles and multiple intelligences; their importance and implications for learning (Adams, 2000; Bloom 1956, Clausen-May, 2005; Green, 1999; Tiberius & Tipping, 1990). The work of Gardner (2011) identifies the variety of intelligences that pupils apply in learning situations, highlighting the fact that not all children learn in the same way and require programmes that reflect their different approaches to learning (Adams, 2000). The scope of Gardner’s work on discrete multiple intelligences is demonstrated by Figure 9. Educators can engage with the widest possible audience when they design activities that utilise their pupils' broad range of intelligences.

**Figure 9:** Howard Gardner’s Multiple Intelligences

*Mathseeds* is designed to appeal to different learning styles and multiple
intelligences. The programme’s content and variety allow all pupils the
opportunity to engage in mathematical learning. The following examples
illustrate how *Mathseeds* caters for multiple intelligences.

*Mathseeds* appeals to those who think logically. There are opportunities within
the programme for pupils to calculate answers, solve problems with numbers,
draw conclusions, explore the relationships between numbers, shapes, and
statistical data, work with different representations of numbers, and gather and
interpret information.

The programme offers opportunities for seeing, saying, counting, reading, and
writing numbers. The *Mathseeds Playroom* also offers opportunities for young
children to hear and sing along with familiar nursery rhymes that reinforce
counting and simple mathematical concepts such as days of the week.

Throughout the programme, children are encouraged to listen and follow
instructions. There are opportunities to read and comprehend word problems
and explore ways of converting problems to algebraic expressions. *Mathseeds*
characters expose pupils to new mathematical expressions and help them
to explore mathematical vocabulary. Research indicates that these aspects
should be modelled in order to enhance pupils’ understanding (Runesson,
2005). At the end of each lesson, pupils can read ebooks that consolidate
new concepts. The texts are professionally narrated which provides a model for
the child’s own reading fluency. Figure 10 shows the layout and content for the
e-book *Near Doubles* for Lesson 91.

**Figure 10:** *Lesson 91*, *Near doubles* e-book

The *Mathseeds* programme features high-quality, colourful animations that have
been designed to appeal to the visual learner. The onscreen graphics are bold,
clear, and engaging. Lesson progression is mapped in a fun and unique way.
pupils are taken to a range of virtual habitats. Stepping stones mark their
progress through each habitat, and on completion of each lesson, pupils
move forward to the next stepping stone. This creates a very powerful and
visual way of helping pupils see the progress they are making and ensures
that they stay motivated toward their goals. Making progress visible to
pupils is articulated in research as being a key goal (Adams & Hamm, 2014;
Marzano, 2007; McLennan & Peel, 2008).

In addition, each *Mathseeds* lesson is accompanied by an ebook with
full-colour illustrations. The programme also has accompanying posters
and worksheets to consolidate learning and increase information processing.

*Mathseeds* offers kinesthetic learners the ability to engage their senses and
create an experience that goes beyond simply learning by rote which Clausen-May
(2005) identifies as crucial. Early number concepts are taught in a very
visual and kinesthetic way and encourage pupils to see numbers as wholes.
The first *Mathseeds* song, "There Is Only One of Me," encourages the pupil to
see and feel that they have only one nose, one face, one mouth, etc.

Bobis (2008) in her research identifies how virtual manipulatives can assist
pupils with number sense and spatial thinking. In *Mathseeds* pupils are
encouraged to subitise early on and the presence of dominoes, dots and
various other engaging items to count are available for all pupils to use—
not just the kinesthetic learners. Research indicates that when given the
appropriate materials, pupils can mentally combine and partition numbers.
This is an important skill prior to the introduction of addition and subtraction
(Bobis, 2008).

Early addition lessons physically show the main character joining two distinct subgroups together to form one group or total. Only when this concept of addition is in place does the programme present addition in the form of a simple number sentence and eventually as a formal algorithm. Figures 11–13 demonstrate the sequential building of this conceptual knowledge.

