Blog Post Six - Games and Simulations

Link to Simulation: GeoGebra

I chose to focus on math simulations for this assignment because I feel as those these are less common and less well known when compared to math games. I found GeoGebra as an open source math simulation program when searching for a simulation or game to examine through this assignment. All of the GeoGebra images and descriptions are resulting from my own experience in creating a log-in and playing with the software myself.

               

(These images show the calculators function to use tools for graphing shapes and lines as well as formulas for representation of those figures.)

GeoGebra.org is an online math simulation website, with a downloadable app version, which offers two main functions. The first function within GeoGebra is its “calculator.” I place the word calculator in quotation marks beacuse it is so much more than that. The calculator function holds many different options as listed below:

- Graphing functions in 2D and 3D

- Graphing shapes in 2D and 3D

- Creating and manipulating shapes using basic construction tools and transformations

- Setting up probability distributions

- Proving a scientific calculator

- Offering tables and spreadsheets for appropriate functions

The second feature of GeoGebra is the math resources. Choosing between topics such as algebra, geometry, measurement, number sense, operations, and probability and statistics, GeoGebra offers both exploration and practice simulations on a large variety of different math topics from fourth to twelfth grade. Choosing an exploration simulation will allow the user to investigate specific mathematical theorem by adjusting measurements or quantities to see how it effects the outcome. On the other hand, a practice resoruces simulation will allow the user to apply knowledge to practice questions in a particular topic. These practices allow the user 3 attempts at answering a problem. If the second attempt is wrong, the software will provide a hint to aid the user in finding the answer. However, if the third attempt is wrong the software will provide the user an explanation of how to solve the problem as well as the final answer.

(This video shows a simulation which demonstrates a geometric theorem regarding how not matter how a polygon is manipulated, the sum of it’s exterior angles is 360 degrees and makes a circle.)

                    

(The left image above shows an example of how the software offers a hint after the second wrong answer in the practice simulations whereas the right image demonstrates how the software explains the problem after the third incorrect answer.)

As I have just found GeoGebra and this is my first exposure to it’s uses for simulation within mathematics classrooms, I truly believe it’s opportunities are endless. Of course, simulations have been found for a variety of uses within the educational world. For example, Bradley & Kendall (2015) discuss how computer simulations can be used in teacher education and training teachers in bullying prevention, classroom management, identifying at-risk students and many other topics. Such simulations are not intended to be a substitue for hands-on classroom experience, however they do have the capacity for providing specific skill-building lessons to teacher candidates (Bradley & Kendall, 2015). However, I beleive that simulations, such as GeoGebra, represent how simulations of mathematic concepts have the capacity for changing how students learn content in their classrooms as well. Where Bradley & Kendall (2015) discuss teacher simulations and how they change how we prepare teachers for situations they will encounter in the field, I believe that GeoGebra and simulations similar to it have the capacity to offer the same opportunities and benefits for students. GeoGebra simulations provide students the unique experience of experimenting with the different properties and theorems that they learn about in class. Many math teachers, such as myself, struggle to find ways to provide students situations where they can experience and visualize math concepts and theorems in easy to understand ways. Much like how Bradley & Kendall (2015) discuss how teacher simulations can provide teachers the opportuntiy to experience situations they may not otherwise be able to practice with in an actual classroom, GeoGebra simulations offer students the opportunity to visualize principals that may not otherwise be easily replicated in the classroom. While it may not be a game per say, GeoGebra does offer a low-stakes opportunity for students to experience relevant simulations to visualize and understand math concepts as they are discussed in class.

While I do believe GeoGebra can be integrated throughout an entire course of study and has appropriate benefits within a variety of concepts and topics, one specific area I can see myself implementing GeoGebra is in discussions of geometry. For example, New York State Next Generation 8th grade math standard “NY-8.G.1 Verify experimentally the properties of rotations, reflections, and translations.” (New York State Department of Education, 2017, 102) Typical mastery of this standard would include having students practice preforming reflections, transplantions and rotations on a paper coordinate grid in an effort to hopefully help them understand that lines match to lines and angles math to angles during all transformations. However, many students tend to loose sight of this understanding because visualizing such theoretical concepts can be difficult, especially on coordinate planes when students are not necessarily comfortable with the concept. However, GeoGebra has a large variety of simulations and practice problems in the area of geometric transformations in addition to the capacity to preform transformations on a coordinate grid through the calculator function. 

(A scroll through of the 6-8th grade math exploration and practice resources for transformations.)

In introducing transformations, I would likely set up classroom activities using small group stations around the room. Ideally, one of these stations would be dedicated for students to experiment with GeoGebra explorations such as “Translating Figures” and “Angle Measures of Rotated Figures,” which are two of the available exploration simulations. My objectives for this station would be: using GeoGebra simulation software students will be able to explain how moving a shape does not change the length of the shapes sides or measure of the shapes angles. In order to further cement the visualization of these simulations I would also have students write/draw the simulation transformations and shapes on their own piece of graph paper that they can later reference in review. These simulations would act as a strong introduction to the concept of translations and rotations as well as the idea that such rigid motions do not change the size of the shape that is being transformed. Finally, I would also have students assess their knowledge after experimenting with these simulations by participating in the “Angle Measures of Translated Figures” practice resource on GeoGebra and further inform them to document their use and answers of this practice resource.

(Images of the “Translating Figures” and “Angle Measures of Rotated Figures” GeoGebra exploration simulations.)

When considering how I would implement GeoGebra within the class, and more specifically within this activity, there are several factors to consider. Firstly, I would aim to scaffold student usage of GeoGebra by demonstrating the program to the class and doing an “I do, we do, and you do” introduction and examples of how I expect them to use the program and document their use on graph paper. While it is not mandatory that users create accounts for GeoGebra, because of how frequently I would like to use the application I would likely have my students set up GeoGebra accounts in the beginning of the school year. Additionally, if students require differentiation I can also select lower-level or higher-level simulations for them to utilize as alternatives to these simulations. Because GeoGebra offers simulations for grades 4 through 12 there are a variety of opportunities for differentiating content by assigning students to do different simulations based on their skill level. Additionally, I would consider showing high-achieving students the calculator function of GeoGebra and inviting them to use that function to create and document their own transformations as another form of differentiation.

(Image of the “Angle Measures of Translated Figures” GeoGebra practice resource. This resource shows how the image is translated visually by moving the image across the screen in real time and then asks the student to fill in the blank of angle measures in the new image.)

Finally, student literacy practices and learning goals with GeoGebra can be assessed through both their submission of documentation from using the program as well as student reflection journals. Students can reflect on their experience with GeoGebra and the course context qualitatively in their reflection journal which can be reviewed by the teacher. Additionally, I would have students submit their documentation of their GeoGebra use as qualitative data towards assessing their completion of literacy practices and learning goals. 

Overall, I am so glad I found GeoGebra while searching for math simulations for this assignment. GeoGebra has endless opportunities for implementation of simulations through exploration and calculator functions as well as practice opportunities. This simulation program is something I look forward to using in the future! 

References

Bradley, E.G., Kendall, B. (2015). A review of computer simulations in teacher education. Journal of Educational Technology Systems, 43(1) 3-12.

New York State Department of Education. (2017). New York State Next Generation Mathematics Learning Standards. https://www.nysed.gov/sites/default/files/programs/standards-instruction/nys-next-generation-mathematics-p-12-standards.pdf#page97