BOUNDED LEARNING PROGRESSIONS - December 2019 Authors: Chelsea Cutting, Centenary Professor Tom Lowrie and the SERC team - Early Learning ...
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BOUNDED LEARNING PROGRESSIONS
December 2019
Authors: Chelsea Cutting, Centenary Professor Tom Lowrie and the SERC team.
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STEM Education Research Centre (SERC)
Table of Contents
1.0 Executive Summary .................................................................................................................................................................................. 3
2.0 Overview of ELSA ...................................................................................................................................................................................... 6
3.0 Apps 1 and 2: Spatial Reasoning ............................................................................................................................................................... 8
4.0 Apps 3 and 4: Logical Reasoning............................................................................................................................................................... 9
5.0 Learning Progressions ............................................................................................................................................................................. 12
5.1 A hybrid approach to Learning Progressions ...................................................................................................................................... 14
6.0 Bounded Learning Progressions ............................................................................................................................................................. 18
6.1 Unpacking the structure of a Bounded Learning Progression ........................................................................................................... 19
6.2 Bounded Learning Progressions: Connected Networks of Learning .................................................................................................. 23
8.0 Conclusion............................................................................................................................................................................................... 36
9.0 References .............................................................................................................................................................................................. 37
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STEM Education Research Centre (SERC)
1.0 Executive Summary
This report provides an overview of the Early Learning STEM Australia (ELSA) project, and explains the theoretical foundation for the
development of Bounded Learning Progressions for ELSA. Bounded Learning Progressions (BLPs) are a new and innovative method for
investigating children’s learning, afforded by the dynamic structure of the ELSA program. The intention of, and foundational to, BLPs are
that they are a focussed, conjectured path of knowledge construction children may follow as they engage with a range of STEM concepts.
In ELSA, BLPs are situated within Spatial Reasoning and Logical Reasoning and are enacted via the children’s engagement in STEM Practices
(Lowrie, Leonard, & Fitzgerald, 2018) and the Engage – Represent – Apply (ERA) framework (Lowrie & Larkin, 2019). Importantly,
underpinning the development of BLPs is a hybrid approach of learning progression methodologies, which are a fusion between a cognitive
levels approach; an observable-strategies-and-learning performance approach; and a Hypothetical Learning Trajectory (HLT) approach.
The vision for developing ELSA within the cognitive areas of Spatial Reasoning and Logical Reasoning, is based on a deliberate, research
informed decision to design and deliver a program that enables sustained conceptual learning within the early years of education. Spatial
Reasoning is not a single ability or skill; it is a form of reasoning that constitutes many spatial skills that are both related and independent
of one another (Uttal & Cohen, 2012). Importantly, there is a strong relationship between spatial ability and success in STEM related tasks,
experiences and professions at all levels of expertise (Stieff, 2007; Uttal & Cohen, 2012); specifically, young children’s spatial reasoning
ability has been found to be the best predictor of success in mathematics and science in grade six and beyond (Mix et al., 2016; Webb,
Lubinski, & Benbow, 2007). Similarly, Logical Reasoning is a complex set of skills and abilities that allow us to process, analyse and critically
interpret information using a range of senses, to make assumptions about, and solve problems, in our world. Logical Reasoning requires
the development of systematic and rational procedures, which are foundational to successful engagement in STEM contexts. As with Spatial
Reasoning, an emphasis on developing Logical Reasoning in ELSA allows children to seek truths, create hypothesis and conjectures, and
critically examine the conceptual connections in familiar and unrelated learning contexts. For true conceptual understanding to occur,
knowledge and skills must be accessible and transferable beyond the discrete disciplines. The use of STEM Practices, enacted through the
twin lenses of Spatial and Logical Reasoning, allow for this authentic and sustained learning to occur.
Unlike curriculum perspectives that focus on progressions of prescribed content within year levels, the ELSA program and the BLPs reflect
the intuitive development of STEM concepts but with an emphasis on the authentic learning connections made possible by the explicit
development of STEM Practices. In real-world contexts, we do not separate the disciplinary knowledge and skills we need to engage with
when solving everyday problems that we encounter. Spatial Reasoning and Logical Reasoning, through the development of STEM Practices,
shift the focus from learning sequences of content in isolation, to developing conceptual understanding and skills. The latter approach
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STEM Education Research Centre (SERC)
enables learners to reason and problem solve in systematic and efficient ways, that connect knowledge across disciplines to develop more
robust and sophisticated ideas about the world. ELSA is a program that allows for this learning to occur, as the BLPs not only demonstrate
more connected, research informed, and authentic pathways of learning appropriate to early childhood education than typical curriculum
sequences provide, and also provide explicit instruction and intentional teaching advice to assist the child’s development of learning, (see
figure 1).
Figure 1: Curriculum based Learning Progression versus ELSA conceptual Bounded Learning Progression structure
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The term BLPs not only incorporates the hybrid approach to the construction of a learning progression such as the one noted above, but
also suggests how learning occurs within the boundary of the ELSA program. That is, the “boundedness” of the BLPs, is the way the
conceptual, theoretical and pedagogical elements of the ELSA program scaffold the development of Spatial Reasoning and Logical
Reasoning by early years children. Thus, the foundation of STEM Practices within an ERA framework provides both the context and
boundary in which learning can occur. Whilst this may appear at first glance to be limiting in terms of what can be achieved, both in terms
of the topics explored in the ELSA program, and also what can be developed in terms of BLPs; the opposite is in fact the case. Many current
forms of learning progressions describe a linear path within a learning area or topic, from least sophisticated to most sophisticated levels
of skills and understanding, without the consideration of how related progressions, directly or indirectly, may enhance or influence learning
in different ways. BLPs provide an innovative and dynamic perspective that challenges these current methodologies. Therefore, we propose
that BLPs are learning maps that describe the possible pathways of learning, which will contribute to achieving elements of Spatial
Reasoning and Logical Reasoning, through the identified STEM concepts within ELSA.
