Phase I

Phase I:

Identifying the Problem and Proposed Solution

Learning Issue:

As a fourth grade teacher of on-grade-level math, I notice every year that my students come in to class frustrated and with very low expectations of themselves. They continually demonstrate a negative attitude towards math and struggle through each unit. In order to counteract this attitude, I try to make every lesson as interesting and engaging as possible, while letting my students know that they are capable of learning and understanding. Every year, one of the most challenging topics for my students is geometry. While some children are able to quickly grasp each concept, a vast majority of my classes struggle through. At the beginning of every unit, students are given a pre-assessment to determine the areas that need the most support. Every year, an average of 80% of my classes score a 60% or below on the geometry pre-assessment. By the end of the unit, this has improved to 70% of students scoring 70% or higher on their post-assessment. It is my goal to get 100% of my students scoring 80% or higher on their post-assessment.

Description of School and Population:

The school that I work at is located in Gaithersburg, Maryland and has a current population of 430 students. The population consists of 38.4% Asian, ≤ 5% African American, ≤ Hispanic, 45.1% White, 7.4% multi-racial, and ≤ American Indian and Pacific Islander. Of these students. 12.1% are enrolled in an ESOL (English as a second language) program, 8.4% receive free and/or reduced meals, and 6.0% receive special education services. The students at this school have a wide variety of needs. Many students are labeled as GT (Gifted and Talented), but there are also many ESOL students with a range of abilities, as well as students with IEPs (Individualized Education Plans) and 504 plans (providing accommodations to regular education students with special needs that influence their learning). These students have specific modifications to their education to support their special needs. There are also many students who are not receiving these services, but have documented interventions from current and previous teachers.

This school is located in a very affluent area of Montgomery County and is fortunate to have a wealth of technology that students have access to on a daily basis. Each classroom comes equipped with an interactive Promethean Board and projector, a single teacher computer, an Elmo document camera, a class set of 30 ActiVotes, one ActivSlate (with pen), one ActivWand, and two ActivPens. There is one monochrome printer and one color printer that are shared by each grade level and located in the team leader's classroom. There is also one computer lab in the school that supports 30 student workstations and one teacher workstation. Each workstation has access to the internet through the Montgomery County Public Schools network. In addition, there is one class set of 30 mobile Netbook computers and 10 digital cameras that teachers can sign out from the Media Center for individual student or whole-class use.

Individuals Involved:

I will be using my Capstone project to support my on-grade-level fourth grade math class. In the class, there are 18 students consisting of 7 girls and 11 boys all between the ages of 9 and 10 years old. There are 2 students with IEPs (Individualized Education Plans) and 2 students with 504 plans (providing accommodations to regular education students with special needs that influence their learning). There is 1 ESOL student who is placed at a level 3 signifying that the student is advanced in their mastery of the English language. There is also 1 RELL student. RELL stands for Reclassified English Language Learner signifying that the student has exiting the ESOL program within the last two years. There are 0 GT (Gifted and Talented) students in the class.

There is one special education para-educator who offers additional support in my math class for 30 minutes on Mondays, Wednesdays, and Fridays. I often assign her to work with small groups of students who need extra support. During this unit, I will be assigning her to either monitor the classroom while I work with small groups or asking her to work with a small group who needs more individual attention.


Approval was granted by my administrator via email.

Technology-Based Solution:

After determining the area of most need in my math class, I have decided to use an online resource that my school has a subscription to called IXL ( This website provides many resources including games, lessons, and activities for students of all math levels from Pre-K through seventh grade. Within each grade level, the math concepts are broken down into specific areas based on the essential questions and objectives of the lesson. After introducing each topic, students will use these online resources to enhance and support their independent learning of each geometry concept as it pertains to the Montgomery County Public Schools current curriculum.

