I teach 4th grade and I love the math I get to teach.  It is really the first year where you get to really work with mental math and look at many strategies to solve problems.  I know there is some of that in primary grades but 4th grade takes so much of that wonderful foundation work that is done in K-3 and moves outward from there.

There is beginning to be a consistency in the literature [Sensible Mathematics included] that is painting a picture of math content knowledge [MCK] that teachers need to teach "sensible mathematics". The characteristics of this MCK build upon the NCTM Process Standards:

• Connections: math, to real situations and other disciplines,
• Communication: the ability to "talk math" to students and understand what students are saying when they talk back to us,
  
• Reasoning & Proof: why, how do you know, can you show me?,
• Representation: use appropriate models,
  
• Problem Solve: have math be in context.

Now to change practices in classrooms and have resources that support this picture.

The non-negotiable skills for the "language of math" is a very thorough and instructive list. It was great to see these skills listed.

At the bottom of page 51 Leinwand lists the goals of which his non-negotiable skills provide a foundation.  The goals are "solve everyday problems, communicate their understanding, and represent and use mathematical ideas."  He claims that anything beyond is "obsolete. . . and no longer valued by society."  Which society?   In U.S.  school settings, the holy grail of mathematics is calculus.  Statistics runs a close second.  One or the other is required by most college programs in science and business, and one needs a whole lot more mathematical literacy than just the basic skills as listed to succeed in calculus and stats.  He hasn't even mentioned irrational numbers (though that may be implied by "using and understanding the number line"), or logarithms (yes, sorry, still an important piece of calculus), or complex numbers, or the concept of infinity and division by zero.  I could go on and on, but what I'm trying to say is that I don't believe we can comment on the appropriateness of his list of non-negotiables without reference to the related goals.  His list is fine for his goals, but insufficient for the goals of many students, especially those headed to 4 year colleges.  

As I read through the list of "basics", I have two competing reactions.  On the one hand, I think that the list is too "basic", that these skills are not enough of a foundation for students.  On the other hand, I think about how beneficial it would be for my students' math success if they actually did have these skills and habits of mind in place.  It is frustrating for my students and for me to work through math workshop where so much of the deeper math is inaccessible because of these obstacles.  It is very difficult to think deeply about a math context when so much of the intermediate pieces are "stumbling blocks" rather than "steps" to the solution.  How best to address thee deficits?  What is the right balance of remediation to instruction? 

After reading the previous posts, I must admit that I would agree with much of what has been said already. Therefor, no sense in repeating any of what was written. As a middle school (7-9^th grade math levels) teacher, I am not as aware of the specific concerns voiced by some of the other teachers at the different grade levels, but acknowledge their concerns.

Although I agree with Steve's non-negotiable's in their purest sense, I believe that we must be a little bit more broad-minded when looking at what is necessary. I believe that algebraic reasoning, estimation, percents, and other areas as listed by the previous respondents need to be addressed as well. Sorry, I did repeat some of what was mentiond before. But, having said all this, I believe that he is on the right track. We must prepare our students for their future and not our past. This implies that they need to have a working knowledge of mathematics, and be able to apply it the most practical real-world situations. I believe the common core standards will help us move forward towards this goal.

I am in great hopes that the new CMP3 materials will be more like the alternatives that were suggested in the reading rather than the traditional approach to problem-solving we have now. Right Shawn?  :-)

In conclusion (cause I'm sick and at home), I believe that the nonnegotiable's need to be addressed in a real sense, that the practices of common core be emphasized on a daily basis, and computation fluency be reinforced. My simplistic, but practical, response. Back to bed!