Utilising BLPs to capture and explore the learning that is possible in the ELSA program reinforces a fundamental tenet of BLPs; namely, that
they are not designed to be a set of “psychological descriptions of learning but are, rather, situated in a larger conceptualisation of the
roles of students and teachers in overall learning ecologies” (Confrey, 2019, p. 8). The tasks and learning experiences designed for each
element of ELSA – that is the digital activities within the Apps and the suggested learning activities in the Experience and Apply phases
provided in the Educator and Families Apps, are not simply stimuli for responses, but instead involve the establishment of specific
conditions for learner engagement and teacher participation, to promote learner’s activity and also to respond with pedagogical agility to
this activity (Confrey, 2019). The range of the experiences offered via the ERA Framework therefore serve two purposes: to allow learners
to explore STEM concepts underpinned by Spatial Reasoning and Logical Reasoning through deep and purposeful engagement with STEM
Practices; and to provide contexts that support children to relate the STEM concepts to their experience and background (Bang & Medin,
2010; Confrey, 2019; Shepard, Penuel, & Pellegrino, 2018), and apply this in meaningful ways beyond their formal educational contexts.
This report details the development of each BLP – using an adaption of Lithner’s (2008) framework for mathematical reasoning, and
importantly highlights the prospective links between concepts and learning domains. This is a novel aspect of the design of BLPs because,
as noted earlier, most current learning progression methodologies focus on linear or hierarchical descriptions of learning. They do so
without the consideration of the synergies between learning domains within Spatial Reasoning and within Logical Reasoning as separate
domains, and without considering the synergies between these two reasoning domains collectively. Finally, this report showcases the
authentic and deep STEM learning that occurs within the play-based ELSA environment. It also demonstrates the scope for connecting this
learning to a range of Early Years Learning Framework (EYLF) outcomes and also to Australian Curriculum Content Descriptors from
Foundation to Year 2, illustrating the powerful learning opportunities across the Early Years of formal learning, made possible by ELSA.
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STEM Education Research Centre (SERC)
2.0 Overview of ELSA
Early Learning STEM Australia (ELSA) is a play-based digital learning program for children in preschool to explore science, technology,
engineering and mathematics (STEM). ELSA allows children to play, experiment and make sense of the world around them – which is also
part of being a child. ELSA's STEM Practices encourage children to ask questions, make predictions, experiment, and reflect on what
happened and why.
Children engage in STEM through play every day, for example, when they:
• create patterns
• draw designs
• build structures
• fill containers
ELSA comprises a collection of integrated resources for educators, families and preschool children. These integrated resources promote
hands-on activities for children through digital, play-based learning experiences rich in STEM Practices, delivered through a series of
applications (apps) for tablets and mobile devices.
The ELSA apps for children support learning through play and are intended to act as a springboard for children to explore the world. The
apps go beyond the screen to encourage active play that supports the development of STEM Practices.
Exploring STEM practices helps children develop sound problem finding and solving skills, as well as ideas, methods and values. Each of the
four ELSA apps for children develops practices that underpin STEM:
• Patterns and relationships
• Location and arrangement
• Representations
• Investigations
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Each App has a particular focus and, at the same time, reinforces concepts developed within the other apps. The ELSA apps for children
are aligned to the Early Years Learning Framework (EYLF) and support child-directed, play-based learning in a variety of preschool settings.
Integrated educator resources, and suggestions for families, support and assist children to make connections between their preschool and
their learning experiences at home. The program is based upon The Experience, Represent, Apply (ERA) pedagogical framework, which
provides early years educators with the opportunity, and the know-how, to integrate digital technologies into STEM activities through
intentional teaching and play-based engagement. The four children’s apps in ELSA are structured around the following conceptual areas
within STEM education (see Figure 2):
Spatial Reasoning
Patterns and Location and
Relationships Arrangement
(App1) (App 2)
Sorting, Ordering, Position, Location,
Patterning, Representing Arrangement, Orientation
Representations Investigations
(App 3) (App 4)
Decoding, Encoding, Observing, Proposing,
Conditionals, Debugging Verifying, Explaining
Logical Reasoning
Figure 2: ELSA Program Conceptualisation
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3.0 Apps 1 and 2: Spatial Reasoning
The term Spatial Reasoning describe a range of mental processes, including mental rotation, spatial orientation and spatial visualisation
that help us represent, analyse, and draw inferences from spatial relations. These spatial relations could be relations between objects (e.g.,
landmarks in a city) or relations within objects (e.g., the structure of the block tower). Spatial reasoning involves the understanding of three
related properties: (1) an awareness of space itself, such as distance and dimensions; (2) the representation of spatial information
(internally in the mind and externally in graphics such as diagrams and maps); and (3) the reasoning involved in interpreting spatial
information and decision making (Carroll, 1993).
Spatial reasoning has been established as a critical skill for everyday tasks such as learning, training, and working (Uttal, Miller & Newcombe,
2013). Spatial reasoning helps us to understand, appreciate, and interpret our three-dimensional world (NCTM, 2000), including navigating
our surroundings or following a diagram while building furniture. A large, and growing, body of research (e.g. Wai, Lubinski, & Benbow,
2009) has demonstrated the link between spatial reasoning and later performance in STEM subjects at school. Spatial reasoning is also a
strong predictor of a STEM career, post-formal education. In particular, developing spatial reasoning has clear and positive impacts on
mathematics achievement (Lowrie, Logan, Harris & Hegarty, 2018).
