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

*ABC Mathseeds* is an innovative teaching and learning program
that focuses on the needs of students learning mathematics in
kindergarten to year 2. The program 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, *ABC 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 students 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
student progress, and provide useful feedback to students,
parents, and other key stakeholders in their schools.
*ABC Mathseeds* is carefully designed to motivate and maximise student
learning to provide the strongest foundation to achieve lifelong
mathematical success.

Sullivan (2011) in his research looked at the goals of school mathematics in first defining what we expect from mathematics programs in our schools. His research pointed to Australian practice as focused on giving “practical and useable mathematics” to children throughout their formal years of schooling. Ernest (2010) was explicit in his description of the two perspectives of mathematics, the practical perspective and the specialised perspective. Both perspectives are important in classroom pedagogy to ensure students receive the skills and content (practical) as well as the understanding (specialised) to use mathematics flexibly throughout their lives.

In its comprehensive design, the Australian Curriculum was built upon two dimensions to explore both perspectives: the content strands and the proficiencies. The content strands detail the mathematical concepts to be explored and the proficiencies look at “how content is explored or developed, that is, the thinking and doing of mathematics” and “the actions in which students can engage when learning and using the content” (ACARA, 2015). The proficiencies set this curriculum apart by linking content to the thoughtful action and active exploration by students at all levels of competency. In developing a national curriculum in this way ACARA has established a balanced and strong framework that aims to be flexible in order to challenge students in exploring mathematics.

In-depth analysis of mathematics and science retention rates in senior years of schooling has seen a steady, slow decline in Australia with figures that are reiterated in developed nations around the world (Kennedy, Lyons and Quinn, 2014, p.35). Increasingly students are opting for non-Calculus based mathematics courses propelling a downward trend in intermediate and advanced calculus based mathematics during senior years.

There are a plethora of reasons for this decline including self-efficacy in the subject, perceptions of difficulty but also usefulness, prior achievement in mathematics, alongside the rate of interest and enjoyment derived from mathematics (Department of Education, 2015). The difficulty for teachers and school administrators is to build up the profile of mathematics not only for the immediate need of university entrance requirements (which can dictate senior student choices) but also for “future aspirations” (Kennedy, Lyons and Quinn, 2014, p.45).

Schools need to make learning interesting and relevant to actively engage students
(Stephens, 2011). This begins in the early years of learning. Research by leading
scientists Prinsley & Johnston (2015) discusses the importance of transforming STEM
education in primary schools. *ABC Mathseeds* offers teachers an engaging, well-structured
program designed to motivate students to want to learn mathematics. By positioning
mathematics as a highly interactive tool for problem solving and reasoning, mathematics
becomes part of how students think and experience success. The program demands a high
achievement in mathematics learning in line with the Australian Government’s
determination to make mathematics a priority in schools (Prinsley & Johnston, 2015).
In the early years of STEM education student engagement and skill growth sets a
trajectory for sustaining higher levels of achievement in mathematics.

There is a strong emphasis on the need to capitalise on number sense in the early years of schooling, and teachers are encouraged to provide children with experiences that will develop number sense and thus improve mathematics outcomes.

Dr Sally Clare Howell and Dr Coral Rae Kemp, Macquarie University Special Education Centre, 2010)

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) 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, students need to explore numbers and engage with them using multiple presentations and a wide variety of different activity types.

*ABC 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 *ABC 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 students in a variety of ways.
The sequence of lessons in *ABC 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 students' thinking, making
connections, structured lessons, tools and representations, feedback, and
assessment for learning (Anthony, & Walshaw, 2009; Jensen, 2005; Sullivan,
2011). *ABC Mathseeds* combines each of these into an engaging environment for young
children. The program focuses on student interaction and features a wide variety
of short instructional movies and highly motivating activities. Students
continually earn rewards which encourages active participation.

All *ABC 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 program offers students opportunities
to engage in practise and review activities, with up to 12 parts. Initial lessons
build on the students’ early mathematical experiences and focus on developing
number sense. Other lessons focus on operations and algebra, geometry, measurement,
and data.

*ABC 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 students identify number eight both in
isolation and when presented as one of three other numbers. Students 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 student through one-to-one correspondence.