**Figure 11:** *Lesson 24*, characters are exploring two distinct groups and joining them together to find the total.

**Figure 12:** *Lesson 51*, characters are adding and locating the final counted numeral as the total on a number line.

**Figure 13:** *Lesson 65*, characters are creating formal number sentences from pictorial representations.

Similarly, subtraction is taught through more than one approach. Pupils physically take items away from the main group when learning how to subtract. They also learn to cover items up, and eventually progress to counting back along a number line, using subtraction number sentences and finally formal algorithms. This multilevel and kinesthetic approach allows pupils to understand why a method works, rather than how to just solve a problem (Clausen-May, 2005).

“Play and learning maths do not have to be mutually exclusive events. Play and games can give young children opportunities to learn and develop foundational math skills.”

Dr Geetha Ramani & Sarah Eason, University of Maryland, 2016

*Mathseeds* is full of playful songs that act as mnemonics to aid memory and
consolidate new concepts. The songs are popular among children and perfect
for those who have sensitivity to music. The *Mathseeds Playroom* has a number
of traditional nursery rhymes and familiar songs that reinforce simple counting
skills and other mathematical ideas.

**Figure 14:** *Lesson 66*, characters singing a fraction song about quarters.

Aspects of rhythm are also used to teach mathematical concepts such as
patterning. According to Mulligan (2010), "an awareness of mathematical
pattern and structure is both critical and salient to mathematical development"
(p.47). In *Mathseeds*, pupils are encouraged to participate in simple dances,
led by the onscreen characters, to demonstrate the idea of repeating patterns.
Figure 14 is an example of one such song from Lesson 66 about fractions.

The *Mathseeds* programme can be used in a variety of ways to promote
interpersonal and intrapersonal skills. It can be used with a whole class or for
a focused group lesson. It encourages talk and discussion, sharing, and group
participation. The programme can also be used on an individual basis for pupils
who prefer to work alone at their own pace. It allows for thoughtful reflection on
individual progress.

*Mathseeds* lessons encourage pupils to think about how they use
mathematics outside of the lesson. This provides opportunities for pupils to
draw on their own experiences and construct their understandings of the real
world (Perry, 2000; Tiberius & Tipping, 1990). In *Mathseeds* the onscreen
characters model how to solve problems through discussion and rationalising.
They effectively teach pupils how to monitor the problem-solving process
and demonstrate for pupils how a collaborative atmosphere enhances learning.

“In order to become capable and strategic learners in mathematics, pupils need to have confidence in their own ability and self-identity as learners of mathematics. Strategies that promote inclusiveness, deep thinking, and ownership, can have a powerful effect on building pupils’ mathematics skills.”

Chris Kyriacou, Professor in Educational Psychology, University of York

“Raising pupil attainment in mathematics is one of those things that is so easy to say, yet is so difficult to achieve, and sustain. In short, it is an enduring challenge in most mathematics classrooms.”

Sue Gifford & Penny Latham, Everyone Learning Project, 2013

When addressing the issue of how to interest and engage pupils, Sullivan
and McDonough (2007) refer to the pupil’s "willingness to persist" (p.698).
This "willingness" is the motivation required for pupils to complete learning
activities. Motivation plays a key role in learning (Gagne & Deci, 2005; Jensen,
2005; Rodionov & Dedovets, 2011; Sullivan & McDonough, 2007; Taylor &
Adelman, 1999). Intrinsic motivation rewards pupils purely for participating
in the activity itself, whereas extrinsic motivation is derived from gaining awards
such as certificates or verbal rewards (Gagne & Deci, 2005; Ryan & Deci,
2000). These important, positive rewards impact pupil motivation (Griffith
& Burns, 2012; Jensen, 2005). *Mathseeds* seeks to provide both intrinsic and
extrinsic motivational rewards in order to produce total satisfaction.