Children use spatial reasoning on a daily basis as they learn to understand the relationships between objects, give and receive directions,
and imagine changes in the position and size of shapes and objects. Given the importance of spatial reasoning for children, in their
interactions with their world and for its impact on later STEM achievement, it is one of the two overarching conceptual pillars for the ELSA
program.
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STEM Education Research Centre (SERC)
4.0 Apps 3 and 4: Logical Reasoning
The term Logical Reasoning describes the use of valid reasoning in some form of activity; and it names the normative study of reasoning or
a branch thereof. In the latter sense, it features most prominently in the subjects of philosophy, mathematics, and sciences, and thus is a
pivotal part of the ELSA program. Logical reasoning is not a single construct, rather a range of processes used in thinking and problem
solving; dealing with the principles and criteria of validity of inference through a systematic approach (Johnson-Laird, 1999). The mental
recognition of cause-and-effect relationship is called ‘reasoning’. It may involve a prediction of an event from an observed cause or the
inference of a cause from an observed event. Logical reasoning is the process of deriving a logical inference, from a hypothesis through
reasoning, and is commonly classified into two forms – deductive and inductive reasoning (Evans, 2002).
By definition, deductive reasoning yields a valid conclusion, which must be true if their premises are true (Johnson-Laird, 1999). For
example: an argument using the rule of modus ponens would be: if p then q, p; therefore q; or, described by the modus tollens: if p then q,
not q; therefore, not p (Goel, 2007; Markovits, Doyon, & Simoneau, 2002). The anatomy of deductive reasoning can be illustrated through
a simple example of deductive reasoning: All parrots can fly. Fred is a parrot. Fred can fly.
Inductive reasoning is concerned with the detection and acknowledgement of regularities and irregularities in order to form rules and make
generalisations (Barkl, Porter, & Ginns, 2012; Klauer & Phye, 2008). It can be considered the opposite of deductive reasoning as it seeks to
make broad generalisations from specific observations. Phye and Klauer (1993) identified a set of cognitive operations and process that
are foundational to inductive reasoning. They are illustrated in the following table (see table 1):
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STEM Education Research Centre (SERC)Table 1: Inductive reasoning cognitive processes
Thinking Process Definition
Generalisation The process of recognising similarities of attributes between objects or events
Discrimination The process of recognising dissimilarity of attributes between objects or events
Recognition of Relations The process of recognising connections between relations of objects or events
Differentiating Relationships The process of recognising discrepancies between relations of objects or events
Cross-Classification The process of considering two attributes simultaneously
System Construction The process of establishing either equivalence of dissimilarity of relationships
Inductive reasoning facilitates problem solving and the development of expertise in learning and performance of STEM related domains;
therefore, it is an important process and skill for young children to develop as they construct knowledge about the world they live in
(Harverty et al. 2000). A concrete example of inductive reasoning is as follows. Galahs have grey and pink feathers. There are grey and pink
feathers on the ground. Perhaps a galah was here recently.
Spatial Reasoning and Logical Reasoning, provide the twin, overarching, conceptual domains underpinning the entire ELSA program. Within
this overarching scope, STEM Practices are explored and developed through the ERA Framework, within ELSA. To capture children’s
learning, and to help children develop increasingly sophisticated ways of thinking and working in STEM contexts within ELSA, the
conceptualisation and design of appropriate Learning Progressions, and the creation of a hybrid methodology to support children’s
learning, were developed.
As highlighted earlier, Spatial and Logical Reasoning provide a vehicle for exploring STEM concepts in a more intuitive, authentic and robust
way, because the learning progressions created are not based on context, rather they are developed on research informed and validated
conjectures about how children’s skills and conceptual understanding develop holistically. For instance, to develop an understanding of
the topic of Time, a child needs to develop the concepts of fractions with relation to: the part-whole relationships of time; measuring and
representing units of time; and representing duration and the passing of time (Frienderwitzer et al., 1999). Time is a construct that is both
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STEM Education Research Centre (SERC)highly spatial and logical in the types of reasoning abilities required and one that is highly interdisciplinary. However, from the perspective
of the Numeracy Learning Progression (NLP) based on the Australian Curriculum, the sequence suggested for developing time is quite
disjointed in terms of the conceptual foundations of the content descriptions provided. For example, in Year one, children are required to
tell the time to the half hour. Telling time to a half hour requires deep knowledge of partitioning fractions, specifically mixed fractions. At
this point in the curriculum, children are only formally introduced to the part whole interpretation of fractions, in the form of half as a unit
fraction - as described by the content descriptor: Recognise and describe one-half as one of two equal parts of a whole (ACMNA016). In
Year two, children are then required to Tell time to the quarter-hour, using the language of 'past' and 'to' (ACARA, ACMMG039 n.d.). To
demonstrate these fractional understanding children must be able to explore the multiplicative and proportional nature of the fraction as
measure rational number interpretation, through spatial reasoning abilities such as spatial proportional reasoning which children as young
as four are capable of (see Mix, Levine & Huttenlocher, 1999; Confrey 2009). These multiplicative and proportional understandings of
fractions are not developed until much later in the Australian Curriculum, long after they are encountered in Year one and two.
