The first sentence in the title of this post could suggest the advocacy of a big focus on academics during the early years. This is not what this is about, however, as we shall soon see. As a teacher, I am from a play-based background.
My current class are now in the final year of kindergarten here in China, which is for 5–6-year-olds. I have been with them since they were 3, so this is now our third year together.
The opportunity to practice maths has always come up naturally as part of our daily activities and in different contexts. We use it to solve real-world problems—but that’s a story for another day.
What’s important here is that I’ve always used transition times to practice short, fun maths questions—a practice the students have also been keen to lead. We’ve practiced counting and simple addition, then moved to subtraction and multiplication, developing techniques together, for example, counting objects or fingers to help us. In addition, we’ve included real-life word problems, which have been an effective way to practice English listening and comprehension, especially with my students being English language learners.
Recently, we’ve explored arithmetic with bigger numbers. Yesterday, a few of the students asked if we could try a new type of question.
On the spot, I thought of an idea and asked one of them, “Do you want to do some algebra?” He asked what algebra was. I told him I’d show him an example.
I asked, “If x + 5 = 7, what is x?”
He initially replied that he didn’t know. I told him not to worry, but to listen again and think about it. After a little thinking time, he exclaimed, “It is 2!” We tried more similar examples, and each time—with a little thought—he was quick to follow what was happening.
I’ve explored this with other students since then as well. They’ve approached the problem in the same open-minded way, also finding success. The most support I’ve given has been to repeat the question slowly, emphasizing its meaning. One of the girls asked, “But what is x?” I replied, “That’s what you need to tell me. Take your time. Think about it.” She did—and she worked it out.
The activity has been met with curiosity and excitement, serving to exercise and celebrate thinking. One of the boys even began creating his own scenarios later, saying, “x is 5 and y is 10. What is x + y?” (I had asked some questions earlier using letters other than x.)
It’s important to note that all of this was done as relaxed, playful activities, following the students’ own curiosity—not as a “class,” for example.
Asking such questions to students of this age—and seeing them tackle them independently—can, of course, make you smile as a teacher. Algebra is something we often associate with an older age group. On reflection, though, questions like the ones I asked are actually well within the range of the mathematical thinking and number sense the students have at this stage. I had a natural feeling at the time that this was something they could try—and it was.
What can we take away, then?
Well, the age is not actually overly important. (Within reason.) Age is very much just a number. Students should develop at their own pace and in their own way. Challenges should always be within their zone of proximal development.
With maths, we first want to focus on the real world and how techniques and skills are used there—contextualization, contextualization. But before diving into explanations or teaching techniques, we should ensure students have space to think and understand. Give them the information they need, then allow time to explore the problem themselves. This helps them gain a feel for what they’re doing and supports the growth of independent thinking and problem-solving.
Looking at maths as a whole, it’s a broad subject—but its different parts, like numbers and algebra, are often directly related. We can highlight these connections to help students see the bigger picture and develop deeper understanding. For something like algebra, it has real purpose that connects naturally to numbers in the real world, and it’s number skills we can use as tools within it. It’s certainly worth introducing such ideas alongside foundational number skills—especially when interest and curiosity lead the way.