Common Core State Standards and NCTM Standards

Having compared the Common Core State Standards with the NV State Standards it is interesting to compare CCSS with the NCTM Standards.

Observations of NCTM Standards

NCTM has five content areas of focus: Number and operations, Algebra, Geometry, Measurement and Data Analysis and Probability (likely/unlikely). Expectations of these standards elaborate on concepts expected to be developed through grade 12, though the standards are chunked into Pre-K - 2, 3 - 5, 6 - 8, and 9 - 12. Most expectations do not specify to what degree students should have mastered the material (i.e. count with understanding and recognize "how many" in sets of objects does not dictate to what number). Some of the expectations use distinct language identifying the action the students should be able to accomplish (i.e. recognize, name, build, draw, compare and sort), but provide an overall goal for the student development in the span identified. With each standard is a reasoning and justification for its inclusion in the standards and examples of student work are shared along with e-examples which are practice points. Sample problems teachers can give their students are evident in the standard explanations.

How does this relate to the Common Core State Standards?

Honestly, I feel I would be more comfortable with Common Core than I would with teaching the NCTM Standards. My reasoning behind this is particularly in the specificity. The fact that the NCTM Standards are bundles into a range of grades scares me a bit. It's understandable that these are standards that can be addressed in the span of the grade levels given, but I would feel more prepared to teach if I had a clear idea of what the student in first grade was taught in mathematics so that I may build on that idea or not formally teach that concept again. I am a very step-by-step tell-me-what-and-how-to-do-it type of teacher. I guess the NCTM Standards just seem too general.

What I did notice about the NCTM Standards not present in CCSS was the content of probability in the range I was looking at. I know CCSS introduces the strand in Grade 6, however, I think students need simple probability reasoning experiences early on to build that foundation.

Both standards are spiral curriculums and gaps exist within both documents. While NCTM seems to have a more meaningful mathematics whole-approach to the standards, CCSS clearly lays it out for each grade level. I feel that the content in NCTM is well worth reading but many teachers may look at the bullet points and skim over the details (though that is where the understanding is embedded). There aren't standard numbers in NCTM that identify how to reference where a standard is addressed in another grade rather a strand has a K-12 repeating focus that is then broken down into the smaller components particular to the grade span.

NCTM can be more beneficial to Common Core if it shared some of the research in a supplemental document teachers must read too, because I see value in sharing these findings with the teacher. I appreciate the focus, dialogue and examples in mathematics present in the NCTM standards but find myself more drawn to the formatting of Common Core.

Resources:
NCTM Principles and Standards: Ch. 4 - Standards for Pre-K - 2
Common Core State Standards Initiative: Mathematics

Having just found the document to the NCTM Focal Points by grade I almost regret my statement that there was not enough specificity. The Grade 2 and Grade 1 focal points identify to which place value the students must have understanding of before leaving and I appreciate the break down by grade. Having read this document now changes almost everything said prior. The focal points were not meant to be the standards that are only taught but more or less gives the teacher more clarification of what it looks like in the particular grade. A focus seems to be centered around the practices of making connections and using the standards in the different contexts of problem solving, reasoning, communication, design and analysis of representations. There is specific consideration of how the standards can be tied in with one another in the focal points.

Additional resource:
Focal Points by Grade

Implementing Common Core

Given the following situation I have my response to both scenarios.

As the resident expert in Common Core Standards, your principal has asked you to design an implementation program for your school. Give two scenarios: a dream, unlimited time, unlimited funds scenario, and reality.

Dream Scenario:

In my dream scenario I would have my school host a summer institute, with extra pay, before the school year that we plan to execute the new standards. The summer institute would focus on reading the standards, establishing acceptable assessments, thinking of units of study that would integrate the standards into a series of lessons and/or finding materials which complement the standards, and designing a curriculum map for a school year.

The focus on the reading would be for the teachers to find the big ideas of content. The teachers would gather as grade-level teams and thoroughly read the new standards discussing any questions they may have. After having read the standards, the teachers would then set benchmark goals for their students so they reach mastery by the end of the year. These benchmark goals would lend itself to the following discussion on assessments.

The second conversation about Common Core would be to establish both formative and summative assessments. The teams would pull together their resources, or create their own assessments that they feel are suitable in addressing each standard. A rubric will be developed as a standard of reference for each assessment or a universal rubric will be decided on. These assessments will be benchmarked on a curriculum map.

