Designing an Engaging Mathematics Framework

The provided content includes a range of academic papers, books, and articles that explore various aspects of education, including mathematics learning, literacy teaching, teacher beliefs, and student motivation. The sources cover topics such as early childhood education, primary school pupils, and the development of numeracy skills in kindergarteners. Additionally, there are resources on learning environments, collaborative problem-solving, and the importance of creative thinking in education. Overall, this diverse range of content can be useful for understanding different perspectives and approaches to teaching and learning.

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World of Math

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Introduction
Globally, the education systems considers Mathematics or Arithmetic a crucial foundation course
for all learners. This is the study of numbers, quantity, patterns, processes, logic and space
among others. Mathematical reasoning comprises of systematic models, which lead to the
acquisition of numeracy skills. Therefore, Math is necessary for making scientific deductions and
developing numeracy. The difference between Math and Numeracy lies in their concepts. The
two also have similarities in application.
Mathematics
The Mathematical calculations facilitate for the development of different discoveries (Sierinska
& Kilpatrick, 2012). Under the mathematic laws, objectivity provides concrete evidence for
applications in real life situations. Its classification includes pure and applied mathematics. Pure
mathematical concepts such as arithmetic is useful in scientific studies like engineering and
physics. It presents ideas and models for studying abstract phenomenon such as abstract research
on space distance. Its ideas also provide solutions in applied mathematics for subjects like social
research. Mathematics simplifies notions and classifies case studies. Algebra, which is part of its
study, provides rules for manipulating numbers. It also comprises of geometry, which focuses on
figures, shapes and sizes.
Numeracy
Numeracy is a skill obtained from studying Mathematics. Learners who have the ability to use
numbers and Math concepts have numeracy skills (Purpura, Hume, Sims, & Lonigan, 2011).
Being literate in Math calls for an ability to reason using numbers. It involves the use of a wide
variety of concepts in problem solving. Referred to as logic reasoning or thinking it consists of
knowledge in calculations, data interpretation, reading charts, processes and numbers. Reasoning

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through numbers calls for an understanding of Mathematical concepts such as arithmetic,
statistics, geometry, and others. Learners have different levels of numeracy therefore the
assessment levels also vary. For example, foundation mathematics teaches basic mathematic
concepts like addition, subtraction and multiplication. Advanced learners know how to make
deductions from complex concepts like ratios, probabilities and matrices. Professional numeracy
involves the use of multiple concepts.
Similarities between Math and Arithmetic
The development of numeracy skills starts at an early stage and develops to maturity depending
on the exposure of the learner. Competency in numeracy skills dictates that the learner has the
ability to process, make interpretation and communicate mathematic concepts effectively. This
calls for a combination of different ideas such as the analysis and interpretation of frequencies,
graphs and trends. Thus, Math and numeracy are similar in application. Their concepts overlap
during application. Both concepts have evolved over time and they apply to real life situations.
Numeracy helps people run bank accounts and make purchases while Math helps business
people to make transactions. Both involve the use of numbers for problem solving. The
application of Mathematics and numbers is evident in the creation of timetables, and setting the
time.

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Part 2: Collection of resources
2.1 Theme: Preschool and early numeracy learning
Evidence: Pirjo, A., Pekka, H., Joannes, E. H., & Jari-Matt, V. (2014). The development of early
numeracy skills in kindergaten in low-average-and high perfomance groups. Journal of Early
Childhood Research, 13(1), 3-16
Description: Pirjo, Pekka, Joannes, & Jari-Matt (2014) note that the development of early
numeracy skills in preschool children is different in all children. Though numeracy starts early,
there are factors which influence the development of numeracy in preschoolers. Teachers support
this development by breaking down complex arithmetic lessons into simple tasks that learners
enjoy.
Rationale: This resource supports the mental capacities and the development of numeracy skills.
Understanding numbers starts with early development of math skills (Stanberry, 2017). Young
learners between 2 and 5 years learn math by counting physical objects from memory. Activities
such as measuring water jars, counting bubbles and building blocks simplify math concepts for
the learners. Numerical skills acquired through interesting math concepts from real world
examples are memorable (Yelland, 2011). However, the mind develops through training and
learning activities. Learners need professionally trained teachers to develop complex numerical
skills. Although there are inborn abilities, this age group also learns numeracy from exposure
(Morales, Calvo, & Bialystok, 2013).
Application: Learning mathematical concepts is easier with practical examples from what
children have seen, touched or interacted with and kid’s games are excellent. Computerized
games and rhymes also use common themes that children can comprehend. Learning through fun

