Statement of purpose:
This review explores research and literature around the notion of numeracy as an embedded part of every key learning area in the curriculum, with a focus on PDHPE. It will consider numeracy across the curriculum and the difference between embedded and integrated numeracy in the school context. Numeracy is mathematical education that provides students with a wide range of knowledge, skills and related activities that help them to develop an understanding of the physical world and social interactions. It gives the students a language and a system through which they can analyse, describe and explain a wide range of experiences, make predictions, and problem solve. Numeracy concepts underpin everyday life, through knowing days of the week, reading days and dates, measurement, spatial awareness, positioning and knowing time. Mathematics can be often seen as a ‘stand-alone’ subject and can be neglected from integration unit of work (Sellars, 2017), however it is clear that numeracy is embedded in all Key Learning Areas (KLAs). For example, measurements and patterns in science, timelines and dates in math and graphing and mapping in geography. The focus of this review will be on how numeracy is embedded into the KLA of PDHPE, with reference to the NSW and Australian Syllabus and current literature. It is essential to understand the importance of embedding KLAs into one another as they influence professional pedagogical practice and enthuses and encourages students in all key learning areas.
Numeracy across the curriculum:
Numeracy is a fundamental component of student learning across all areas of the school curriculum, as students are required to effectively apply mathematical skills in a range of subjects and contexts (Geiger et al., 2015a; Kissane, 2012). For this reason, it is crucial that educators view numeracy as a central part of the curriculum, rather than simply an “educational by-product that develops as a result of studies in these subjects” (Bennison, 2015, p. 561). Different curriculum contexts demand distinctive knowledge and skills, which conveys that students need to have the disposition and competence to select and use the numeracy appropriate for a context or situation (Siemon et al., 2011; Steen, cited in Goos et al., 2012). Therefore, it is critical that teachers foster the development of students’ numeracy capabilities as opportunities arise within each curriculum area (Bennison, 2015). Development of numeracy and problem-solving skills prepare students to live, reflect and contribute to society (Geiger et al., 2015b; Goos et al., 2012; Kissane, 2012).
Physical education is defined as meeting the physical needs of the student and the need for movement experiences, challenges and play. It develops a desire for daily physical activity and encourages constructive use of free time and participation in physical activities through the rest of their lives (Delaney, 2012).
Numeracy – embedded or integrated into PDHPE:
Relevant within this review is the contrast between ‘embedded’ and ‘integrated’, with embedded defined as ingrained within, foundational to, or an integral component of, and integrated defined as combining two components or linking various aspects (Oxford University Press, 2017; Oxford University Press, 2017b). This review is pertinent as recognition of the embedded nature of numeracy in KLAs such as PDHPE is essential in understanding and influencing professional pedagogical practice.
Numeracy in PDHPE is often referred to as being integrated rather than embedded. A large body of research supports the view that integrating physical activity in lessons produces positive outcomes, academic achievement, engagement, sedentary time and staying on task (Bartholomew & Jowers, 2011; Beck et al., 2016; Grieco, Jowers, Errisuriz, & Bartholomew, 2016; Martin & Murtagh, 2015; Mullender-Wijnsma et. al., 2015; Mullender-Wijnsma et. al., 2016; Riley, Lubans, Holmes, & Morgan, 2016).
This integration is extremely effective and efficient in enriching numeracy through enjoyment and achievement. Physically activities reflected in the literature clearly show links to numeracy skills such as; number, operations, spatial awareness, patterns, sequences, fractions, time, data, length, and problem solving (Bartholomew & Jowers, 2011; Beck et al., Mullender-Wijnsma et. al., 2016) thus, authenticating the fundamental numeracy concepts within the KLA PDHPE. Research into numeracy and PDHPE integration clearly shows that there is an interrelation between Mathematics and PDHPE; however further research needs to be done into the fundamental role that numeracy plays in PDHPE learning. This will then highlight, and pin point the importance of this integration and provide clear details of how students benefit from this integration.
