Draft Project Outline and Annotated Bibliography
Name: Sushmita (Sushi) Roy (working individually)
Project Title: The Terrace Garden Morning: Teaching Measurement, Classification, and Spatial Reasoning Through Outdoor Plant Care in an Anganwadi Setting
Grade Level / Age: Ages 3–6 (preschool/foundational stage)
Context: Anganwadi centre (India's public early childhood care and education system) serving children from rural and peri-urban households in Rajasthan, India. Designed for an Anganwadi worker facilitating a mixed-age group of approximately 15–20 children with minimal purchased materials.
Design: I will create a step-by-step activity narrative with embedded mathematical language prompts, materials lists, and variations for the three age bands (3–4, 4–5, 5–6). I will map each activity element to the BC Kindergarten Mathematics Curriculum (specifically: direct comparative measurement, sorting by single attribute, equality as balance, and the Big Idea "We can describe, measure, and compare spatial relationships") as well as to India's Aadharshila curriculum, to show dual curricular alignment. The BC curriculum's explicit reference to Bishop's (1988) cultural mathematical practices and to connecting mathematics to "daily activities, local and traditional practices" provides a strong frame for the project's culturally responsive design.
Try out: I do not currently have access to children aged 3–6 for a live pilot. Instead, I plan to do a detailed walkthrough with a peer or classmate acting as co-facilitator: we will lay out the materials, run through the activity sequence step by step, test the mathematical language prompts, and identify where the design would need adaptation. I will document the walkthrough with photographs and reflections, noting what worked in the sequence, where prompts felt natural or forced, and what I would revise for an actual classroom implementation. This approach is consistent with design-based research traditions where iterative refinement begins with structured rehearsal before live testing (Cobb et al., 2003).
Positionality connection: I grew up in India and have spent the past year immersed in households where children's everyday reasoning — measuring, sorting, building, estimating — was abundant but unnamed. This project is my attempt to close the gap my thesis documented: to design the activity that would make household mathematical knowledge visible and extendable within the institution that currently cannot see it.
Annotated Bibliography
Clements, D. H., & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968–970.Clements and Sarama present evidence that early mathematics interventions grounded in developmental learning trajectories significantly improve young children's mathematical understanding. Their concept of learning trajectories — where instruction begins from where children currently are and builds toward more formal reasoning — directly informs the "recognise–name–extend" sequence in my project. The idea that effective early maths teaching starts by identifying existing competence and then designing the next step is foundational to this activity design.
Ginsburg, H. P., Lin, C.-L., Ness, D., & Seo, K.-H. (2003). Young American and Chinese children's everyday mathematical activity. Mathematical Thinking and Learning, 5(4), 235–258. Ginsburg et al. demonstrate that young children's everyday mathematical activity is more complex and more integrated than what typically appears in formal early mathematics curricula. Their finding that children naturally engage in measurement, pattern, and spatial reasoning during free play and household routines supports the design principle of this project: rather than importing decontextualised math tasks, the activity begins from a routine (garden care) that already compresses multiple mathematical domains.
Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge University Press.Lave's foundational study demonstrates that mathematical reasoning in everyday settings is organised by practical goals and material constraints rather than by decontextualised problems, and that people perform significantly better in situated contexts than on structurally equivalent pencil-and-paper tasks. This work grounds the project's core premise: that measurement with household containers in a real garden is not a simplified version of "real" mathematics but a different and legitimate form of mathematical practice that the Anganwadi can build on.
Moll, L. C., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of knowledge for teaching: Using a qualitative approach to connect homes and classrooms. Theory Into Practice, 31(2), 132–141. Moll et al. established the Funds of Knowledge framework, arguing that households accumulate historically developed knowledge through labour, social networks, and material practices, and that this knowledge can serve as a resource for classroom instruction. This is the theoretical backbone of my project: the garden activity is designed not as an imported school task but as a deliberate bridge between what children already do at home (water plants, sort seeds, arrange pots) and the mathematical language and reasoning that institutions can extend.
