I got an email from a reader last week asking about the impact of technology on the CRA sequence of instruction, so I thought I’d blog about it. First, let me remind you that CRA stands for concrete, representational, and abstract. From Van de Walle (pg 99):
“…this model reflects a sequence that moves from an instructional focus on concrete representations (manipulative materials) and models to semi-concrete representations (drawings or pictures) and images to abstraction (using only numerals or mentally solving problems).”
Lots of problems occur when we skip steps in this instructional model or move too quickly through them. For example, before students start practicing with traditional flashcards (very abstract), they need to have lots of concrete and representational experiences to develop understanding.
Van de Walle makes a great point, however, that the stages need to overlap. That is, we need to connect the abstract to the concrete and representational along the way.
“…it is essential that there is parallel modeling of number symbols throughout this continuum to explicitly relate the concrete models and visual representations to the corresponding numerals.”
What this means is that while you are using base-10 blocks to model addition or subtraction with regrouping, you need to also show the connection to the algorithm or students will never move past the concrete or representational stage.
Now back to the original question about technology. Are virtual manipulatives, such as the ones you find at the National Library of Virtual Manipulatives or NCTM’s Illuminations website, concrete learning? My thinking is that virtual manipulatives actually fall between concrete and representational. They are clearly not as concrete as holding manipulatives in your hands, yet because of the interactive nature, they are more concrete than representational. My advice? Use virtual manipulatives, but not to the exclusion of true hands-on learning. Also, consider the age and developmental stage of the child.
|The Factorize interactive activity at NCTM’s Illuminations website|
I think what’s important is that when choosing technology, whether it’s computer programs, websites, or apps, you have to consider the CRA stages, just like you would when choosing any instructional activity.
I hope this all makes sense. I would love to hear your comments!