number line mastery through game apps timothy smith college of education california state...

Number Line Number Line Mastery Through Mastery Through

Game AppsGame AppsTimothy SmithTimothy Smith

College of EducationCollege of EducationCalifornia State University, SacramentoCalifornia State University, Sacramento

United StatesUnited [email protected]@csus.edu

Digital Game Apps and Number Line Digital Game Apps and Number Line TheoryTheory

Numerical value: Conceptual understandingNumerical value: Conceptual understanding Young children relate whole numbers to physical Young children relate whole numbers to physical

objects (Varma & Schwartz, 2011), thus making it objects (Varma & Schwartz, 2011), thus making it difficult to comprehend higher magnitude numbers.difficult to comprehend higher magnitude numbers.

Children and adults begin to create mental number Children and adults begin to create mental number lines to envision numerical values (Thompson & lines to envision numerical values (Thompson & Siegler, 2010).Siegler, 2010).

Children gradually develop mental coordinates on Children gradually develop mental coordinates on the number line to represent linear magnitudes the number line to represent linear magnitudes (Saxe et al, 2013).(Saxe et al, 2013).

Given two number lines, one generic and one Given two number lines, one generic and one themed (game-like), students placed numbers themed (game-like), students placed numbers more accurately on the themed number line (Saxe more accurately on the themed number line (Saxe et al, 2013).et al, 2013).

Digital applications and the learning environmentDigital applications and the learning environment When digital games in the classroom mimic real world When digital games in the classroom mimic real world

situations, students are more engaged (Bennet et al, situations, students are more engaged (Bennet et al, 2009).2009).

Teachers must never take a passive role when using digital Teachers must never take a passive role when using digital games (Reynolds, 2008).games (Reynolds, 2008).

Using video games earlier in childhood reduces the Using video games earlier in childhood reduces the cognitive load later on when video games are used as a cognitive load later on when video games are used as a learning tool (Moreno, 2002).learning tool (Moreno, 2002).

The new set of Common Core State Standards is a catalyst The new set of Common Core State Standards is a catalyst for integrating digital applications into the learning for integrating digital applications into the learning environment.environment.

The use of technology as a tool, particularly for modeling, The use of technology as a tool, particularly for modeling, provides connections between graphical, verbal, and provides connections between graphical, verbal, and tabular descriptions of mathematical relationships and tabular descriptions of mathematical relationships and concepts (Sokolowski & Gonzalez, 2011).concepts (Sokolowski & Gonzalez, 2011).


Game apps and the classroom teacherGame apps and the classroom teacher The variety of technological skill levels among teachers The variety of technological skill levels among teachers

makes it challenging to provide professional development makes it challenging to provide professional development to in-service and pre-service teachers (Lawrence, 2011).to in-service and pre-service teachers (Lawrence, 2011).

Fortunately, products abound that make it easy to Fortunately, products abound that make it easy to differentiate professional development modules (Smith & differentiate professional development modules (Smith & Straight, 2011).Straight, 2011).

Inexpensive (and free) software for creating customized Inexpensive (and free) software for creating customized classroom apps is available to teachers, even those classroom apps is available to teachers, even those teachers with little or no experience in coding (Miller & teachers with little or no experience in coding (Miller & Doering, 2011).Doering, 2011).


Platform choicesPlatform choices The proliferation of app software has coincided with the The proliferation of app software has coincided with the

growth of laptops and mobile devices in the classroom growth of laptops and mobile devices in the classroom (Smith & Straight, 2011).(Smith & Straight, 2011).

SCRATCH software from the Massachusetts Institute of SCRATCH software from the Massachusetts Institute of Technology was so user-friendly that elementary and Technology was so user-friendly that elementary and middle school students were able to create their own middle school students were able to create their own games (Smith & Jeffries, 2011). games (Smith & Jeffries, 2011).

The Games Design Toolkit from the Learning Games The Games Design Toolkit from the Learning Games Network and FableVision developed the Game Design Network and FableVision developed the Game Design Toolkit to help teachers design their own games (The Toolkit to help teachers design their own games (The Education Arcade, 2014).Education Arcade, 2014).


The not-so-final productThe not-so-final product GameMaker Studio was chosen for this project because it is free GameMaker Studio was chosen for this project because it is free

and novice-friendly. A windows platform was chosen, but other and novice-friendly. A windows platform was chosen, but other platforms were equally user-friendly.platforms were equally user-friendly.

Two levels of the game were created for this paper. The first was a Two levels of the game were created for this paper. The first was a second grade level model representing whole numbers (not shown second grade level model representing whole numbers (not shown in the Powerpoint) and the other model was fifth/sixth grade level in the Powerpoint) and the other model was fifth/sixth grade level with larger magnitude numbers and negative integer solutions.with larger magnitude numbers and negative integer solutions.

The second grade design features a horizontal number line with a The second grade design features a horizontal number line with a bunny hopping in the direction of the correct number line position. bunny hopping in the direction of the correct number line position. The background and parameters are easily customizable. The background and parameters are easily customizable.

