Monthly Archives: November 2018

Action-Consequence-Reflection Activities for GeoGebra

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.


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 f\left(x\right)=x^n , and can toggle between positive and negative leading coefficients. Capture power funct border

In Function Transformations, students investigate the effects of the parameters a, h, and k on the desired parent function.Capture funct transf border


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.Capture DR lin quad border


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.Screen Shot 2018-11-29 at 9.52.52 PM


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.Capture int ext border

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.Capture right tri border


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.


Testing Tips: Using Calculators on Class Assessments

If you’ve been using TI graphing calculators in your teaching, you may have contemplated how to implement the calculators for in-class testing.  Whether you are giving a short quiz, a chapter test, or end-of-term exam, read my post on the TI BulleTIn Board Blog for some tips for how to use TI calculators successfully on class assessments.

Testing Tips: Using Calculators on Class Assessments

There is much more in the full post, but here is a summary:

  • Determine the Objectives: decide which math skills and problems you will assess with and without the calculator.
  • Separate the Sections: separate the calculator and non-calculator problems into two sections.
  • Set up the Handhelds: to be sure the calculators are useful tools for students and don’t interfere with assessing their math knowledge, set up the handhelds for security and equity.
  • Electronic Quizzes with TI-Nspire CX Navigator: take advantage of electronic quizzes if your classroom has the TI-Nspire Navigator System.

Screen Shot 2018-09-07 at 3.57.07 PM

End of Quarter Feedback Is a Two-Way Street

[Note: this is an excerpt from my blog post on the TI BulleTIn Board.]

With the first marking period winding down here in the northeastern US, teachers and students are focusing on the grading process.  How might we make end-of-marking period evaluations into a constructive tool for the teacher AND the students?  Here is one idea…

Rating clipboardAt the end of a marking period, students’ grades indicate their progress and achievement in math class.  It is also a great time to encourage reflection and feedback on what teaching and learning practices have played out in the classroom and what changes can be made so the class is more productive in the future.  Here is how I have turned my end-of-quarter evaluations into valuable conversations about how to make math class better for all of us.


My Four Questions

My students answer these four open-ended prompts.  Names are optional.

  1. Tell me something specific you did well or are proud of this quarter.
  2. Tell me something specific you want to improve for next quarter.
  3. Tell me something you think I did well.
  4. Tell me something you want me to change or improve.

I give students time to reflect and write, and the ground rules are that they can’t say “nothing” and can’t propose major changes like “stop giving homework/tests”.  Because I require them to be specific, they have to find some details about their learning and my teaching to discuss.  Most of the time, students write about things that are actionable in their evaluations.

I feel that this process makes evaluation a two-way street, since students are commenting on me and my teaching but also on themselves.  By asking them to name what they are going to do differently for the coming quarter, I place the responsibility on their shoulders for making changes in their class performance.  The set of four questions opens the door for us to communicate constructively about improving our math class experience for everyone.

What Will You Do?

I’m interested in what other teachers find useful for end-of-marking period feedback.  Let me know what works for you and your students here in the comments or on Twitter (AT KarenCampe).

Notes and Resources:

Some helpful blog posts about End-of-Quarter/Semester feedback are here and here from Sarah Carter (twitter AT mathequalslove) and here from Jac Richardson (twitter AT jacrichardson).  Thanks so much for sharing!

Read the full post on the TI BulleTIn Board:

End-of-Marking Period Feedback Is a Two-Way Street