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and games or audiovisual shapes children’s memory. Children in preschool learn counting by
shapes, numbers and simple charts. In order to acquire numeracy, learners draw, classify and
count different items. Singing in numerical themes is one way to motivate arithmetic learning.
The preschool themes come to life with experiences that children can connect and interact with
when learning. Among these are video clips of activities done with parents and caregivers. Math
in the real world reveals challenges and opportunities. Buying items at the groceries provides a
number of math ideas for learners. This is a chance for children to learn math addition,
subtraction, and shapes. Using a video on the market place reminds children of shopping
experiences. Using their favorite fruits helps them to add fruits and vegetables. This age may not
be conversant with pricing but will learn counting and subtracting items. Age, vocabulary and
attention abilities are some factors, which determine the effectiveness of the learning process
(Melissa, Lisa, & Halberda, 2013). Videos, toys, the internet, books, and magazines are some
useful learning resources for preschool mathematics.
2.2 Theme: Planned Play and Incidental Play Experiences
Evidence: Robinson, K. (2011). Out of our minds: Learning to be creative. John Wiley & Sons
Description: Using interesting and creative ideas stimulates the learner’s mind (Robinson, 2011).
Play based learning curriculum consists of creative games such as dancing, ball games and
building blocks. In order to develop numeracy effectively, a teacher adds incidental play
experiences in the learning environment. Leaning math is interesting with colorful blocks made
of different shapes.

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Rationale: Structured play needs planned and incidental experiences because children can
recognize shapes and symbols depending on familiarity. Shaping a student’s attitude towards
math calls for the incorporation of fun in learning. Further research shows the importance of
building blocks in helping students to learn math (Clements, Sarama, Spitler, Lange, & Wolfe,
2011). The resource identifies planned play as effective in the development of math because it
relies on research evidence. Planned play includes outdoor and indoor activities that children
enjoy. Psychologists and educational researchers encourage the use of creativity in solving
problems and brainstorming. However, learning outcome is not always positive and it hinders the
child’s ability to become independent in creativity.
Application: Creating a conducive learning environment fosters learning through Incidental play.
Children develop math ideas through incidences like drawing. The combination of songs and
sequence images helps young learners to connect numbers and their symbols. Having a song
board in the play school connects the learner to unplanned learning. This environment is
conducive for children with mental challenges like Autism (Baron-Cohen, Tager-Flusberg, &
Lombardo, 2013). Shaping arithmetic skills needs both planned and incidental learning activities.
This is important because it replaces negative behavior with attention and interactive behavior.
Family members and caregivers are important elements in incidental learning because children
also grasp information from observation and repeated action (Jonassen & Land, 2012). Effective
and efficient learning involves both formal and informal processes. ECD learning is important in
shaping futures math careers therefore a learning institution needs a good plan. Planned play is
effective in mentorship programs and professional training. Planned play sticks within the
curriculum in order to ensure that learners understand variety of concepts. On the other hand,
incidental learning is good for reflective, experimental and impromptu learning. An integrated

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model provides a comprehensive approach that caters for classroom and out of class learning for
the effective development of numeracy (Entwistle, 2013).
2.3 Theme: Mathematics in primary school
Evidence: Beswick, K. (2012). Teachers' beliefs about school mathematics and mathematicians'
mathematics and their relationship to practice. Educational Studies in mathematics, 79(1), 127-
147
Description: Learning mathematics in primary school forms the foundation of careers in
mathematics, but does not shape a mathematician. School mathematics has a different focus
from its practice in real life. The classroom math has different activities from what
mathematician practice. Based on these differences, it is difficult to predict a student’s outcome
at primary level.
Rationale: A successful learning experience in math could lead to a mathematician career.
However, the field of mathematics practice is highly diversified. Primary level learners have a
wide variety of subjects to choose from and this makes it hard to predict a student’s trend or
career choice. A good mathematics foundation prepares learners for careers in different sectors
including sciences and technology careers (McAleavy, 2012). In order to shape a primary school
student into a mathematician the student needs exposure to a math-oriented curriculum. This is
important in sharpening the ability to memorize, develop progression and focus on numeracy
continuously.
Application: Mathematics as a subject is complex. It requires a comprehensive learning approach
that encourages innovative and friendly training. This is a better option than coercive training,
which affects the learner’s attitude. The process of training future mathematicians follows

