Journal Articles


Johnson, H. L., Olson, G., Tsinnajinnie, B., & Bechtold, L. (2023). Boundary transitions within, across and beyond a set of digital resources: Brokering in College Algebra. Digital Experiences in Mathematics Education. 7(2), 209-231. [OPEN ACCESS]

Olson, G., Johnson, H. L., Robinson, R., Knurek, R., & Whitmore, K. A. (2023). Anchoring inverse and injective functions with techtivities. PRIMUS. [OPEN ACCESS]


Johnson, H. L. (2022). Task design for graphs: Rethink multiple representations with variation theory. Mathematical Thinking and Learning. 24(2), 91-98. [OPEN ACCESS]

Johnson, H. L., Tzur, R., Gardner, A., Hodkowski, N., Lewis, A., & McClintock, E. (2022). A new angle: A teacher’s transformation of mathematics teaching practice and engagement in quantitative reasoning. Research in Mathematics Education. 24(1), 88-108. [OPEN ACCESS]

Olson, G. & Johnson, H. L. (2022). Promote students’ function reasoning with techtivities. PRIMUS. 32(5), 610-620. [OPEN ACCESS]

Tzur, R., Johnson, H. L., Davis, A., Hodkowski, N., Harrington, C., Wei, B., & Norton, A. (2022). A stage-sensitive, written assessment of multiplicative double counting for grades 3-8. Studies in Educational Evaluation. 74. Article 101152.


Tzur, R., Johnson, H. L., Norton, A., Davis, A., Wang, X., Ferrara, M., Harrington, C., & Hodkowski, N. M. (2021). Children’s spontaneous additive strategy relates to multiplicative reasoning. Cognition and Instruction. [OPEN ACCESS]


Johnson, H. L., McClintock, E., & Gardner, A. (2020). Opportunities for reasoning: Digital task design to promote students’ conceptions of graphs as relationships between quantities. Digital Experiences in Mathematics Education. 6(3), 340-366. (OPEN ACCESS)

Tzur, R., Johnson, H. L., Hodkowski, N., Nathenson-Mejia, S., Davis, A., & Gardner, A. (2020). Beyond getting answers: Promoting conceptual understanding of multiplication. Australian Primary Mathematics Classroom, 25(4), 35-40. LINK TO RESEARCH GATE FILE


Johnson, H. L., Dunlap, J., Verma, G., McClintock, E., Debay, D., & Bourdeaux, B. (2019). Video based teaching playgrounds: Designing online learning opportunities to foster professional noticing of teaching practices. Tech Trends. 63(2), 160-169. DOWNLOAD


Johnson, H. L & McClintock, E. (2018). A link between students’ discernment of variation in unidirectional change and their use of quantitative variational reasoning. Educational Studies in Mathematics97(3), 299-316. (OPEN ACCESS)

Johnson, H. L., Olson, G., Gardner, A., & Smith, A. (2018). From soliciting answers to eliciting reasoning: Questioning our questions in digital math tasks. Colorado Mathematics Teacher, 51(1), 2. [OPEN ACCESS]


Johnson, H. L., Coles, A., & Clarke, D. (2017). Mathematical tasks and the student: Navigating “tensions of intentions” between designers, teachers, and students. ZDM: The International Journal on Mathematics Education, 49(6), 813–822. 49(6). (OPEN ACCESS)

Johnson, H. L., McClintock, E., & Hornbein, P. (2017). Ferris wheels and filling bottles: a case of a student’s transfer of covariational reasoning across tasks with different backgrounds and features. ZDM: The International Journal on Mathematics Education, 49(6), 851–864. DOWNLOAD


Dunlap, J. C., Verma, G., & Johnson, H. L. (2016). Presence+Experience: A framework for the purposeful design of presence in online courses. Tech Trends, 60(2), 145-151. DOWNLOAD

Johnson, H. L., Hornbein, P., & Azeem, S. (2016). Investigating functions with a Ferris wheel. Mathematics Teacher. 110(5), 345-351. Link to abstract.

Johnson, H. L., Hornbein, P., & Bryson, D. (2016). Designing online playgrounds for learning mathematics. Mathematics Teacher, 110(4), 298-303. Link to abstract.


Johnson, H. L. (2015) Secondary students’ quantification of ratio and rate: A framework for reasoning about change in covarying quantities. Mathematical Thinking and Learning, 17(1), 64-90. DOWNLOAD

Johnson, H. L. (2015). Together yet separate: Students’ associating amounts of change in quantities involved in rate of change. Educational Studies in Mathematics, 89(1), 89-110. DOWNLOAD


Johnson, H. L. (2014). A role of context in constructivist model building: What problem is the learner solving? Constructivist Foundations, 9(3), 339-341. Link to title page.

Johnson, H. L., Blume, G.W., Shimizu, J., Graysay, D., & Konnova, S. (2014). A teacher’s conception of definition and use of examples when doing and teaching mathematics. Mathematical Thinking and Learning, 16(4), 285-311.  DOWNLOAD


Johnson, H. L. (2013). Predicting amounts of change in quantities. Mathematics Teaching in the Middle School. 19(5), 260-265. Link to title page.

Johnson, H. L. (2013). Reasoning about quantities that change together. Mathematics Teacher, 106(9), 704-708. Link to title page.

Castillo-Garsow, C., Johnson, H. L., & Moore, K. (2013). Chunky and smooth images of change. For the Learning of Mathematics, 33(3), 31-37. Link to PDF.

Tzur, R., Johnson, H. L., McClintock, E., Xin, Y. P., Si, L., Woodward, J., Hord, C., & Jin, X. (2013). Distinguishing schemes and tasks in children’s development of multiplicative reasoning. PNA, 7(3), 85-101. Link to PDF.


Johnson, H. L. (2012). Reasoning about variation in the intensity of change in covarying quantities involved in rate of change. Journal of Mathematical Behavior, 31(3), 313-330. DOWNLOAD


Johnson, H. L. (2010). Investigating the fundamental theorem of calculus. Mathematics Teacher, 103(6), 430-435. Link to abstract.