Rewards reinforce existing learning and encourage new learning to occur. The brain responds favourably to rewards, the potential for rewards (prediction) and to unexpected rewards (surprise). It releases a sudden burst of dopamine that makes the pupil feel good and motivated to continue with the task (Bear, Connors & Paradiso, 2007; Jensen, 2005).

The *Mathseeds* programme rewards pupils with a cute pet that hatches from
an acorn at the end of each lesson sequence. The first time this happens is
an unexpected surprise for the pupil. After subsequent lessons the pupil
knows it will happen (prediction) but they still have the element of surprise as
they do not know what each pet will be until it hatches.

According to Edward de Bono, "Humour is by far the most significant activity
of the human brain" (de Bono cited by Griffith & Burns, 2012). The
*Mathseeds* programme actively motivates pupils through its elements of humour
and playfulness. Each hatching pet has its own unique character that pupils
can enjoy. In addition, the five key characters are role models for pupils;
exploring new mathematical challenges and having fun whilst they learn.

Learning is an ongoing, dynamic process and the learning environment must
continuously change to reflect this (Taylor & Adelman, 1999). The *Mathseeds*
programme moves through different locations, with regard to the lessons and
reward maps. The key characters remain the same but they present the lessons
intermittently to maintain pupil interest. The huge range of interactive
activities are uniquely written and animated in different styles to prevent
pupils from becoming bored and demotivated.

According to Taylor & Adelman (1999), "One of the most powerful factors
for keeping a person on task is the expectation of feeling some sense of
satisfaction when the task is completed" (p.266). *Mathseeds* rewards pupils
with golden acorns at the completion of each lesson and activity. These get
banked and can later be spent on clothes for the pupil’s avatar (online
character) or furniture for their personal tree house.

After the completion of five lessons, pupils participate in an online quiz.
If they pass, their efforts are rewarded with a printable gold, silver, or
bronze certificate with their name on it. Providing a representation of a very personal accomplishment can be a valuable
motivator to improve pupil achievement (Marzano, Pickering & Pollock,
2001). The range of rewards that *Mathseeds* offers pupils actively
encourages them to engage with the programme, explore it, learn from it and
value their progress.

“I am more and more convinced of a need for planned consolidation, so that after every mathematical task, whether it was a practice exercise, a problem-solving activity, a game, or whatever, there needs to be some kind of interaction that reviews the core mathematical idea, together with its language, and its representations, and focuses on how it arose and how it might be recognised in future.”

Anne Watson, Oxford University, 2014

Assessment is necessary to monitor progress, to identify strengths and weaknesses, and to inform further instruction. *Mathseeds* weaves pupil-facing assessment seamlessly throughout the programme. Detailed reports keep teachers informed as to where individual pupils are in reaching their goals. This enables teachers and school leadership staff to make informed judgments about pupil understanding against national standards and benchmarks.

*Mathseeds* includes both summative and formative assessment opportunities. These
assessments present pupils with multiple avenues to show their knowledge and have
distinct structures to cater for a wide range of pupils.

*Mathseeds* provides multiple opportunities for informal assessment through the range
of interactive activity types. These increase in difficulty by gradually removing
supports like reminders and visual manipulatives as pupils demonstrate competency.
The gradual removal of scaffolds reduces the potential for anxiety and boosts pupil
success. For pupils, interactive activities offer immediate feedback and the ability
to correct errors. These are critical to ensure pupils continually self-monitor their
understanding.

*Mathseeds End-of-Map Quizzes* and *Driving Tests* provide formal assessment opportunities.
At the completion of every five lessons pupils complete a 15 question assessment quiz. This
assesses pupil understanding of the content covered in the latest map with results appearing
in teacher reports. The *Driving Tests* are 10 question tests that assess pupil knowledge in
essential mathematics skills. These assessments have responsive feedback that requires pupils
to redo questions answered incorrectly. This allows pupils to critically evaluate incorrect
responses to reinforce correct mathematical thinking.

