When I choose to use technology in my math teaching, I want to be sure that the technology tool supports the learning, and helps students to develop conceptual understanding. The Action-Consequence-Reflection cycle is one structure that I use towards this goal. I’ve written about Action-Consequence-Reflection activities before, in **this post** and **this post**, and I recently had an article published in the North American GeoGebra Journal, “**Using Action-Consequence-Reflection GeoGebra Activities To Make Math Stick**.”

In the Action-Consequence-Reflection cycle, students

- Perform a mathematical action
- Observe a mathematical consequence
- Reflect on the result and reason about the underlying mathematical concepts

The reflection component is, in my view, the critical component for making learning deeper and more durable. The article includes the following six activities that use the cycle to help “make the math stick” for students. Each of the GeoGebra applets is accompanied by a lab worksheet for students to record their observations and answer reflective questions.

**EXPLORING GRAPHS & SLIDERS:**

The first two activities use dynamic sliders so that students can make changes to a function’s equation and observe corresponding changes on the graph.

In Power Functions, students control the exponent n in the function , and can toggle between positive and negative leading coefficients.

In Function Transformations, students investigate the effects of the parameters *a, h,* and *k* on the desired parent function.

**INTERACTIVE VISUALIZERS: **

Using the power of visualization to deepen understanding, the Domain and Range applet highlights sections of the appropriate axis as students manipulate linear and quadratic functions.

**UNDERSTANDING STRUCTURE:**

In the Rational Functions activity, students explore how the algebraic structure of functions relates to important graph features. The handout includes extensions allowing investigation of other rational function scenarios not already covered.

**INVESTIGATING INVARIANTS:**

The last two activities have students looking for invariants—something about the mathematical situation that stays the same while other things change.

In Interior & Exterior Angles, students investigate relationships among the angles of a triangle and form conjectures about the sums that do and don’t change as the shape of the triangle changes.

In Right Triangle Invariants, the applet links the geometry figure to a numerical table of values, and students discover several invariant properties occurring in right triangles.

**PLANNING FOR REFLECTION:**

Simply using these robust technology activities will not guarantee student learning and conceptual understanding; it is imperative that we as teachers plan for reflection by including focusing questions, discussion of students’ mathematical thinking, and clear lesson summaries with the activity. Use the provided lab worksheets or adapt them for your needs. Capitalize on the power of the Action-Consequence-Reflection cycle to make the math stick for your students’ success!

**Notes and Resources:**

This post contains excerpts from the full article (pdf available **here**) from Vol 7 No 1 (2018): *North American GeoGebra Journal*.

The *North American GeoGebra Journal* (NAGJ) is a peer-reviewed journal highlighting the use of GeoGebra in teaching and learning school mathematics (grades K-16). The website for the NAGJ is **here**.

My GeoGebra Action-Consequence-Reflection applets are in this **GeoGebra book**, or they can found by entering “kdcampe” into the GeoGebra search box. Thanks to Tim Brzezinski, Marie Nabbout, and Steve Phelps for their assistance with some of the GeoGebra applets.