Author A. J. Hackenberg
Amy J. Hackenberg is a newly tenured faculty member at Indiana University-Bloomington. She does research on how middle school students learn to reason algebraically; relationships between students’ rational number knowledge and algebraic reasoning; and how student-teacher relationships influence mathematical learning. She is the principal investigator of the project “Investigating Differentiated Instruction and Relationships between Rational Number Knowledge and Algebraic Reasoning in Middle School” funded by an Early Career Development grant from the National Science Foundation. In this project she is learning to teach, in one classroom, students operating with at least two different levels of units coordinations. Prior to working at the university level Amy taught middle and high school students for 9 years in Los Angeles and the Chicago area.

Publications Found: 13 · Show All Abstracts

Hackenberg A. J. (2005) A model of mathematical learning and caring relations. For the Learning of Mathematics 25: 45–51. Fulltext at
Hackenberg A. J. (2007) Units coordination and the construction of improper fractions: A revision of the splitting hypothesis. Journal of Mathematical Behavior 26: 27–47. Fulltext at
Hackenberg A. J. (2010) Mathematical caring relations in action. Journal for Research in Mathematics Education 41(3): 236–273.
Hackenberg A. J. (2010) Mathematical caring relations: A challenging case. Mathematics Education Research Journal 22(3): 57–83.
Hackenberg A. J. (2010) Students’ reasoning with reversible multiplicative relationships. Cognition and Instruction 28(4): 1–50.
Hackenberg A. J. (2013) Holding together. For the Learning of Mathematics 33: 16–17.
Hackenberg A. J. (2013) The fractional knowledge and algebraic reasoning of students with the first multiplicative concept. Journal of Mathematical Behavior 33: 1. Fulltext at
Hackenberg A. J. & Lawler B. R. (2002) An ethics of liberation emerging from a radical constructivist foundation. In: Valero P. & Skovsmose O. (eds.) Proceedings of the 3rd International MES Conference. Centre for Research in Learning Mathematics, Copenhagen: 1–13. Fulltext at
Hackenberg A. J. & Sevinc S. (2022) Middle school students’ construction of reciprocal reasoning with unknowns. The Journal of Mathematical Behavior 65: 100929.
Hackenberg A. J. & Tillema E. S. (2009) Students’ whole number multiplicative concepts: A critical constructive resource for fraction composition schemes. Journal of Mathematical Behavior 28: 1–18.
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