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learning theories such as constructivism, which has instrumental and progressive learning
(Jonassen & Land, 2012). Its effect supports knowledge obtained from the cognitive abilities and
the nurturing environment. As a result, the learner can pursue different interests. A learner’s
attitude is important in an arithmetic based career. Choosing to focus on numeracy prepares a
learner for an independent professional development. A mathematician’s career needs an in-
depth analysis of concepts giving the learner confidence. The primary school learning
environment helps the student to learn standard procedures while discovering strategies for
solving mathematical problems. This stage motivates and removes any anxieties that the student
may have. Primary arithmetic shapes the cognitive in order to prepare the learner for complex
problems in future. Different grades have concepts to develop the reasoning capacity in stages
(Mrbee, 2017). Among these is Meta recognition, rules of calculation, concepts and
identification of facts.
2.4 Theme: Math and the learning environment
Evidence: Charlesworth, R. (2015). Math and science for young children. Cengage.
Description: The learning environment determines the successful implementation of science and
math subjects. It encourages awareness creation through the stimulation of ideas. Education in
numeracy combines extrinsic factors such as assessments, curriculum, professional instruction
and coaching. Mathematical skills mature over time hence a conducive environment caters for
different approaches including classroom, audio visual and outdoor learning.
Rationale: An example of a stimulating math-learning environment is the Princeton International
School of Mathematics and Science (PRISMS, 2016). In this environment, learners experiment
and share knowledge. The students also participate in the content development of the curriculum.

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The authenticity of the curriculum has in mind the learner’s ability and motivations. As a result,
its evaluation and learning processes shape the learner into becoming mathematicians and
scientists. Although this conditioned learning is effective in focusing the learner’s attention, it
limits the student’s creative abilities to innovate and diversify into different careers. This may
also have monotony, which affects the motivation and students efficiency.
Application: Researchers support a mixed learning environment because it is inclusive (Salvia,
Ysseldyke, & Witmer, 2012). A math-learning environment is exclusive and it targets specific
qualifications and learners. Students wishing to join such learning institutions need to pass
certain tests. Its curriculum design provides an opportunity for professional development.
Students have a chance to explore each other and widen their curiosity. Having common
standards of learning within the learning environment encourages the development of the subject
and it encourages competence ( National Research Council, 2012). The learning environment is
crucial for individuals and teams. Behaviorist propose the use of rewards for a positive outcome
in a learning environment. Math students need both intrinsic and extrinsic motivation in order to
succeed (Sadler, Sonnert, Hazari, & Tai, 2012). Pursuing a career in mathematics calls for inner
drive. Evidently, learners in preschool, primary and high school levels learn math at different
levels because children have multiple intellectual abilities. However, specialization in
professional development calls for a focus. When designing the learning environment for the
development of numeracy skills, it is important to consider the teaching strategies. This
encourages consistency and learners can gain knowledge by exploration.

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Theme: Motivating learners for numeracy skills
Evidence: Attard, C. (2014). I dont like it, I dont love it, and I dont mind. Introducing a
framework for engagement with mathematics. Curriculum Perspective, 34(3), 1-14
Description: The primary and secondary school curriculum comprises of mathematics as one of
the major subjects. The significance of numeracy skills is evident in learner’s literacy levels.
However, a good number of learners lack the passion for math. How can teachers motivate
learners to develop a passion and open mind for mathematics?
Rationale: The process of learning numeracy through mathematics is important. Its agenda is to
prepare competent learners ready for the professional and real life application. The environment
needs an effective environment for reasoning, planning and learning. Factors affecting the
learner include foundational learning, exposure to the external environment and individual drive
(Dabbah & Kitsantas, 2012). Each student has a perception on his or her learning environment.
Some students learn better through exploration while others embrace learning through the social
environment. Learning environments have both formal and informal approaches in order to
accommodate all kinds of learners. However, having an environment that motivates all
individuals is impossible.
Application: The development of numeracy skills has different effects on learners. Some pursue
math courses in order to develop problem-solving skills. In other incidences learner intends to
understand the basic concepts. However motivating them towards pursuing math related careers
takes individual efforts (Posamentier, 2013). Every learning institution needs to invest in quality
teachers and curriculum development for intrinsic and extrinsic motivation. The performance of
the learning teams depends on the personality of the teachers, the classroom environment,
motivation from the school and learning techniques. The development of numeracy is a

