Generating Initial Codes:
When developing the codes for Algebraic Thinking, the first step I took was accessing the NCTM Standards. I downloaded the standards and wrote down the different standards that were listed. I knew the standards were grades 3-5, but I felt that each standard could be addressed at each grade level, but not as in-depth as in the 5th grade. From there, I looked at CCSD standards and Common Core standards. I found a few additional 3rd grade standards from CCSD and nothing new from Common Core (in the sense that Common Core standards didn’t have anything new that NCTM or CCSD had listed). From there, I took the standards and tried to organize them in a logical way. So, I referred to the resources received from the Algebraic Summer Course and used equalities, relational thinking, conjectures and proof as my concepts. Then, I placed the standards within each of the concepts.
While developing the codes I did consider general topics that third grade students may come across and found my codes to be pretty much complete. I did not closely think about specific examples that typical third grade students may come across. This created holes within my coding and made it incomplete. When going back and revising the codes, I need to be thinking about what specific types of examples students may come across in a variety of texts.
Feelings of Experience
Initially, I did not feel too frustrated by this experience. I tried to use Dr. Olson's example to guide my own coding. It wasn’t frustrating until I posted it and Dr. Shih brought to my attention the lack of completeness. I believe this task would have been easier if I did go through the NCTM algebraic thinking document a bit closer because this document gives examples of the types of thinking students would do with these standards. This may have made my coding more complete. From this process, I did learn the NCTM Algebraic Thinking standards. I knew they had the standards, but I was not quite aware of what they were exactly. In addition, I learned that I need to learn more about algebraic thinking. I have a limited knowledge and need to make it more complete to create my coding.
Saturday, October 16, 2010
Saturday, September 25, 2010
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.
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.
Sunday, September 12, 2010
Common Core Implemenation
Dream Common Core Implementation
Given the opportunity to provide my staff about information on the Common Core Standards I would have the staff come in two weeks before school began and paid the teachers $30/hour money (or more!) for their time spent looking at the standards and planning to use the standards. In my plan as you will read there will be documents pre-created for teachers to use at their disposal such as common core assessments, Correlation Report between current NV Standards and Common Core, and curriculum alignment to match their current curriculum to the common core standards. I believe with these documents and the steps below, the teachers will learn the common core and be ready to work with them throughout the year. I have limited to two weeks because even in my dreams teachers would probably only be able to look at the standards for two weeks straight. Any more time than that may cause burn out!
I.Introduction to Common Core Standards (Day 1)
a.Teachers will be shown the NCTM Common Core Standards PowerPoint: NCTM PowerPoint. This PowerPoint shows how the Common Core Standards were developed, how the standards are formatted and general ideas that would cover most questions about the standards. During and after the presentation, there will be time for questions and answers.
b.Teachers will then be provided with a copy of their grade level standards and a Standards Correlation Report comparing CCSD standards and the Common Core Standards.
c.Teachers will then be given time to meet in their grade levels to discuss the differences between the two groups of standards and come up with any questions they may have about the standards.
II.Discussing Grade Level Common Core Standards (Day 2 & 3)
a.The teachers will come together again and discuss their questions/concerns about the standards for their grade level. There will be a “Common Core standards” expert to answer the questions about the standards. (Remember, in my dream!)
b.Teachers will then meet with the grade below them and the grade above them (in two separate meeting times) to discuss their vertical alignment. This should allow teachers to see what students are expected to come in with and what they need to be ready for in the next grade level.
III.Assessments (Day 4 & 5)
a.During another meeting, teachers will be given sample tests to show them samples of test questions their students will need to be prepared for in the spring.
b.In addition, teachers will be given benchmark tests that will be given each trimester to the students to determine their acquisition of the content being taught. This will help teachers see what their students do not know throughout the year and concepts that need to be re-taught without having to create the assessments themselves.
IV.Curriculum (Day 6-10)
a.Teachers will be given a curriculum alignment to the new Common Core Standards. This alignment will show teachers which lessons need to be taught and the best possible order.
b.Once given the curriculum alignment, teachers will work with their grade levels to determine long term plans.
