Common Core vs. NCTM Standards & Focal Points

Common Core vs. NCTM Standards
Going through the 3rd grade Common Core standards I noticed that there seemed to be large gaps and differences as compared to the NCTM Standards grades 3-5. Just looking at the standards for both, it is obvious that each group finds a need to focus on Numbers and Operation since these are the largest sections of both. From there in the NCTM Standards, other areas such as measurement and geometry have a similar number of expectations. However, in the Common Core Standards this is not the case.

Review number and operations, I noticed initially that both groups find that multiplication and division are important for students to understand and represent in a variety of ways. A big difference is where the NCTM standards also include the continued use of addition and subtraction as a strategy of multiplication and addition and the Common Core Standards do not. The CCS focus on using number lines to develop understanding of number and addition/subtraction are only during development of place value to 1000. The NCTM standards would like an in-depth look at fractions using a variety of models such as parts of a collection, as locations on number lines and as division of whole numbers. The CCS only uses the number line and once mentioned using a visual fraction model to teach students about fractions. There are other areas not mentioned in CCS but were in the NCTM standards, such as estimation, decimals, and understanding the effects of multiplying and dividing whole numbers.

The algebra standards for NCTM focuses on understanding patterns, relations and functions, representing and analyzing mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contexts. The CCS only had standards related to represent and analyze mathematical situations and structures using algebraic symbols. The other areas of algebra were not mentioned.

The geometry standards for NCTM focuses on two and three dimensional shapes by analyzing the characteristics, describe spatial relations, apply transformations and use visualizations to solve problems. The CCS standards only focused on two-dimensional shapes and the attributes of those shapes. For measurement, the focus for the CCS is on volume, perimeter, area and time. The NCTM standards looks at weight and temperature in addition to the ideas listed in CCS. As for data analysis and probability, CCS only mention students creating and reading bar graphs, picture graphs and line plots. There is no mention of students collecting data or any probability, which is discussed in the NCTM standards.

As for NCTM’s problem solving standard, communication standard, connections standard and representation standards there was limited mention of these in the CCS. The CCS does mention mathematical practices that include some ideas from the NCTM problem solving and communication standards. However, there is no mention of any ideas from NCTM connections and representation standards.

Curriculum Focal Points vs. Common Core
Reviewing the 3rd grade Curriculum Focal Points as compared to the Common Core Standards, I found that there were a lot of similarities. Actually, it looked as if the Common Core Standards were taken directly off the page for the CFP. Of course, there were a few ideas that the common core standards did not have, such as estimation or congruence and symmetry, but overall they are quite similar.

I do have one concern. These CFP are recommendations of what should be focused on and as I understand them are not meant to be the only ideas taught in the third grade. The CFP was created as a suggestion to curriculum developers, not standards developers. The Focal Points are focuses not all that needs to be learned. Also, they should be addressed in contexts that encourage problem solving, reasoning, communication, making connections, and designing and analyzing representations. This is something the CCS are certainly not doing.