How to Guide Children's Mathematical Development

Knowing where your learners are at and where they are going. 

Understanding the developmental journey of your learners — where they've been, where they are, and where they're headed — is pivotal in effective teaching.

Developmental trajectories of mathematics are an important part of meeting learners where they are at. They equip educators with the insight to identify areas for reinforcement or nudges in thinking. I often get asked by educators  "How do I know what questions to ask to children?" And the response isn't always straightforward. As stated by Drs. Julie Sarama and Douglas H. Clements on Learning and Teaching with Learning Trajectories “Research shows that when teachers understand how children develop mathematics understanding, they are more effective in questioning, analyzing, and providing activities that further children’s development than teachers who are unaware of the development process.” Thus, knowing what to ask depends on our understanding of how children learn. Our ability to craft meaningful questions hinges on our confidence and knowledge of developmental trajectories.

There are several resources about understanding the development of learning mathematics, in fact there are so many that it can get overwhelming!

I’ve narrowed down a few of my favourites to help you get started on your ongoing learning journey. I say ongoing, because the more I dive into children's development the more questions I have…and the more I learn! As you continue along this learning journey, I encourage you to be kind to yourself. You can’t know it all. Take the time to notice and name the ideas or theories in action so it becomes second nature to recognize how children are processing their world through a mathematical lens. 

• In Pam Harris’ model of Developing Mathematical Reasoning, she helps us understand the scope of reasoning through development, not chonological age. Starting at counting, through addition and multiplication to proportional and functional reasoning. I highly suggest taking some time to dig into her FREE online course, developing mathematical reasoning or listening to her podcast here. Below is her Development of Mathematical Reasoning.   
• I am a huge advocate of Cathy Fosnot’s Landscapes for Learning to understand the complexities and trajectories of content based math learning. Fosnot has trajectories for number sense, multiplication, data representation and more! You can check out some of her work here and watch some of her YouTube videos here. Below is one of her landscapes for learning. 

• Douglas Clements is well known for his work around early learning mathematical development. You can check out his website here and find information about development, as well as games and resources to support the implementation. You can also listen to this podcast here. 
• One of my favourite books (and a relatively quick read!) is How Children Develop Number Concepts; a guide to critical learning phases by Kathy Richardson. In this read, you can vividly make connections to the learners in your class as well as create and implement concrete examples in action. 

Reflection Questions:

• How do you currently incorporate knowledge of learning trajectories into your teaching practice?
• How can you leverage the insights gained from resources like those mentioned to enhance your teaching effectiveness?
• In what ways can ongoing learning about children's mathematical development impact your instructional approach and classroom environment?
• How does knowledge of these trajectories help clarify your assessment practices?