Whilst the Australian Curriculum NLP is intended to show connections across the content descriptions of each discipline, and also between
the indicators within the numeracy progression and their elements, the actual learning progressions themselves are descriptions of
content. Thus they can become an exercise in mapping content from the NLP across the disciplines, as opposed to the form in which ELSA
Learning Progressions have been developed. That is, regardless of curriculum or discipline, the learning progressions developed within the
boundary of ELSA describe authentic, intuitive and empirically validated progressions of learning that a child will typically undertake when
constructing their STEM understanding, knowledge and skills. Therefore, when a child is engaging with a particular topic such as patterning,
the child is led through a range of learning experiences (developed from a deep understanding of the appropriate range of related concepts
and underpinned by the relevant elements of Spatial or Logical reasoning), that are required to develop an understanding of early
patterning. Unlike the Australian Curriculum NLP, ELSA not only provides evidence based conjectured paths of learning children will typically
develop, but also provides authentic intentional teaching and play based learning advice to enable children to develop the next stage of
learning. This will be detailed in the following section.
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STEM Education Research Centre (SERC)5.0 Learning Progressions
The idea of what constitutes a Learning Progression (LP) (sometimes referred to as Learning Trajectories [LT]) has its root within
developmental psychology fields, with the underlying premise that children are not ‘miniature or incomplete’ adults; rather, they are
capable and confident beings in their own right that continuously build their understanding of the world through their interactions and
experiences in a range of everyday contexts (Confrey, 2019). The contexts and interactions that children experience are as unique as the
children themselves. Thus, there is a tension that exists between both the formal curriculums and learning frameworks provided by
educational bodies; and what and how children actually develop their conceptual understanding, skills and practices in their everyday
worlds. In pre-school and early years settings within Australia, a significant level of flexibility and agency is provided to, and indeed required
from, educators so that they can develop nuanced educational experiences for the children in their care, enacted through the EYLF.
However, in the more formal school context, educators are bound by a prescribed curriculum; which often lack a fine-grained
understanding of how children’s learning and ideas evolve over time in each topic within a discipline area (Loboto & Walters, 2017). This
has been a catalyst for research into LPs, to help align and uncover how discipline based conceptual ideas evolve to enable and inform
developmentally appropriate curriculum for each age and/or stage of learning. Moreover, there are many advocates who have
demonstrated the great potential of a LP approach to curriculum design (see Battista, 2011; Clements & Sarama 2004, 2017/2019; Confrey,
Maloney, & Nguyen, 2014) to offer a more authentic, conceptual and research driven approach to educating children, informing education
policy and the professional development of educators.
Although the terms LP and LT are often used interchangeably; there are, however, variations in meaning and use and consequent variations
in their theoretical foundations and intention. Table 2 briefly illustrates the subtle differences between LPs and LTs.
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STEM Education Research Centre (SERC)Table 2: Learning Progressions versus Learning Trajectories
Learning Progression (LP) Learning Trajectory (LT)
• A sequence of successively more complex ways of thinking about an • A detailed description of the sequence of thoughts, ways of reasoning,
idea that might reasonably follow one another in a student’s learning and strategies that a student employs while involved in learning a
(Smith et al., 2006). topic, including specification of how the student deals with all
• Not developmentally inevitable as they do depend on instruction; instructional tasks and social interactions during this sequence
however, they do not typically include descriptions of instruction. (Battista, 2011; Simon 1995).
• Based on research synthesis and conceptual analysis, making use of • Include detailed descriptions of instruction.
current research on children’s learning (NRC, 2007). • Two types of LT – Hypothetical and actual. Hypothetical LT have three
• “Are anchored one end by what is known about the concepts and components: A goal (research based “big ideas”), the learning activities
reasoning of students…at the other end, LP’s are anchored by societal and the hypothetical learning process – that is, a prediction of how the
expectations; thus, LP’s provide “intermediate” understandings students thinking and understanding will evolve in the context of the
between these anchor points that… contribute to building a more learning activities (Simon, 1995). Actual learning trajectories can be
mature understanding” (NRC, 2007). specified only during and after a student has progressed though such a
• Different in time spans they describe – can be the development of learning path. Thus, the actual learning trajectory is not knowable in
children’s thinking over a span of years, or the progression of thinking advance (Simon, 1995).
through a particular topic or instructional unit (Battista, 2011). • Are descriptions of children’s thinking and learning in a specific domain
• Differ in grain size of descriptions. Some may be minute to minute and a related, conjectured route through a set of instructional tasks
changes in student development of thought, while others are more designed to engender those mental processes or actions hypothesised
global progressions through school curricula. to move children though a developmental progression of levels of
• Differ in audience – some are written for researchers, standards thinking, created with the intent of supporting children’s achievement
writers, assessment developers (formative and summative) and some of specific goals in that domain (Clements & Sarama, 2004).
for teachers (Battista, 2011). • If one is designing and testing a curriculum (program of instruction/
• Foundational differences on which they are designed. Some are built unit of work etc.) then you are more likely to develop a learning
on the synthesis of extant research; others synthesise extant research trajectory based on the sequence of learning tasks in that curriculum
and then perform additional research to elaborate (such as (Battista, 2011).
longitudinal or cross-sectional research).
• Differ in how they describe student learning. Some have numerical
measures of student progress; others focus on describing the
categories of student’s cognitive structures and reasoning (Battista,
2011).
• If one is focussing on a formative assessment system that applies to
many curricula, one is more likely to develop a learning progression
based on many assessment tasks, not those in a fixed sequence
(Battista, 2011).
