Joseph S. Kozlowski

ABSRACT The purpose of this study was to explore how kindergarten students (aged 5–6 years) engaged with mathematics as they learned programming with robot coding toys. We video-recorded 16 teaching sessions of kindergarten students’ (N = 36) mathematical and programming activities. Students worked in small groups (4–5 students) with robot coding toys on the floor in their classrooms, solving tasks that involved programming these toys to move to various locations on a grid. Drawing on a semiotic mediation perspective, we analyzed video data to identify the mathematics concepts and skills students demonstrated and the overlapping mathematics-programming knowledge exhibited by the students during these programming tasks. We found that kindergarten children used spatial, measurement, and number knowledge, and the design of the tasks, affordances of the robots, and types of programming knowledge influenced how the students engaged with mathematics. The paper concludes with a discussion about the intersections of mathematics and programming knowledge in early childhood, and how programming robot toys elicited opportunities for students to engage with mathematics in dynamic and interconnected ways, thus creating an entry point to reassert mathematics beyond the traditional school content and curriculum.

Background and Context: There is a need for early childhood assessments of computational thinking (CT). However, there is not consensus on a guiding framework, definition, or set of proxies in which to measure CT. We are addressing this problem by using Evidence Centered Design (ECD) to develop an assessment of kindergarten-aged children’s CT. Objective: To present a design case on the development of the assessment, specifically the algorithmic thinking (AT) tasks and to share validity evidence that emerged. Method: We focus on the AT sub-component of CT and present the principled assessment design process using ECD. Findings: Our operationalization of CT includes spatial reasoning as a sub-component. Pilot results showed an acceptable internal consistency reliability for the AT items and critical design decisions that contributed to validity evidence. Implications: An important contribution of this work is the inclusion of spatial reasoning in our definition of early childhood CT.

Student ability to demonstrate mathematical creativity positively affects their mathematical learning. Further, creativity-based mathematical instruction (CBMI) may enhance divergent thinking and precipitate a highly creative mathematical learning environment . In this literature review and discussion, it is posited that CBMI has distinctively beneficial influences on mathematically gifted students’ learning processes and products. With CBMI, a value is placed on creative output, which differs from dispositions generated in algorithmically based classrooms, which may arrest creative or divergent thought. Procedure-based teacher instruction abates mathematically gifted students’ creative possibilities and restricts their thinking potential. By placing unnecessary constraints on mathematical thought, teachers restrict mathematically gifted students’ ability to produce divergent thoughts that may lead to creative products. Contemporary interpretations of giftedness include creativity as a characteristic, and therefore should be considered in mathematical learning episodes. By incorporating CBMI and promoting a mathematical environment in which creativity is valued, mathematics classrooms are raising the learning ceiling for mathematically gifted students. CBMI allows students to explore concepts and construct understanding conceptually and creatively.