Early Years
High quality instruction in mathematics and high quality free play need not compete for time in the classroom. Engaging in both makes each richer, and children benefit in every way.
(Sarama & Clements, 2009a, p. 331)
Kindergarten Curriculum & Support Documents
The understanding that children, families, and educators share about themselves and each other, and about the roles they play in children’s learning, has a profound impact on what happens in the Kindergarten classroom. The view of children, families, and educators provided in the following descriptions is at the heart of Ontario’s approach to pedagogy for the early years. When educators in early years and Kindergarten programs reflect on and come to share these perspectives, and when they work towards greater consistency in pedagogical approach, they help strengthen and transform programs for children across the province.
Continua of Curriculum Expectations Grades K-2
Conceptual Understandings (K), Big Ideas from Dr. Small (K-3), Curriculum Expectations
Early Counting Principles
Student’s effectiveness in using operations depends on the counting strategies they have available, on their ability to combine and partition numbers, and on their sense of place value.
(Guide to Effective Instruction in Mathematics Gr. 1-3, NSN, pg. 20)
These concepts do not necessarily occur in a linear order. For example, some students learn parts of one concept, move on to another concept, and then move back again to the first concept.
(Guide to Effective Instruction in Mathematics Gr. 1-3, NSN, pg. 11)
Computation Strategies Booklet
Counting Principles
SK/1 Scope and Sequence
The K-2 Scope and Sequence is intended to be used as a guide for educators planning for Kindergarten and Grade 1 combined classrooms, to assist in choosing provocations and opportunities that will aid in “mathematizing” the learning environment – which Clements and Sarama (2013) indicate can create a wide variety of opportunities for children to learn about mathematics. In addition to mathematizing the environment it is very "important to be attuned to children’s mathematical thinking – that is, to regard young children as being capable of potentially complex thinking. Keeping in mind the question 'Why have we chosen this learning for this child at this time in this context?' to help educators in providing differentiated ways of supporting children’s learning. Throughout the day, the educators can create an effective environment to support young children’s learning of mathematics by providing mathematics experiences that focus on particular mathematical concepts and by identifying and embedding significant mathematics learning experiences in play, daily routines, and classroom experiences. "(Kindergarten Curriculum, 2016 - Page 80, Page 84). Intentional, purposeful teacher interactions are necessary to ensure that mathematical learning is maximized during play (Baroody, Lai, & Mix, 2006; deVries, Thomas, & Warren, 2007; Balfanz, 1999; Ginsburg, Lee, & Boyd, 2008).
Early Years Professional Development
Number Sense Trajectory
Number Sense Trajectory from Clements & Sarama with games to support each principles from G. Fletcher.
The lessons provided are samples of an instructional trajectory, designed to promote early stages of algebraic reasoning. They are the fundamental lessons which will allow students to analyze and create increasingly complex patterns. It is intended that they be started early in the year and revisited with opportunities in-between and beyond these lessons to practice and deepen understanding at centres and through games, to create, analyze and name a variety of patterns generated by students using a variety of materials (e.g. concrete manipulatives, interactive white board, virtual manipulatives).
It is intended that teachers and learning teams use these research-informed lessons, adapting them to their students’ needs.
Early Math Learning
Learning Trajectories
Intention Play-Based Learning
Integragted Concrete Concepts
Intentional Instruction
Professional Reading/Videos
Growing evidence indicates that early mathematics plays a significant role in later education. From an analysis of six longitudinal studies, Duncan and colleagues found that early mathematics skills were more powerful predictors of later academic achievement in both mathematics and reading than attentional, socioemotional or reading skills (2007, p. 1428).
In addition, the differences in mathematical experiences that children receive in their early years “have long-lasting implications for later school achievement, becoming more pronounced during elementary school … and continuing on into middle school and high school” (Klibanoff, 2006, p. 59). Such findings raise a critical question:
How can educators take advantage of the mathematical knowledge and experience that children bring to early primary classrooms?
Maximizing Student Mathematical Learning in the Early Years, pg. 1-2.
Mathematically literate students demonstrate the capacity to “formulate, employ and interpret mathematics” (OECD, 2012, p. 4); they view themselves as mathematicians, knowing that mathematics can be used to understand important issues and to solve meaningful problems, not just in school but in life. By extension, the physical environment for mathematics learning should include:
- Spaces where students can use manipulatives to solve problems and record their solutions.
- Board and/or wall space to display student solutions for Math Congress and Bansho – student solutions should be easily visible from the group gathering space.