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continuous process and visible change in individuals is important. Classroom and out of class
challenges stimulate the learner but practical application gives them the interest. The use of
puzzles and games makes the games practical. Learning math is important for numeracy skills. It
provides important skills for everyday life. Baking requires accurate measures of ingredients, and
surveyors make use of perimeter, circumference and length measurements to allocate land.
Numeracy helps professionals and leaners across different levels. Its wide knowledge comprises
of different theories and symbols for problem solving, estimation, measurements and
mathematical ideas. This makes math subjects useful across different industries. Students should
learn about its wide variety of definitions for different subjects of study, scientific and artistic
applications (Brophy, 2013).
Theme: New modalities and math
Evidence: Beschorner, B., & Hutchinson, A. (2013). Ipads as a literacy teaching tool in early
childhood. Online Submission, 1(1), 16-24
Description: Beschorner & Hutchinson ( 2013) agrees that the use of technoloogy is important
today. Young children use ICT applications and devices for classroom learning. The use of ipads
as a teaching method is preschool has its pros and cons. In mathematics, the counting games
support the learner’s by boosting their thinking ability.
Rationale: The new modalities of teaching and learning mathematics includes ICT applications
and devices. These technology tools enhance learning through lively digital experiences. This
gives children the exposure to modern learning techniques. Although there have been concerns
that the use of computer in learning alters the teaching modalities, there are some play school

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games that are beneficial. Incorporating them in the planned and incidental play has more
benefits than harm. The creative use of ICT in the development of numeracy skills needs
effective model that will not hinder social development of the child. Preschool learning is
supposed to be holistic (Desoete, Ceulemans, De Weerdt, & Pieters, 2012).
Application: The use of counting games within an Early Childhood context is effective and does
not inhibit play behavior. In order to create an engaging activity using ICT, devices such as iPads
have computer supported learning (CSCL) themes, which young people enjoy (Light & Blaye).
Research on the use of tablets for home and school learning environments agrees that tablets
have practical applications for learning numeracy (Neumann & Neumann, 2014). However, in
order to avoid misusing technology in learning, the effective use of the iPad, is important. This
will distinguish between its impact as a teaching support tool and its effective use by learners and
teachers. Children can easily learn about mathematic symbols and shapes through the images and
pictures portrayed in audiovisual technology. Educational software provides 3D and animation
characters for easy learning. The games improve children’ creativity and problem solving skills
for a positive attitude in learners. However, technology may not be affordable for all students.
Teachers also need to monitor preschooler’s use of technology for the greatest benefits. Web
based platforms provide a wider scope of understanding and it enhances the instructional
delivery modules. It also encourages learners to explore mathematics with an open mind for
future development.
Conclusion
Numeracy is the ability to understand and interpret patterns, formulations and logic and
applications is numeracy. Useful for theoretical applications, it provides practical approaches for
daily functions and operations. Mathematical subjects prepare learners by equipping them with

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these skills. Early childhood development shapes the trend for the future. However, it takes a
continuous learning process for a learner to focus on a career in math. This may not happen in
preschool nor primary level. Whether physical or digital, the learning environment needs to have
important elements that encourage the development of a mathematician. This includes teachers,
learning platforms, curriculum and the social surrounding.
References

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National Research Council. (2012). A framework for K-12 science education: Practices,
crosscutting concepts and core ideas. National Academies Press.
Attard, C. (2014). I dont like it, I dont love it, and I dont mind. Introducing a framework for
engagement with mathematics. Curriculum Perspective, 34(3), 1-14.
Baron-Cohen, S., Tager-Flusberg, H., & Lombardo, M. (2013). Understanding other minds:
Perspectives from developmental social neuroscience. Oxford University Press.
Beschorner, B., & Hutchinson, A. (2013). Ipads as a literacy teaching tool in early childhood.
Online Submission, 1(1), 16-24.
Beswick, K. (2012). Teachers' beliefs about school mathematics and mathematicians'
mathematics and their relationship to practice. Educational Studies in mathematics,
79(1), 127-147.
Bishop, E., & Bridges, D. (2012). Constructive analysis. Springer Science & Business Media.
Brophy, J. (2013). Motivating students to learn. Routledge.
Charlesworth, R. (2015). Math and science for young children. Cengage.
Clements, C. D., Sarama, J., Spitler, M. A., Lange, A., & Wolfe, C. B. (2011). Mathematics
learned by young children in an intervention based on learning trajectories: A large-scale
cluster randomized trial. Journal for Research in Mathematics Education, 42(2), 127-
166.
Dabbah, N., & Kitsantas, A. (2012). Personal Learning Environments, social media, self
regulated: A natural formula for connecting formal and informal learning. The Internet
and higher education, 15(1), 3-8.