In preparation of the curriculum map, the teachers will gather together and decide as a team how they want to teach the standards. Using our current math program, Investigations, the grade levels will choose whether they want to teach particular units because they’ve worked well in the past and align with Common Core, or if they want to supplement the program with something more appropriate. This is where the lesson planning and units of study designing will take place. Having this conversation may take the most amount of time because the teachers have to find teaching grounds they all feel comfortable with and also feel is best for the students. A great brainstorming time will take place and teachers, perhaps cross-grade-level, will have a share time on how they perceive their teams designing units of study. Each grade-level team will decide at this time on at least one standard they’d like to present a lesson study on. A lesson study is a professional development process that examines teaching practices with the goal of becoming more effective. Teachers collaboratively plan, one teaches, all observe and all critique a lesson. Our school has had experience with this and knows the protocol. This will be ongoing throughout the year as we practice the new Common Core State Standards.

Lastly, the professional development in regards to the roll out of the new standards will expect the teams to develop a curriculum map. This map will focus on math and serve as a pacing guide for each teacher. Curriculum maps will include vocabulary, Kathy Richardson Stations, the standards, benchmark dates and relevant text alignments. All the lesson study planning and use of current math program and supplement materials will be presented on this curriculum map.

Ideally, all teachers would be “on board” to this idea. Funds would available to compensate the teachers for this extra time they are putting in. If unit studies require more funding it will be supplied so long as it is rational. Teachers would be given technology such as laptops, smartboards, elmos and computer programs as needed. Substitutes would be brought in for Lesson Study planning, execution and debriefing. All would be excited for the new standards and would continue sharing ideas as we learn and adapt to this new way of teaching.

Reality Scenario:

In reality, teachers may only be compensated up to two days considering the funding. The two days would be spent reading the new standards and finding the gaps in our current math program that do not address the standards. Units of study in Investigations would be realigned to match Common Core and teacher would have to pull together resources or design their own for the gaps. A new curriculum map would be designed around the standards and will include vocabulary, stations, texts and lessons. Teachers would establish appropriate assessments and design new ones for the lessons they’ve chosen to fill the gaps. Grade-levels would just have to “make it work with what we have”.

Common Core State Standards vs. NV State Standards

Looking closely at the Common Core State Standards I chose to focus on the development of the mathematics within the three year span of Grades 1-3 because I teach Grade 2. Having this opportunity with the current Nevada standards has helped me identify what my students should know as they enter second grade and what they will need before they move on to third. As I compared the curriculum of the CCSS with the NV Standards, I was able to identify differences, similarities and overall goal expectations.

Observations of NV Standards

In my observations of the NV Standards I notice the standards following a spiral curriculum with the content developed in sophistication over time. For example, students identify, model, read and write place value positions of 1s and 10s in first grade (1.1.1), extend this to include 100s in second grade (1.2.1), and further develop this idea to include 1000s in third grade (1.3.1). Many of the standards follow this procedure and are identified by strand indicators. Strand categories in the NV Standards are Numbers/Number Sense/Computation, Patterns/Functions/Algebra, Measurement, Spatial Relationships/Geometry/Logic, and Data Analysis.

Specific quantities are identified for applicable standards such as stating the range of sums students should know, time to nearest minute/hour, fraction denominators and value positions. Verbs are clear enough to understand what is expected so teachers know what their students need to do to show understanding (i.e. identify, read, write, compare, order, generate, model, extend, sketch, describe). I have the impression Numbers/Number Sense/Computation is emphasized since more standards exist within that strand.

From the Perspective of a Teacher and the Mathematics

As a teacher who has only taught using the NV Standards, the development of the curriculum of the NV Standards is simple for me to understand. I appreciate the specific detailing in the way each standard is written and I have few, if any, questions on what is expected. Some of the standards can be integrated together when teaching a lesson which makes it more meaningful to me in my teaching. However, I do feel that there are more standards that stand alone or are disjointed from everything else that it almost seems that the only way it can be taught, in a manner so it can be assessed, is as a mini-lesson. For example, read and write number words to 20 and identify ordinal positions first to twentieth (1.2.3). These standards seem practical in nature, but seem a little out of place in ways of being a report card standard/grade.