Another assessment component can be found in the *Teacher Toolkit*, where teachers can choose
from a range of printable assessment tasks that can be used with individual pupils, groups or the whole class.
This provides teachers with the rich assessment data to aid both in reporting
and to inform targeted teaching.

“One of the chief benefits of mobile devices is that they enable learning anywhere, anytime. This allows a shift away from the industrial era model where the classroom is the central place of learning driven by the teacher and limited to instruction within the school day. In deploying mobile devices, the teacher is no longer at the centre of the learning process and the instructional time can transcend the school day.”

Dr Kristy Goodwin, Institute of Early Childhood, Macquarie University, 2012

As technology permeates all aspects of interactions, it has become "an ubiquitous tool for teaching and learning" (Li & Ma, 2010, p.215).

Cheung & Slavin (2013) identify that as technology permeates 21st century
living, the question for teachers shouldn’t be whether to use educational
technology but rather what applications ensure it is in the best
way for pupils (p.102). Technology that enables the manipulation of virtual
objects is powerful (Hoyles & Noss, 2009), as are regenerative question designs
that afford endless practise opportunities. By its design, the *Mathseeds*
programme takes advantage of the inherent benefits of computer technology.

The programme allows children to manipulate objects in a variety of ways, to experiment without fear of failure and test out their new skills through a range of practise opportunities. Accessible on desktop and mobile devices, it bridges the home and school divide working to connect family and school communities in the learning process.

Research indicates the most powerful potential for tools are where meaningful
interactions operate alongside sound teaching and learning strategies (Coley,
Cradler & Engel, 2000) and guided support (Moyer et al., 2005). *Mathseeds* is
an innovative interactive teaching and learning resource designed by educators
to connect pupils to the key concepts of number sense. In teaching and
learning sequences, pupils play with virtual manipulatives in short, focused
sequences. This teaching is always linked to content in the lesson that follows
and is a scaffold to provide guided support for activities within the lesson
sequence.

*Mathseeds* is an interactive Web-based programme that incorporates a huge
range of highly structured, effective, research-based activities. It combines
rigorous learning with high-interest level activities, taking into consideration
the needs, learning styles and future direction of learners in the 21st century.
*Mathseeds* has been built on best practices in pedagogical research alongside
core curriculum initiatives, creating a programme that is both educationally sound
and highly motivating. *Mathseeds* lessons provide an engaging environment
for young children who learn best through play. The instructional elements and
interactive activities are set in contexts that are meaningful and relevant. The
programme offers a range of age-appropriate rewards that actively encourage
pupils to engage with the programme, explore it, learn from it and value
their progress.

*Mathseeds* is designed to seamlessly connect learning between school and
home, making learning possible anywhere and easily accessible on different
devices. Its comprehensive assessment and reporting procedures allow
pupils, parents, and teachers to receive instant feedback on progress and
achievements made. Written by experts with over 25 years of experience in
creating high-quality educational resources, *Mathseeds* has been carefully
designed to maximise pupil learning and to equip pupils with the strongest
foundation possible to achieve lifelong mathematical success.

Adams, T. L. (2000). Helping children learn mathematics through multiple
intelligences and standards for school mathematics. *Childhood Education, 77*, (2),
86–94.

Adams, D. & Hamm, M. (2014). *Teaching math, science and technology in schools
today: Guidelines for engaging both eager and reluctant learners.* Plymouth:
Rowman & Littlefield Education.

Anthony, G., & Walshaw, M. (2009). Characteristics of effective teaching of
mathematics: A view from the West. *Journal of Mathematics Education, 2* (2),
147–164.

Askew, M. (2016) *Transforming primary mathematics: understanding classroom tasks, tools
and talk.* Routledge: New York.

Attard, C. (2012). Engagement with mathematics: What does it mean and what
does it look like? *Australian Primary Mathematics Classroom, 17* (1), 9–13.