Research-Based Evidence:

Mathematics Education in Elementary School

A Literature Review


In today’s world, technology is everywhere.  There is not a single day where people don’t encounter some kind of technology, whether they’re on their way to work, sitting in a meeting, or relaxing with their families.  Advances are constantly being made to improve our lives through technology.  In fact, Carlson (2005) refers to the current generation of children as the Millenial or Net generation because of the amount of technology that they are exposed to on a daily basis.  Television and movies are a common social gathering and computer programs such as Skype, Twitter, and email are the most convenient forms of communication.  Texting via cell phones is an even more immediate form of keeping in touch and airmail is beginning to be used less and less.  The college application process has changed from paper-based to almost completely online.  Credit card companies are “going paperless” and sending out their bills via email and people don’t even need to leave their homes to go grocery shopping (e.g. Peapod Home Delivery).  Televisions, computers, videogame systems, and cell phones are commonly seen and used around the ordinary household. 

            Along with all of the technology that children see in their homes, there has been an increase in the technology within schools.  From class sets of laptop computers to interactive Promethean Boards, students are now using technology as a part of their daily learning.  Exposure to all of this technology is changing the way that children view the world.  Children are learning in vastly different ways and teachers need to adapt their teaching and assessment methods to meet these needs.  The advances of modern technology have forced significant changes in the way professionals teach and assess student learning through the increased access and understanding of newer and more interactive classroom technology (Musso, 2009).

            In addition to an increased use of technology in schools, there has been greater emphasis placed on teachers and administrators to implement more science and math based programs. National studies have shown that American schools are falling behind in the fields of science, technology, engineering, and math, otherwise referred to as STEM (National Association of Education Statistics, 2011; OECD PSA, 2003). However, the reaction to this research is most commonly seen in middle and high school programs. In reality, the best time to introduce programs like this is during the elementary school years. It is at this time that students are more likely to form an interest in science and math disciplines (Dejarnette, 2012).

Using Technology to Teach Math

            Elementary education sets the standard for all future learning that children will do. Along with reading, science, and social studies, children spend a significant amount of their elementary school experience studying math. The basic ideas that these students form about math will support their learning through middle school, high school, and beyond. This is why it’s not only important to provide students with strong mathematical knowledge, but also a positive outlook and acceptance of math. Every year, my students come into class and tell me that they don’t like math because it is hard. This stereotype is commonly accepted and passed along from generation to generation of students. Unfortunately, this belief can lead to a very negative attitude towards math and makes it challenging for students to learn. This negative attitude and low performance can lead to math anxiety and phobia in young students (Mundia, 2012).

            By integrating technology into education, teachers can engage their students more in the learning process and help build their interest in lessons. This positive environment serves as a battering ram to break down the previously formed negative ideas towards math. However, merely adding technology to a lesson doesn’t mean that it’s going to increase student learning and achievement (Roblyer & Doering, 2010). While technology does serve to motivate students and gain their attention, it is the way that the technology is used that makes the biggest impact on student learning. Teachers need to use technology as a support tool to their lessons, not as a means to teach the lessons.

            In her study of best practices for teaching mathematics, Marilyn Burns emphasizes that “children need to learn mathematical concepts and to see relationships among those concepts. Mathematical concepts and relationships are abstract ideas that people learn through the process of sense making and constructing understanding” (Burns, 2007, pg 27). By using specific technological tools with students, they can construct meaning of mathematic concepts while making personal connections. This combination of strategies makes the mathematical concepts learned in elementary school more accessible and easy to remember for students as they progress through their education.

Concrete and Virtual Manipulatives in Teaching Math

            One very important aspect of teaching math in elementary school is the use of manipulatives. Manipulatives are defined as, “physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics,” (Boggan, Harper, & Whitmire, 2007, pg 1). These objects can be used to support almost any mathematical concept as part of whole-group instruction or independent practice (Burns, 2007; Linder, 2012). The use of manipulatives allows students to play with mathematical concepts and make their own sense out of these abstract ideas (Burns, 2007). They add a visual meaning that can be easier for young students to remember.

