Common Core Mathematics standards

First of all, let's look at the Standards for Mathematical Practice in the Common Core Standards for Mathematics...  There are 8 overall standards:

1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning

These standards are what administrators/teachers WANT children to do.  This, I suppose, is the GOAL of the education.  So, let's look at the specific goals for Kindergarten math...

In Kindergarten, instructional time should focus on two critical areas: (1) representing, relating and operating on whole numbers, initially with sets of objects; (2) describing shapes and space.  More learning time in Kindergarten should be devoted to number than to other topics.

 Ok, fine.  So they want kids to know what numbers are, what written numbers look like, how to relate small numbers (0-10) to objects to written numbers (the number "5" to 5 eggs, etc.), and they want kids to get a handle on general geometric shapes (triangles, squares, etc.) and relate them to real-life objects.  Sounds fine.  The rest of the standards are separated into sections:

• Counting and cardinality
• Know number names and the count sequence (up to 100)
• Count to tell the number of objects
• Compare numbers
• Operations and algebraic thinking
• Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from
• Number and operations in base ten
• Work with numbers 11-19 to gain foundations for place value
• Measurement and data
• Describe and compare measurable attributes
• Classify objects and count the number of objects in each category
• Geometry
• Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres)
• Analyze, compare, create and compose shapes

 There are grade-level overviews for every grade, K-5.  I have read through K-3 in detail, and they're all pretty much the same, building on what the children should have learned the previous year.  I think the separate sections of the standards (counting, operations, etc.) are pretty straightforward and reasonable.  Sure, Kindergartners should be learning place value in the teens.  Yes they should be identifying geometrical shapes and drawing triangles and squares.  What I don't clearly understand is how the specifics relate to the 8 overall standards mentioned above. 

Let's take the first standard as an example.  "Make sense of problems and persevere in solving them."  The text goes on to say

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.  They analyze givens, constraints, relationships, and goals.  They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.

 So, is the goal to teach this kind of thing to younger children, in elementary school?  I definitely don't remember analyzing math problems in such a way until high school.  Further...

They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution.  They monitor and evaluate their progress and change course if necessary.  Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need.  

I can't think of anyone that I know who approaches math this way.  Definitely not in high school or earlier.  Sure, monitoring your progress and changing course if necessary is a hugely helpful skill, but most people I knew in my calculus classes in college didn't have it.  As a goal, it is lofty.

Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.  Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem.  Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?"  They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

I don't know if, especially in more complex math, students do check their answers using a different method.   Again, all of these points are lofty goals.  The major problem with these standards as they are written is that they really don't offer any advice in reaching these goals.  They lay out the goals, and then say some things children should be learning in specific grades that are really basic, such as Kindergartners should be counting to 100. 

I don't believe that these standards make math any more "approachable" than it was when I was taught in elementary school.  The goal for proficient students to be able to "model with mathematics" tries to bring math and the "real world" together, but that's about it.  The overall Kindergarten standard says, "More learning time in Kindergarten should be devoted to number than to other topics."  Does that mean to the exclusion of other subjects?  Do these standards take into account that mathematics can be taught right alongside everyday subjects such as baking, or exercise, or traveling, or any number of other subjects?  It is my feeling that topics and subjects are already too segmented in public school, and these new standards do nothing to change that.  Overall, I see a continuation of the status quo.