National Research Council. (2009). Mathematics learning in early childhood: Paths toward excellence and equity. National Academies Press. This comprehensive report identifies measurement, spatial reasoning, and classification as core mathematical domains for early childhood, alongside number and operations. It argues that young children's informal mathematical knowledge — developed through everyday activity — provides a critical foundation for later formal learning, and that effective pedagogy builds on rather than replaces this foundation. The report's framework directly supports the curricular alignment of this project's activity elements.
Rogoff, B. (2003). The cultural nature of human development. Oxford University Press. Rogoff's concept of guided participation — where children learn through increasingly responsible involvement in culturally meaningful activities rather than through decontextualised instruction — provides the pedagogical model for this project. The garden activity is structured so that children participate at their developmental level (pouring water, sorting seeds, placing pots) within a shared routine that has real purpose, with the adult's role being to notice and extend reasoning rather than to deliver content.
Tippett, C. D., & Milford, T. M. (2017). Findings from a pre-kindergarten classroom: Making the case for STEM in early childhood education. International Journal of Science and Mathematics Education, 15(Suppl 1), 67–86.Tippett and Milford show that when STEM is integrated into ordinary pre-K activities in age-appropriate ways, young children engage meaningfully in STEM practices and families recognise this learning as valuable. Their finding that integration works better than subject separation reinforces the bundled design of this project, where measurement, classification, and spatial reasoning are encountered together within a single garden routine rather than taught as isolated topics.
Calabrese Barton, A., & Tan, E. (2009). Funds of knowledge and discourses and hybrid space. Journal of Research in Science Teaching, 46(1), 50–73. Calabrese Barton and Tan extend the Funds of Knowledge framework into science education, showing how students' everyday expertise becomes scientifically productive when it is explicitly recognised, reframed in disciplinary terms, and extended through further inquiry. Their concept of "hybrid space" — where home knowledge and school knowledge meet productively — directly informs the design of the garden activity as a space where household measurement practices and institutional mathematical language can meet.
Robertson, J. (2017). Messy maths: A playful, outdoor approach for early years. Independent Thinking Press.Robertson provides the most comprehensive practitioner resource on outdoor mathematics for ages 3–6. Her central argument — that outdoor spaces make maths real by connecting hands, heart, and head — directly supports this project's design logic. Chapters on measurement, pattern, and the "mathematical garden" offer concrete activity structures (using containers for capacity comparison, natural objects for sorting, garden spaces for spatial planning) that I adapt for the Anganwadi/Rajasthani context. Robertson's emphasis on mathematical vocabulary embedded in outdoor routines aligns with the "naming" step of the recognise–name–extend pedagogy.
Pecaski McLennan, D. (2020). Embracing math: Cultivating a mindset for exploring and learning. NAEYC. Pecaski McLennan, a Canadian kindergarten teacher and recipient of the 2020 Prime Minister Award for Excellence in Teaching STEM, demonstrates how mathematical inquiry can be integrated across art, outdoor exploration, and literacy in early childhood classrooms. Her chapters on math in outdoor spaces and math through art provide practical models for the arts-integrated and outdoor elements of this project. Her approach — noticing the math children are already doing and extending it through conversation — closely mirrors the recognise–name–extend sequence this project proposes.
British Columbia Ministry of Education. (2019). Mathematics curriculum: Kindergarten. Government of British Columbia. https://curriculum.gov.bc.ca/curriculum/mathematics/k The BC Kindergarten mathematics curriculum provides the curricular alignment for this project. Relevant content standards include: direct comparative measurement (longer than, shorter than, heavier than, holds more/holds less); sorting objects using a single attribute; equality as balance (modelling with a pan balance); and repeating patterns. The curriculum's Big Idea — "We can describe, measure, and compare spatial relationships" — maps directly onto the garden activity's measurement and spatial reasoning components. The curriculum also explicitly references Bishop's (1988) six cultural mathematical practices (counting, measuring, locating, designing, playing, explaining) and encourages connecting mathematics to "daily activities, local and traditional practices, the environment," which grounds the project's culturally responsive design.