The mathematics progression of the standards seems to err on the easy side. Like my principal says, the standards and those that will be tested are the "floor" and the minimum of what students should understand. Because they're stated as grade-level standards, I feel that many teachers choose to teach just those concepts in order to feel like they have covered the material and expectations. Place value makes sense to me and I do not argue with the development of it over the three year span. What I would like to see more of in terms of the mathematics is a connection between ideas and deeper algebraic concepts. The students are capable of algebra and problem solving at a young age and think it should be included in the mathematics curriculum.

Observations of Common Core State Standards

In the CCSS the standards follow the spiral curriculum. Each idea is brought into more depth as the students progress through school. For example, the second grade standard in add and subtract within 20 is for students to "fluently add and subtract within 20 using mental strategies…" (pg.19) A footnote references a first grade standard, 1.OA.6, for a list of mental strategies; thus, clarification is given and specifically refers back to a concept taught in the previous year.

Quantities are identified for ranges of computations and specific examples are used with some standards as an illustration of what is expected (i.e. "for example, determine the unknown number that makes the equation true in each of the equations 8 x ? – 48, 5 = __ / 3, 6x6=?" pg.23) Several standards reference the Glossary at the end of the document which provides clarity of the language and additional information such as examples to use and definition of terms. Table 1 is formatted in the Cognitively Guided Instruction (CGI) framework and offers practical word problems.

Standards are presented in four strands, Operations/Algebraic Thinking, Number and Operations in Base Ten, Number and Operations – Fractions (3rd grade), Measurement/Data, and Geometry. Each strand is expanded into an overview of the strand, and further divided into examples and objectives. The verbs in each standard are more application based in nature such as use addition and subtraction to, solve, apply, understand as, relate, determine by relating, interpret, distinguish, compose, partition. Emphases in content (based on the number of standards dedicated to that strand) change with each year. First grade has more emphasis in Operations/Algebraic Thinking, second grade focuses on Measurement/Data and Geometry, and third grade emphasizes Operations/Algebraic Thinking.

From the Perspective of a Teacher and the Mathematics

As a teacher, I think the CCSS appear to be more challenging to teach. More thought needs to be activated in planning and execution because the standards are embedded with connecting ideas. Coming up with assessments of these standards will require careful planning because the standards ask the students to use application techniques in their problem solving.

To make a connection to literacy, I see the CCSS to follow more of a "whole-language" approach as opposed to phonics; so in this content, the concepts are more cohesive and teach an overall idea and then come back to fill in the detailing, instead of being detail focused. Specifically, I found in Second Grade Geometry (2.G) students "partition rectangles into rows and columns of same-size squares and count to find the total number of them" (pg.20) and later (3.G) use these partitions to express area. Concepts are introduced and then later identified with a vocabulary word.

From the perspective of the mathematics, I am satisfied with what is expected to be taught to the students. The concepts are practical for the students at their age and developmentally appropriate to stimulate deep thinking. As mentioned earlier, the emphases in strands vary with the grade level. I think the reason for this is the maturity of the student and their capabilities. While students in Grade 1 might focus on Operations, Grade 2 students will focus more on Geometry because spatial understandings might be more developed at that age. There seems to have been more thought in this regard. Properties of operations are introduced at a young age and I think making a point of it helps the little ones begin to make connections with their ideas about algebra.

In conclusion, the NV Standards and CCSS have similarities in what is deemed appropriate; in some examples, the progression of place value, time and fractions. Differences occur in placement of introduction to ideas such as skip counting and understanding coin value. Some concepts, altogether, are not mentioned such as calendar, estimation, patterns and ordinal numbers (standards represented in NV State but not in CC). It is difficult to really compare the two otherwise because the NV State Standards are very specific standards and the Common Core State Standards are broad but encompassing. Both have their pros and cons and gaps can be found in both. As everything else, I expect the CCSS to be revised as it becomes more practiced.

Surprisingly, I find myself to be more in favor of CCSS than I had expected. I feel like I understand the direction the developers chose to take in the construction of these new standards. The "whole-math" concept appeals to me as something that can be attainable with a challenge. I believe with attentive inspection of the standards, and careful planning, the conceptual understandings and achievement of our students as mathematical thinkers can be profit from the Common Core State Standards.

Resources:
Common Core State Standards >> Mathematics
Power Standards K-12 CCSD >> Mathematics