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									Running head: USABILITY OF VIRTUAL MANIPULATIVES                           1

              Usability Testing of Virtual Manipulatives by User Profile

                                    Michael Ota

                          The University of Texas at Austin

                                College of Education

                    EDC 385G Design/Strategies for New Media

                                     Dr. Min Liu

                                   April 25, 2010
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                    2

                     Usability Testing of Virtual Manipulatives by User Profile

         Universal design (UD) was originally developed for architectural design so that

individuals with physical disabilities would have greater access to physical spaces inherently

open to the individuals without disabilities. UD is the foundation for the design, development,

and implementation of assistive technology (AT) in education so that students with physical

disabilities can gain greater access to the general education setting (Elder-Hindshaw, Nelson,

Manset-Williamson, & Dunn, 2006; Crow, 2008). A consequence of the inclusion model in

educational reform (i.e., where students with atypical needs have a right to be included in general

education), UD is gaining acceptance for designing curriculum and educational environments for

all typical and atypical students (Scott et al., 2003).

Usability of Online Learning

         The last twenty years have provided a seemingly unlimited advancement of affordances

in educational materials, especially with online access. Theoretically, the technology is available

to design, develop, and implement tools needed to achieve a universally accessible general

education. Unfortunately, the research shows that UD is not consistently followed in online

learning (Grabinger, Aplin, & Ponnappa-Brenner, 2008; Pisha & Coyne, 2001; Scott et al.,


         The needs of online learners with physical and cognitive disabilities require alternative or

enhanced features so that access is available and/or unfettered. Students with physical disabilities

can greatly benefit from screen readers, descriptions of figures and diagrams, layouts that have

organized headings, available closed captions, text captioning for video or other forms of multi-

media, limited synchronous activities, and additional time to complete asynchronous activities

(Crow, 2008). Research has found that designing universal access can improve the usability of
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                       3

the technology for all learners. This would include limiting content to the appropriate level for

the target user, providing choices in features for accessibility and providing live tech support. In

addition, tools should be dynamic, tactile and intuitive at any age and for any purpose

(Simoncelli & Hinson, 2008). Grabinger et al. (2008) found that the most effective online layouts

and functionalities met the requirements of 5 symptomatic needs of cognitive disabilities

(attention and memory, language, executive function, problem solving and reasoning, and social

function) through 3 lenses (recognition, strategic, and affective). Online materials that follow the

key elements of usability (information, interface and interaction) were found to be effective for

students of all ages, abilities and purpose because the interfaces were organized, non-cluttered

and included the freedom of choice in features (like text-to-speech). More importantly, it has

been found that the most effective platforms for both students and teachers are flat in design

where the interaction has limited external links and layers for searching of materials (Keeler and

Horney, 2007).

Research Question

       A great deal of research and development is dedicated to online or computer-based

manipulatives in primary and secondary mathematics. Although this research reports on the

effectiveness of the tools in terms of academic achievement, it does not provide evidence as to

whether or not the design of the platforms on which these tools reside are useful in terms of

interaction, interface and information. Thus, this study will examine whether or not the 3 most

popular sites for virtual math manipulatives (VMs) are easy and intuitive to navigate and use for

students of various ages. Furthermore, we will examine the usefulness of these sites to teachers

who are attempting to plan to use a VM in their lessons.

Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                     4

       Since the reenactment of No Child Left Behind (2006) and the Individuals with

Disabilities Education Act (2004), educators have been held to a higher standard for instructional

materials, particularly for those in digital form. Teachers must use tools, activities and lessons

that are based on or are themselves scientifically proven methods of instruction (Pisha & Stahl,

2005). As a result, researchers have studied the essential components of websites that meet this

standard in addition to outlining instructional design principles that will guide developers. In

other words, they have identified what works and doesn’t work. However, these researchers did

not include usability in their studies (Reimer & Moyer, 2005; Underwood et al., 2005).

       Established usability testing for math websites or virtual math manipulatives is almost

nonexistent. Therefore, principles on testing, data collection and analysis by Moggridge (2007)

and Rubin and Chisnell (2008) (among many others within these same standards) were

referenced and/or implemented as a theoretical foundation for the following methodology.