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STEM Education Research Centre (SERC)As described in Table 2, there are some strong similarities, but also subtle differences, between the construction and the intention of a LP
or LT. Despite the nuanced differences between the two, the commonalities between the intention, structure and affordances of learning
progressions/ trajectories are evident in two ways. Firstly, the notion that both acknowledge that learning takes place over a sustained
period, and that teaching involves identifying where learners are in their learning journey and recognising the importance of providing
carefully considered, challenging but achievable learning experiences which will support learners to progress to the next step in their
particular journey (Siemon et al., 2017). Secondly, the intention of either a LP or LT is, to varying extents and in different ways, is to suggest
hypothesised pathways of learning children may take when constructing knowledge and skills, which is derived from a variety of sources;
namely, a synthesis of current and relevant literature; the design and trial of learning activities aimed at progressing learning within the
hypothesised framework; and the employment of empirical evaluation methods to assess where learners are in their journey and the
efficacy of both the framework and the teaching materials and approaches used (Siemon et al., 2017). Using either a LP or a LT thus provides
educators with a fine-grain analysis and understanding regarding how children learn, at each age and/or stage of development, the targeted
STEM concepts and skills. LPs and LTs also contribute to the wider educational and research community by providing empirical evidence in
relation to how children learn, which can be used to shape policy and curriculum development on strong educational foundations.
5.1 A hybrid approach to Learning Progressions
As indicated above, there are very clear and common intentions for the development of a LP or LT. However, LP and LT can also be based
upon the different methodological considerations guiding their construction. Based on the affordances of the learning possible within the
play-based learning environment that is the ELSA program, and the targeted age range of children (4-7-year old) ELSA can cater for – a
hybrid approach to the development of ELSA LPs was created and used to understand children’s learning.
The theoretical roots of a LP within ELSA are characterised by a fusion between a cognitive levels approach; observable strategies / learning
performance approach; and, the Hypothetical Learning Trajectory (HLT) approach.
A cognitive levels approach to constructing a LP is predominantly used for diagnostic assessment purposes, which can include identifying
and classifying partially productive understanding of learning, generally within broad education topics such as “geometry” or “life cycles”
etc. (Lobato & Walters, 2017). Cognitive levels LPs generally describe students' ways of reasoning about a topic, irrespective of curriculum,
and focus on understanding and reacting to students' current cognitive structures (Battista, 2011). They include a beginning ‘level’ or
anchoring starting point and end in a deeper, more sophisticated benchmark of a learning goal. In relation to ELSA, this is incorporated in
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STEM Education Research Centre (SERC)the adaption of Lithner’s (2008) model, whereby our LPs move through three main phases: beginning with - reasoning as object, then -
reasoning as process, and finally the most sophisticated demonstration of reasoning - reasoning as concept phase. These phases will be
elaborated upon in the following section. Additionally, the diagnostic and assessment for learning affordances this type of progression
permits, across a range of topics and/or areas of learning, are important characteristics of the LP developed for ELSA.
The most common method for developing a cognitive levels LP involves cross-sectional, clinical interviews over multiple ages, which
become “compilations of empirical observations of the thinking of many students” (Battista, 2004). A downfall of this type of LP
methodology; however, is that it does not examine the influence of innovative educational and intentional teaching opportunities – such
as that offered in ERA framework within ELSA - and also does not consider learning construction in the ‘messiness’ of everyday, play based
learning experiences vital in early years education. Therefore, whilst utilising aspects of this approach to help map the cognitive patterns
in student thinking to understand the conceptual structures for achieving a range of learning goals, if we relied solely upon such an
approach, we would not be able to determine a progression of understanding and how this is influenced by the intentional teaching
opportunities across the overarching domains of Spatial Reasoning and Logical Reasoning possible within ELSA.
The second theoretical perspective that underpins our LPs is the observable strategies and learning performance approach to developing
a LP. This type of LP typically identifies proficiency levels in terms of strategies or other observable behaviours (Lobato & Walters, 2017).
The intention of this type of LP is to draw connections between the sophistication in student strategies, whilst considering the impact
variables such as task complexity, cultural context and the learning environment have on learning. This method therefore highlights the
fundamental role the STEM Practices (Lowrie, Leonard, & Fitzgerald, 2018) play, in underpinning all learning within the ELSA program. This
type of learning progression can be constructed upon existing research (such as disciplinary logic/ curricular coherence approaches) or, it
can be a product of research (Lobato & Walters, 2017) such as through the collection of empirical data enabled through the digital activities
in ELSA. Thus, there is no prototypical method for the construction of this type of LP, which aligns seamlessly to the innovative and dynamic
nature of ELSA. This methodology allows for the revision of the LPs as more empirical learning evidence is collected; for example, the ways
in which children are demonstrating their knowledge through their engagement in STEM Practices and the application of these practices
in the performance tasks provided. This approach allows for cognitive levels to inform the development of this hybrid approach to
developing a LP, and it can be more specific to the conceptual aims and learning goals explored within ELSA. This methodology of learning
progression construction lends itself to the formal design of measures to empirically validate the LP (Confrey, Maloney, Nguyen, & Rupp,
2014), because knowledge states are encapsulated within the learning performances (Lobato & Walters, 2017).