- Space to post co-created reference charts such as glossary terms and past and current summaries of learning that specifically support the development of the big ideas currently under study.
- Instructional materials organized in such a way as to provide easy selection and access for all students; may include mathematics manipulatives, calculators and other mathematical tools, mathematical texts, hand-held technology.
The Third Teacher, pg. 2.
From edugains.ca
Please click on the link above to access resources and materials designed to support educators to engage numeracy through the day. This is a video series that explores elements of numeracy in a Kindergarten classroom, including:
- Thinking About Numeracy Throughout the Day
- Making Mathematics Thinking and Learning Visible Throughout the Day
- Prompting Children's Mathematical Thinking
- Engaging in Children's Play to Make Mathematics Learning Visible
- Mathematics in Inquiry – Responding to Children's Ideas
- Analyzing Documentation and Observation to Inform Learning
- Co-constructing Learning
- Children Learning from and with Each Other
- Reflections on Making Numeracy Visible and Intentional Based on Observations
Math can be seamlessly integrated into children’s ongoing play and activities. But this usually requires a knowledgeable adult who creates a supportive environment and provides challenges, suggestions, tasks and language.”
(Samara & Clements, Building Blocks, 2009, p. 332-333)
From edugains.ca
Please click on the link above to access resources and materials designed to support educators to engage numeracy through the day. This is a video series that explores elements of numeracy in a Kindergarten classroom, including:
- What do early learning environments look like and sound like? How are educator teams rethinking the learning environment? Rethinking the learning environment and the impact on learning.
- Rethinking the learning environment: what materials are educator teams removing?
- Thinking deeply about the learning environment - planning the materials and spaces to make learning visible.
- Co-constructing and negotiating the learning environment – including the children's voices and ideas.
The learning environment is often referred to as the “third teacher” because when carefully designed it supports and enhances children’s learning and their development of self-regulation competencies.
From edugains.ca
The learning environment includes the indoor and outdoor space and materials, the daily routines, schedules and rules as well as the inter-relationships between children, adults and all of these elements. Watch the following video clips and read the research brief to reflect on your practices and think about what you could do to invite investigation and create learning environments that value children as competent, capable and curious learners.
From edugains.ca
Please click on the link above to access resources and materials designed to support educators to engage numeracy through the day. This is a video series that explores elements of numeracy in a Kindergarten classroom, including:
- What does play-based learning look like and sound like?
- How are educator teams rethinking their role in play-based learning?
- How do educator teams co-construct learning through play and make learning visible?
- How are educator teams analyzing their observations and documentation to inform learning in play?
- What are some strategies that educator teams use to support children's play-based learning?
- Following children's thinking to respond, extend and challenge.
Learning in play is a highly complex and intellectual process that requires careful, planned, and intentional observation, interpretation, and analysis. This requires educators to have and continue to acquire an extensive knowledge base of how learning happens in play, how different children develop in play, how concepts are revealed and the critical role of the adult in making the learning visible.”
(Adapted from Trawick-Smith & Dziurgot, (2010)
From edugains.ca
Please click on the link above to access resources and materials designed to support educators to engage numeracy through the day. This is a video series that explores elements of numeracy in a Kindergarten classroom, including:
- What does inquiry-based learning look like and sound like? How are educator teams repeating, removing, and rethinking their theme-based planning and moving to inquiry?
- How are educator teams repeating, removing and rethinking their inquiry-based planning?
- Reflections on inquiry: the power of inquiry co-constructing and making learning visible.
- What does it look like and sound like to co-construct inquiry with the children? Listening in on a classroom inquiry
Educators become the leaders of a “community of inquiry.” They do not wait for development to happen rather they foster, provoke, and scaffold it by deepening children’s current understanding so new knowledge systems and new connections among them may be continuously generated.
(Adapted from Eun 2010, Bruner 1996)
"As part of our 'rethink' about creating a positive classroom climate for mathematics learning, we intentionally worked at changing the language we used when talking with the children. In addition, we created many community events that included parent and student engagement. There is no limit or ceiling to the math learning. When we put out the manipulatives the children took charge and demonstrated way more thinking and learning than we anticipated.” (K-3 Educators)
• suggestions of rich contexts for exploring mathematical ideas and developing mathematical skills and concepts
• details of linked mathematics learning goals
• descriptions of the mathematical journey that the learners may take through the task
• suggestions for prompts and questions to elicit mathematical responses from the children