Website Search

       Underwood, Hoadley, and Lee (2005) and Reimer and Moyer (2005) collectively

reported that the 3 most prominent websites for virtual math manipulatives are the National

Library of Virtual Manipulatives (, the Math Forum Math Tools

( and the Shodor Foundation Project Interactive

( We used 3 search engines on April 2, 2010:, and Our search consisted of three layers:

general, age and purpose. For a general search, we used the keywords “math manipulatives,”

“virtual manipulatives” and “virtual math manipulatives” in all 3 search engines. Searching by

age, we used the keywords “preschool,” “middle school” and “teacher.” And a search based on
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                      5

purpose consisted of the keywords “activities,” “tools,” “lessons” and “lesson plans.” The results

consistently listed the NLVM, Math Forum and Shodor websites in the top ten.


          Three individuals participated, varying in age, computer competency levels and

occupation. The first to participate was a male preschool student age 3 years 5 months and of

Asian-Caucasian ethnicity; the second participant was a Hispanic-Caucasian female student age

13 years enrolled in middle school TAG classes (in particular, algebra 1 in 7th grade); the last

participant was a Caucasian female teacher at age 32 who taught special education and holds a

bachelor’s degree. All three have average to above-average proficiency with computers, online

activity and virtual manipulatives (self reported). It should be noted here that all 3 participants

are related to the researcher.


          All 3 participants completed the study at the researcher’s home on the same computer in

a secluded den. The Mac Mini computer was connected to a high definition 20+ inch color

monitor and high speed Internet. Participants could use the keyboard, touch pad and/or

traditional mouse to navigate the 3 sites. A webcam and microphone was attached to the monitor

of the computer, which was used in conjunction with Camtasia to record each session.


          Each session was conducted one at a time conducted with one participant sitting at the

desk with the computer while the other participants were not in the home. In each session, the

participant was debriefed about the study, using language relevant to the participant’s age and

education. He/she was also instructed not to answer any questions or perform any task that made

him/her feel uncomfortable. In addition, each participant was informed that the data and results
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                    6

collected from the study would not be shared with anyone except the professor and other

researchers in the class.

       Pre-questionnaire. Participants were verbally asked questions about their comfort level

with computer hardware, computer software, Internet use and virtual manipulatives. Each

participant was asked to rate his/her comfort level on a scale of “1” to “5,” “5” representing very

comfortable or on a scale of “no” or “yes,” depending on his/her age. The researcher did ask

unscripted, follow-up questions for clarifications of responses.

       Data collection. The researcher logged onto the tools, activities or lesson plans section

(depending on the occupation of the participant) for each of the 3 sites (NLVM, Math Forum and

Shodor Foundation) one at a time in the same order. He then instructed the participant to search

(excluding the preschooler), find and click on a link of a manipulative that he/she either found

interesting or was currently studying/teaching. Guidance was given if the participant: 1)

exhausted the search on his/her own and did not receive satisfying results; or 2) needed help with

troubleshooting the technology and/or with navigating the website. The researcher sat in a chair

next to the participant and watched the same screen. No judgment was given on what the

participant chose as a virtual manipulative and reassurance was given with statements like

“There is no right answer.” No other instructions were given as far as search techniques or

navigation within the site. The researcher did use hand-on-hand guidance for the preschooler if

he had difficulty navigating the site, and did ask follow-up questions for areas of difficulty.

       Notes were taken by the researcher on how the participant searched for the topic, on ease

of navigation and on difficulties experienced when executing the tasks, all within the site up to

exploring with the VM. Data on ease and difficulty with the VM was only noted if it pertained to

an overall usability issue that was exhibited or could be relevant to the host site.
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                      7

       Post-questionnaire. Once the 3 sites had been explored, each participant was asked to

verbally state which site was liked best and why (excluding the preschooler), to explain which

site(s) was easiest to find the virtual manipulative pertaining to the topic in mind (excluding the

preschooler), and to rate overall satisfaction (using the scale previously mentioned) of each site.

The researcher did ask follow-up questions for clarifying responses.

                                         Data and Results

       Each participant provided a different perspective on good and ineffective design of the

interface, information and interaction of the websites. This occurred due in large part to the

participant’s age and purpose, but also due to unforeseen actions and uses that he/she attempted.

Technology Competence and Experience

       Each participant was able to respond to the pre-questionnaire. The results are shown in

Table 1 below. Overall, the participants were fully capable of completing the tasks of the study.

Experience levels warranted physical and technical guidance for the preschooler, but the effects

of that assistance by the researcher are negligible.

