# data[].attributes.body
S: Substitution

A: Augmentation

M: Modification

R: Redefinition

*Enhancement

*Transformation

*Practical Application

# data[].attributes.body
a. Substitution and Augmentation (Enhancement)

Substitution: I can technology to replace traditional tools without changing the task!

Ex: Use Google Slides instead of a whiteboard to deliver notes on solving equations.

Augmentation: Improve tasks slightly using digital tools

Ex: Practice solving equations or factoring using self-checking Google Forms or Quizizz.

Ex: Use Desmos to graph equations and inequalities, offering immediate visual feedback on slope and intercept.

b. Modification and Redefinition (Transformation)

Modification: Redesign tasks using technology

Ex: Students create videos explaining the steps to solve a system of equations using Flip

Redefinition: Create entirely new learning tasks not possible without technology

Ex: Engage students in global math collaboration using tools like Padlet walls or a shared digital space where they analyze patterns in data collected from around the world.

# data[].attributes.body
a. Content Knowledge (CK)

b. Pedagogical Knowledge (PK)

c. Technological Knowledge (TK)

# data[].attributes.body
a. Content Knowledge (CK)

Key topics: linear equations, inequalities, systems of equations, functions, exponents.

b. Pedagogical Knowledge (PK)

Use inquiry-based and collaborative learning strategies.

Scaffold tasks to allow for student exploration before formal instruction (ex: "Notice and Wonder" prompts).

c. Technological Knowledge (TK)

Tools like Desmos, GeoGebra, Flip, Padlet, and Quizizz.

Classroom management platforms like Google Classroom for organizing assignments.

d. TPACK in Action – Sample Unit: Linear Functions

Content: Students learn to graph linear equations and interpret slope and y-intercept in context.

Pedagogy: Use real-world contexts (ex: rate of change scenarios), encourage student-led exploration.

Technology: Students explore linear relationships using Desmos activities like “Marble Slides,” and submit reflections on Flip.

# data[].attributes.body
Different Conceptual Visualization!

I'd love to use Desmos activities for students to experiment with graphing and transformations in real time, such as exploring slope, to have a more engaging, fun way to learn concepts.

I also think GeoGebra for geometric representations of algebraic ideas (like parabolas or transformations) can also be enjoyable and helpful for students to see

Promote Inquiry

ASU has majorly focused on taking any opportunities we can to involve inquiry and discovery opportunities, and I feel online software can greatly expand on this

Students can also use graphing software to test hypotheses about systems of equations or quadratic behavior.

Enhance Creativity and Teamwork

I can create group tasks where students create mind maps connecting vocabulary, examples, and strategies that allows them to see their peers' thoughts as well

Students can record tutorials explaining factoring or completing the square, then provide peer feedback.

Flipped Classroom Opportunities

If students complete a lesson in their own time, I can use class time to address misunderstandings and apply knowledge to deeper problems.

Students can prepare for in-class stations by reviewing content through interactive apps or videos at home that I created or use outside sources for.

Additional Resource: https://www.edutopia.org/article/effective-technology-use-math-class/

# data[].attributes.attachment_link.readable_text
Ensuring that the technology we bring into math classes fosters active engagement is key.

Incorporating technology in mathematics classrooms enables educators to craft powerful collaborative learning experiences that support problem solving and flexible thinking. With strategic integration of both content-specific and content-neutral technology, students and teachers can construct their learning together in authentic ways that elevate mathematics learning.

Until recently, one of educators' primary concerns around educational technology was the lack of access that existed in many American schools. That gap has decreased, but a new digital divide has emerged: The updated 2017 National Education Technology Plan explains that in today's classrooms many students are using technology as a tool for passive learning rather than engaging in active learning experiences that promote student agency.

The Importance of Content-Specific Pedagogy

In order to create technology-infused experiences that support active mathematics learning, educators must of course have pedagogical content knowledge (PCK)-an understanding of best practices specific to mathematics.

One method a teacher can use to analyze the effectiveness of technology integration is the Technological Pedagogical Content Knowledge (TPACK) framework. This tool supports careful educator reflection on pedagogy, content, and technology not only as separate entities but as overlapping and intersecting domains.
Reproduced by permission of the publisher, ©2012 by tpack.org
For example, when planning to integrate technology into a lesson, educators can take into account the technology knowledge the students will need, the mathematics content knowledge they'll need, and the best practices for teaching both the technology and the math. This process is extremely important because without it, the technology may be integrated in a way that is pedagogically inappropriate for mathematics instruction.

