A New Perspective…Non-Negotiables

As math departments we are reliant on programs to set the foundation of our curriculum.  We are reliant because the risk/reward is too great to try and go it alone.  Are we good enough as mathematicians to plan a strong enough sequence to teach students?  Are we strong enough as educators to know the best methods of instruction to access the rigor students need to succeed?  These questions, along with many more, prevent us as teachers from “going it alone.”  So we look for programs that set our sequence.  I wonder though, how many schools consider the things that are non-negotiable.  Those things that are vital to student learning and must be able to continue regardless of the math curriculum.  What are they?

The Non-Negotiables are the foundation of a series of posts that will follow over the coming weeks.  They include rigor that challenges all students at the level  they are at and pushes them farther,  resources that force teachers to engage in best practices in instruction, group work that requires a high level of classroom discourse, and engaging resources that are up to date with real use of images and video.  It also includes opportunities for teachers to differentiate the learning for students.  Whether you are focusing on the mathematical practices as stated in the Common Core State Standards or the instruction based on Charlotte Danielson’s framework supported by most educator effectiveness programs; the non-negotiables don’t change.

Where do we begin.  It makes the most sense to begin with the end in mind.  Not how we teach but what we expect of our students.  Norman Webb created Depth’s of Knowledge (DOK) in the late 1990’s.  It has just taken some time to catch on.  Webb’s DOK is about the complexity of the task.  It contains 4-levels that form the foundation for the expectations of instruction.

  • Level 1:  Recall and Reproduction
    • No rigorous thought beyond remembering the right information.  Although this is changing it is still the area where most math instruction and assessments live.  It also takes the least amount of thought.
  • Level 2:  Skills and Concepts
    • Using the main skills and extending them when a decision needs to be made.  This is the essence of math instruction.  This is where students start to connect their learning.  It is also the area where too many teachers maximize their time in the classroom.
  • Level 3:  Strategic Thinking
    • Justification of an answer is a main component of DOK 3.  This needs to be the focus of our instruction.  We want students to be applying their learning at this level.  These are non-routine situations that require time to problem solve, explain and process multiple conditions of the problem or task.
  • Level 4:  Extended Thinking
    • This level requires research in addition to everything in DOK 3.  Typically, this level takes a significant amount of time.  For all intensive purposes we don’t plan for DOK 4.  If they happen, great.

In the classroom the expectation is that we push the envelope and engage students in questions that make them think.  Questions that make them apply their learning and most importantly explain their thinking using complete sentences.  The problem is that in my time leading this charge it has been painfully obvious that these prompts are not easy to come up with.  Certain teachers have a skill set that includes making prompts that fit a DOK 3 level.  Most do not.  That is why we need a program that supports these levels of instruction.  Most programs offer more rigorous questions that encourage thinking but qualify them as SMARTER Balanced or PARCC questions.  They find their way into a separate portion of the textbook.  A portion, that is very easy to skip.

We need a resource that incorporates these questions not as a section, but as a rule.  The rigor expected of our students needs to increase.  In other words, DOK 3 questions need to be the norm.  They force students to think and explain their reasoning in a manner that will also enable students to retain their knowledge.