This blog gives an insight into a kindergarten classroom and what authentic learning of mathematics might look like. Examples include mathematics that is a natural part of children’s play, child-initiated inquiries, and teacher-led investigations.
Sean Walker is a Kindergarten teacher at International School Of Paris. After teaching for 25 years, this is the first time for Sean teaching in Early Years. He leads face-to-face and online workshops for the IB and is particularly interested in play, conceptual learning and inquiry.
As educators, we have a key role in helping children understand mathematical ideas in their play, their lives, and their world. Mathematical processes and big ideas should be explored in authentic contexts.
Numeracy involves the capabilities (knowledge, skills and dispositions) needed to understand and use mathematics concepts in a wide range of contexts. Numeracy is a language that we use to communicate. Young learners are developing their numeracy capabilities every day. Through play, they explore and make sense of the world by finding patterns, manipulating shapes, measuring, sorting, comparing, locating, counting and grouping, estimating, connecting, playing with possibilities, posing problems and solving them. The early years in the PYP (Primary Years Programme)
I value inquiry and conceptual learning so that children develop as curious mathematicians, making sense of complex ideas through engaging and relevant contexts. Halliday’s framework of learning, learning about and learning through still resonates with me. It reminds me of the importance of the behaviours, passion and mindset of a person actively engaged in a discipline (learning), alongside the mathematical knowledge, skills and concepts that are targeted (learning about) and how the discipline is truly connected to other disciplines and contexts (learning through). I have written more about Halliday in my blog.
In her book, Concept-Based Mathematics, Jennifer Wathall highlights the importance of processes in maths. Concepts are drawn from these processes as they provide lenses to move beyond just “doing maths” and understanding the why behind the maths.
This post reflects on the mathematics in my kindergarten class for the first three months of the school year.
Each morning, the children move their photo to take their own attendance. As a class, we then think about how many children are in school that day and how we know. Various strategies are shared.
There is a morning message each day. The day of the week, the month, the year, and the actual date all present opportunities to read different numbers and words and explore patterns.
There is also a maths question that focuses on a big idea. We spent several weeks subitizing and comparing counting strategies using number dots and we are now focusing on estimation using different objects. The phrase “How many…?” has been part of both. This has inspired different wonderings and interest groups going around school to count the number of steps, teachers, and rooms.
This week, a group was building a Lego wall thinking about shape, orientation, space, and area as they showed determination to add a layer without any gaps. Construction is a popular choice. As children were trying to build the tallest structures, they started to compare the heights of things. I added a metre stick to their play which prompted them to see who and what was taller and shorter than one metre. Construction often involves exploration of shape, size, space using different materials such as Magna-Tiles, Kapla, and interconnecting sticks.
Many of the children love to draw and colour. Introducing different types of paper (triangular, squared and, isometric paper) has inspired children to play with design, pattern, and symmetry.
There are games, mazes, and puzzles for children to play with. These require logic, reasoning and strategic thinking which frame fascinating conversation about process. Some children choose to play with Bee-Bots, exploring direction and distance.
Building on the children’s interests in Pop Its, we have Pop Its with different numbers and arrangements. By writing numbers up to 100, this has appealed to many children who, despite struggling with numbers in the ‘teens’, recognised patterns and popped numbers to 100.
We have lots of loose parts in our learning environment. Their open-ended nature offers infinite possibilities. Children have sorted buttons, designed tube-bracelets with patterns and built water walls with tubes and pipes outside. Children have been playing with balance scales to make comparisons.
When forming digits in the air, in salt or on paper, many children struggle with where to start and often reverse the digits. We have numbers on display as a model.
There is a spiral staircase that connects the Early Years hallway to the playground. We had the numerals 1-10 in September and Kindergarten would often count forwards and backwards. We just changed the numbers (0-20), skip counting in 2’s. This has generated lots of dialogue and choral counting.
In the classroom, there are models and tools to support mathematical thinking. I often use these with groups of children to target specific concepts. These include number lines, 100-squares, 10 frames, Numicon, Rekenreks and games such as bingo. There are also whole-class maths lessons that focus on specific mathematical concepts and skills. Explicit instruction, high-level questioning and modelling mathematical language in rich contexts are not the enemies of inquiry-based learning. Jo Boaler’s Mindset Mathematics – Grade K – is a wonderful resource for ideas for these focused investigations.
Stories are a daily feature in kindergarten. Stories might be picture books, poems, rhymes, songs, or videos. Often, the stories are based on numbers, patterns, repetition, measurement or shape and space.
Using the city as a classroom
At least once a week, we venture into Paris. Last week, we walked along streets to notice 2D and 3D shapes. Shape hunts like this are examples of low-floor, high-ceiling explorations that allow everyone to participate but place no limits on learning. Some of these five-year-olds spotted shapes with seven, nine and 12-sides and wanted to learn their names. One child asked, “What is the name of a two-sided shape?” This question was launched back to the class as they were challenged to draw a two-sided shape. A different day, children tallied the different shapes they saw.
We visit a nature trail to play, go on scavenger hunts and do team challenges. Many children count the number of things they find or design shapes using materials. Children are noticing and reading larger numbers more.
Sometimes, children explore different areas based on their interests. One group was curious about the fruit and vegetable shop. They noticed the prices of different items, and spontaneously compared the prices of different produce.
Another group was interested in the Metro. A worker gave the children a Metro map. The children were fascinated with this network of lines and directions, and how to navigate this symbolic representation of Paris. Some children then made their own maps.
Our current unit of inquiry for how the world works focuses on the concept of structures. We walked to the River Seine to observe bridges. Reflecting on the trip, some children were interested in measurements linked to the bridge we walked across (its height and distance across).
I introduced Google Maps and children explored symbols for units of measurement. Some children chose to continue playing with this app and Google Earth to explore place, direction, and measurement.