   Participant by      Comfort Level       Comfort Level      Comfort Level      Comfort Level
   Occupation          with Hardware       with Software       with Internet       with VM
   Preschool                 5                   5                   3                 5
   Middle School             3                   4                   5                 4
   Teacher                   4                   4                   5                 4

Table 1. Some of the participants were unfamiliar or not capable of using the scale. Thus,
comparable words were used to represent the ratings on the scale. For instance, the participant
was given a choice between “No,” “I think so,” or “Yes.” The results have been transformed to a
scale of 1 to 5, with 5 representing “very comfortable.”

Navigating through the Tasks

       Overall, each participant found it difficult to find the tool or activity he/she had in mind

on all 3 sites. Each website had a different layout and search capabilities. Figures 1, 2 and 3

below show the home page for each site. In Figure 1, a user in the NLVM site must move the
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                       8

mouse pointer over the boxes by category and age group and click on the box that is highlighted

in white; if he or she wanted to search by a particular topic, the user would have to notice the

search box on the upper right area of the screen and realize the box to the left of the label

“Search” in intended for input. This is a different design than that of the Math Forum site, shown

in Figure 2, where the search features are prominently displayed at the top of the page utilizing a

keyword search engine or a drop down menu by age, category and type of materials (i.e., tool,

activity, or lesson). The Shodor Foundation home page uses a tabular layout where the user may

search by keywords, category or type of materials; however, there are no search capabilities by


       In addition, the teacher found it to be particularly challenging to find pertinent lesson

plans for the topic and virtual manipulative sought. The NLVM home page required the teacher

to click through the same levels as the students, then click on the buttons at the top of the screen

to access standards and teacher notes (which are available to all users). The Math Forum and

Shodor Foundation home pages allowed the teacher to “one-click” her way to lessons, but had to

stumble upon or be guided to the drop-down menus that enable the functionality.

Figure 1. NLVM home page.

Figure 2. Math Forum home page.

Figure 3. Shodor Foundation home page.
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                   11

       Preschool student. The preschooler was not required to search for a topic, which the

researcher chose (counting whole numbers in pre-kindergarten), due to experience and cognitive

capabilities. However, he was asked to find and click on a virtual manipulative he found

interesting, of skills he was capable. The easiest navigation for him of the 3 sites was the Shodor

Foundation (Figure 3); this may have been greatly influenced by the fact that he was currently

learning how to read an analog clock and the first virtual manipulative in the results list was

“Clock Arithmetic.” He had slightly less difficulty navigating the results list in the NLVM site

(Figure 4), where the pictures (although small) drew his attention to a counting manipulative.

The least useful site for the preschooler was Math Forum; the list had no graphic icons, required

an unstable “over” movement with the mouse pointer in order to reveal detailed information

(Figure 5), and often led to irrelevant or dead links. The researcher had to assist the participant in

choosing an appropriate link on this site.
Running head: USABILITY OF VIRTUAL MANIPULATIVES                              12

Figure 4. NLVM results list for pre-kindergarten and number and operations.
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                  13

Figure 5. Math Forum results for pre-kindergarten and number sense.

       There are few points to note about the actual VMs and their usability for the preschooler.

First, none of them had automatic voice over (VO) or the option to have VO that could be

verbally describing the tasks. Shown in Figure 6 is the VM “Let’s count!” on the Math Forum

site, which has written directions but no intuitive action. The participant did not know what to do

and randomly clicked on different areas of the screen until he became frustrated. Second, the

layout of the counting numbers VM in “Clock Arithmetic” in the Shodor Foundation site (Figure

7) had buttons in close proximately to each other and with small real estate for clicking. This

made it difficult for this participant to navigate the VM, which is contrary to his previously

demonstrated abilities and frustrated him to point where he stated, “I can’t do it,” for subsequent

tasks. The researcher at that point used hand-on-hand guidance until his confidence returned.
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                  14

Figure 6. Counting VM on Math Forum.

Figure 7. Shodor Foundation VM on counting numbers.

       Middle-school student. The middle school student was capable of using the search

engines or given filters. She indicated that her current studies in math touched on graphing of

parabolas. She was then instructed to find a VM that would help her in that topic. She found the

matrix of categories and ages easy to navigate; although, she clicked on the broad category of

algebra instead of using the cross reference of “Algebra” and “9-12” and had to look through

over 100 topics in order to find one on graphing parabolas. She did have considerable difficulty
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                15

with the Math Forum site, first inputting keywords in the search box on the top left of the screen

and then having difficulty finding a category that matched her topic in the “Browse” drop-down

menus (Figure 8). The search resulted in no relevant links, links that had little relevancy or VMs

that required cash payment or an unsupported platform (e.g., Java Applet). This become so futile

that the researcher had to stop her after 10 minutes and redirect to any VM of interest, not

necessarily one that was pertinent to her topic of study. Her easiest navigation and search was in

the Shodor Foundation site, which had a tab of “Algebra” and large, descriptive graph icons that

allowed her to scroll down and find the “GraphIt” VM.

