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Numbers Are Radical

Pedagogic Theory
Core Pedagogic Theory

Teaching an activity-based curriculum drives classroom success. In that spirit, this page explains some of my theories and why they are beneficial in the classroom.


Every teacher faces the challenge of finding the "right" materials to complement their lesson plans. Materials are rarely perfect as is. With a little creativity, I can modify or combine materials with a computer and other common supplies. This allowes me to go beyond my budgetary limitations and tailor my lessons to specifically meet students’ needs.


Technology in and outside the classroom is essential to creating an engaging environment. Over the last few years, I have increased on my own knowledge of technology through self-study and university course work. The success of my classroom instruction depends on my ability to manipulate the latest technologies. Outside the classroom, I use a variety of technology and computer programs to write and develop lessons. During any lesson, students use technology in combination with activities such as creating a foldable, practicing new skills, playing a game, or completing interactive notes.

The newest technologies allow us to try things in physical and virtual classrooms that were not possible before. What you use depends fundamentally on what you are trying to accomplish.

Grill and Drill vs. Rehearsal

Because students are usually well engaged for the first fifteen minutes of class, they can recall what they have “taken in” by the end of class. Asking them closing questions is good but will they remember the information 24 hours later? 

The technique of “Grill and Drill” or repeating information to memorize is not effective for long-term learning. I use two types of active rehearsal: rote and elaborative. Rote rehearsal is best when students need to remember exact information such as formulas. A memory or matching game can be used to perform rote rehearsal as well. Elaborative rehearsal is best for learning a process or using prior knowledge to probe into the meaning of mathematical processes.

My teaching goal is to train students to use rehearsal activities. Elaborative rehearsal should be used in the classroom more often than other types of rehearsal. Some examples would be student developed games, interactive booklets, or puzzles. This requires the student to dig deeper into resources and ask questions that are beyond the scope of the traditional lecture or worksheet.




This rehearsal activity helps students gain a more detailed understanding beyond “divide by the reciprocal”. Adding a visual representation that aids students’ understanding and is more likely to be recalled from long-term memory.

After this initial rehearsal, a good elaborative rehearsal would be a game requiring students to work with mixed numbers. Mixed numbers would include the new use of reciprocals and the prior knowledge of mixed numbers.

dividing fractions.png
and Technology

Creativity and technology go hand-in-hand.

Applying creativity to technology will aid in the creation of engaging lessons and materials.

The continued search for technology and training in their use will only increase a teacher’s ability to create engaging lessons and materials.


"There is almost no long-term retention of cognitive concepts without rehearsal"


p. 86, David Sousa, How the Brain Learns, 2001


"At some point in most lessons, students should be up and moving around,
talking about the new learning."

p. 231, David Sousa, How the Brain Learns, 2001​



2010 - present

2010 - present

Time Well Spent

During a learning episode, students remember more information from the first and last 15 minutes. The timespan between the 15 minute intervals must include other rehearsal activities or the information gained is likely to decay.

A form of elaborative rehearsal such as a game, using technology to find information, or a student created crossword puzzle. Modern teacher guides often have more activity options to help with this. I prefer to use the textbooks problems and worksheet for homework practice.


Remember, many worksheets can be quickly tuned into a game, activity, or foldable with a bit of teacher creativity!

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