The third perspective underpinning the construction of the LP in ELSA is the Hypothetical Learning Trajectory (HLT). This methodology is
characterised by a change in focus from the learner and the knowledge and skills displayed within a particular learning domain, to an
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STEM Education Research Centre (SERC)emphasis on the teaching supports for learning as part of a model of teacher’s decision-making process in curriculum and education
development (Loboto & Walters, 2017). First conceived by Simon (1995), a HLT consists of three main elements: a learning goal; the
selection of tasks that will promote student learning towards the identified goal; and a hypothesis about the process or path of student
learning (Simon & Tzur, 2004). Clements and Sarama (2004) elaborate, stating that HLTs are:
descriptions of children’s thinking and learning in a specific mathematical domain and a related, conjectured route through a set
of instructional tasks designed to engender those mental processes or actions hypothesized to move children through a
developmental progression of levels of thinking, created with the intent of supporting children’s achievement of specific goals in
that mathematical domain. (p. 83)
HLTs are commonly situated in a constructivist, socio-constructivist and/or social cultural paradigm of learning. That is, these foregrounding
theories exert a profound influence on the meaning of these progressions, because they define the likely catalysts for learning
development, and provide a theoretical base for explaining the movement between the steps identified within the progressions (Confrey,
2019; Simon et al., 2010; Simon & Tzur, 2004). This is a critical feature of such an approach, in that its design and development is ongoing,
iterative, context specific, and is informed by the interpretivist nature of seeking information from students regarding their engagement
and integration within a learning experience (Lehrer & Schauble, 2015). Thus, the power of an HLT comes from the nexus between the
developmental path a child is conjectured to explore within a defined concept, and the carefully selected teaching and learning experiences
that are developed and selected to promote this learning (Daro, Mosher, & Cocoran, 2011). This is an essential feature of the ELSA program,
and is evident in the way each of the activities within the Represent (digital) phase have been constructed within a specific learning area
or topic, in addition to the educational activities and opportunities promoted in the E and A phases through the Educator and Families App
across other learning areas and activities.
Utilising this hybrid approach to developing learning progressions gives rise to our new and innovative learning progression methodology-
Bounded Learning Progressions (BLPs). In line with the definitions described above, the intention and foundation of our BLPs is that they
are a focussed, conjectured path of knowledge construction for a range of STEM concepts, that manifest within Spatial Reasoning and
Logical Reasoning, through the engagement in STEM Practices (Lowrie, Leonard, & Fitzgerald, 2018) and the ERA framework (Lowrie &
Larkin, 2019). Importantly, underpinning this hybrid approach is a strong premise that BLPs are not designed to be a set of “psychological
descriptions of learning but are, rather, situated in a larger conceptualisation of the roles of students and teachers in overall learning
ecologies” (Confrey, 2019 p. 8). The tasks and learning experiences designed for each element of ELSA, are not simply stimuli for responses,
but involve setting up specific conditions for learner engagement and teacher participation, to promote and respond with pedagogical
agility to learners’ activity (Confrey, 2019). Thus, the digital activities, teaching suggestions and off app learning experiences provided are
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STEM Education Research Centre (SERC)designed for two purposes: to introduce and allow learners to explore conceptual learning within Spatial Reasoning and Logical Reasoning
domains, through deep and purposeful engagement with STEM Practices; and to provide contexts that support children to relate STEM
concepts to their experience and background, and apply this new knowledge in meaningful ways (Bang & Medin, 2010; Confrey, 2019;
Shepard, Penuel, & Pellegrino, 2018).
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STEM Education Research Centre (SERC)6.0 Bounded Learning Progressions
The term BLPs not only incorporates the hybrid approach to the construction of such a learning progression noted above, but also suggests
how learning occurs within the boundary of the ELSA program. That is, the “boundedness” of the BLPs, is the way the conceptual,
theoretical and pedagogical elements of the ELSA program, scaffolds the development of Spatial Reasoning and Logical Reasoning by early
years' children. That is, the foundation of STEM practices within an ERA framework provides the context and boundary for learning to
occur.
Whilst this may appear at first glance to be limiting in terms of what can be achieved, both in terms of the topics explored in the ELSA
program, and also what can be developed in terms of BLPs; the opposite is in fact the case. Many current forms of learning progressions
describe a linear path within a learning area or topic, from least sophisticated to most sophisticated levels of skills and understanding,
without the consideration of how related progressions, directly or indirectly, may enhance or influence learning in different ways. BLPs
provide an innovative and dynamic perspective that challenges these current methodologies. Thus, we define BLPs as learning maps that
describe the possible pathways of learning, which will contribute to achieving different layers of reasoning, through the identified STEM
concepts within ELSA (see Figure 3).
Figure 3: Bounded Learning Progression Conceptualisation
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STEM Education Research Centre (SERC)Specifically, BLPs are identified, established, revised and re-developed within the domains of Spatial and Logical Reasoning, through a series
of learning foci detailed in each of the Apps, which give a lens in which the STEM Practices, concepts and pedagogical innovativeness of
the ERA is supported. That is Spatial Reasoning and Logical Reasoning are developed through the STEM Practices, which are not a series of
discrete, disciplinary content, but rather provide a way to think of diverse engagement with STEM without specific recourse to content. As
such, it supports thinking about STEM engagement by artists, doctors, and any other field or activity that makes use of STEM Practices.
STEM connects to the real world not on the basis of disciplinary content, but through the diverse use of the sayings, doings and relatings
of STEM (Lowrie, Leonard, & Fitzgerald, 2018). Therefore, through the ‘funnel’ of the above diagram, it is the STEM Practices that influence
and develop the sayings, doings and relatings of STEM concepts. However, we acknowledge the difficulty many Early Childhood Educators
face in translating these big ideas and concepts into practical actions within the individualised and child-centred learning environments.
Therefore, the Experience – Represent – Apply (ERA) heuristic is the third ‘ingredient’ shaping the development of the BLPs. The ERA
heuristic asks designers and educators to create learning activities that use or enact forms of STEM practice comprising of three cyclic
stages, with the intent of each phase as follows and expressed in term of ELSA’s app-based activity (Lowrie & Larkin, 2019; Lowrie, Leonard,
& Fitzgerald, 2018):
• Experience. This is what children already know. Children’s lived experiences are used as the foundation for concept development
through social engagement and language.