**Figure 3:** *Lesson 14*, narrator is guiding student 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 *ABC 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 *ABC 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 program.
In addition to the core lessons, the Driving Test area of the program 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
program focuses on building fluency with basic facts, this section brings mental
arithmetic to life, where students can engage in a huge range of fun activities
that develop number fact fluency.

"In the mathematics classroom engaged students are: actively participating—group discussions, practical, relevant activities and homework tasks genuinely valuing—'This learning will be useful to me in my life outside the classroom' reflectively involved in deep understanding of mathematical concepts and applications, and expertise."

Dr Catherine Attard, Lecturer in Primary Mathematics, 2012

Research indicates that mathematical engagement occurs when students 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 students 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 students 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 students 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 *ABC Mathseeds* activities bring mathematical concepts
to life. And with more than 350 different activities, students are always
seeing content that is new and interesting. For students working through the
program, the *ABC 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 *ABC Mathseeds* are the instructional movies and interactive activities
that make up the beginning of each lesson. Both the movies 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 students 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 students. The *ABC Mathseeds* instructional video sequence
is interspersed with short, interactive activities that serve as practise and
consolidation, as well as a method for keeping students focused.

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

The *ABC 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*, students continue simple patterns.

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

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

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

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 students
using virtual manipulatives and software as opposed to concrete materials.
*ABC Mathseeds* lessons use short and varied activities to maintain student interest
and regular rewards to g motivation. The activities are playful so that
students see them as an extension of how they play—and this means students
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 *ABC Mathseeds* instructional movies end with a song. This acts as an
additional way for students to remember mathematical concepts in a fun and
engaging way (Hayes, 2009; Jensen 2005).

One important feature of the *ABC Mathseeds* instructional format is that on
completion of every activity, the student receives immediate encouragement,
feedback, and error correction in a nonthreatening way. Feedback in the early
stages of learning is essential for keeping students 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. Students 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 students vital
opportunities to review, revise, and repeat new skills (Jensen, 2005). They allow
students 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 *ABC Mathseeds* program
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 students 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 students. 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 students apply in learning situations, highlighting the fact that not all children learn in the same way and require programs 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 students' broad range of intelligences.

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

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

**Logical/Mathematical**

*ABC Mathseeds* appeals to those who think logically. There are opportunities within
the program for students 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.

**Verbal/Linguistic**

The program offers opportunities for seeing, saying, counting, reading, and
writing numbers. The *ABC 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 program, 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. *ABC Mathseeds*
characters expose students to new mathematical expressions and help them
to explore mathematical vocabulary. Research indicates that these aspects
should be modelled in order to enhance students’ understanding (Runesson,
2005). At the end of each lesson, students 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

**Visual/Spatial**

The *ABC Mathseeds* program 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.
Students are taken to a range of virtual habitats. Stepping stones mark their
progress through each habitat, and on completion of each lesson, students
move forward to the next stepping stone. This creates a very powerful and
visual way of helping students see the progress they are making and ensures
that they stay motivated toward their goals. Making progress visible to
students is articulated in research as being a key goal (Adams & Hamm, 2014;
Marzano, 2007; McLennan & Peel, 2008).

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

**Bodily/Kinesthetic**

*ABC 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 students to see numbers as wholes.
The first *ABC Mathseeds* song, "There Is Only One of Me," encourages the student 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
students with number sense and spatial thinking. In *ABC Mathseeds* students are
encouraged to subitise early on and the presence of dominoes, dots and
various other engaging items to count are available for all students to use—
not just the kinesthetic learners. Research indicates that when given the
appropriate materials, students 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 program 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. Students 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 students to understand why a method works, rather than how to just solve a problem (Clausen-May, 2005).

**Musical**

*ABC 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 *ABC 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 *ABC Mathseeds*, students 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.

**Interpersonal/Intrapersonal**

The *ABC Mathseeds* program 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 program can also be used on an individual basis for students
who prefer to work alone at their own pace. It allows for thoughtful reflection on
individual progress.

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

“A student’s motivation for learning is generally regarded as one of the most critical determinants of the success and quality of any learning outcome.”

Sheri Coates Broussard & M. E. Betsy Garrison, Louisiana State University"

When addressing the issue of how to interest and engage students, Sullivan
and McDonough (2007) refer to the student’s "willingness to persist" (p.698).
This "willingness" is the motivation required for students 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 students 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 student motivation (Griffith
& Burns, 2012; Jensen, 2005). *ABC 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 student feel good and motivated to continue with the task (Bear, Connors & Paradiso, 2007; Jensen, 2005).