Back, J., Sayers, J. & Andrews, P. (2013) *The development of foundational number
sense in England and Hungary: a case study comparison.* Conference Proceedings: CERME 2013.

Bear, M., Connors, B. & Paradiso, M. (2001). *Neuroscience. Exploring the brain.*
Baltimore, MD: Lippincott Williams & Wilkins.

Bloom, B. (1956). *Taxonomy of educational objectives.* New York: David Mackay.

Bobis, J. (2008). Early spatial thinking and the development of number sense.
*Australian Primary Mathematics Classroom, 13* (3), 4–9.

Bruner, J. (1960). *The Process of Education.* Cambridge: Harvard University Press.

Cain, C., Doggett, M., Faulkner, V., & Hale, C. (2007). *The components of number
sense*. Raleigh, NC: NC Math Foundations Training, Exceptional Children’s Division
of the North Carolina Department of Public Instruction (NCDPI).

Cheung, A. C. K. & Slavin, R. E. (2013). The effectiveness of educational
technology applications for enhancing mathematics achievement in K–12
classrooms: A meta-analysis. *Educational Research Review, 9*, 88–113.

Clausen-May, T. (2005). *Teaching maths to pupils with different learning styles*.
London: Paul Chapman Publishing.

Clements, D. & Sarama, J. (2009). *Learning and teaching early math: The
learning trajectories approach*. New York: Routledge.

Coley, R., Cradleer, J. & Engel, P.K. (2000). *Computers and the classroom:
The status of technology in U.S schools*. Princeton: Policy Information Center,
Educational Testing Service.

Cross, C. T., Woods, T. A. & Schweingruber, H. (Eds.) *Mathematics learning in early
childhood: Paths toward excellence and equity*. Washington, D.C.: National Academy
Press.

Department of Education (2015) *National curriculum assessments at key stage 2 in England.*
Sheffield: Education Data Division, Department of Education. Accessed from
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/456343/SFR30_2015_text.pdf

Department of Education (2016) *Educational Excellence Everywhere.* London: Williams Lea Group
on behalf of Her Majesty’s Stationery Office. Accessed from
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/508550/Educational_excellence_everywhere__print_ready_.pdf

Edelson, D. C., & Joseph, D. M. (2001). *Motivating educational psychology
interactive*. Valdosta, GA: Valdosta State University.

Faulkner, V. N. (2009). The components of number sense: An instructional model
for teachers. *Teaching Exceptional Children, 41* (5), 24–30.

Fredricks, J., McColskey, W., Meli, J., Mordica, J., Montrosse, B., and Mooney, K.
(2011). *Measuring pupil engagement in upper elementary through high school:
A description of 21 instruments*. (Issues & Answers Report, REL 2011–No. 098).
Washington, D.C: U.S. Department of Education, Institute of Education Sciences,
National Center for Education Evaluation and Regional Assistance, Regional
Educational Laboratory Southeast.

Fuchs, L. S., & Fuchs, D. (2001). Principles for the prevention and intervention of
mathematics difficulties. *Learning Disabilities Research & Practice, 16* (2), 85–95.

Gagne, M. & Deci, E. L. (2005). Self-determination theory and work motivation.
*Journal of Organized Behavior, 26*, 331–362.

Gardner, H. (2011). *Frames of mind: The theory of multiple intelligences (3rd ed.)*.
New York: Basic Books.

Garnett, S. (2005). *Using brainpower in the classroom: Five steps to accelerate
learning*. London: Routledge.

Gersten, R. & Chard, D. J. (1999). Number sense: Rethinking math instruction for
pupils with learning disabilities. *The Journal of Special Education, 33*, 18–28.

Gifford, S. & Latham, P. (2013) Removing the glass ceiling on mathematical achievement
in primary classrooms: Engaging all pupils in mathematical learning. *Mathematics Teaching 232*,
pp. 31–34.

