1. Mathematics- Module C Diana Roscoe & Crystal Lancour
Using A Comparison Tool to Inform the Path Forward for the Delaware Mathematics Community
Mathematics- Module C
Diana Roscoe & Crystal Lancour
Welcome to mathematics session for Module C designed to share a few key findings from a recent comparison of the CCSS to our DE standards and GLEs. These findings will help to inform the path forward for DE mathematics educators.
Welcome
Back!!

2. ACHIEVE’s Comparison Tool
Math specialists from districts, charters, and the University of Delaware joined the Department of Education math associates in a process that compared the Common Core State Standards (CCSS) with the Delaware Standards. This group of educators used the newly developed web based technology tool from ACHIEVE to first identify the grade level expectations (GLEs) that aligned with the CCSS, rate the match, identify possible grade level shifts, and record notes regarding the alignment. Then a report was provided in order to analyze the comparison of the two standards documents.

3. Math Common Core State Standards Analysis
While 92% of the Common Core MATH standards were matched, or aligned, to DE’s standards, it is important to take a deeper look at these matches and examine the strength of the match (as - excellent, good, or weak), as well as possible shifts across grade spans or grade levels. Consider that some grade-level differences may include instances where the DE standards might introduce a concept before or after that same content is introduced the Common Core. These differences will have implications for classroom instruction, professional development, curriculum materials, and assessment in DE.

4. Content Alignment – (Single Match)
Common Core Standard
Delaware GLE
Grade Difference
Match
CC.7.SP.2 Use random sampling to draw inferences about a population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
DE Analyze: Analyze a representative sample to make inferences about a population -1
3 = Excellent match between the two documents
As the DE team completed the comparison, one observation noted was that for most grade levels over half the DE GLEs were an “excellent match” to a Common Core standards bullet. There are two ways to rate an alignment as excellent. As demonstrated here, the content in one Common Core standard aligned well with one DE GLE.

5. Content Alignment – (Multiple Match)
Common Core Standard
Delaware GLE
Grade Difference
Match
Note
CC.K.CC.1 Know number names and the count sequence. Count to 100 by ones and by tens.
DE.K.1.2 Number sense: Connect number words and numerals (up to 10) to the quantities they represent using various physical models and representations
3 = Excellent match between the two documents
In Gr. K DE requires counting to only 10 and in Gr. 1 to 50. However DE Gr1 requires also skip counting by 2s and 5s in addition to 1s and 10s and also addresses sequencing numbers to 100 in Gr. 1.
DE Number sense: Count sets of objects up to 50 by 1s, 2s, 5s, and 10s -1
DE Number sense: Sequence numbers and explain which is larger, which is smaller, and what is between other numbers up to 100
Another way to rate an excellent match is by aligning the content of one Common Core standard to more than one DE GLE. Notice that any one of these three DE GLEs does not capture the full meaning of this Common Core standard. However, when grouped together, all three DE GLEs result the same conceptual understanding for students.

6. CC Standard - Not Matched to DE
Common Core
Delaware
CC.9-12.N.VM.4 (+) Perform operations on vectors. Add and subtract vectors.
None…
Some DE high school GLEs did not align to CCSS content. DE design teams wrote their high school GLEs for all students. They focused more on problem-based goals and less on abstract mathematical structure. The DE GLEs promote the development of procedural fluency through contextualized problem solving. The only occurrences of a “no match” to CCSS happens in the high school grade band.

7. How do our DE GLEs compare to the Common Core in high school?
Some formal topics in HS are intended for accelerated students and are labeled as STEM. These are indicated in the Common Core document by a ‘+’ symbol. This graph represents the alignment ratings of DE high school GLEs to the CCSS excluding the STEM content.
High School Common Core standards will add focus on structure and procedural fluency for all students in the Function and Geometry strand. The CC standards that did not match DE high school GLEs are in the areas of: polynomial operations; formal function notation; proof function theorems; geometric constructions; modeling circle symmetry; and conic sections.

8. How do our DE Math standards compare to the Common Core at each grade K-8?
This graph represents the alignment ratings of DE GLEs in grades K – 8. Some grades demonstrated a stronger content alignment than others. Please take a moment to make some of your own observations.

9. Content Alignment – (Multiple Match)
Common Core Standard
Delaware GLE
Grade Difference
Match
Note
CC.K.CC.1 Know number names and the count sequence. Count to 100 by ones and by tens.
DE.K.1.2 Number sense: Connect number words and numerals (up to 10) to the quantities they represent using various physical models and representations
3 = Excellent match between the two documents
In Gr. K DE requires counting to only 10 and in Gr. 1 to 50. However DE Gr1 requires also skip counting by 2s and 5s in addition to 1s and 10s and also addresses sequencing numbers to 100 in Gr. 1.
DE Number sense: Count sets of objects up to 50 by 1s, 2s, 5s, and 10s -1
DE Number sense: Sequence numbers and explain which is larger, which is smaller, and what is between other numbers up to 100
Let’s refer back to the earlier example of an excellent content alignment/match. Although the content is aligned, it may now be introduced at a different grade level.
Grades K-5 will experience a shift from including a study of algebraic foundational concepts such as patterning, statistics and probability to a more in-depth focus on number and geometry exclusively. Many of the mathematical concepts taught in grades K - 8 are shifted one to two grade levels below where they are currently introduced and/or mastered in Delaware.
Think about what that might mean for adoption and implementation of the new standards. Consider the implications for classroom instruction, professional development, and curriculum materials in your school/district. The Common Core Standards that were not matched to DE GLEs or that change grade levels will be helpful in determining next steps with respect to adoption, implementation, and DCAS item development.

10. Over 15 states have already adopted!
We are not alone!
Over 15 states have already adopted!
The Common Core State Standards Initiative began in 2009, when 48 states, 2 territories and the District of Columbia signed a memorandum of agreement with the Council of Chief State School Officers (CCSSO) and the National Governors Association (NGA). They committed to a state-led process to establish a single set of clear educational standards for ELA and mathematics that states can share and voluntarily adopt.
This session has highlighted key findings from the comparison conducted between the CCSS and the DE GLEs for mathematics. Teachers in DE will become a part of local, state, and national collaboration to effectively implement the common core standards. Success as well as barriers to success will need to be analyzed and problem-solved on a large, collective scale. As you finish Module D and continue to work in Professional learning communities, you will dig deeper into these CCSS and help to design our path forward.