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Desoete, A., Ceulemans, A., De Weerdt, F., & Pieters, S. (2012). Can we predct mathematical
learning from symbolic and non symbolic comparison tasks in kidergarten? Findings
from a longitudinal study. British Journal of Educational Psychology, 82(1), 64-81.
Entwistle, N. (2013). Styles of learning and teaching: An integrated outline of educational
psychology for students, teachers and lecturers. Routledge.
Jonassen, D., & Land, S. (2012). Theoretical foundations of learning environments. Routledge.
Light, P., & Blaye, A. (n.d.). Collaborative problem solving with hypercard: The influence of
peer interaction on planning and information handling strategies. In C. O'Malley,
Computer Supported Collaborative Learning.
McAleavy, T. (2012, July 20). Exploring different approaches to teaching primary maths. The
Guardian. Retrieved September 16, 2017, from https://www.theguardian.com/teacher-
network/2012/jul/20/primary-maths-programme
Melissa, E. l., Lisa, F., & Halberda, J. (2013). Is appropriate number precision a stable or math
ability? Learning and individual differences, 25, 126-133.
Morales, J., Calvo, A., & Bialystok, E. (2013). Working memory development in monolingual
and bilingual children. Journal of experimental child psychology, 114(2), 187-202.
Mrbee, T. (2017, June 23). Developing reasoning skills in primary school pupils. Retrieved
September 14, 2017, from thirdspacelearning:
https://www.thirdspacelearning.com/blog/2017/developing-reasoning-how-to-improve-
maths-reasoning-skills-in-primary-school-pupils

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Neumann, D., & Neumann, M. (2014). Touch screen tablets and emergent literacy. Early
Childhood Educational Journal, 42(4), 231-239.
Pirjo, A., Pekka, H., Joannes, E. H., & Jari-Matt, V. (2014). The development of early numeracy
skills in kindergaten in low-average-and high perfomance groups. Journal of Early
Childhood Research, 13(1), 3-16.
Posamentier, A. (2013, November 1). 9 strategies for motivating students in mathematics:
Keeping your hioigh school math students engaged with these techniques. Edutopia.
Retrieved September 16, 2017, from https://www.edutopia.org/blog/9-strategies-
motivating-students-mathematics-alfred-posamentier
PRISMS. (2016). Princeton International School of Mathematics and Science. Retrieved from
prismsus.org: http://www.prismsus.org/
Purpura, D. J., Hume, L. E., Sims, D., & Lonigan, C. (2011). Early literacy and early numeracy:
the value of including early literacy skills in the prediction of numeracy development.
Journal of experimental child psychology, 110(4), 647-658.
Robinson, K. (2011). Out of our minds: Learning to be creative. John Wiley & Sons.
Sadler, P. M., Sonnert, G., Hazari, Z., & Tai, R. (2012). Stability and volatility of STEM career
interest in high school: A gender study. Science Education, 96(3), 411-427.
Salvia, J., Ysseldyke, J., & Witmer, S. (2012). Assessment: in special and inclusive education.
Cengage Learning.
Sierinska, A., & Kilpatrick, J. (2012). Mathematics education as a research domain: A search
for identity. Springer Science & Business Media.

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Stanberry, K. (2017). Understanding numbers and counting skills in preschoolers. Retrieved
from getreadytoread.org: http://www.getreadytoread.org/early-learning-childhood-
basics/early-math/understanding-numbers-and-counting-skills-in-preschoolers
Yelland, N. (2011). Reconceptualising play and learning in the lives of young children.
Ausralian Journal of Early Childhood, 36(2), 4.