TIMSS, NAEP, No Surprises

TIMSS was released earlier this year and schools in the United States were alarmed about our performance in relation to other democratic nations. Then the NAEP report came out and we congratulated ourselves for scoring better but still poorly. 
What is wrong with math education in the US? 
I can answer this question in one word. Cohesion. 
The plethora of choices teachers have to sort through from free online curriculum sources and published supplemental and core programs has made lesson planning into the process of choosing content from a variety of sources which are not aligned to each other. 

Cohesion consists not only of standards alignment but also of vocabulary, teaching practices, visual and procedural models and teaching approaches. 
Why does Singapore math have results? Because of Cohesion. 
Singapore Math is a set of carefully planned pedagogical practices combined with materials to support cohesion. 

Take the trajectory of subtraction:
In Kindergarten, students consider taking sets apart, comparing quantities, and taking away. All without learning the algorithm for subtraction, they use concrete objects and real world context to think about subtraction. Finally, at the end of the year, we introduce an abstract symbol (-) that can help us to represent these situations. 

In First Grade, students consider part-whole relationships and the mathematical idea of hierarchical inclusion or the understanding that numbers are made up of smaller numbers inside of them. We use length models to think about comparison and difference.  From this perspective we can consider subtraction using ten frames, towers of ten, and other concrete and pictorial representations. We can then introduce the number bond and the abstract form of subtraction for simple differences. 

​In Second Grade, we are ready to consider subtraction using base ten materials and carefully constructed number strings to consider regrouping physical materials and renaming place values. Each problem is a distinct diagnostic guiding us to gain insight from the problems before and after. 
Consider this series of learning objectives: 
I can tell subtraction stories for "take from" situations.
I can write a subtraction equation using - and =.
I can tell subtraction stories for "take apart" situations.
I can count back to subtract.
I can use number bonds to subtract.
I can write a fact family.
I can relate addition and subtraction.
I can compare two numbers by subtraction.
I can subtract ones from a 2-digit number within 20.
I can subtract ones from a 2-digit number by subtracting from a 10.
I can count back to subtract with 20
I can use addition facts to subtract.


Each I can statement is carefully curated with specific vocabulary and models. Each I can statement builds upon the one before it and leads to the one after it. 
So my question, do you believe in cohesion? I do.