Mathematics in Kindergarten

There are so many different views about and practices in math(s) in the Early Years, including the ideas that it's all around us, it's part of a transdisciplinary programme and it's a natural part of how children play. 

While I agree with these views, I think as educators, we have an important role in helping children understand mathematical ideas that are indeed in their play, their lives and their world. Mathematical processes and big ideas should be explored explicitly in authentic contexts. A recent tweet by Dr Helen Williams reminded me that thinking is not always a feature when learning mathematics. 

In the recent IB publication, The Early Years in the PYP, the reasons why symbolic exploration and expression is important for early learners are explained: "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."

Although this is my first year teaching Kindergarten, my beliefs and guiding principles from my career stay strong. 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 for any single discipline. 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 here in the context of language. 

In her book, Concept-Based Mathematics, Jennifer Wathall reminds us of 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 is a chance to reflect on the mathematics in my Kindergarten class so far this year. 

Routines

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, explore patterns, consider what has changed and what has stayed the same and anticipate what is to come the next day. 

There is also a maths task that focuses on a big idea as part of the morning routine. We spent several weeks subitising and comparing counting strategies using number dots and we are now focusing on estimation using different objects in the classroom. Part of both of these has been the phrasing "How many...?" This has inspired several different wonderings and interest groups going around school to find out how many steps, teachers and rooms we have. 

Play

As children play, there are often mathematical ides being explored. This week, a group of children were building a Lego wall thinking about shape, orientation, space and area as they showed great determination to add a layer without any gaps. 

Many of the children love to draw and colour. Introducing different types of paper (triangular, squared and, soon, isometric paper) has inspired children to play with design, pattern and symmetry. 

Construction is also another popular choice. Recently, 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 1 metre. 

Construction often involves exploration of shape, size, space using different materials such as Magna-Tiles, Kapla and interconnecting sticks. 

Some children choose to play with Bee-Bots, exploring direction and distance. 

There are games, mazes and puzzles for children to play with too. These often require logic, reasoning and strategic thinking which frame fascinating conversations with the children about process. 

Building on the children's interests in Pop Its, we have Pop Its with different numbers and arrangements. This one has the standard 100-square written on and has appealed to many children who, despite struggling with numbers in the 'teens', recognised patterns and popped numbers to 100. 

Learning Environments

The learning environment is instrumental in supporting and provoking mathematical thinking. We are lucky to have lots of loose parts in the classroom. The open-ended nature of these materials offers infinite possibilities and learning beyond mathematics. Within mathematics, children have sorted buttons, counted beads, designed tube-bracelets with patterns and built water walls with tubes and pipes outside. Recently, several children have been playing with balance scales in the classroom and making comparisons about how heavy objects are. 

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 in the class to serve as a model and reference point for where to start. 

There is a spiral staircase that connects the Early Years hallway to the playground. We had the numerals 1-10 at the start of the year and these 5-year olds would often count forwards and backwards as they walked and read the numbers. A couple of weeks ago, we changed the numbers starting from 0 and going to 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 small groups of children to target specific number concepts. These include number lines, 100-squares, 10 frames, Numicon, Rekenreks and games such as bingo. There are also some whole-class maths lessons that focus on very 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

Stories are a daily feature in Kindergarten. Stories might be from picture books, poems, rhymes, songs or videos. So often, the stories are based on numbers, patterns, repetition, measurement concepts or the use of shape and space. 

Paris as a Classroom

We regularly seek opportunities to experience, extend and apply learning beyond the school's walls. At least once a week, we venture into Paris. Last week, we walked along nearby streets to look at architecture and notice 2D and 3D shapes. Shape hunts like this are examples of low-floor, high-ceiling explorations that allow all children to participate but place no limits on learning. Some of these 5-year olds spotted shapes with 7, 9 and 12-sides and wanted to learn the names of these shapes. Walking back to school, one child asked, "What is the name of a 2-sided shape?" This question was launched back to the class the next day as they were challenged to draw a 2-sided shape. A different day, children tallied the number of different shapes they saw. 

We regularly visit a nearby 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 natural materials. En route, children are noticing and reading larger numbers more and more. 

Sometimes, children explore different areas based on their interests. A few weeks ago, one group was curious about the local fruit and vegetable shop and the jobs of those who worked there. Observing, they noticed the transactions of buying and selling and the prices of different items. They spontaneously started to compare the prices of different produce, understanding the notation for Euros. 

 

Another group was interested in the Metro and who worked there. One of the workers kindly 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 the city they lived in. Some children were inspired to make their own maps back at school. 

Our current unit of inquiry is under the transdisciplinary theme of How the world works and focuses on the concept of structures. Last week, 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 our inquiry then took on a new angle with symbols to show units of measurement. Some children chose to continue playing with this app and Google Earth to explore place, direction and measurement. 

Reflections on your Practice

What mathematical learning opportunities do your young learners have?

What other opportunities might be possible?

How do mathematical processes play a role in the learning and teaching of mathematics?

How might there be more opportunities for children to play and be playful with mathematical ideas?