Remediation should be systematic...

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I have had the wonderful opportunity to work with interventionist and Special Educators all over the world. Each time I get asked, is Singapore math for "my" kids. 

Good intervention needs to be systematic and not just focused on fact fluency. 
There are four main principles of good intervention: 

1. Use of the Concrete to Pictorial to Abstract approach
2. A Systematic approach to number strings
3. A recognition to production to extension approach. 
4. Contextual Relevance

Back in graduate school at Northwestern, when the field of learning disabilities was still in its infancy, my mentor, Dr. Doris Johnson used an analogy of a black box to describe learning disabilities. 

She said, we need to be thinking about the input (how we are giving students the information); cognitive load and processing inside the box (or the student's mind) and the output (how they will communicate their understanding) 

To me intervention lies in the bridges. How can I systematically increase the cognitive load while creating bridges between the Concrete, Pictorial, and Abstract? How can I help students to generalize rather than learn discrete tasks. 

For instance: Grade 3 standard of subtracting across zeros, when given a subtraction story:

1. Does a student recognize when regrouping is necessary? Using tens frames, in the concrete, with numbers less than 20? If I show them 15 -7 can they tell me that they will have to break into the full ten? 
2. Can they produce the regrouping themselves?  Still in Concrete with number less than 20? 
3. Can they recognize when regrouping is necessary with base ten materials with numbers less than 100?  In problems that only require regrouping in the ones place? 
4. Can they produce a regrouping in the concrete with regrouping in the ones place.? 

etc....

As soon as I see an understanding in this trajectory, I quickly move to the next. And by systematically moving through steps, I can help a student to grow not only their understanding of content by their mindset of success.  Ohio has produced some amazing support for breaking down the standards. See them on the Great Teaching Resources pages.