Creating Meaningful Visualizations for Teaching Mathematics: Lesson 1
Introduction
Visualizations are pictures, diagrams, or charts used to organize thoughts and make sense of problems. They can be both formal, meaning precise and/or drawn to scale, or informal sketches. Visualizations can sometimes refer to mental imagery people use to think about problems. Edens and Potter state, “[Visualizations] assist students to learn to ‘unpack’ the structure of a problem” (2008). Visualizations help students to think and process mathematical ideas when solving problems. With the implementation of the Common Core State Standards, students are expected to use visualizations effectively (See Standards for Mathematical Practice).
All students learn differently. Using visualizations can assist visual and kinesthetic learners make sense of mathematics. As we discussed in Unit 1, it is difficult for students to learn with understanding if they are simply mimicking teacher practices and we want our learners to be active and independent thinkers. Encouraging the use of visualization can help mold students into effective problem solvers.
By the end of this lesson, participants will be able to answer and reflect on the following questions:
- What are visualizations and why are them important in mathematics curricula?
- What do effective and ineffective visualizations look like?
Assignment
Research Use an electronic database, academic journal, or print literature in a local library to find a case study that relates to effective or ineffective visualizations. For example, case studies that explore the types of diagrams students create or study effectiveness of the models students draw in relation to a given problem might be useful for this purpose.
Review Common Core State Standards: Standards for Mathematical Practice.
Reflection As you are reading, think about why visualizations are important in the mathematics curricula. In a two-three paragraph reflection, discuss the findings of your case study and why visualizations are important in mathematics. Identify your case study and be sure to cite the study in APA format at the end of your reflection.
For further reading, consider Guzman, located in the Resources and References section at the end of this lesson to learn about specific types of visualization. This is not required.
Resources and References
Anderson-Pence, K. L., Moyer-Packenham, P. p., Westenskow, A. a., Shumway, J. j., & Jordan, K. k. (2014). Relationships Between Visual Static Models and Students' Written Solutions to Fraction Tasks. International Journal For Mathematics Teaching & Learning, 1-18.
Edens K, Potter E. How Students "Unpack" the Structure of a Word Problem: Graphic Representations and Problem Solving. School Science And Mathematics [serial online]. May 1, 2008;108(5):184-196. Available from: ERIC, Ipswich, MA. Accessed February 23, 2015.
Guzman, M. The Role of Visualization In the Teaching and Learning of Mathematical Analysis. Universidad Complutense de Madrid. Accessed May 8, 2015 via http://www.math.uoc.gr/~ictm2/Proceedings/invGuz.pdf
Links
Next Lesson: Creating Meaningful Visualizations for Teaching Mathematics: Lesson 2
Back to Unit 2: Unit 2: Creating Meaningful Visualizations for Teaching Mathematics
Mini-Course: Using Visualizations to Teach Mathematics with Understanding (Spring 2015 Mini-Course)
Portfolio Page: Melissa Connor's Portfolio Page for Spring 2015 Mini-Course