Research & SoTL

Career History

Juan Carlos Ponce Campuzano

Background

Bachelor of Science: Mathematics

Autonomous University of the State of Mexico - Mexico

Thesis titled: Continuum theory - Whitney reversible strong sequential properties

Masters: Mathematics Education

Cinvestav - Mexico

Thesis titled: A case study with high school teachers on the role played by the Fundamental Theorem of Calculus.

PhD: Mathematics Education

Cinvestav - Mexico

Thesis titled: The Fundamental Theorem of Calculus: a study about some concepts, formulas and methods related to their application.

Research and SoTL

My applied research interests include:

  1. the historical development of mathematical concepts and how this can be used for teaching and learning in university mathematics; and
  1. the effectiveness of interactive mathematics software for enhancing students’ mathematical thinking, understanding and confidence.

Examples at UQ in my role as a Learning designer

Collaboration with academics

Science and Mathematics Simulations (SciMS) project.

Website: https://teaching.smp.uq.edu.au/scims

  • Prof. Tim McIntyre
  • Prof. Tony Roberts
  • Dr. Margaret Wegener
  • A/Prof. Kelly Matthews
  • Dr. Elise Kenny
  • Isaac Lenton
  1. Ponce Campuzano, J. C., Roberts, A. P., Matthews, K., Wegener, M. J., Kenny, E. P., & McIntyre, T. J. (2019). Dynamic visualisation of line integrals of vector fields: a didactic proposal. International Journal of Mathematical Education in Science and Technology.  50: 6, pp. 934-949.
  2. 13th Asia-Pacific Physics Conference in conjunction with the 22nd Australian Institute of Physics Congress, Brisbane, Australia. 4-9 December 2016.

2016

Examples at UQ in my role as a Learning designer

Collaboration with academics

Science and Mathematics Simulations (SciMS) project.

Website: https://teaching.smp.uq.edu.au/scims

  • Prof. Tim McIntyre
  • Prof. Tony Roberts
  • Dr. Margaret Wegener
  • A/Prof. Kelly Matthews
  • Dr. Elise Kenny
  • Isaac Lenton

Included in the

Australian Council of Deans of Sience Repository

2017

Examples at UQ in my role as a Learning designer

Collaboration with academics & students

Science and Mathematics Simulations (SciMS) project.

  • Prof. Tim McIntyre
  • Prof. Tony Roberts
  • Dr. Margaret Wegener
  • A/Prof. Kelly Matthews
  • Dr. Elise Kenny
  • Yitong T. Bu
  • Jeremy Edirisinghe

2016

Australian Conference on Science and Mathematics Education,

Brisbane, Australia. September 2016.

Examples at UQ in my role as a Learning designer

Collaboration with academics

SCIE1000/1100 Online Modules for Support and Enrichment

Course website: https://teaching.smp.uq.edu.au/SCIE1000

  • Prof. Tim McIntyre
  • Dr Sara Davies
  • Dr. Adam Piggott

2019

Included in the

Australian Council of Deans of Sience Repository

Examples at UQ in my role as a Learning designer

Collaboration with academics

SCIE1000 in 2017

  • Prof. Peter Adams
  • A/Prof. Kelly Matthews
  • Prof. John Rice - The University of Sydney

Ponce Campuzano, J. C., Matthews, K. & Adams, P. (2018). On the use of history of mathematics: an introduction to Galileo’s study of free fall motion. International Journal of Mathematical Education in Science and Technology. 49: 4, 517-529

Application and report of an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, based on Galileo’s experiments designed to investigate the motion of falling bodies, and his geometrical explanation of his results, via simple dynamic geometric applets.

Examples at UQ in my role as a Learning designer

Collaboration with academics

UQ Extend/edX/LearnX, 2018-2023

  • Dr. Poh Wah Hillock
  • Prof. Anthony Roberts
  • Michael Jennings
  • Wenbo Li
  • A/Prof. Cecilia Gonzalez Tokman

Work across four first-year courses (MATH1040, MATH1050, MATH1051, MATH1052) on the Digital Learning Uplift (DLU) to enhance the student experience through engagement in course (re)design and development.

Examples at UQ in my role as a Learning designer

Collaboration with academics

UQ Extend/edX/LearnX, 2018-2023

  1. Hillock, P. & Ponce Campuzano, J. C. (2021). Course redesign for flexible delivery and increased engagement in first year mathematics. 13th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics. Auckland, New Zealand.
  • Dr. Poh Wah Hillock
  • Prof. Anthony Roberts
  • Michael Jennings
  • Wenbo Li
  • A/Prof. Cecilia Gonzalez Tokman

Work across four first-year courses (MATH1040, MATH1050, MATH1051, MATH1052) on the Digital Learning Uplift (DLU) to enhance the student experience through engagement in course (re)design and development.

