I currently work in a classroom where six students fall somewhere on the Autism Spectrum Disorder. Working one-on-one with these students is often difficult because they have below average memory retention, making concepts harder to grasp and build upon. My students range in age from 2nd grade to 5th grade but all of them do work with numbers. Exercises include addition and subtraction, skip counting, and for some, simply writing out numbers. As instruction expanded into other areas such as reading, writing, music, etc. I’ve found the knowledge of numbers to be extremely important and widespread. Our students also tend to struggle with hand/motor coordination which ultimately affects their ability to independently write certain numbers and shapes. This difficulty is most often associated with the younger students. With all of this information, I’ve decided to create a counting tool to help my students work with numbers in a way that allows them to rely on a physical object. The fact that our work is created using a 3-D printer is wonderful because my students also greatly benefit from tactile touch within their learning experiences. My tool will be palm-sized written numbers 1-10 with a hole in each number indicating its value or ‘how many’. For example, there will be one hole in 1 and ten holes in 10. I’m hoping this will allow my students to not only visibly see the written representation of numbers 1-10 but to also physically feel what each of these individual numbers represent.

Throughout the chapters that we have read in both of our textbooks, direct modeling forms the basis of how students begin to develop their concepts of numbers and their corresponding values. The importance of representation as seen in direct modeling is something that I hope to embody with my counting tool. Students within the direct modeling stage are not able to abstractly work with numbers presented to them so their reliance on physical representation is key. I want my tool to align with the goal similar to that of *Children’s Mathematics*: “to provide a basis for developing understanding of basic number concept and operations by connecting them to children’s surprisingly rich intuitive conceptions and giving them an opportunity to extend these concepts in ways that make sense to them” (Carpenter, Fennema, Loef Franke, Levi, Empson, 2015, p.5). My decision to add holes to each of the numbers is with the hope of encouraging my students to make their own personal conclusion as to what each hole represents. Some may need to look and touch all ten numbers in order to understand, others may only need look. I want my students to reach this conclusion on their own so they come to terms with the written and valued representations of numbers 1-10 supported by their own thoughts, ideas, and connections.

This tool values the importance of the role that tangible interaction and hands-on-experience plays within mathematics. In order to continue and build upon number problems and operations, students need to feel comfortable understanding what a number means. Being able to have a visual representation of a value is a crucial foundation in furthering math capabilities and overall confidence. Numbers 1-10 also allow students to observe the patterns that are formed within the base ten system. Additionally, counting strategies can be made more accessible when students are able to tangibly recognize and ‘feel’ number relationships. A hundreds chart has been known to be helpful for students to recognize certain patterns amongst number groups but this tool doesn’t provide a hands on approach. We know that number facts are not learned by habitual repetition. My tool can be the bridge that gaps the hundreds chart to a more abstract concept of number facts. The pieces are interactive and can be used in a variety of different situations.

In order to measure the success of my tool, I would hope that my students would be able to make the connection of written and valued representation without the help of physical objects. I do think it’s important though, that my students take their time in order to get comfortable with the tool and use it for a variety of number related concepts, not just simple counting from 1-10. If I were to say a number aloud and then my student could show me (with fingers, counters, tallies, etc.) how much that number represented then I would consider my tool a success. If the tool failed, my students would not have been able to make the connection between the written and valued representations of the provided numbers. This would not be their fault but a fault in design that I would need to work to adjust after observing the challenges it presented to my students. I wouldn’t want my tool to be used in any type of testing, I only want it as a support system for my students. If it doesn’t work, it is my responsibility to fix it. If it does, then that’s wonderful for the students who it helps. The testing aspect gets too technical and takes away from the purpose of the tool which is just to give some students a different way of learning or understanding new or difficult information.