Project Title: The Terrace Garden Morning: Teaching Measurement, Classification, and Spatial Reasoning Through Outdoor Plant Care in an Anganwadi Setting
Grade Level / Age: Ages 3–6 (preschool/foundational stage)
Context: Anganwadi centre (India's public early childhood care and education system) serving children from rural and peri-urban households in Rajasthan, India. Designed for an Anganwadi worker facilitating a mixed-age group of approximately 15–20 children with minimal purchased materials.
Brief Description
This project designs a 45-minute outdoor activity sequence centred on terrace/courtyard garden care — a routine already present in many rural Indian households — that integrates measurement, classification, proportional reasoning, and spatial thinking through embodied, arts-based, and outdoor approaches.
The mathematical focus is measurement using non-standard units, with classification and spatial reasoning woven in as supporting domains. Children pour water into plant pots using household containers (cups, bowls, small vessels), compare quantities ("Which holds more? Which plant needs more?"), sort seeds and leaves by observable properties, and collaboratively plan a simple garden layout by arranging pots and drawing a map.
The design draws directly from my MA thesis research, in which I spent four weeks conducting fieldwork in one Anganwadi and ten connected households in Udaipur, Rajasthan. I documented children as young as three engaging in sophisticated mathematical reasoning through everyday routines — measuring water portions for plants using a fractional rule ("half a container"), operating balance scales at vegetable carts, sorting grains with steel strainers, and proportioning roti dough. However, these competencies were not recognised or extended within the Anganwadi's pedagogical routines, in part because the system's activity calendar and assessment instruments have no category for science and frame learning through discrete, decontextualised tasks.
This project operationalizes the "recognise–name–extend" pedagogy I proposed in my thesis: the Anganwadi worker begins by noticing what children already know from home (recognition), gives mathematical language to what they are doing (naming), and then adds one small prompt that pushes reasoning further — "What if we use a bigger cup? Will the plant need more or fewer pours?" (extension). The activity requires no purchased materials: soil, water, seeds, leaves, containers, sticks, and chalk are sufficient. It is designed to be feasible within the time, resource, and staffing constraints that Anganwadi workers actually face.
How I plan to research, design, and try out the ideas:
This project designs a 45-minute outdoor activity sequence centred on terrace/courtyard garden care — a routine already present in many rural Indian households — that integrates measurement, classification, proportional reasoning, and spatial thinking through embodied, arts-based, and outdoor approaches.
The mathematical focus is measurement using non-standard units, with classification and spatial reasoning woven in as supporting domains. Children pour water into plant pots using household containers (cups, bowls, small vessels), compare quantities ("Which holds more? Which plant needs more?"), sort seeds and leaves by observable properties, and collaboratively plan a simple garden layout by arranging pots and drawing a map.
The design draws directly from my MA thesis research, in which I spent four weeks conducting fieldwork in one Anganwadi and ten connected households in Udaipur, Rajasthan. I documented children as young as three engaging in sophisticated mathematical reasoning through everyday routines — measuring water portions for plants using a fractional rule ("half a container"), operating balance scales at vegetable carts, sorting grains with steel strainers, and proportioning roti dough. However, these competencies were not recognised or extended within the Anganwadi's pedagogical routines, in part because the system's activity calendar and assessment instruments have no category for science and frame learning through discrete, decontextualised tasks.
This project operationalizes the "recognise–name–extend" pedagogy I proposed in my thesis: the Anganwadi worker begins by noticing what children already know from home (recognition), gives mathematical language to what they are doing (naming), and then adds one small prompt that pushes reasoning further — "What if we use a bigger cup? Will the plant need more or fewer pours?" (extension). The activity requires no purchased materials: soil, water, seeds, leaves, containers, sticks, and chalk are sufficient. It is designed to be feasible within the time, resource, and staffing constraints that Anganwadi workers actually face.