V.On-going Professional Development (3-4 full school days)
a.Throughout the year prior to the next trimester, teachers will be given time to work with their grade level to determine the next set of standards to be taught and to discuss the standards alignment with the curriculum to make long range plans. They will also determine questions they have about the standards that will be submitted to ‘the expert’.
VI.Overall Estimated Time for Professional Development
a.Introduction- 1 day
b.Meeting with various grade levels-2 days
c.Assessment Overview- 1 day
d.Curriculum Alignment- 1 week
e.Professional Development Throughout the year – 3 to 4 FULL Days
Reality
I.Common Core Standards Implementation
a.Teachers will be shown the NCTM PowerPoint. Questions will be asked and answers will be given to the best possible extent.
b.Teachers will then be given the Common Core Standards for their grade level. Grade levels will meet to discuss common core standards and to determine how to use current curriculum to teach these standards.
c.During grade level meetings throughout the year, teachers will discuss implementation of standards, assessments used with the standards and curriculum alignment with standards.
d.Professional Development will be given from the district and teachers will be encouraged to attend these meetings for more clarification.
II.Overall Estimated Time for Professional Development
a.Introduction to standards- 1.5 days
b.Professional Development throughout year- 250-500 minutes (50 minute periods)
Given the opportunity to provide my staff about information on the Common Core Standards I would have the staff come in two weeks before school began and paid the teachers $30/hour money (or more!) for their time spent looking at the standards and planning to use the standards. In my plan as you will read there will be documents pre-created for teachers to use at their disposal such as common core assessments, Correlation Report between current NV Standards and Common Core, and curriculum alignment to match their current curriculum to the common core standards. I believe with these documents and the steps below, the teachers will learn the common core and be ready to work with them throughout the year. I have limited to two weeks because even in my dreams teachers would probably only be able to look at the standards for two weeks straight. Any more time than that may cause burn out!
I.Introduction to Common Core Standards (Day 1)
a.Teachers will be shown the NCTM Common Core Standards PowerPoint: NCTM PowerPoint. This PowerPoint shows how the Common Core Standards were developed, how the standards are formatted and general ideas that would cover most questions about the standards. During and after the presentation, there will be time for questions and answers.
b.Teachers will then be provided with a copy of their grade level standards and a Standards Correlation Report comparing CCSD standards and the Common Core Standards.
c.Teachers will then be given time to meet in their grade levels to discuss the differences between the two groups of standards and come up with any questions they may have about the standards.
II.Discussing Grade Level Common Core Standards (Day 2 & 3)
a.The teachers will come together again and discuss their questions/concerns about the standards for their grade level. There will be a “Common Core standards” expert to answer the questions about the standards. (Remember, in my dream!)
b.Teachers will then meet with the grade below them and the grade above them (in two separate meeting times) to discuss their vertical alignment. This should allow teachers to see what students are expected to come in with and what they need to be ready for in the next grade level.
III.Assessments (Day 4 & 5)
a.During another meeting, teachers will be given sample tests to show them samples of test questions their students will need to be prepared for in the spring.
b.In addition, teachers will be given benchmark tests that will be given each trimester to the students to determine their acquisition of the content being taught. This will help teachers see what their students do not know throughout the year and concepts that need to be re-taught without having to create the assessments themselves.
IV.Curriculum (Day 6-10)
a.Teachers will be given a curriculum alignment to the new Common Core Standards. This alignment will show teachers which lessons need to be taught and the best possible order.
b.Once given the curriculum alignment, teachers will work with their grade levels to determine long term plans.
V.On-going Professional Development (3-4 full school days)
a.Throughout the year prior to the next trimester, teachers will be given time to work with their grade level to determine the next set of standards to be taught and to discuss the standards alignment with the curriculum to make long range plans. They will also determine questions they have about the standards that will be submitted to ‘the expert’.
