Teachers and Mathematics Educators as Designers and Users of Objects to Think With: Our Partnership with the National Technology Leadership Summit (NTLS)

“The concrete operational stage is crucial in a child's development of logical thinking. Manipulatives provide the hands-on experience necessary for understanding abstract mathematical concepts.”

- Jean Piaget

The NTLS is a coalition of 12 national teacher education associations created with the goal of collaborating across disciplinary lines on issues related to teaching and learning with technology. NTLS includes national teacher educator associations in the four STEM content areas: science education (Association for Science Teacher Education, ASTE), educational technology (Society for Information Technology and Teacher Education, SITE), engineering education (International Technology and Engineering Educators Association, ITEEA), and mathematics education, represented by our organization, AMTE. There are also associations representing the humanities. AMTE has contributed to the NTLS work in several ways, one of which has been through the publication of an open-source peer-reviewed journal, the Contemporary Issues in Technology and Teacher Education (CITE Journal, www.citejournal.org). The mathematics section of the journal, referred to as CITE-Math, is managed by AMTE.

For a long time, manipulative materials have been an important tool for the learning and teaching of mathematics. Given the availability of digital fabrication tools such as 3-D printers and laser cutters, and the growing presence of maker spaces in K–12 schools, the possibility for teachers, educators, and students to invent and create original manipulative materials is now a reality. To support this type of development and to allow teachers and educators to learn from and benefit from what others create, NTLS has created a new section of the CITE Journal titled "Objects to Think With." This work will be supported by an ecosystem for open-source educational models and associated instructional supports. This ecosystem will include an organizational structure to manage the objects created and related instructional supports, a CAD library of peer-reviewed objects to think with, a community that will contribute educational objects and related instructional materials, and a community of users that will use the objects to address instructional objectives. Details about the status of this work and future plans are described in Glen Bull et al. (2023).

This new type of publication and related CAD library opens collaboration and research opportunities for mathematics teacher educators and teachers. Teachers can now design and create manipulative materials that embody the ideas of their students to help them develop a deeper understanding of the concepts. Teacher educators can collaborate with teachers to research what takes place when these “objects to think with” are used in the classroom. An example of the types of materials that can be designed and how they were used is reported by Grenstein and Fernández (2023). I invite AMTE members to consider contributing to the new section of the CITE Journal.

Enrique Galindo

References

Bull, G., Shapiro, D., Cohen, J., Borowczak, A., Galindo, E., Lassiter, S., & Slykhuis, D. (2023). Establishing an educational CAD model ecosystem. Contemporary Issues in Technology and Teacher Education, 23(3), 393-413.

Greenstein, S., & Fernández, E. (2023). Learning mathematics with mathematical objects: Cases of teacher-made mathematical manipulatives. Contemporary Issues in Technology and Teacher Education, 23(1), 103-115.