Programming as a language for young children to express and explore mathematics in school
Authors: Goldenberg E. Paul , Carter Cynthia J. 
Published: June 2021

AbstractNatural language helps express mathematical thinking and contexts. Conventional mathematical notation (CMN) best suits expressions and equations. Each is essential; each also has limitations, especially for learners. Our research studies how programming can be a advantageous third language that can also help restore mathematical connections that are hidden by topic‐centred curricula. Restoring opportunities for surprise and delight reclaims mathematics' creative nature. Studies of children's use of language in mathematics and their programming behaviours guide our iterative design/redesign of mathematical microworlds in which students, ages 7–11, use programming in their regular school lessons as a language for learning mathematics. Though driven by mathematics, not coding, the microworlds develop the programming over time so that it continues to support children's developing mathematical ideas. This paper briefly describes microworlds EDC has tested with well over 400 7‐to‐8‐year‐olds in school, and others tested (or about to be tested) with over 200 8‐to‐11‐year‐olds. Our challenge was to satisfy schools' topical orientation and fit easily within regular classroom study but use and foreshadow other mathematical learning to remove the siloes. The design/redesign research and evaluation is exploratory, without formal methodology. We are also more formally studying effects on children's learning. That ongoing study is not reported here.
Practitioner notesWhat is already known

Active learning—doing—supports learning.
Collaborative learning—doing together—supports learning.
Classroom discourse—focused, relevant discussion, not just listening—supports learning.
Clear articulation of one's thinking, even just to oneself, helps develop that thinking.
What this paper adds

The common languages we use for classroom mathematics—natural language for conveying the meaning and context of mathematical situations and for explaining our reasoning; and the formal (written) language of conventional mathematical notation, the symbols we use in mathematical expressions and equations—are both essential but each presents hurdles that necessitate the other. Yet, even together, they are insufficient especially for young learners.
Programming, appropriately designed and used, can be the third language that both reduces barriers and provides the missing expressive and creative capabilities children need.
Appropriate design for use in regular mathematics classrooms requires making key mathematical content obvious, strong and the ‘driver’ of the activities, and requires reducing tech ‘overhead’ to near zero.
Continued usefulness across the grades requires developing children's sophistication and knowledge with the language; the powerful ways that children rapidly acquire facility with (natural) language provides guidance for ways they can learn a formal language as well.
Implications for policy and/or practice

Mathematics teaching can take advantage of the ways children learn through experimentation and attention to the results, and of the ways children use their language brain even for mathematics.
In particular, programming—in microworlds driven by the mathematical content, designed to minimise distraction and overhead, open to exploration and discovery en route to focused aims, and in which children self‐evaluate—can allow clear articulation of thought, experimentation with immediate feedback.
As it aids the mathematics, it also builds computational thinking and satisfies schools' increasing concerns to broaden access to ideas of computer science.