The *ABC Mathseeds* program rewards students 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 student. After subsequent lessons the student
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
*ABC Mathseeds* program actively motivates students through its elements of humour
and playfulness. Each hatching pet has its own unique character that students
can enjoy. In addition, the five key characters are role models for students;
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 *ABC Mathseeds*
program 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 student interest. The huge range of interactive
activities are uniquely written and animated in different styles to prevent
students 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). *ABC Mathseeds* rewards students
with golden acorns at the completion of each lesson and activity. These get
banked and can later be spent on clothes for the student’s avatar (online
character) or furniture for their personal tree house.

After the completion of five lessons, students 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 student achievement (Marzano, Pickering & Pollock,
2001). The range of rewards that *ABC Mathseeds* offers students actively
encourages them to engage with the program, explore it, learn from it and
value their progress.

“Choosing engaging experiences as contexts for a variety of tasks assists in making mathematics inclusive, and these tasks can be effectively differentiated both for students experiencing difficulty and those who complete tasks easily.”

Australian Curriculum Assessment and Reporting Authority, 2015"

Assessment is necessary to monitor progress, to identify strengths and weaknesses,
and to inform further instruction (ACARA, 2015). *ABC Mathseeds* weaves student-facing
assessment seamlessly throughout the program. Detailed reports keep teachers informed
as to where individual students are in reaching their goals. By basing all lessons
and assessment on the Australian Curriculum achievement standards, teachers and school
leadership staff can make informed judgments about student understanding against
national standards.

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

*ABC 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 students demonstrate competency.
The gradual removal of scaffolds reduces the potential for anxiety and boosts student
success. For students, interactive activities offer immediate feedback and the ability
to correct errors. These are critical to ensure students continually self-monitor their
understanding.

*ABC Mathseeds End-of-Map Quizzes* and *Driving Tests* provide formal assessment opportunities.
At the completion of every five lessons students complete a 15 question assessment quiz. This
assesses student understanding of the content covered in the latest map with results appearing
in teacher reports. The *Driving Tests* are 10 question tests that assess student knowledge in
essential mathematics skills. These assessments have responsive feedback that requires students
to redo questions answered incorrectly. This allows students 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 Australian Curriculum assessment tasks that can be used with individual
students, groups or the whole class. In the Australian Curriculum, the achievement standards allow
teachers “to make a balanced judgement about the quality of learning demonstrated” (ACARA, 2015).
To do this, teachers need data and *ABC Mathseeds* provides 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 students (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 *ABC Mathseeds*
program takes advantage of the inherent benefits of computer technology.

The program 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). *ABC Mathseeds* is
an innovative interactive teaching and learning resource designed by educators
to connect students to the key concepts of number sense. In teaching and
learning sequences, students 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.

*ABC Mathseeds* is an interactive Web-based program 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.
*ABC Mathseeds* has been built on best practices in pedagogical research alongside
core curriculum initiatives, creating a program that is both educationally sound
and highly motivating. *ABC 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
program offers a range of age-appropriate rewards that actively encourage
students to engage with the program, explore it, learn from it and value
their progress.

*ABC 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
students, 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, *ABC Mathseeds* has been carefully
designed to maximise student learning and to equip students 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.

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

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) *Mathematics by inquiry roundtable key messages*. Retrieved
29 April 2016 from
https://docs.education.gov.au/system/files/doc/other/maths_by_inquiry_roundtable_key_messages.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 student 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
students with learning disabilities. *The Journal of Special Education, 33*, 18–28.

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 students 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
students 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 students’ mathematics learning. *Educational Psychology Review, 22* (3),
215–243.

Manner, B. (2001). Learning styles and multiple intelligences in students. *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 student 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.

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.

Prinsley, R. & Johnston, E. (2015) *Transforming STEM teaching in Australian primary
schools: everybody’s business – Position Paper*. Canberra: Australia.

Queensland Studies Authority (2006). *Developing early mathematical
understandings*. Retrieved February 7, 2015, from www.qcaa.qld.edu.au/
downloads/p_10/ey_lt_maths_understandings.pdf

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 student 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.

Willis, J. (2014). Neuroscience reveals that boredom hurts: Students 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.

**Click to download the Report as a PDF**