This page will address the following questions:

What does Deep Conceptual Understanding mean in math instruction?

Developing a deep conceptual understanding in our students means teaching more than how to get the answers. Instead, we need to support students' ability to access concepts from a number of different perspectives. We need to convey to students that math is more than memorization and procedures. The goals is for all students deeply understand and be able to operate easily within a math concept before moving on. We need students to demonstrate deep conceptual understanding of core math concepts by applying them to new situations and by writing and speaking about their understanding.

An EngageNY video on Mathematical Instructional Shifts 2-6. The discussion of Shift 4, Deep Conceptual Knowledge, takes place from 21:34 to 25:15

What can I do, as a teacher, to help my students develop a deep conceptual understanding?

• ask yourself what mastery/proficiency looks like for different math concepts 
• spend time to deepen your own understanding (see links below)
• address the 8 standards of mathematical practice daily (though you do not to engage all 8 everyday, some of the 8 should be part of every problem and activity)   
• develop the 8 practices of math practice in your class as a way to help students understand that math requires more of them than memorizing and repeating a procedure 
• incorporate problem-based, student centered activities 
• engage students in tasks before it is modeled
• get comfortable and flexible with your own depth of content knowledge. You don't need to know all the ways that student might do it. You can keep learning by testing the soundness of student work (teaching them how to do the same) 

How can teachers deepen their own conceptual understanding of math?

• The Content Progressions for the Common Core Math Standards

The Common Core State Standards in Mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels. These documents can be very helpful for teachers when planning lessons because they identify common student misconceptions. Teachers should choose problems that draw out these misconceptions, so that they can be explored. In addition to describing common student misconceptions the content progressions offer pedagogical suggestions for dealing with those misconceptions. They are also helpful in helping teachers develop their own conceptual understanding.

• Deepening Teacher Conceptual Knowledge of Foundational Mathematics