How I plan to research, design, and try out the ideas:
Research: I will draw on the literature I have already reviewed for my thesis (Funds of Knowledge, situated cognition, early mathematics, embodied learning) and supplement it with 3–4 sources on outdoor mathematics pedagogy and arts-integrated math approaches from this course.
Design: I will create a step-by-step activity narrative with embedded mathematical language prompts, materials lists, and variations for the three age bands (3–4, 4–5, 5–6). I will map each activity element to the BC Kindergarten Mathematics Curriculum (specifically: direct comparative measurement, sorting by single attribute, equality as balance, and the Big Idea "We can describe, measure, and compare spatial relationships") as well as to India's Aadharshila curriculum, to show dual curricular alignment. The BC curriculum's explicit reference to Bishop's (1988) cultural mathematical practices and to connecting mathematics to "daily activities, local and traditional practices" provides a strong frame for the project's culturally responsive design.
Try out: I do not currently have access to children aged 3–6 for a live pilot. Instead, I plan to do a detailed walkthrough with a peer or classmate acting as co-facilitator: we will lay out the materials, run through the activity sequence step by step, test the mathematical language prompts, and identify where the design would need adaptation. I will document the walkthrough with photographs and reflections, noting what worked in the sequence, where prompts felt natural or forced, and what I would revise for an actual classroom implementation. This approach is consistent with design-based research traditions where iterative refinement begins with structured rehearsal before live testing (Cobb et al., 2003).
Positionality connection: I grew up in India and have spent the past year immersed in households where children's everyday reasoning — measuring, sorting, building, estimating — was abundant but unnamed. This project is my attempt to close the gap my thesis documented: to design the activity that would make household mathematical knowledge visible and extendable within the institution that currently cannot see it.
Annotated Bibliography
Clements, D. H., & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968–970.Clements and Sarama present evidence that early mathematics interventions grounded in developmental learning trajectories significantly improve young children's mathematical understanding. Their concept of learning trajectories — where instruction begins from where children currently are and builds toward more formal reasoning — directly informs the "recognise–name–extend" sequence in my project. The idea that effective early maths teaching starts by identifying existing competence and then designing the next step is foundational to this activity design.
Ginsburg, H. P., Lin, C.-L., Ness, D., & Seo, K.-H. (2003). Young American and Chinese children's everyday mathematical activity. Mathematical Thinking and Learning, 5(4), 235–258. Ginsburg et al. demonstrate that young children's everyday mathematical activity is more complex and more integrated than what typically appears in formal early mathematics curricula. Their finding that children naturally engage in measurement, pattern, and spatial reasoning during free play and household routines supports the design principle of this project: rather than importing decontextualised math tasks, the activity begins from a routine (garden care) that already compresses multiple mathematical domains.
Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge University Press.Lave's foundational study demonstrates that mathematical reasoning in everyday settings is organised by practical goals and material constraints rather than by decontextualised problems, and that people perform significantly better in situated contexts than on structurally equivalent pencil-and-paper tasks. This work grounds the project's core premise: that measurement with household containers in a real garden is not a simplified version of "real" mathematics but a different and legitimate form of mathematical practice that the Anganwadi can build on.
Moll, L. C., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of knowledge for teaching: Using a qualitative approach to connect homes and classrooms. Theory Into Practice, 31(2), 132–141. Moll et al. established the Funds of Knowledge framework, arguing that households accumulate historically developed knowledge through labour, social networks, and material practices, and that this knowledge can serve as a resource for classroom instruction. This is the theoretical backbone of my project: the garden activity is designed not as an imported school task but as a deliberate bridge between what children already do at home (water plants, sort seeds, arrange pots) and the mathematical language and reasoning that institutions can extend.