Figure 8. Math Tools search engine.

Figure 9. Math Forum search results for the middle school student.
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                    16

Figure 10. Shodor Foundation search results for the middle school student.

       Teacher. The purpose, as directed by the researcher, for the teacher was to navigate

through the sites and find lesson plans supporting the VMs on a current topic taught (in her case,

multiplying polynomials). As indicated by the teacher, a lesson plan would consist of standards,

notes to the teacher and instructions on how to facilitate use of the VM. In addition, the lesson

plans should not be apparent and readily available to the student. Given these constraints, both

the NLVM and Math Forum sites failed the usability test for teachers. As seen in Figures 11 and

12, the teacher notes are clearly marked at the top banner of the screen and are accessible to the

students. In addition, the participant commented that the notes were neither to the depth nor in

the form normally written in instructional materials. When she clicked on the instructions button,

the site gave the same directions given to the student with no answers or further guidance (Figure

13). Finally, when she clicked on the standards button, the site hyperlinked to a page on the

NCTM website, which was not specific to the VM and too general for her to fully understand the

goal of the materials.
Running head: USABILITY OF VIRTUAL MANIPULATIVES                    17

Figure 11. NLVM screen layout of a VM on multiplying polynomials.

Figure 12. NLVM teacher notes on multiplying polynomials.
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                   19

Figure 13. NCTM standards for secondary algebra, hyperlinked from NLVM.

       The Math Forum, when the teacher was able to find a readily available lesson on a topic,

was just as unclear and shallow as the lessons on the NLVM site. Searching by keywords or

browsing by topic and/or resource type yielded no or very little results. Unfortunately, she was

not able to find a lesson on multiplying polynomials; instead she found a lesson on addition and
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                  20

subtraction of polynomials. As seen in Figures 13 and 14, this provided very little resources; the

one resource that was available consisted of a hyperlink to another site that required registration.

This participant expressed a desire to stop on that site and the researcher allowed her to move on

to the Shodor Foundation site.

Figure 14. Math Forum results for both student tools and teacher lessons.

Figure 15. Math Forum hyperlink to lesson on polynomial operations.
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                   21

       On the Shodor Foundation site, the teacher was able to quickly ascertain that the topic on

multiplying polynomials was not available by clicking on the “Algebra” tab and scrolling down

the page. She did comment on the sparseness of resources. She then clicked on a comparable

topic and found it difficult to locate any link to lesson plans. The researcher then directed her to

the “Jump To:” menu at the top of the screen; the teacher immediately found “Lessons” and

clicked on the plan for Venn diagrams (Figures 16 and 17). She verbally reported that the results

list was clear, easy to read, informative and not cluttered. This satisfaction of the Shodor

Foundation site continued after exploring the actual lesson plan on Venn diagrams. According to

her, the site was organized and relevant to the information customary in lesson plans (Figure 18).

Also, she gave high marks on the standards drop-down menu, mainly because she could examine

detailed standards for Texas within the same page of the lesson plan (Figures 19 and 20).

Figure 16. Shodor Foundation “Jump To:” drop-down menu.

Figure 17. Shodor Foundation site results on lessons.

Figure 18. Lesson plan page on Venn diagrams
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                 23

Figure 19. Standards drop down menu on Shodor Foundation site.

Figure 20. Texas standards imbedded on the same screen as the lesson plan.

Reflective Usability

       Once the tasks were complete, each participant was asked which site he/she liked best

and why (excluding the preschooler), to explain which site(s) was easiest to find the virtual

manipulative (excluding the preschooler), and to rate overall satisfaction (using the scale

previously mentioned) of each site. Table 2 shows that the Shodor Foundation had the highest

marks by all participants; this was confirmed after a review of the data by the researcher, noting
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                    24

the level of enthusiasm and lack of frustration when compared to their experiences on the other

sites. The site with the lowest marks was the Math Forum site; this was also confirmed by a

review of the data, noting a greater frustration level with finding VMs or lesson plans pertinent

to their current topic. In addition, the participants spent the most time on the Math Forum site,

with an average of 12 minutes of the average total session time of 20 minutes. This time was not

spent exploring, but in searching for relevant tools, activities and/or lesson plans. The two eldest

participants also indicated, as answers to the first 2 post-questions, that the Shodor Foundation

site was the easiest to use because of the smaller number of levels needed to navigate, good use

of graphic icons, clear, concise and organized layout, and pertinent and intuitive information.

