[Note: Based on feedback from readers, it seems this post needs some context. This is part of a series on exploring a new number system in a course for preservice elementary teachers. The purpose of this unit is to provide these future educators with an experience of what it is like to learn concepts of number and operation using a conceptual approach. In this final post of the series I describe the days leading up to the unit's final assessment. You can see the entire series by clicking on the Wumania tag at the bottom of the post.]
As we near the Wumanian number system assessment, some of the preservice elementary teachers express concern about their ability to demonstrate their fluency in computing with multi-digit numbers. I suggest that they consider putting the expressions into context using one of the Cognitively Guided Instruction stories types presented in the article, Using Student Interviews to Guide Classroom Instruction: An Action Research Project (PDF). We also try connecting the stories to manipulatives (the blocks introduced at the beginning of the unit - see below) using the approaches presented in Teaching without Telling: Computational Fluency and Understanding through Invention (PDF) and Second Graders Cirumvent Addition and Subtraction Difficulties (NCTM). In the process, I explicitly point out my use of practitioner journals to inform my instruction.
As we near the Wumanian number system assessment, some of the preservice elementary teachers express concern about their ability to demonstrate their fluency in computing with multi-digit numbers. I suggest that they consider putting the expressions into context using one of the Cognitively Guided Instruction stories types presented in the article, Using Student Interviews to Guide Classroom Instruction: An Action Research Project (PDF). We also try connecting the stories to manipulatives (the blocks introduced at the beginning of the unit - see below) using the approaches presented in Teaching without Telling: Computational Fluency and Understanding through Invention (PDF) and Second Graders Cirumvent Addition and Subtraction Difficulties (NCTM). In the process, I explicitly point out my use of practitioner journals to inform my instruction.
Because not everyone needs support in this area, I am in the habit of posting on our class website PowerPoint Think Alouds of how I might go about solving some of the problems on this practice sheet.
Learners with access to the internet can download the Think Alouds and watch them at their convenience. This is how those first PowerPoints looked.
With current technological tools, like Jing, here is what I can post now.
These Think Alouds provide the learners who are struggling to apply the approaches they have read about a model of the approaches in action. It also models how teachers can use technology to offer different levels of support to learners. Some might call me the Wumanian Sal Khan, but I can assure you that these productions were not one-take affairs.
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