• Represent. Children will play a variety of games on the apps to engage with, and represent, STEM concepts. These representations
will include creating images, interpreting pictures, visualising and using symbols.
• Applications. Children will build on their learning from the on-app activities through a range of off-app activities, guided by their
educators and their families.
The BLPs are designed to reflect these elements of both pedagogical and conceptual authenticity, within child-centred play-based learning
experiences.
6.1 Unpacking the structure of a Bounded Learning Progression
As described earlier, when outlining the methodological construction of a BLP, one of the features that helps determine the level of
sophistication a child is working at, as well as providing a diagnostic map for how interrelated experiences and activities can assist in the
child in moving to the next level of sophistication, is the adaption of Lithner’s (2008) framework for mathematical reasoning, which we
suggest applies more broadly to both Spatial Reasoning and Logical Reasoning. This framework has been adopted in a variety of studies,
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STEM Education Research Centre (SERC)including those situated in preschool settings (see Sumpter, 2016; Sumpter & Hedefalk, 2018). Moreover, this framework is adapted
because it helps us to look at the foundation of the learning through the development of STEM Practices, and how they are used in play-
based, early childhood, learning environments. In our adaption, these phases are: reasoning as object, reasoning as process and reasoning
as concept, illustrated in Figure 4, and evident in both Spatial Reasoning and Logical Reasoning.
Figure 4: The framework of the Bounded Learning Progression
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STEM Education Research Centre (SERC)Reasoning as object considers the objects (within an activity or learning experience) as fundamental entities. That is, they are considered
as the “thing” that one is doing something with (Lithner, 2008; Sumpter, 2016). This can be typically evidenced in the form of comparing,
classifying and analysing specific objects to notice similarities and differences in properties, their attributes and orientation or position
(Clements & Sarama, 2009). It can also include disembedding, which is isolating and attending to one aspect of a context or scene
(Newcombe & Shipley, 2015). Seriation by trial and error or intuition is evident, and children explore and discover (generally with
assistance) that there can be sequences, rules and patterns within and between simple objects and/ or sequential contexts (Clements &
Sarama, 2009).
Reasoning as process considers the process(es) applied to an object or context, with a sequence of these changes being a procedure
(Lithner, 2008; Sumpter, 2016). This can be in the form of the child looking at a range of possible solutions, procedures, and strategies to
be considered, and trialling and applying them in various contexts – both on App (in the R phase) or off app in the E and A phases. Reasoning
as process also demonstrates an understanding of the relationship between the information explored, the objects of concern and the
processes applied to these objects. Cause and effect and conditional reasoning are typically emergent in this phase, although not
necessarily with a secure understanding. Newcombe and Shipley’s (2015) identification of penetrative thinking, mental transformation and
sequential thinking are also illustrative of this level of reasoning. In terms of Clements and Sarama’s (2009) work, this phase might be
interpreted as their ‘picture maker’ phase, where the child is demonstrating flexibility in integrating parts of a structure, utilising trial and
error, with some aspects of logical reasoning emerging and some systematic and/ or unsystematic use of spatial relations when constructing
and assembling objects and shapes.
Reasoning as concept is where children are applying, in our case, STEM concepts built from the deep understanding of the interactions
between the objects, their transformations (or processes performed) and their properties (Lithner, 2008; Sumpter, 2016). This phase
includes compositional reasoning, which is evident when the learner can represent functions and combine them without explicit instruction
- hypothesising the outcome of the composition (Piantadosi & Aslin, 2016) with the provision of clear conclusions about the overarching
concept (Sumpter, 2016). For example, Clements and Sarama (2014) explain this phase as the ability to compose shapes with specific
intention, anticipation, and understanding what 2D shape or 3D object will be produced with a composition of two or more other (simple
and familiar) 2D shapes or 3D objects. It may also be the application of a framework the child creates when exploring patterning. For
example, given objects in an ABBABB pattern, a child can recognise and reason the core unit of the pattern as AAB and then represent this
pattern with either different objects or with movement – e.g. clap, clap, jump. This is what Clements and Sarama (2009) identify as a
‘Pattern Unit Recogniser’, which is the ability to “translate patterns into new media; that is abstract and generalise the pattern” (Clements
& Sarama, 2017/2019). Whilst this is not an exhaustive description of all the learning examples that exemplify this level of thinking and
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STEM Education Research Centre (SERC)working, its underlying foundations are the demonstration of the desired conceptual ideas and the ability to apply systematic and robust
Spatial Reasoning and Logical Reasoning in a range of different contexts.
An important element to the three phases of sophistication for reasoning is that they should be considered, somewhat paradoxically, as
both hierarchical and cyclical in nature. As presented in each of the phases above, there is a hierarchical shift from simple to complex levels
of reasoning. However, as illustrated in Figure 4, the three phases are highly cyclical, in that the construction of complex and sophisticated
thinking within a reasoning through concept phase, affords new possibilities and provocations for thinking about different objects, to start
a new cycle of reasoning in related and unrelated domains. This resonates strongly with the ERA pedagogical approach where an A
experience in one cycle flows into a subsequent E experience in the next cycle of ERA.
The inclusion of this adapted aspect of Lithner’ (2008) model allows for, in the ELSA BLPs, the diagnosis and formative assessment of the
characteristics of children’s thinking across a learning domain. That is, when a child’s learning development is mapped across their
engagement within an App, and or across multiple Apps (automatically in many of the digital R activities), and across E and A opportunities
in observable, anecdotal form, themes can be determined about the overall level of sophistication a child is demonstrating at a particular
point in time. This flexibility in determining the collective level of sophistication a child is demonstrating provides valuable formative
information for the educator, that is authentic to the child’s experiences and needs. This is a very important affordance of the BLPs in ELSA
and will be elaborated upon further in this document.
