iPads and Geometry for Pre-service Teachers

Carla Gerberry & Sheila Doran, Xavier University


In recent decades, there has been an increased emphasis on incorporating innovation and technology in the classroom at all grade levels (National Council of Teachers of Mathematics [NCTM] 2000; Banister, 2010). The recommendations for this integration of technology are expressly prominent in areas of mathematics: computer algebra systems, dynamic geometry environments, and statistics and probability. In addition to the suggestions from the NCTM, the new Common Core State Standards for Mathematics (CCSS-M, 2010) confirm the use of technological tools by students in exploration and development of mathematical understanding.

NCTM values the use of technology so much that they have dedicated their 2000 document Principles and Standards for School Mathematics to discussing their recommendations. The NCTM suggests technology scaffold students’ learning as they work through inquiries. With the innovations in technology today and the endorsements from these two major groups, technology in the classroom is more prevalent and important than ever. With this, teacher preparation programs should focus on incorporating these technologies into the classroom as well. The importance of this is two-fold: First, according to the Conference Board of the Mathematical Sciences, pre-service teachers (PSTs) need exposure to new technologies (Conference Board of the Mathematical Sciences [CBMS], 2012); second, PSTs should engage in the very practices they will be teaching their students in order to support their students’ learning in the classroom (Li, 2013). In this paper, we will discuss how we incorporated technology (specifically, iPads) into a geometry course for PSTs of early and middle childhood in order to help them develop problem-solving skills through technology and prepare them for technology use in their future classrooms.

The Geometer’s Sketchpad (GSP), a computer software program used in geometry classrooms in a K-12 setting, was a part of the curriculum in our geometry and measurement content courses for early and middle childhood PSTs in order to supplement and enhance regular classroom activities and expose them to technology relevant in their future classrooms. PSTs would test and observe properties of geometry by constructing geometric figures, easily dragging points and lines or transforming objects. However, the rate at which students learn to use GSP varies across the class, leading to classroom time management issues. We wanted to examine how incorporating Sketchpad Explorer (SE), an app used on tablets and iPads for exploration with less programming requirements, into activities might elicit a better understanding of certain topics in the course and better prepare our PSTs for their future classroom.

Because of the increasing use of iPads in schools and by students at home, as well as the opportunity to use Sketchpad Explorer, we believed our PSTs would benefit from working with iPads in their mathematics content courses. Subjects were early childhood PSTs, including Montessori education majors, and middle childhood PSTs, both with and without a math concentration, and intervention specialists (K-12) PSTs. Sketchpad Explorer allows the student to interact with documents previously created on GSP. The student opens the activity with the SE app and immediately explores the design by dragging figures or touching action buttons. In order to incorporate the use of the iPads in the courses, we examined our student learning objectives, the course outlines, and activities previously used with GSP. We opened and assessed every SE activity on The Geometer’s Sketchpad Sketch Exchange  (http://sketchexchange.keypress.com) related to topics in our courses. The SE app also included activities that were assessed. While searching for other activities for the iPad, we found the Math Is Fun website (http://www.mathisfun.com/) which provided good review explanations for the students along with quiz questions that could be used as formative assessments. While the students were not able to take the iPads outside of the classroom for practice on SE, they could, and did, access Math Is Fun for review on their own time.

Research shows that PSTs struggle with conceptual understanding of geometry in elementary and middle school mathematics content courses (Aslan-Tutak & Adams, 2015). Questions were developed about the concepts within the SE app activities to help the students make connections and develop understanding of the topics. Use of the iPads elicited more group discussions because the students were in pods and used the iPads simultaneously. Students more readily asked each other questions about how to use the iPad and the geometry concepts as they worked, whereas they used GSP in isolation at computer stations. Although some groups finished before others, students within groups finished together once all were satisfied they understood the concepts embedded in the activity. When using GSP, some students would not complete the construction of the design, requiring more work outside of class.

During the semester, students reflected on their use of the iPads as well as how the activities they completed (with or without technology) met CCSSM.MP.1. The reflections, when mentioning the iPads, were positive. Benefits from the iPads are clear from these reflections. The PSTs used the iPads as learning supports. Some examples of that are indicated here in student reflections:

 “Using the I-pad makes it easier to remember because we learned the rules through experience with the different figures”.

We used our assigned iPads to look at activities that concern polygons, prisms, polyhedrons, and quadrilaterals. It was easier to understand the lesson because it was hands on and we were able to drag corners, make things bigger or smaller, or organize data”.

The activities on the iPads personally helped me a lot to distinguish between different polyhedra. I was able to practice problems on the iPad quizzes and then easily recall them later on, on my actual quiz”.

While using the iPad for this activity, we were able to physically touch, move, and drag the angles and sides of the objects to see if they fit the right criteria for the type of shape we were looking to find”.

The use of the iPad in this course also aligns with findings from previous research (e.g. Dick & Burrill, 2009; Pegrym, Howitt & Striepe, 2013). Students learned to reflect by using the instant feedback obtained when dragging objects and by seeing many perspectives of figures. As noted by the students, this helped them remember and understand better. They also claimed to gain experience with hands-on activities and with ways to use technology in their future mathematics classrooms. Through classroom discussion, students identified ways to incorporate these activities in their elementary and middle school classrooms.


iPads are excellent tools for enriching classroom content (Perry, Thrasher & Lee, 2014). Overall, incorporating iPads into these geometry courses supplemented pre-service teacher learning. As evidenced from their comments, students preferred having hands on activities guided by the Sketch Explorer app. Introducing the app to replace The GSP (which was used regularly in previous courses) accomplished at least two things. First, students were able to begin the activity more quickly. The app removed the learning curve for constructing the designs on GSP. When using GSP, students have to be instructed how to use the software so that they understand the features. A second benefit to Sketch Explorer was the students’ ability to help each other quickly with the app and activities. Most of the class had been exposed to iPads before and were familiar with how they worked. In future semesters, the authors hope to create new original activities on The Geometer’s Sketchpad for the Sketchpad Explorer with explicit connections to the course. Another hope is to use the iPads in other mathematics content courses for the elementary education PSTs. Lastly, we would like to select additional apps for other concepts in the Geometry and Measurement courses.


Aslan-Tutak, F., & Adams, T. L. (2015). A study of geometry content knowledge of elementary preservice teachers. International Electronic Journal of Elementary Education, 7(3), 301-318.

Banister, S. (2010). Integrating the iPod touch in K-12 education: Visions and vices. Computers in the Schools, 27 (2): 121-131.

Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for Mathematics (CCSS-M).Washington, DC: National Governors Association Center fo Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/Math/Practice

Conference Board of the Mathematical Sciences (2012) The mathematical education of teachers II . Providence, RI: American Mathematical Society in cooperation with Mathematical Association of American.

Dick, T. & Burrill, G. (2009). Technology and teaching and learning mathematics at the secondary level: Implications for teacher preparation and development. Presentation at the Association of Mathematics Teacher Educators, Orlando FL.

Li, X. (2013). Conceptualizing and cultivating mathematical practices in school classrooms. Journal of Mathematics Education, 6(1), 60-73.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

Pegrum, M., Howitt, C., & Striepe, Michelle. (2013). Learning to take the tablet: How pre-service teachers use iPads to facilitate their learning. Australasian Journal of Educational Technology, 29 (4): 465-479.

Perry, A., Thrasher, E., & Lee, H. (2014). High-leverage iPad apps for the mathematics classroom. The Mathematics Teacher, 107 (9): 706-711.