The fifth/sixth grade design features either a drone flying up and The fifth/sixth grade design features either a drone flying up and down a vertical number line or a flying fish moving up and down a down a vertical number line or a flying fish moving up and down a vertical number line where the water represents zero magnitude vertical number line where the water represents zero magnitude and below the water line are negative numerical values. Both and below the water line are negative numerical values. Both designs allow for easy background and parametric changes.designs allow for easy background and parametric changes.



This model was labeled as a fifth grade model because of the drone graphics and the higher magnitude numerical parameters.

Digital Game Apps and Number Line TheoryDigital Game Apps and Number Line Theory

This version is a flying fish with a vertical number line. This version is a flying fish with a vertical number line. Notice that the number line extends into negative Notice that the number line extends into negative integers. It can be easily modified to different integers. It can be easily modified to different numerical magnitudes.numerical magnitudes.

Digital Game Apps and Number Line TheoryDigital Game Apps and Number Line TheoryChanging the parametersChanging the parametersProfessional development modules (videos) will be made Professional development modules (videos) will be made

that detail in five simple steps (shown below) how to that detail in five simple steps (shown below) how to change the parameters. Other modules will be made change the parameters. Other modules will be made showing how to change the other aspects of the game.showing how to change the other aspects of the game.

Step 1: Find the obj_globals under the Objects menu, Step 1: Find the obj_globals under the Objects menu, then click to open itthen click to open it

Step 2: Find the "Create" button under the Events Step 2: Find the "Create" button under the Events category of obj_globals. This is where all of the category of obj_globals. This is where all of the parameters that the game uses are defined.parameters that the game uses are defined.

Step 3: Find the "Execute a piece of code" action under Step 3: Find the "Execute a piece of code" action under the Actions sub-category. This is where the code is the Actions sub-category. This is where the code is stored that will initialize the game parameters.stored that will initialize the game parameters.

Step 4 and Step 5: These two specific lines of code will Step 4 and Step 5: These two specific lines of code will define the maximum and minimum height, define the maximum and minimum height, respectively. When they are altered, the game respectively. When they are altered, the game program will automatically adjust the playing field and program will automatically adjust the playing field and problem parameters that generate the integer ranges problem parameters that generate the integer ranges to better suit the new number line range.to better suit the new number line range.


Example of a screen shot showing steps in modify the Example of a screen shot showing steps in modify the game.game.

ReferencesReferencesBennett, C., Sundholm, T., Weigant, A., Su, B., & Rodriguez, C. D. (2009) Educational games in the PK-12

environment. 32nd Annual Convention of the Association of Educational Communications and Technology, 30.Common Core State Standards. (n.d.). Retrieved October 13, 2014 from the Common Core State Standards site:

http://www.cde.ca.gov/re/cc/.Lawrence, E. (2011, March). Engaging the 21st Century Learner in P-12 Course Content: Creating Technology-Rich

Teacher Education Programs. In Society for Information Technology & Teacher Education International Conference (Vol. 2011, No. 1, pp. 974-977).

Miller, C., & Doering, A. (2011, October). The Apps Class: K-12 Teachers as Designers of Contemporary Mobile Education. In World Conference on E-Learning in Corporate, Government, Healthcare, and HigherEducation (Vol. 2011, No. 1, pp. 2039-2044).

Moreno, R. (2002). Who Learns Best with Multiple Representations? Cognitive Theory Implications for Individual Differences in Multimedia Learning. In P. Barker & S. Rebelsky (Eds.), Proceedings of World Conference on Educational Multimedia, Hypermedia and Telecommunications 2002 (pp. 1380-1385).

Reynolds, C. (2008). Video gaming in the classroom: friend or foe?. In K. McFerrin et al. (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference 2008 (pp. 3582-3589). Chesapeake, VA: AACE.

Saxe, G. B., Diakow, R., & Gearhart, M. (2013). Towards curricular coherence in integers and fractions: A study of the efficacy of a lesson sequence that uses the number line as the principal representational context. ZDM, 45(3), 343-364.

Smith, B. & Jeffries, M. (2011). Creating Content-Based Video Games in the Elementary Education Classroom. In M. Koehler & P. Mishra (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference 2011 (pp. 2242-2243). Chesapeake, VA: AACE.

Smith, J., & Straight, R. (2011, March). The Development and Delivery of Custom Mobile Apps for K-12 Learning: Viable Options for Educators. In Society for Information Technology & Teacher Education International Conference (Vol. 2011, No. 1, pp. 3102-3107).

Sokolowski, A., & Gonzalez y Gonzalez, E. (2011, March). Teachers’ perspective on utilizing graphical representations to enhance the process of mathematical modeling. In Society for Information Technology & Teacher Education International Conference (Vol. 2011, No. 1, pp. 4068-4075).

The Education Arcade (2014, November 5). Retrieved from http://education.mit.edu/ Thompson, C. A., & Siegler, R. S. (2010). Linear numerical-magnitude representations aid children’s memory for

numbers. Psychological Science, 21(9), 1274-1281.Varma, S., & Schwartz, D. L. (2011). The mental representation of integers: an abstract-to-concrete shift in the

understanding of mathematical concepts. Cognition, 121(3), 363-385.

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