Author(s)

Ying Zhang ¹, Zhen Li ¹

Affiliation(s)

¹ School of Mathematical Sciences, University of Jinan, Jinan, 250022, Shandong, China

Corresponding Author

Ying Zhang

ABSTRACT

This study develops an ACT-R theory-based instructional design for the fundamental theorem of spatial vectors, addressing three dilemmas: abstract spatial concept comprehension, superficial theorem understanding, and fragmented cognitive structure. Through four cognitive stages (declarative, procedural, automated, reflective feedback), it designs hierarchical teaching strategies. The design helps students construct a systematic cognitive system of vector theorems, and provides a replicable framework for applying cognitive psychology to mathematical theorem teaching, guiding master's students in education to conduct research-based instructional design.

KEYWORDS

ACT-R Theory, Spatial Vectors; Mathematical Theorem Teaching; Instructional Design; Cognitive Development

CITE THIS PAPER

Ying Zhang, Zhen Li. Research on Instructional Design of Mathematical Theorems Based on ACT-R Theory—Taking the Fundamental Theorem of Spatial Vectors as an Example. Advances in Educational Technology and Psychology (2026). Vol. 10, No. 1, 86-91. DOI: http://dx.doi.org/10.23977/aetp.2026.100111.

REFERENCES

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[3] Ministry of Education of the People's Republic of China. General High School Mathematics Curriculum Standards (2017 Edition, Revised in 2020)[S]. Beijing: People's Education Press, 2020.
[4] Anderson, J. R., Fincham, J. M., & Douglass, S. The role of examples and rules in the acquisition of a cognitive skill[J]. Journal of Experimental Psychology: Learning, Memory, and Cognition, 1997, 23(4), 932-945.
[5] Wang, G. M., & Wei, Q. P. Research on the evaluation of high school mathematics learning quality based on SOLO classification theory[J]. Journal of Mathematics Education, 2017, 26(6), 65-69.

Sponsors, Associates, and Links

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• Curriculum and Teaching Methodology
  
  
• Transactions on Comparative Education
  
  
• Applied & Educational Psychology
  
  
• Advances in Vocational and Technical Education
  
  
• Adult and Higher Education