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Reflection One
Technology Applications in a Mathematics Education Setting
Technology Applications in a Mathematics Education Setting
Introduction:
In classrooms around the world, from chalkboards to dry-erase boards and traditional textbooks, they are giving way to tablets, interactive apps, and virtual simulations. Today, innovative technology applications are making math more engaging, accessible, and tailored to individual learners than ever before. From gamified learning platforms to Artificial Intelligence (A.I.)-driven tutoring systems, educators and students now have a diverse toolkit to explore mathematical concepts in both dynamic and intuitive ways. This blog explores how these technological tools are reshaping math education, bridging learning gaps, and inspiring a new generation of problem-solvers.
Discussion:
I must say that I have not, over the years, been the biggest supporter of certain technology (A.I.) in the classroom due to the potential crutch it can provide to students. However, I still do see the benefits of it and with all technology being introduced and monitored appropriately, students can achieve a high understanding and success rate in and out of the classroom.
From various readings and discussion through class, the text Introduction to Focus in High School Mathematics: Technology to Support Reasoning and Sense Making (FHS), standouts to me initially because of the different classifications of technology applications. By categorizing these applications, it helps one differentiate the types of implications of technology and its effect on enhancing the mathematical reason of students. As seen below, the types of technology are categorized by Conveyance Technologies and Mathematical Action Technologies (National Council of Teachers of Mathematics, 2010). In my years, I have had limited experience or exposure rather to Mathematical Action toolkits but not much to the Conveyance side of things. I'll explain further later but first let's get a better understanding of the two.
Types of Technology
Types of Technology
Conveyance Technology:
Generally, technologies that are tools for presentation and communication (e.g., document cameras, projectors, collaboration platforms). These support discourse, but do not themselves embody mathematical content.
Mathematical Action Technologies:
Generally, technological tools that respond to user input with mathematically meaningful actions (e.g., graphing calculators, dynamic geometry software, simulations). These technologies actively support student exploration and discovery.
As displayed above in the video, both technologies are demonstrated. Conveyance Technology via the projector and projector screen likewise Mathematical Action Technology through the interactive interaction of the students input via the stylus. There are myriad interactive apps and things that amplify student engagement (GeoGebra, MathWay, Khan Academy, etc.) just as much as well. These are similar experiences I shared in my upbringing but because of new advancements students now have another tool accessible to them via (drumroll please) A.I.! This integration has changed the game of reality and educational interaction in a drastic way. For both the good and the worse, but let's focus only on the good for now.
This leads into my next point of how the advancements made in the realm of A.I. helps connect the gap of student(s) learning. Meaning, just as there are two overarching categories of technological applications, there are two major learning styles that navigates kids understanding of material. As discussed in Relational Understanding and Instrumental Understanding, the two are Relational Mathematics and Instrumental Mathematics (Skemp, 1978).
Learning Styles
Learning Styles
Instrumental Mathematics
Defined as knowing rules without understanding the reasons behind them.
Example: Knowing the formula area = length × breadth and being able to use it, without understanding why it works.
Often gives quick, correct answers and short-term success.
Encourages memorization and rule-following without deeper comprehension.
Relational Mathematics
Defined as knowing both what to do and why—a deeper, connected comprehension.
Enables students to apply knowledge flexibly and adapt to new problems.
Builds a more lasting, self-motivating, and satisfying learning experience.
Often, instrumental instructing is viewed as harmful in comparison to relational due to the dependency instrumental provides on external sources and the easier, immediate gratification of success. This often leads to temporary memorization of rules versus long-term retention of building block components (ideas and concepts). This mismatch is frequent and through the assistance of A.I., students and instructors now have the opportunity to engage with the software to obtain more understanding and creativity of content.
Students can utilize the platform for problem solving after attempting on their own, explanation of course materials in more rudimentary or technical ways (whichever they prefer), and real-world applications where the software can depict and/or systemize the use of the material. Similarly, teachers can call on the platform for "ingenuitive" lesson planning ideas that can leads to better classroom engagement and success. It can sharpen teachers' creative ability in terms of "what questions could I ask that I could not ask before?" (National Council of Teachers of Mathematics, 2010, p. xvi) and drive the success rate of asking more thought-provoking questions. This, overall, yields the next generation of students into becoming better problem-solvers.
I'm excited to explore more about the advancement and involvement of technology applications in a learner setting and look forward to ways I can incorporate it myself. As aforementioned, I haven't always been the biggest advocate of it but with proper utilization, it is the ever-changing force that we as a society can continue to benefit from. Technology is an instrument (tool) that when played in tune and unison with the band (classroom/education realm) will make an appeasing and beautiful song like no other.
References:
National Council Of Teachers Of Mathematics. (2010). Focus in high school mathematics: reasoning and sense making. Reston, Va. National Council Of Teachers Of Mathematics.
Skemp, R. R. (1978). Relational Understanding and Instrumental Understanding. The Arithmetic Teacher, 26(3), 9–15. http://www.jstor.org/stable/41187667?origin=JSTOR-pdf
PPT - Beyond Behaviorism Learning for Understanding PowerPoint ... (2025). Bing. https://sl.bing.net/kZ7v0IR1tEO
(2025). Thetechedvocate.org. https://www.thetechedvocate.org/wp-content/uploads/2019/08/Teaching-Math-with-Technology-quote-AU.jpg
(2025). Youtu.be. https://youtu.be/lrkkPlJjHo4
(2025). Slideplayer.com. https://images.slideplayer.com/24/7367913/slides/slide_8.jpg
(2025). Wordpress.com. https://buildingmathematicians.files.wordpress.com/2016/07/instrumental.png?w=300&h=161
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