Numeracy: foundation of the PDHPE syllabus pyramid
It is clear that numeracy concepts are integrated into all the strands of PDHPE, many mathematical concepts are fundamental in the acquisition and understanding of PDHPE skills. The numeracy concepts of communicating, reasoning, logic and justification are central to the skill strands in PDHPE. For example, the communication strand contains concepts of transitionary periods, sequencing, critical thinking skills, reasoning for understanding good health (BOS, 2007). Decision making involves mathamatical data, measuring and understanding the difference between healthy and unhealthy products. Chance and probability are involved when looking at and making safety decisions. Interacting involves adaptive reasoning when looking at logical thought and explanation strategies, events and dates (BoS, 2007; Kilpatrick, Swafford, & Findell, 2001; Sullivan, 2011). In the Moving strand the concepts that are embedded are direction, sequencing, distance, speed, position and patterns. Understanding is developed through appreciation of these of these embedded strands as they increase student engagement, and deeper and conceptual understanding. (BoS, 2007; Kilpatrick et al., 2001; Sullivan, 2011). The most significant embedment of these skill outcomes is the Problem-Solving strand. Patterns, sequences, chance and probability, mapping and data, strategic ability formed through interpreting, understanding and solving of problems, and adaptive reasoning developed through logical consideration of issues, reflection on outcomes, and explanation and justification of solutions (BoS, 2007; Kilpatrick et al., 2001; Sullivan, 2011).
Numeracy is linked throughout the PDHPE ‘knowledge and understanding’ strands with the strongest links in measurement, spatial awareness, patterns and logic. Within the Active Lifestyle strand Numeracy skill embedded are time, sequencing, space, logic, data, patterns and trends, reasoning, logic, and laterality, which is pertinent within the primary school context (BoS, 2007). In the Dance and gymnastics strand the numeracy concepts are very similar such as time, duration, direction, sequencing, patterns, spatial awareness, angles and preciseness. Student understanding is developed through appreciating how to perform these tasks (BoS, 2007; Kilpatrick et al., 2001; Sullivan, 2011). Growth and Development incorporates gathering and interpreting data relating to personal characteristics and life changes, sequencing, measurement, analysing, reasoning, and logic through devising strategies. Interpersonal relationships involves gathering of data and adaptive reasoning through logical thought, explanation and reason of communication, cooperation and relationships (BoS, 2007, Kilpatrick et al., 2001; Sullivan, 2011). Vital to the Personal Health Choices strand are the numerical, statistics, data, reasoning and logic concepts that will relate to vitamins, exercise and foods. Safe Living encompassing statistics, data, patterns and trends relating to behaviour and personal wellbeing, and logic through devising strategies and action plans (BoS, 2007). The Games and Sports strand includes area and perimeter of sports fields, time, spatial awareness relating to sporting positions and roles of players and numerical data relating to scores and sporting leader boards. Importantly problem solving is vital as it is central to decision making relating to the playing of the game and the strategic decisions that need to be made. (BoS, 2007). This shows how numeracy in integrated through all parts of the PDHPE syllabus, it provides students with the opportunity to engage and develop a deep understanding of the value of numeracy skills in their everyday lives. This integration can also provide students with practical ideas of mathematic skills they are learning in the classroom (Thompson, 2015).
Thus, with the embedment of numeracy in PDHPE; students are able to use their knowledge of calculation, estimation and measurement when understanding information in regard to nutrition, fitness and navigation in sporting activities. Students use spatial reasoning in movement activities when developing concepts and strategies for individual and team sports. Through using statistical reasoning, knowledge of patterns and data students will be able to interpret and analyse health and physical activity information and make predictions and inform health behaviour and practices ("Numeracy in the NSW Syllabuses for the Australian curriculum", 2018).
Easy Minds program
As outlined above numeracy is foundational throughout physical activities, and physical activity can be better integrated into other KLAs. EASY (Encouraging Activity to Stimulate Young) Minds is a new approach combating students disinterest in math and moving (Riley et al., 2016). The aim of the EASY Minds study was to evaluate the impact of a primary school-based physical activity integration program delivered by trained classroom teachers on objectively measured physical activity and a range of educational outcomes. Research has found that higher levels of physical fitness are linked to improved academic performance. In recent times, there has been increasing pressure on schools to demonstrate academic success, including the publication of comparisons of school performance in literacy and numeracy. There has been less pressure to demonstrate a school’s success in promoting physical activity. Nevertheless, schools have a responsibility to encourage the physical development of all students, helping them master fundamental movement skills and develop a positive attitude to physical activity including sport (Physical Activity in Government Primary Schools, 2018). Results from the EASY Minds cluster randomised controlled trial demonstrated that children who received the intervention achieved significantly improved physical activity across the school day; increased physical activity and moderate-to-vigorous physical activity during mathematics lessons; reduced sedentary time across the school day and during mathematics; and improved on-task behaviour in class (Riley, Lubans, Morgan & Young, 2015).