Using PCK to Spot Unhealthy Apps and Websites

Teachers start from their understanding of PCK, or best practices for mathematics instruction, in choosing effective technology tools for the mathematics classroom. We know that mathematics should not be focused on speed or quick answer finding. And timed fact testing is a known trigger of math anxiety, which can lead to low mathematics achievement and mathematics avoidance. Yet math apps and websites that focus on speed and rote memorization are readily available and widely used.

This use of technology can promote fear and stress, and it also sends inaccurate messages about the purpose of mathematics. Math is about thinking deeply, discovering patterns, and making connections. Automaticity with math facts and math skills is critical, but how we get students to automaticity matters. A focus on memorization without understanding promotes a joyless, nonsensical form of mathematics that requires remembering a large amount of seemingly disconnected information.

In addition, technology that simply transfers a gradual release-the "I do, we do, you do" structure-to an online format is a form of passive learning that strips math of student agency and rigor. Although gradually releasing responsibility is an effective model in other content areas, in mathematics this model is best flipped to give students the agency to decide what strategies they want to use and how they might solve a problem.

That's because students should productively struggle with math. We need them to problem solve rather than learn to repeat a specific list of procedures given by the teacher. Problem solving skills are more valuable than memorization, and they're the true work of mathematicians. If we're integrating technology into our classrooms to engage students in real-world experiences, our students must be given opportunities to do real mathematics.

Technology That Fosters Deep Mathematical Thinking

When used appropriately, both content-specific and content-neutral technology can be effective in the math classroom. Research indicates that content-specific apps and websites that focus on math learning with the use of virtual manipulatives are highly effective, and in some cases more efficient than physical manipulatives.

The Math Learning Center, for example, provides several manipulative options, such as rekenreks, geoboards, number lines, and number frames. Apps and websites that provide these types of virtual tools are easy to use, support students with conceptual understanding, and increase student access to math tools.

Content-neutral technology includes tools such as virtual whiteboards, handheld clickers, and student collaboration apps. Virtual whiteboard and websites, such as Explain Everything, promote self reflection, enable students to make their learning visible and share and connect ideas, and have been linked with high-level student thinking and teacher questioning.

But content-neutral technology that promotes fast answering, such as handheld clickers, is associated with decreased cognitive demand, most likely due to the likelihood of being used with minimal student discourse.

Being a Critical Consumer of Technology

The educational technology market is flooded with new apps, tech tools, and gadgets, and in some instances, teachers are commended for increased technology use whether it supports healthy math learning or not. Technology can have a truly positive impact on student learning, but it should not replace teaching or ignore research-based best practices for math instruction.

If we believe that students of mathematics need opportunities for discussing math, creating and connecting visuals, analyzing models, discovering patterns, and making generalizations, the technology that we introduce into our classrooms should match those values.

There was a time when simply getting technology into the hands of our students was a goal, but the time has come to slow down and plan for technology integration that truly supports healthy and productive mathematics learning.

# data[].attributes.attachment_link.description
Ensuring that the technology we bring into math classes fosters active engagement is key.

# data[].attributes.body
a. When I Will Use Technology

When I start teaching Algebra 1, I plan to use technology to help students explore big ideas. For example, when we get to graphing parabolas or linear functions, I’ll use tools like Desmos so students can play around with parameters and actually see how the graph changes. It’ll make those abstract ideas feel way more concrete.

I’ll also use tools like Formative or Quizizz to check for understanding. I want students to get instant feedback, and I’ll use their responses to figure out which concepts we need to revisit. It’ll make formative assessment feel more like a conversation than a quiz. I can also do this through game-like activities as well that shows me how much they understand!

Whenever I’m designing lessons where inquiry or exploration is the focus, I’ll bring in tech that lets students experiment. I want them to be able to ask “what if?” and use the tools to figure it out on their own.

b. When I Won’t Use Technology

When I’m introducing foundational skills like solving basic linear equations, I’ll probably lean more on hands-on practice or even manipulatives. I want students to focus on the process without screens pulling their attention away.

There will also be moments when students just need a break from tech. Maybe we’ll do a whiteboard round-robin, a math talk, or a gallery walk. I think switching things up like that will keep students engaged and give them different ways to connect with the content.

And honestly, if I find that a tech tool is adding confusion instead of clarity, I won’t use it. I’ll always ask myself: Is this helping my students learn better? If the answer’s no, I’ll go with something simpler that gets the job done. I want to teach in a way that is fun, engaging, and relatable to my students.