Journal Articles

Johnson, H. L., Dunlap, J., Verma, G., McClintock, E., Debay, D., & Bourdeaux, B. (2018). Video based teaching playgrounds: Designing online learning opportunities to foster professional noticing of teaching practices. Tech Trends. doi: 10.1007/s11528-018-0286-5 TeachingPlaygrounds_AAM

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. doi: 10.1007/s10649-017-9799-7 (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). doi: 10.1007/s11858-017-0894-0 (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. doi: 10.1007/s11858-017-0866-4  JohnsonEtAl_FerrisWheelFillinBottle_AAM

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. doi: 10.1007/s11528-016-0029-4   P+Eframework_AAM

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. doi: 10.1080/10986065.2015.981946  HLJohnson_QuantRatioRate_AAM

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. doi: 10.1007/s10649-014-9590-y  HLJohnson_TogetherYetSeparate_AAM

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. doi: 10.1080/10986065.2014.953018  JohnsonEtAl_RolesOfDefs&Exs_PrePrint

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. doi: 10.1016/j.jmathb.2012.01.001   Johnson_JMB_AAM

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