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news & tips

A collection of helpful articles on teachers and teaching

Don’t Teach Your Dog to Talk: Increasing Retention in Math

Each year as we work to help our students learn new skills in math, it seems that too many of them do not know or do not remember much of what they should have learned in previous years.  As a result, there is a great deal of backtracking, re-teaching and hair pulling.  Making this situation even more stressful is the emphasis placed on standardized tests and the supporting curriculum that students must master.  Instructional time is limited.  So I ask you to stop and think: what can remedy this situation?

While listening to one of my colleagues present material to her social studies teachers one day, something she said really stuck with me.  “I taught my dog to talk,” she told the teachers.  Heads cocked sideways.  Snickers could be heard from the corner of the room.  “I taught my dog to talk,” she repeated.  “He cannot talk, but I taught him.”  This caught their attention.


Who is doing the majority of the work in the classroom?  Where is the energy in your classroom?  If you reflect on these questions honestly and the answer is you, a shift needs to occur.  A teacher’s time and energy is best spent planning and creating learning opportunities for students.  So what type of teaching can help us make this shift?


The 5E Lesson Model was introduced by Roger Bybee.  Originally presented as a model for teaching science concepts, the benefits for the math teacher are equally strong.  Rooted in constructivism, the 5E Lesson Model places the emphasis on students developing understanding of a concept first by drawing on their prior knowledge, then by explaining the concept and finally by applying this information in a new context.


The stages of the 5E Model develop as follows.  First Engage the students.  This can be as easy as presenting a question for them to think about or even showing them an item, picture or diagram.  Get their minds on the topic.  Once you have hooked the students, then provide an experience for them to Explore.  This is not the time to directly teach new material, but to access their prior knowledge and give them a common experience from which to work and to discuss.  Each and every one of your students comes to class with different set of background knowledge.  The Explore provides a common ground for all from which to work.


The Explain stage is where the new information is presented and discussed.  Using the experience from the Explore, guide students through a discussion that allows them to see the new information.  Add what you need to as a teacher to clarify the concept, making sure that the quantity of student talk exceeds that of the teacher.  Once it appears that the students grasp the new information you set them up to learn from the experiences of the Explore, move the students to the Elaborate phase.  In this fourth stage of the lesson model, students apply the new concept in a new setting as they begin to really make sense of the information.  Close out the lesson with the final step: Evaluate.  Formative assessment takes place throughout the lesson, helping the teacher gauge student understanding.  The fifth segment of the lesson model allows both the learner and the instructor to evaluate how well the new concept has been grasped.


What might this look like in the math classroom?  Let’s examine an example of how to help students identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.  Engage students with a game of “I have, who has?” using squares and square roots.  Have students Explore a quadratic function machine using a program such as Geometer’s Sketch Pad to examine integers that form a Pythagorean triple.  For the Explain, students work through solutions to the equation


x2 + (x+1) 2 = (x+2) 2


with the assistance of the teacher who guides them to understand the quadratic function machine they explored.  In the Elaborate, students work in groups to solve a set of problems of increasing complexity.  To Evaluate their understanding, students solve a series of three problems similar to those presented in the elaborate, but this time they work alone.

The power of the 5E lesson comes from the Explore.  One of the teachers I coached offered the best explanation I have heard as to why the Explore is so valuable.  He made an analogy to water flowing down a river.  The Explore is like a rock in the middle that catches objects in the water that might otherwise float on by.  The common experience provides the brain a place to attach the new information and vocabulary. 

There are variations on and loops within the 5E Lesson Model teachers can apply once they become skilled in its application.  As you work to learn how to use this model, I offer you a few words of caution.  A 5E lesson may take several days to work through.  Rarely, if ever, can a 5E lesson be taught within a single class period, even if you are teaching on a block schedule.  Secondly, try to keep from telling students new information until you are well within the Explain.  Allow students to work through the Explore and figure out what is being presented. 


Have students do as much of the explaining and talking as you guide them to understand.  The goal is for the students to make sense of the information for themselves. 

Shifting from a more traditional teaching method to the 5E Lesson Model takes time and practice.  Having students construct their own learning promotes retention and understanding, and avoids those situations in which you teach your dog to talk.


Anne Douglas is Dean of Instruction for Sam Houston Math, Science and Technology Center, a comprehensive high school in Houston, TX.

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