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
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
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