National Research Council. (2009). Mathematics learning in early childhood: Paths toward excellence and equity. National Academies Press. This comprehensive report identifies measurement, spatial reasoning, and classification as core mathematical domains for early childhood, alongside number and operations. It argues that young children's informal mathematical knowledge — developed through everyday activity — provides a critical foundation for later formal learning, and that effective pedagogy builds on rather than replaces this foundation. The report's framework directly supports the curricular alignment of this project's activity elements.
Rogoff, B. (2003). The cultural nature of human development. Oxford University Press. Rogoff's concept of guided participation — where children learn through increasingly responsible involvement in culturally meaningful activities rather than through decontextualised instruction — provides the pedagogical model for this project. The garden activity is structured so that children participate at their developmental level (pouring water, sorting seeds, placing pots) within a shared routine that has real purpose, with the adult's role being to notice and extend reasoning rather than to deliver content.
Tippett, C. D., & Milford, T. M. (2017). Findings from a pre-kindergarten classroom: Making the case for STEM in early childhood education. International Journal of Science and Mathematics Education, 15(Suppl 1), 67–86.Tippett and Milford show that when STEM is integrated into ordinary pre-K activities in age-appropriate ways, young children engage meaningfully in STEM practices and families recognise this learning as valuable. Their finding that integration works better than subject separation reinforces the bundled design of this project, where measurement, classification, and spatial reasoning are encountered together within a single garden routine rather than taught as isolated topics.
Calabrese Barton, A., & Tan, E. (2009). Funds of knowledge and discourses and hybrid space. Journal of Research in Science Teaching, 46(1), 50–73. Calabrese Barton and Tan extend the Funds of Knowledge framework into science education, showing how students' everyday expertise becomes scientifically productive when it is explicitly recognised, reframed in disciplinary terms, and extended through further inquiry. Their concept of "hybrid space" — where home knowledge and school knowledge meet productively — directly informs the design of the garden activity as a space where household measurement practices and institutional mathematical language can meet.
Robertson, J. (2017). Messy maths: A playful, outdoor approach for early years. Independent Thinking Press.Robertson provides the most comprehensive practitioner resource on outdoor mathematics for ages 3–6. Her central argument — that outdoor spaces make maths real by connecting hands, heart, and head — directly supports this project's design logic. Chapters on measurement, pattern, and the "mathematical garden" offer concrete activity structures (using containers for capacity comparison, natural objects for sorting, garden spaces for spatial planning) that I adapt for the Anganwadi/Rajasthani context. Robertson's emphasis on mathematical vocabulary embedded in outdoor routines aligns with the "naming" step of the recognise–name–extend pedagogy.
Pecaski McLennan, D. (2020). Embracing math: Cultivating a mindset for exploring and learning. NAEYC. Pecaski McLennan, a Canadian kindergarten teacher and recipient of the 2020 Prime Minister Award for Excellence in Teaching STEM, demonstrates how mathematical inquiry can be integrated across art, outdoor exploration, and literacy in early childhood classrooms. Her chapters on math in outdoor spaces and math through art provide practical models for the arts-integrated and outdoor elements of this project. Her approach — noticing the math children are already doing and extending it through conversation — closely mirrors the recognise–name–extend sequence this project proposes.
British Columbia Ministry of Education. (2019). Mathematics curriculum: Kindergarten. Government of British Columbia. https://curriculum.gov.bc.ca/curriculum/mathematics/k The BC Kindergarten mathematics curriculum provides the curricular alignment for this project. Relevant content standards include: direct comparative measurement (longer than, shorter than, heavier than, holds more/holds less); sorting objects using a single attribute; equality as balance (modelling with a pan balance); and repeating patterns. The curriculum's Big Idea — "We can describe, measure, and compare spatial relationships" — maps directly onto the garden activity's measurement and spatial reasoning components. The curriculum also explicitly references Bishop's (1988) six cultural mathematical practices (counting, measuring, locating, designing, playing, explaining) and encourages connecting mathematics to "daily activities, local and traditional practices, the environment," which grounds the project's culturally responsive design.
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