Examples at UQ in my role as a Learning designer

Collaboration with academics & students

Live Scripts: Interactive activities for
learning mathematics and MATLAB

www.dynamicmath.xyz/matlab/math1051/

www.dynamicmath.xyz/matlab/math1052/

  • Dr. Poh Wah Hillock
  • Dr. Sam Kault
  • Wenbo Li
  • Kyle Clunies-Ross
  • Thomas Reay
  • Marcus Flook
  • Dylan Cowley
  • Marcus Flook
  • Christina Tang-Fujiwara
  • Andrew Mengene
  • Liam Timms
  • Emma Comino
  • Montana Wickens

2020

Align the programming component with the course content

Examples at UQ in my role as a Tutor & Lecturer

MATH1040: Mathematical Foundations - Tutor

MATH1050: Mathematical Foundations II - Tutor

MATH3401: Complex Analysis - Tutor and Super tutor

2014-2021

f(z)=\displaystyle\sum_{n=0}^{\infty} a_n(z-z_0)^n+\displaystyle\sum_{n=1}^{\infty}\frac{b_n}{(z-z_0)^n},
R_1 <|z-z_0|< R_2.
a_n=\frac{1}{2\pi i}\displaystyle \oint_C \frac{f(z)dz}{(z-z_0)^{n+1}}\quad (n=0,1,2,\ldots)
b_n=\frac{1}{2\pi i}\displaystyle \oint_C \frac{f(z)dz}{(z-z_0)^{-n+1}}\quad (n=1,2,\ldots)

\(f(z)=\exp\left(\dfrac{1}{z}\right)\)

Examples at UQ in my role as a Tutor & Lecturer

MATH3401: Complex Analysis - Tutor and Super tutor

2014-2021

Domain coloring for representing complex functions

Examples at UQ in my role as a Tutor & Lecturer

Domain coloring: Online open-source tools

  1. Ponce Campuzano, J. C. (2023). The hidden beauty of complex numbers. Mathematics Teacher: Learning and Teaching PK-12: For the Love of Mathematics. NCTM. Vol 116 (4), p. 308.
  2. Ponce Campuzano, J. C. (2021). Domain colouring for visualising and exploring the beauty of complex functions. Australian Mathematical Society Gazette. Vol. 48, No. 4, pp. 162-170.
  3. Ponce Campuzano, J. C. (2019). The use of phase portraits to visualize and investigate isolated singular points of complex functions. International Journal of Mathematical Education in Science and Technology. 50:7. 999-1010.

dynamicmath.xyz/domain-coloring/

2018

Examples at UQ in my role as a Tutor & Lecturer

Online interactive textbook

complex-analysis.com

2019

Examples at UQ in my role as a Tutor & Lecturer

MATH2001/7000: Calculus & Linear Algebra II
Lecturer. Notes: dynamicmath.xyz/math2001/

2022-2023

MATH1052 Multivariate Calculus & ODEs
Course coordinator/Lecturer. Notes: dynamicmath.xyz/math1052/

MATH2400/7400: Mathematical Analysis
Course coordinator/Lecturer. Notes: dynamicmath.xyz/math2400/

\displaystyle \int_a^b \mathbf F\left(\mathbf r\right)\cdot \mathbf r'(t)~dt

Examples at UQ in my role as a Tutor & Lecturer

MATH2001/7000: Calculus & Linear Algebra II

2022-2023

Collaboration with Bradley Welch, Bachelor of Secondary Teaching (Mathematics), UQ.

Co-authored paper on linear algebra: Recently published paper in the International Journal of Mathematics Education, Science and Technology.

Applying matrix diagonalisation

Collaborators Overseas

2021:

Dr Carolina Guerrero Ortiz, Pontificia Universidad Católica de Valparaíso (Chile): Online teaching for the course Data modelling and interpretation using GeoGebra classroom (2021)

Since 2014:

Dr Miguel Ángel Maldonado Aguilar, Universidad de Zacatecas (Mexico): Collaboration on the research on mathematics and mathematics education and co-authored of online book: An Invitation to Topology: https://topologia-general.github.io/

2017-2018:

Dr Luis R. Pino-Fan, Universidad de Los Lagos (Spain), collaboration on mathematics education research.

Collaborators Overseas

In Spaish: https://topologia-general.github.io/

Conferences, Seminars & Workshops

  1. Queensland Mathematics Summer School UQ (13 Jan 2023)
  2. AUSTMS/AMSI Teaching Seminar (25 Aug 2022)
  3. Herenga Delta (22-25 Nov 2021)
  4. FYiMaths Forum (8-9 Jul 2021)
  5. FYIMaths (16 Dec 2020)
  6. Mathematical Educational Software Interest Group (11 Dec 2020)

Conferences, Seminar & Workshops (Spanish)

  1. 6to Congreso Internacional de Matemática Educativa (7 Sep 2020)
  2. V Jornadas de GeoGebra Valencia (19 Nov 2021)
  3. Clases de Objetos y Colores Dinámicos  (11 Nov 2020)
  4. Curvas Misteriosas (29 Oct 2020)
  5. Representación de funciones complejas en GeoGebra. (20 Dec 2019)

Thanks