España 
Italia 
United States 
Brasil 
Chile
Ecuador
Mexico
Colombia
Perú
Hey! What’s up? 👋
I’m back to talk to you about the importance of thoroughly understanding students’ learning journey regarding Numbers and Operations. Understanding the path followed by our students is essential not only for designing effective teaching strategies but also for identifying their difficulties and reinforcing these concepts.
The process and the different stages
In this process, students go through various stages that develop progressively. It is important to note, however, that most of these stages take place simultaneously and are revisited cyclically throughout their learning. Here are some examples:
1. Quantifiers
The first step arises very naturally when students start getting familiar with terms such as many, few, none, all, etc. They also start learning how to compare quantities: as many as, more/fewer than, etc.
2. Rote counting:
Here, students start to count aloud by ordering sequences, counting backward, or starting to count from numbers other than 1.
3. Base-10 number system:
This is when students begin to associate numerals with their names. They also practice number representations and put them in ascending and descending order.
4. Cardinal counting:
This reinforces students’ ability to count items one by one, as well as to instantly recognize quantities (subitizing) and group items in a meaningful way.
To sum up, cardinality is developed through progressive skills:
- Learning how to count numbers in order.
- Assigning a number to each object (one-to-one correspondence).
- Understanding that the last number counted indicates the total quantity.
- Recognizing that each successive number represents one more unit.
5. Additive thinking:
Later, everything learned is integrated to lay the foundation for operations like addition.
Do you see how understanding this journey will help you tailor your teaching strategies and provide more targeted support to your students when they need it? 🙂
If you would like to further explore how this process begins in the classroom and discover practical strategies to support your students naturally and progressively, I recommend reading When and How Do Children Enter the World of Numbers?. In this article, Mequè Edo explains, in an accessible and well-founded manner, that numerical learning is built from everyday experiences and playful activities.
For example, the author shows how simple activities, such as counting objects in the environment, can become the starting point for students to understand the essence of numbers.
Big hug,
Judith, from Innovamat
