Episode 193: Beyond the Template – Making the Lesh Translation Model Meaningful

Episode 192 – A Math Task All Teachers Should be Doing

Problems of Representation in the Teaching and Learning of Mathematics edited by Claude Janvier 

I did track down the original source! Lesh, R. (1979). Mathematical learning disabilities: Considerations for identification, diagnosis, and remediation. In R. Lesh, D. Mierkiewicz, & M. Kantowski (Eds.), Applied mathematical problem solving. Columbus, OH: ERIC. 

Welcome fellow Recovering Traditionalists to Episode 193: Beyond the Template – Making the Lesh Translation Model Meaningful

In the last episode I shared about the Lesh Translation Model and an activity you can use with your students centered around that model.  

The Lesh Model is shared a lot but I like to track down original sources.  The first reference of The Lesh Translation Model was in 1979 and I wasn’t able to get that, however I did find the book that most people reference when sharing about the Lesh Model and that is Problems of Representation in the Teaching and Learning of Mathematics from 1987.  The book is based on a collection of papers presented at a symposium.

I read the chapter by Lesh, Post, and Behr, Chapter 4, in which they discuss what is now called the Lesh Model, but what I want to share with you today is from Chapter 16 – Representing Representing: Notes Following the Conference by John Mason.  The Chapters at the end of the book are reactions or responses to the papers and this particular part really called out to me because of last week’s episode:

“As with any framework, there is the immediate danger that what is intended as an attention focuser will turn into a mechanical scheme for generating yet more useless student activity…” he goes on to say “…When other agents attempt to institute frameworks in curriculum, the result is yet more routine exercises for students under the guise of fancy terminology.”

So in the last episode, I’m afraid that maybe I did that by giving you that template to use to do The Translation Task.  I meant to share it as a way to get your attention to focus on the Lesh Model, I don’t want that to become a useless student activity. Today I want to caution you against it becoming a routine exercise that becomes mindless for the students.  Two quick ways exercises become too routine and mindless:

1. You do them predictably at certain times
2. You don’t spend time discussing 

If you downloaded The Translation Task Template, please don’t use it to do something like “Translation Task Tuesday.” Use the template to help build your students’ understanding around a concept or to help you assess what they already know. And when you do use it, make sure you spend time not only discussing what they put into the 5 different representations but what’s really important is spending time discussing how those 5 representations are similar and yet different.  The key is to focus on developing the connections between the different representations.

The Translation Task Template is meant to help you focus, and bring attention to, the 5 different representations. However, The Translation Task isn’t the only way you should be exposing students to the different types of math representations.  It’s just one activity.  You should be including all 5 representations when helping your students develop their understanding of any mathematical topic.

If you want more information about the Lesh Translation Model and The Translation Task Template I’ve link up last week’s episode.

Until next week, my fellow Recovering Traditionalists, keep letting your students explore math, keep questioning, and most importantly, keep Building Math Minds.

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