Green, F. E. (1999). Brain and learning research: Implications for meeting the needs
of diverse learners. *Education, 111* (4), 682–687.

Griffith, A. & Burns, M. (2012). *Outstanding teaching: Engaging learners*. Wales:
Crown House Publishing.

Hayes, O. C. (2009). *The use of melodic and rhythmic mnemonics to improve
memory and recall in elementary pupils in the content areas*. Unpublished
Ph.D., Dominican University of California.

Hattie, J. & Timperley, H. (2007). The power of feedback. *Review of Educational
Research, 77* (1), 81–112.

Highfield, K. & Mulligan, J. (2007). The role of dynamic interactive technological
tools in preschoolers’ mathematical patterning. In J. Watson & K. Beswick (Eds.),
*Mathematics: Essential research, essential practice* (pp.372–381). Adelaide:
Mathematics Education Research Group of Australasia Inc.

House, J. D. (2006). Mathematics beliefs and achievement of elementary school
pupils in Japan and the United States: Results from the third international
mathematics and science study. *The Journal of Genetic Psychology, 167* (1), 31–45.

Howell, S. & Kemp, C. (2009). An international perspective of early number sense:
Identifying components predictive of difficulties in early mathematics achievement.
*Australian Journal of Learning Disabilities, 11* (4), 197–207.

Hoyles, C. & Noss, R. (2009). The technological mediation of mathematics and its
learning. *Human Development, 52*, 129–147.

Jensen, E. (2005). *Teaching with the brain in mind*. Alexandria, VA: Association for
Supervision & Curriculum Development.

Jordan, N. C., Glutting, J. & Ramineni, C. (2009). The importance of number sense
to mathematics achievement in first and third grades. *Learning and Individual
Differences, 20*, 82–88.

Jordan, N. C., Kaplan, N., Locuniak, M. N. & Ramineni, C. (2007). Predicting first-grade
math achievement from developmental number sense trajectories. *Learning
Disabilities Research & Practice, 22* (1), 36–46.

Kennedy, J., Lyons, T., Quinn, F. (2014). The continuing decline of science and mathematics
enrolments in Australian high schools. *Teaching Science, 6* (2), pp. 34-46.

Kilpatrick, J., Swafford, J. & Findell, B. (Eds.) *Adding it up: Helping children learn
mathematics*. Washington, D.C.: National Academy Press.

Klibanoff, R. S., Levine, S. C., Huttenlocher, J., Vasilyeva, M. & Hedges, L. V. (2006).
Preschool children’s mathematical knowledge: The effect of teacher “Math Talk”.
*Developmental Psychology, 42* (1), 59–69.

Li, Q. & Ma, X. (2010). A meta-analysis of the effect of computer technology on
school pupils’ mathematics learning. *Educational Psychology Review, 22* (3),
215–243.

Manner, B. (2001). Learning styles and multiple intelligences in pupils. *Journal
of College Science Teaching, 30* (6), 390–393.

Marzano, R. J. (2007). *The art and science of teaching: A comprehensive
framework for effective instruction*. Alexandria, VA: Association for Supervision
and Curriculum Development.

Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). *Classroom instruction that
works: Research-based strategies for increasing pupil achievement*. Alexandria,
VA: Association for Supervision and Curriculum Development.

McLennan, B. & Peel, K. (2008). Motivational pedagogy: Locking in the learning.
*The Australian Education Leader, 30* (1), 22–27.

Moyer, P., Niezgoda, D. & Stanley, M. (2005). Young children’s use of virtual
manipulatives and other forms of mathematical representation. In W. Masalski & P. Elliott (Eds.), *Technology-supported mathematics learning environments*
(pp. 17–34). Reston: NCTM.

Mulligan, J. T. (2010). Reconceptualising early mathematics learning.
In C. Glascodine and K. Hoad (Eds.) *Teaching mathematics? Make it count*.
Proceedings of the Annual Conference of the Australian Council for Educational
Research (pp. 47–52). Camberwell: ACER.

