Early Math Concepts Using Stages Math: Number Sense

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Madalaine Pugliese: Assistive Technology Graduate Program Coordinator, Simmons College & Stages Math: Number Sense Author

Empowering Teachers with Universal Design for Learning

Truly effective mathematics learning support in the form of software for skills practice is generally considered one of the least developed areas of assistive and educational technologies, which put it squarely in the sights of Madalaine Pugliese of Simmons College. She authored Stages Math: Number Sense software, which is designed to foster the development of precisely that – fundamental numerical concepts and relations for primary grades – such as counting of money, math facts, and focally important to the project, number line concepts.

Number Sense effectively has a dual GUI design, with one interface set up to offer logical interactions for young children, and a behind-the-scenes interface that teachers use to control content and challenges kids experience, down to the level of differentiated scaffolds and accessibility for adaptive device users. More importantly, this “teacher side” includes a plethora of Universal Design settings that will permit a spectrum of accessibility depending on a child’s needs – including visual and auditory cueing scaffolds. These work with a range of external accessible switches and other third party input devices to create a complete accessibility learning solution for mathematics.

Madalaine’s experience with education led her to the realization that teachers are experts in curriculum creation and delivery, but that most cannot, logistically, manage to become technology experts as well. There’s very little time to interrupt the teaching and learning process to deal with settings and features on the fly during instruction, and one project teacher commented that in mainstreaming, it is “Very important to keep all kids working.” Therefore, one of the key design considerations of the technology was keeping teachers at the center of the equation with “proactive settings” that are prepared for learners in advance to avoid interruption and expand teacher capacity. This has the effect of making the software usable and effective for kids through manageable adoption and deployment. She explains,

When you are thinking about UDL, you want to make sure that any student who sits down in front of the software can use it without stopping the flow of what’s going on in the classroom. Some students need extra help, some need fewer questions, some need reading support, some need accessibility considerations and, some need customized feedback. We found this to be extremely helpful in our study. Those considerations are made in advance by the teacher and saved specifically for each unique learner.

Elaborating on this last point, she adds that “Diagnostic information produced by Number Sense influenced teacher’s decisions on strategic direct instruction based on reports it produces” throughout the study. This allowed for flexibility even within the parameters of a complex single-subject A-B-C research design. “That’s very rare in the design of math software, this level of detail,” Madalaine adds, “You might get record keeping, but Number Sense gives more than just whether they got it right or wrong, including the actual pattern of their responses.” This input includes targeted information that helps select “off-computer extension” exercises.

Still, the system does also permit the activation of another set of fast “reactive settings” that can be brought into play quickly when needed during instruction as needs are recognized in real time. For instance, one young subject in the study who was counting money kept restarting his count repeatedly after losing his place. A support scaffold was selected for him that kept track of the money counted so far and gave him verbal reminders, which effectively supported him to move forward.

In regard to these auditory reinforcers, Madalaine explains,

It is important for students to hear their own names in the interactions with the software – we customized under ‘rewards and incorrect feedback’ the kind of support we would want the kids to hear from a teacher.

Generating Scientifically- Based Research Outcomes

Number Sense has been acquired by Cambium Learning Technologies, a growing vendor of access technologies. It was necessary to perform a study to confirm the actual efficacy of the logical design of the software’s feature sets, and the NCTI Tech in the Works award was precisely suited to launching a collaboration project to obtain experimental data in the real-world context of a school setting.

As the software author, Madalaine was acutely aware that while she could organize assets to perform an unbiased assessment, she could not, herself, be a part of the research team. Therefore, Russell Maguire, a respected researcher in Behavior Education at Simmons College, was recruited to head up the research design and implementation. Karen Janowski of EdTech Solutions provided additional AT and research support, while teachers and AT support teams at the selected school constituted final critical partners.

The KeyMath3™ Diagnostic Assessment was used to verify teacher reports of child subjects’ math levels and needs, while corresponding reports generated by the software itself provided outcomes data. A researcher was always present during brief, concentrated treatments even as general class instruction was going on for the classroom at-large, focusing on K-2nd grade children.

Both statistical analysis and qualitative observation confirmed a majority of students acquired substantial new mathematical capabilities within a comparatively short period of time, that the software itself was effective in both informing prescriptive teaching and research outcomes, and that students also developed new computer literacies as a result of interactions.

Perhaps an even stronger outcome of the study is that the deployment has continued, and the district is utilizing Stages Math: Number Sense broadly not just for students with disabilities, but to meet a broad range of developmental needs prescriptively among the general student body. It is meeting common instructional needs in natural scholastic settings.

Collaboration in Schools

The strengths of the outcomes of the project were rooted not only in effective software design, but also in the configuration of an effective team. This began with Russell McGuire, the head researcher, who, like Madalaine, had very strong pre-existing relationships with the school district and teachers as a consultant on managing behavior among special needs students. These relationships meant that trust and communication pathways were already in place.

Madalaine feels one of the strongest links in the collaboration team was the project AT Team itself. They served as liaisons with school district IT personnel, working around potential problems with installations and permissions on networks, worked behind the scenes to help configure Universal Design settings based on student needs, and taught teachers how to connect peripheral input devices. In turn, one member of that team has countered,

From an overall process perspective for a first time implementer, it was overwhelming and amazing to watch how research unfolds. The work that goes into it, from the application for the grant/research, to the specific details for the research team was eye-opening. Collaborating with an unfamiliar team of teachers, volunteering their time and flexibility to their schedule was the gel that held this project together. Without their willingness to participate and allow strangers to come into their classroom for six weeks, pulling students and interrupting their daily schedule, this project would never have happened.

Outlining the investment of Cambium Learning Technologies in the project, Madalaine continues,

Publishers usually provide ’stuff’. In this case, they provided more than software, including Intellikeys keyboards. They acquired Intellitools just about the time they bought Stages Math: Number Sense, so they really looked at this as an opportunity to see how effective they were in working together, much more than publishers typically do for a study. The grant provided touch screens as well.

Madalaine returns to the importance of understanding teachers’ position in closing comments on collaboration, and points to potential improvements for general teacher preparation in the United States:

In AT collaborations, it’s really important to be a good listener when it comes to curriculum. I don’t think general educators are trained in such a way that folding in all these different differentiations, strategies, and tools comes easily. They’re prepared with good rich curriculum ideas and ways to access their progress from a standard point of view. But when kids are not developing typically, when other kinds of tools might be needed, I don’t think we do a very good job of that kind of consideration in teacher prep programs.

Highlighting the importance of on the ground collaboration within the schools themselves, she finishes,

AT specialists are absolutely prepared for those ‘what ifs’. The AT people were really great listeners, had curriculum in mind first, and realized that teachers understood that we were there to support curriculum and identify helpful strategies. This combination was really powerful: collaborating together, we got some really nice diagnostic, prescriptive rhythms going.