            Participant by           NLVM            Math Forum            Shodor
            Occupation                                                   Foundation
            Preschool                   5                  5                 5
            Middle School               4                  2                 4
            Teacher                     1                  1                 5

Table 2. Some of the participants were unfamiliar or not capable of using the scale. Thus,
comparable words were used to represent the ratings on the scale. For instance, the participant
was given a choice between “I didn’t like it,” “Maybe,” or “I liked it.” The results have been
transformed to a scale of 1 to 5, with 5 representing “I liked it.”


       This study on virtual math manipulatives explored the usability of 3 of the most popular

sites with regard to age and purpose of the user. The researcher had a general procedure for

collecting data, instructing participants on the given tasks and analyzed the data based on

recorded digital video. The goal of the study and its research questions was to determine the ease

of use and barriers to access. Conclusions would be based on principles of instructional and

universal design: unfettered and flexible access for all individuals. Based on the data collected on

the use by the aforementioned 3 participants, all 3 sites have severe flaws in their design, which
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                  25

may create barriers to individuals with physical or cognitive disabilities, limitations due to

developmental age, or specialized needs.

Recommendations for Higher Degree of Usability

       In order to provide a more universally designed site for virtual manipulatives, the

following parameters are recommended:

       1)      Provide a simple yet clearly labeled search matrix, such as the one found on the

               NLVM and Math Forum sites.

       2)      Depending on the age and/or abilities of the user, text, graphics and sound should

               be readily enlarged and available.

       3)      Sites should clearly separate purpose of use; thus, students should be prevented

               from gaining access to the teacher materials.

       4)      Online materials should be organized in the same manner as on paper in

               traditional platforms (i.e., teacher edition books) but with the dynamic

               affordances of technology.

       5)      The use of drop-down menus should be limited since they have a tendency to hide

               the features and functions available, and buttons should be large and spaced

               reasonably from each other to allow those individuals with limited physical range

               to click on the desired button.

       6)      Outside, external links should be avoided when possible so that users feel there is

               cohesiveness to the site.

       7)      Navigation should be tabular (e.g., breadcrumbs) with text and graphic icons so

               that users of any age or ability can easily go back and forth in their search and use

               of VMs. However, no individual should have to click through more than 3 levels
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                       26

                (i.e., pages, actions or portals) in order to arrive at his/her desired tool, activity or

                lesson plan.

        8)      Unnecessary graphics (i.e., site trademarks and ads) should be eliminated since it

                reduces available real estate for large icons and concise, precise information.

        9)      To the point it does not detract from a simply organized layout, the home page of

                the site should be just as inviting and exciting as the VMs themselves.

        10)     Organized headings that can embed expanding and collapsible information should

                be the cornerstone of the overall layout.


        Other than a need for a larger sample size and control group, limitations to the results of

this study included possible bias due to the relationship between the researcher and participants.

The capabilities of the preschooler and subsequent guidance required to complete tasks may have

some bias effect on the results; also, he did not answer all questions in the pre- and post-

interviews, which essentially provides incomplete and incomparable data to the data of the other

participants. Furthermore, a limited script and use of follow-up questions, although designed to

simulate the environment the user would experience independently with the sites, could be

source of compounding factors. Perhaps more training and guidance, arguably what school

districts provide, on the features and functionality on each site would garner more favorably

usability results.


        Overall, educational websites lack usability and universal design. They are often rushed

to production without the labor-intensive features that require websites to be accessible. As a

result, teachers, parents and students are less likely to use the tools that are necessary to complete
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                                    27

technology-math standards. As seen with the teacher’s navigation in the study, most sites require

3 to 4 clicks before arriving at needed tool, activity or lesson plan. This scaffolding is a barrier to

those with disabilities or an abhorrence of online materials. Until designers consistently develop

online sites and materials that meet the needs of as many users as reasonably possible, the

affordances of VMs and like technology will be accessible to only a small, elite set of learners.
Running head: USABILITY OF VIRTUAL MANIPULATIVES                                               28


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Running head: USABILITY OF VIRTUAL MANIPULATIVES                                               29

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