Children’s thoughts about mathematics are reflections of their experiences (Steffe, von Glasersfeld, Richards, & Cobb, 1983).
Let’s take a look:
In the AIMS blog, there has been a good bit of talk about the “mathematics of children” (Steffe, 1991). This covers a lot of ground. When we talk about the way that children construct math concepts, we are talking about numerous dynamic parts that include, but are not limited to, the following examples from the video 1) viable language connections, 2) children’s non-verbal cues, 3) the importance of math autonomy, and 4) the importance of fun and spontaneity.
Viable Language Connections
At all ages, but particularly in the preschool classroom, there is a need for the teacher to be aware of the language he/she is using with the children. Consistency and accuracy can support the experiences children need to form their own viable understanding of the vocabulary.
In the video examples, the three children clearly understand what it means to “count backwards”. While their ways of thinking are certainly viable to them, their understanding just isn’t consistent with what the teacher is meaning! This is okay. With a variety of consistent experiences with “backwards” counting, they will soon develop a “backwards” count that can be useful when thinking about numbers.
Accuracy is also important. If the adult says, “Let’s go,” the child may get up and go instead of counting as the adult intended. If asked to “touch the dots”, it may not be clear to him that the adult is actually cueing him to count them.
As teachers, we sometimes get so focused on a lesson or activity that we want to finish that we forget about the importance of the child’s intrinsic motivation. If the children aren’t motivated (or if they are just plain tired), maybe we need to stop and re-think our plan for tomorrow. Our educational culture sometimes “requires” that we follow through with the plan and finish the lesson of the day, when it is more productive to follow the lead of the children.
Imposing adult mathematics on children denies them the chance to invent it themselves and, subsequently, to own it (Piaget, 1966). Instead, as teachers let’s provide activities and games that encourage children to develop intrinsic mathematical goals. This leads to both math autonomy and further intrinsic mathematical goals (Kamii, 1985).
Fun and Spontaneity
Finally, we shouldn’t underestimate the value of fun and spontaneity in the classroom. If as teachers we can loosen up a little bit and enjoy the fun moments with the children, we can stay connected and better understand how those growing minds are working. Be the child!
Emotion is key to learning (Immordino-Yang, 2016), and there is no substitute for joy in mathematics (Wager & Parks, 2017)!