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STEM Education Research Centre (SERC)6.2 Bounded Learning Progressions: Connected Networks of Learning
The construction of a bounded learning progression will incorporate a series of Progress Indicators (PI), which describe the likely steps and
levels of knowing a child may exhibit when developing their understanding on a specific concept (see Figure 5).
Figure 5: Progress Indicators within a BLP
Each PI will have a description of what that step in the BLP looks like in practice. The PI will also list the associated “I Can” statement(s),
which are captured ‘on App’ during the Representation phase of the ERA loop, and also the “I Can” statements that can be observed and
identified by the educator during the suggested E and A activities. As indicated previously, what is innovative about the structure and
affordances of the ELSA BLP is the connectedness these BLPs provide between concepts, and the wider domains of Spatial Reasoning and
Logical Reasoning. Thus, where appropriate, the progress indicators for each BLP will have links to where that specific set of knowledge
and skills can be enhanced, supported and evidenced in other Apps’ E, R and A activities (see Figure 6).
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STEM Education Research Centre (SERC)Figure 6: BLP as connected networks of learning
The BLP depicted in figure 6 is an example of the structure and interconnectedness of learning created in ELSA. In this example the concept
of Decoding is the focus for the BLP (App 3 - Activity 1). The first two progress indicators have been provided in the BLP (in this example),
which indicate the start of a child’s reasoning capabilities for this concept, formulated by current and relevant literature, that is - reasoning
as object phase. The example PIs indicated here are accompanied by a description of what learning and reasoning at this level may look
like in practice. Importantly there are connections to other relevant BLPs and ERA learning experiences that likely will, in different ways,
enhance and develop this child’s understanding of the concept of decoding. For example, a child who is demonstrating they are a
“Representation Senser” in the above BLP, likely means they have an awareness of the role pictorial representations play in communicating
meaning (including a procedure or sequence) but may not be able to describe all the attributes of the representations or apply this
knowledge consistently. This may mean that they are able to decode the simple, three step, pictorial instructions in Activity 1 and build the
drum, but building the guitar and marimba is too challenging at this level. This PI is developed and supported in the empirical data we can
collect in the on-App engagement of the child, that is, we know empirically that building the drum through the representations presented
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STEM Education Research Centre (SERC)in this activity is easier for most children to achieve than building the guitar or the marimba. This PI and “I Can” statements, also relate to
the child recognising that the symbolic representations in Activity 4 on this App represent different sounds for different instruments,
however, the child at this level may not be able to apply this understanding in a systematic or purposeful way other than by trial and error
to make music. To encourage this child’s success in developing decoding skills and understanding the meaning of pictorial and symbolic
representations, the educator may also refer the child to App 1, Activity 1, where they decode pictorial sequences to recreate a story and
Activity 2 where they can practice decoding pictorial representations of familiar and unfamiliar food items to determine different attributes
in sorting their lunch boxes, thus assisting the child to move to the next progress indicator (level) within the BLP.
Building upon figure 6, which illustrated the connections that occur between a Spatial Reasoning BLP (Patterns and Relationships) and a
Logical Reasoning BLP (Decoding), the following figure (Figure 7) exemplifies the connection between all four Apps and their associated
ERA activities that are possible within ELSA. Here, within the two PIs for the BLP of Sorting, we can see connections to the Representations
app and activities (Activity 1 - Decoding); the Investigations app where children need to recognise spare parts and their properties and
attributes to solve a water problem (Activity 1 – Let’s Tinker with Spare Parts), and a range of off app learning opportunities that are
suggested on the educator app in the E and the A phases.
Figure 7: An example of connectedness across all four Apps.
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STEM Education Research Centre (SERC)Moreover, by engaging in the ELSA program, children are developing deep conceptual ideas in connected ways, which are reflected in the
discrete discipline requirements in the Australian Curriculum, as described in Table 3 (NB – Only descriptors relevant to the example above
are listed in this table):
Table 3: Australian Curriculum content alignment with ELSA
Foundation Year 1 Year 2
Content Sort, describe and name familiar two- Investigate and describe number Compare and order several shapes
Descriptors: dimensional shapes and three-dimensional patterns formed by skip-counting and objects based on length, area,
Mathematics objects in the environment (ACMMG009) and patterns with objects volume and capacity using
(ACMNA018) appropriate uniform informal units
Sort and classify familiar objects and (ACMMG037
explain the basis for these classifications. Recognise and classify familiar two-
Copy, continue and create patterns with dimensional shapes and three-
objects and drawings (ACMNA005) dimensional objects using obvious
features (ACMMG022)
Content Objects are made of materials that have Science involves observing, asking A push or a pull affects how an
Descriptors: observable properties (ACSSU003 questions about, and describing object moves or changes shape
Science changes in, objects and events (ACSSU033)
The way objects move depends on a (ACSHE021)
variety of factors, including their size and Use informal measurements to
shape (ACSSU005) Use informal measurements to collect and record observations,
collect and record observations, using digital technologies as
Engage in discussions about observations using digital technologies as appropriate (ACSIS039)
and represent ideas (ACSIS233 appropriate (ACSIS026)
Represent and communicate
Represent and communicate observations and ideas in a variety
observations and ideas in a variety of ways (ACSIS042
of ways (ACSIS029
General Level 1b Level 2
Capability Recognising and using patterns and Recognising and using patterns and relationships
Numeracy relationships Typically, by the end of Year 2, students:
Continuum Typically, by the end of Foundation Year, • Recognise and use patterns and relationships
Elements students: • Identify, describe and create everyday patterns
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