Traditionally, manipulatives are small objects that can be used to model specific math concepts. However, in this age of technology, there are an increasing number of virtual manipulative programs available on the internet or in software packages. These virtual manipulatives allow for all of the same exploration as physical manipulatives, with some additional features. Many virtual manipulatives allow students to backtrack and trace their previous actions, as well as connecting multiple sets of manipulatives (Manches, O’Malley, & Benford, 2010). This allows students to not only practice different concepts, but connect ideas and expand on their mathematical knowledge. A large part of mathematical reasoning encourages students to be able to take their knowledge of basic concepts and apply them to newer and more challenging concepts. Being able to see this modeled virtually will encourage students to make these connections on their own in the future.

Rather than just memorizing formulas and other mathematic concepts, students use this manipulatives to experiment with additional ways to solve problems. In many math concepts, there is not just one way to solve a problem. By being able to manipulate the data or shapes in question (either physically or virtually), students are able to form opinions about the concepts and create new ways to solve problems. The use of manipulatives increases student learning and understanding while allowing students to make personal and mathematical connections (Boggan, Harper, & Whitmire, 2010).


In conclusion, the use of virtual tools during mathematics lessons has value for students of all ages and should be promoted by school boards and administration because of their numerous benefits. It is important to consider that, in supporting the use of virtual tools and web-based learning, we are not talking about converting every aspect of the classroom to an online or technologically-based environment, but rather using these resources to enhance learning and engage students (Appana, 2008). In addition, the use of virtual tools can be used to connect the home and school environment to make learning more collaborative and accessible.

Particularly when it comes to mathematics, virtual manipulatives and online lessons can be a very positive influence on student learning. The use of technology can make learning and mathematical practice feel more like a game for students and may increase their motivation to learn and practice their skills. In addition, many of the available tools are user friendly and easy to learn whether in a school environment or at home. In his article discussing the pros and cons of the online classroom environment, Robert Taylor (2002) states that online lessons and tools promote “cognitive learning – where the student uses memorization … analytical skills, evaluates data and uses this knowledge to arrive at solutions” (p. 25). These independent work skills are worth promoting for students to succeed in today’s ever changing technological world.



Appana, S. (2008). A review of benefits and limitations of online learning in the context of the student, the instructor, and the tenured faculty. International Journal on E-Learning, 7(1), 18 p.

Boggan, M.; Harper, S.; Whitmire, A. (2010). Using manipulatives to teach elementary mathematics. Journal of Instructional Pedagogies. 3(1). pg 1-6.

Burns, M. (2007). About Teaching Mathematics: A K-8 Resource. Math Solutions Publications: Sauslito, CA.

Carlson, S. (2005). The net generation in the classroom. Chronicle of Higher Education, 52(7), pg 34-37.

Dejarnette, N. K. (2012). America’s children: Providing early exposure to STEM (science, technology, engineering, and math) initiatives. Education. 133(1). pg 77-84.

Linder, S. M. (2012). Interactive whiteboards in early childhood mathematics. Young Children. 67(3). pg 26-35.

Manches, A.; O’Malley, C.; Benford, S. (2010). The role of physical representations in solving number problems: A comparison of young children’s use of physical and virtual materials. Computers and Education. 54(3). pg 622-640.

Mundia, L. (2012). The assessment of math learning difficulties in a primary grade-4 child with high support needs: Mixed methods approach. International Electronic Journal of Elementary Education. 4(2). pg 347-366.

Musso, M. & Cascallar, E. (2009). New approaches for improved quality in educational assessment: Using automated predictive systems in reading and mathematics. Problems of Education in the 21st Century, 17(1). pg 134-151.

National Association for Education Statistics. (2011). Mapping state proficiency standards onto the NAEP scales: Variation and change in state standards for reading and mathematics , 2005-2009). Retrieved from

Organization for Economic Cooperation and Development Program for Student Assessment (OECD PSA). (2003). International comparison of math, reading, and science skills among 15-year-olds. Retrieved from International Comparison of Math, Reading, and Science Skills Among 15-Year-Olds —

Roblyer, M. D. & Doering, A. H. (2010). Integrating Educational Technology into Teaching. Allyn & Bacon: Boston, MA.

Taylor, R. W. (2002). Pros and cons of online learning – a faculty perspective. Journal of European Industrial Training, 26(1), 14 p.

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