Math Reflections with Dr. E (April 2021)

As I mentioned last month, I often refer to the IES Practice Guides when I’m reviewing best practices. Originally published in April 2009, Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades was updated last month, and I’ve found myself going back to the document several times in recent weeks. 

IES Practice Guide #26 is a little more targeted than the previous one, as it  “provides evidence-based practices that can help teachers tailor their instructional approaches and/or their mathematics intervention programs to meet the needs of their students.”


Recommended Practice #1- Providing Systematic Instruction 

I think back on the science fiction of my youth and the idea that future humans would be able to take a pill or download a file into our computerized brains and suddenly have infinite skills, knowledge and wisdom. It’s 2021, and while we haven’t yet figured out how to do that, could it have less to do with a lack of technology and more to do with the basic ways in which humans learn?

It was interesting to see systematic instruction was the first of the recommendations and I wondered why? Was it because systematic instruction is the backbone of an effective curriculum program? Or because it reinforces that learning- the ability to retrieve information for use- can only be built one brick at a time? 

Systematic instruction is composed of multiple best practices- layering information- building it the way we do a house- foundation prep, infrastructure, walls, paint, etc. It also means those other best practices are systematically designed with multiple steps adding up to a practice that supports student learning, especially for the struggling student.

That made me reflect on how the TouchMath program has been built layer upon layer, following the manner in which the human brain learns mathematics starting with number sense and building base 10, additive then multiplicative thinking and so on, until students are moving through and beyond algebra. 

Each chunk of knowledge provides the foundation for the next and the instructional practices and learning schema become more sophisticated as the teacher and student more easily retrieve skills and knowledge.

Specifically, systematic instruction at TouchMath includes:

  • Ensuring concepts are built incrementally and intentionally through our scope and sequence
  • Making it easy to dropdown to the foundational skill if a student is struggling with a concept
  • Reviewing and connecting the previously taught and retrievable skills before embarking on a new step at every appropriate opportunity. 
  • Making sure to look at where the student is in their understanding of the concept and if there is any question they have not mastered it in the abstract, providing pictorial and perhaps even concrete representations for the student. 
    • The use of the CRA – build, draw, write or 3,2,1 dimensional representations are critical systematic steps in the development of the concept.

It’s always exciting to me when my thinking on a topic is confirmed by research, and that’s exactly what happened here with the first recommendation (and, as you’ll soon see, with all six!).

How do you incorporate systematic instruction into math? Is this a topic on which you’d like to see us offer a webinar? Let me know! My email is always open ([email protected]).