National Curriculum Council (1989). *Mathematics: non-statutory guidance.*
York: National Curriculum Council.

National Numeracy: For everyone, for life (2016) *What is the issue?* Accessed from
https://www.nationalnumeracy.org.uk/

Perry, B. (2000). *Early childhood numeracy. Australian Association of Mathematics
Teachers*. Retrieved February 2, 2015 from www.aamt.edu.au/content/
download/1252/25269/file/perry.pdf

Poldrack, R. A., Clark, J., Pare-Blagoev, E.J., Shohamy, D., Creso Moyano, J., Myers,
C. & Gluck, M.A. (2001). Interactive memory systems in the human brain. *Nature,
414*, 546–550.

Ramani, G. B. & Eason, S. H. (2015) It all adds up: learning early math through play
and games. *Phi Delta Kappan, 96* (8), pp. 27–32.

Rays, R. E., Lindquist, M., Lambdin, D. V. & Smith, N. L. (2012). *Helping children
learn mathematics* (10th ed.). United States: John Wiley & Sons.

Renninger, K. A. (2000). Individual interest and its implications for understanding
intrinsic motivation. In C. Sansone and J. M. Harackiewicz (Eds.) *Intrinsic
motivation: Controversies and new directions* (pp. 373–404). San Diego, CA:
Academic Press.

Rodionov, M. & Dedovets, Z. (2011). Increasing learner’s level of motivation in
mathematics education through the use of uncomplicated situations. *Literacy
Information and Computer Education Journal, 2* (2), 366–371.

Roschelle, J. M., Pea, R. D., Hoadley, C. M., Gordin, D. N. & Means, B. M. (2000).
Changing how and what children learn in school with computer-based technologies.
*The Future of Children: Children and Computer Technology, 10* (2), 76–101.

Runesson, U. (2005). Beyond discourse and interaction. Variation: A critical aspect
for teaching and learning mathematics. *Cambridge Journal of Education, 35* (1),
69–87.

Ryan, M. & Deci, E. L. (2000). Intrinsic and extrinsic motivations: Classic
definitions and new directions. *Contemporary Educational Psychology, 25*, 54–67.

Stephens, M. (2011). *Engagement in mathematics: defining the challenge and promoting
good practices*. Research Monograph 9, Melbourne: Department of Education and Early
Childhood Development.

Sullivan, P. (2011). *Teaching mathematics using research-informed strategies*.
Camberwell, Vic: ACER Press.

Sullivan, P. & McDonough, A. (2007). Eliciting positive pupil motivation for
learning mathematics. *Mathematics: Essential Research, Essential Practice:
30th Annual Conference of the Mathematics Education Research Group of
Australasia, 2*, 698–707.

Taylor, L. & Adelman, H. (1999). Personalizing classroom instruction to account
for motivational and developmental factors. *Reading & Writing Quarterly, 15*,
255–276.

Tiberius, R. & Tipping, J. (1990). *Twelve principles of effective teaching and
learning for which there is substantial empirical support*. Toronto: University of
Toronto.

Turvill, R. (2016) *Number sense as a sorting mechanism in primary mathematics education.*
CERME 9—Ninth Congress of the European Society for Research in Mathematics Education,
Prague, Czech Republic. pp. 1658–1663.

Watson, A., Jones, K., Pratt, D. (2016). *Key ideas in teaching mathematics*. London: Nuffield
Foundation. Accessed from http://www.nuffieldfoundation.org/key-ideas-teaching-mathematics

Watson, A. (2014). Consolidation *Mathematics Teaching 243*, pp.19–22.

Willis, J. (2014). Neuroscience reveals that boredom hurts: pupils who seem
to willfully defy admonishments to focus on their work may not be doing so
intentionally but rather as a normal, age-appropriate brain reaction. *Phi Delta
Kappan. 95* (8), 28–32.

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