EASY Minds demonstrated a significant improvement in ‘on task’ behaviour and thus movement-based learning may potentially result in increased time ‘on task’. The strengths of the EASY Minds feasibility study are that it is an innovative and unique programme that specifically integrates Physical Activity across the mathematics curriculum and maintaining the integrity of the mathematics lesson outcomes. (Riley, Lubans, Morgan & Young, 2015). The traditional use of teacher-centered approaches in mathematics can be recognised as disengaging; students can view numeracy as a set of isolated procedures and fail to see the real-life applications to their learning outside of the classroom therefore it is important to improve student’s enjoyment of mathematics by addressing subject disengagement (Riley et al., 2016). Innovative teaching methods that provide positive mathematical learning experiences can help enhance students’ experiences and outcomes in mathematics. Through integrating physical activity into mathematic lessons as a novel pedagogical strategy, teachers are able to improve the engagement levels of students in mathematics (Riley et al., 2016). Pedagogical frameworks such as the NSW Quality Teaching model was designed to improve pedagogy and enhance student learning, the model supports teachers to develop their capacity to deliver engaging lessons. The engaging pedagogies that the Easy Minds program works to promote aligns with the NSW Quality Teaching model for example ‘Intellectual Quality’ is evident in the program as mathematical concepts and ideas were central to all activities and resources used were especially chosen to promote mathematical understanding and physical activity (Riley et al., 2016). Pedagogy that treats knowledge as something that requires active construction and requires students to engage in higher order thinking. (NSW DET, 2003). Easy Minds promotes student desire to be more innovative in their learning in terms of incorporating physical activity and outdoor activities into their learning and the program forces teachers to be more creative and forward thinking by implementing a movement-based approach to teaching mathematical concepts (Riley et al., 2016).
Discussion
Through placing emphasis on embedding Numeracy and PDHPE students are given the opportunity to transfer and apply their mathematical knowledge and skills to PDHPE activities. They also learn to appreciate the use of their mathematical skills and apply them to real world problems (Sellars, 2017). It is important to emphasise though that this integration must not take way from the PDHPE curriculum but used to elevate and enhance learning (Thompson, 2015). The Australian curriculum places emphasis on the importance of knowledge integration and teaching students to recognise mathematic skills that are used outside the mathematic classroom. Integrating these KLAs has the potential to provide positive mathematic learning experiences, that has the ability to enhance student’s experiences and outcomes in these learning areas (Sellars, 2017).
One of the greatest barrier to the promotion of physical activity are the beliefs, attitudes and perceptions of teachers (Martin & Murtagh, 2015; Riley et al., 2016). Placing importance on the embedment of numeracy within PDHPE, acknowledgment and research will no doubt be impacted and promoted; thus, influencing teachers, professional practice and educational pedagogy. This will then help to achieve goals in the PDHPE and Numeracy syllabus. It will also help in striving to achieve set the goals set out in the Melbourne Declaration by providing students with stimulating learning experiences and facilitate personal learning abilities (Ministerial Council for Education, Employment, Training and Youth Affairs [MCEETYA], 2008). Ensuring students have the fundamental numeracy skills as a foundation for success in PDHPE, teachers are able to facilitate the ability to think deeply and logically in this integration of KLAs.
Teachers need to acquire research-based teaching ideas, resources and practice classroom management skills to engage students more effectively in numeracy by including physical activity in the context of maths lessons (Riley, Lubans, Morgan & Young, 2015).
Thus, in light of the reviewed concepts the research it is evident that numeracy skills are important to all learning in PDHPE and vice versa.
Future direction
Further research needs to be undertaken into the ways teachers can gain a better understanding of the potential benefits integration can bring to the teaching of other KLAs. Professional learning for teachers is of utmost importance as through this they are able to adapt pedagogical approaches to their learning and be informed of innovative interventions such as PDHPE integration having potential to positively affect attitudes and engagement (Riley et al., 2016). Research into this area may include how teachers will acquire research-based teaching ideas, resources and practice classroom management skills to engage students more effectively in mathematics by including physical activity in the context of maths lessons. This further research can inform teachers on how to facilitate integrated learning in these KLAs and create awareness on how this embedment impacts teaching and learning. More value will also be paced on the KLA of PDHPE facilitating further engagement, authentic and quality learning.
Conclusion
According to ACARA, “numeracy is the capacity, confidence and disposition to use mathematics to meet the demands of learning, school, home, work, community and civic life.” (National Curriculum Board (Australia), 2009). What this demonstrates is that the mathematic skills that are learned within the classroom are not just left there but are integrated into different areas in everyday life. Integrating curriculum is a holistic approach to teaching content across the curriculum and strives to develop deep knowledge and understanding. Research into the embedded nature of Numeracy in PDHPE is crucial in influencing teaching practices and pedagogy so that quality teaching and learning can be achieved.