# Using Visualizations to Teach Mathematics with Understanding (Spring 2015 Mini-Course)

## Contents

**My Topic/Purpose**

This course, *Using Visualizations to Teach Mathematics with Understanding*, will focus on how teachers can use and create visualizations to teach mathematics with understanding. Creating meaningful visualizations can enhance learning in the classroom by helping students conceptualize the big ideas of our lessons. When we use visualizations in the classroom, our students begin to develop their own visualization skills to help them solve problems. These skills can help our students become active and effective learners. In this course, participants will answer and reflect on the following questions:

- What does it mean to teach/learn with understanding?
- What are the advantages of teaching/learning with understanding?
- What are the differences between reform teaching methods and traditional teaching methods?
- What can teachers do to promote learning with understanding?
- What are visualizations and why are them important in mathematics curricula?
- What do effective and ineffective visualizations look like?
- How do you determine if a visualization is an accurate representation for a given problem?
- How do you create meaningful visualizations to supplement mathematics instruction?
- What are some tools and strategies you can use to create visualizations to teach mathematics with understanding in the classroom?
- How can we transfer these skills to our students?

By the end of this course, participants will develop their skills to recognize and create quality visualizations to teach mathematics with understanding.

**Learning Outcomes**

This course will help teachers develop effective visualization skills and provide them with tools and strategies to teach mathematics with understanding. By the end of the course, learners will:

- Conceptualize the idea of teaching and learning with understanding.
- Identify what visualizations are.
- Identify characteristics of meaningful and effective visualizations.
- Develop skills to create visualizations.
- Explore tools and strategies for using visualizations in the classroom and how to transfer these skills to students for his/her own use.

**Unit 1: What do we mean by “Learning with Understanding”?**

**Objective:** Participants will **compare and contrast** reform teaching methods, methods that encourage teaching for understanding, and traditional teaching methods

- Participants will explain the advantages of learning with understanding by completing a two paragraph refection.
- Participants will compare reform teaching methods and traditional teaching methods by analyzing research.
- Participants will clarify any misconceptions about learning with understanding in a class discussion.

Begin: Unit 1: What do we mean by “Learning with Understanding”?

**Unit 2: Creating Meaningful Visualizations for Teaching Mathematics**

**Objectives:** Participants will **identify** advantages of using visualizations for teaching and learning mathematics with understanding. Additionally, participants will **identify** characteristics of meaningful visualizations for supplementing lesson with understanding and **develop strategies** to create useful visualizations for this purpose.

- Participants will identify how visualizations supplement learning with understanding by collecting and analyzing research.
- Participants will explain if and/or when visualizations are useful tools for students.
- Participants will clarify any misconceptions about the importance of visualizations in a class discussion.

Begin: Unit 2: Creating Meaningful Visualizations for Teaching Mathematics

**Unit 3: Putting Ideas into Practice**

**Objectives:** Firstly, participants will **analyze** a series of visualizations created with Geometer's Sketchpad to model strategies for designing classroom lessons and/or materials. Secondly, participants will be able to **construct** a visualization for a given mathematical concept. Finally, participants will **reflect** on ways to transfer skills for using visualizations in mathematics to students by collaborating in a peer discussion.

- Participants will analyze a series of visualizations created with Geometer's Sketchpad to model strategies for designing classroom lessons and/or materials for using visualizations to teach mathematics with understanding.
- Participants will analyze lessons created by teachers and write a reflection on how they integrated visualization into their lessons to teach mathematics with understanding.

- Participants will construct a visualization.
- Participants will create a lesson with visualizations.
- Participants will critique lessons created by their peers.
- Participants will reflect on ways to transfer skills for creating visualizations to learn with understanding to students using a class discussion.

Begin: Unit 3: Putting Ideas into Practice

**References and Resources**

- 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.

- Carpenter, T. and R. Lehrer. (1999). Chapter 2: "Teaching and Learning Mathematics with Understanding." From:
*Classrooms That Promote Understanding*edited by Elizabeth Fennema and Thomas A. Romberg. Mahwah, NJ: Erlbaum. (Accessed via books.google.com). pp 19-32.

- Common Core State Standards. http://www.corestandards.org/Math/

- Dimmel, J. and P. Herbst. (2015). "Semiotic Structure of Geometry Diagrams." Journal for Research in Mathematics Education. Volume 26. Number 2.

- 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.

- Engage NY. Grade 6 Mathematics Curriculum: Module 1, Topic A, Lesson 3. Accessed May 8, 2015 via: https://www.engageny.org/resource/grade-6-mathematics-module-1-topic-lesson-3

- Geometer's Sketchpad: https://www.mheonline.com/programMHID/view/00000SPAD/

- GeoGebra: https://www.geogebra.org

- Goldin, G. A. (2002). Representation in mathematical learning and problem solving. Handbook of International Research in Mathematics Education. March 1, 2002. Available from: Routledge, New York, NY. Retrieved from: https://books.google.com/books?id=LDGRAgAAQBAJ&dq=Goldin,+G.+A.+(2002).+Representation+in+mathematical+learning+and+problem+solving.&lr=&source=gbs_navlinks_s 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

- "How Math Comes to Mind: Intuition, Visualization, and Teaching." Princeton University. Accessed May 13, 2015 via: https://mediacentral.princeton.edu/media/How+Math+Comes+to+MindA+Intuition,+Visualization,+and+Teaching/1_0bfnmopc

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**Links**

**About Me:** Melissa Connor

**Portfolio Page:** Melissa Connor's Portfolio Page for Spring 2015 Mini-Course