VI.Overall Estimated Time for Professional Development
a.Introduction- 1 day
b.Meeting with various grade levels-2 days
c.Assessment Overview- 1 day
d.Curriculum Alignment- 1 week
e.Professional Development Throughout the year – 3 to 4 FULL Days
Reality
I.Common Core Standards Implementation
a.Teachers will be shown the NCTM PowerPoint. Questions will be asked and answers will be given to the best possible extent.
b.Teachers will then be given the Common Core Standards for their grade level. Grade levels will meet to discuss common core standards and to determine how to use current curriculum to teach these standards.
c.During grade level meetings throughout the year, teachers will discuss implementation of standards, assessments used with the standards and curriculum alignment with standards.
d.Professional Development will be given from the district and teachers will be encouraged to attend these meetings for more clarification.
II.Overall Estimated Time for Professional Development
a.Introduction to standards- 1.5 days
b.Professional Development throughout year- 250-500 minutes (50 minute periods)
Sunday, September 5, 2010
Common Core Standards –Grade Span Reflection
As a third grade teacher, when preparing for my year I look at what my students have learned and what they need to learn to be successful in the next grade. So for looking at the Common Core Standards, I chose grades 2nd, 3rd and 4th to compare. My focus is to compare how the standards build upon each other as the grades get higher and whether or not the mathematics seems grade/age appropriate.
Observation of Standards
Looking at the Common Core Standards (CCS), I noticed through the grade levels the standards do build upon each other. For example, in measurement for second grade students are required to read time to the nearest 5 minutes and in third grade they are to know it to the nearest minute. This shows that the writers are developing skills based on the previous grades knowledge. Of course, this is not completely consistent throughout the document, but overall there is a continuous building of skills. I also took note of the examples that were provided for many of the standards. These ideas help clarify what a teacher is to teach, but the examples can also be limiting for a teacher to think that is all they have to teach (that one example). The Nevada Standards and CCSD are very long in comparison to the CCS, but they are very thorough in showing teachers what is expected to be taught.
Comparing NV/CCSD Standards to CCS
As I mentioned before, the CCS are limited in their number of topics covered and explanation of what is expected as compared to our CCSD Standards. However, there are some similarities and differences among our standards and CCS.
Similarities
The CCS has a strong emphasis on Operations and Algebraic Thinking and Number and Operation in Base Ten. CCSD has a similar approach by focusing on these areas in the Power Standards. In addition in these areas, the expectation of student learning is similar. In CCS second grade students are supposed to work with numbers up to the 1000s, third grade they work with numbers in the 1000s and in fourth grade up to and into the millions. This strongly correlates with the CCSD standards. In addition when it comes to operation, second grade students are expected to add and subtract with numbers within 100, third grade students move to multiplication and division within 100 and fourth grade students develop multiplication and division further. These standards match quite similarly.
Differences
There are several similarities, but unfortunately there are a lot more differences. In the CCS, there is a strong focus on the topics mentioned above, but limited on measurement, data and geometry, especially in grades 2 and 3. For example, in grade 2 students are only expected to focus on drawing shapes. They only focus on 2D shapes and the cube. In CCSD standards, grade 2 students are expected to work with 2D and 3D shapes. In third grade, students are expected to identify the attributes of shapes, which match CCSD standards, but are not expected to discuss lines and angles. In fact, only in 4th grade in CCS are students expected to discuss lines, rays, angles, and symmetry. This seems to be a little late to expect students to develop all this knowledge in one grade level. CCSD standards gradually develop the concepts in geometry. The CCS seems to limit the information until higher intermediate grades.
Overall View
The CCS have positive points, as well as negative points. Looking at them as a teacher, they are definitely more focused and would probably be easier to teach than my current CCSD standards. There are not as many standards and within the standards the strands limit what I can teach. In addition, the examples are provided to help guide my instruction, which can be helpful when trying to decode the language of the standards. Looking at the CCS from a mathematics approach, I question the strength and effectiveness they will have on student learning. The CCS have a strong emphasis on number, but little on geometry, data and measurement. This is concerning since students need to apply their knowledge of number to a variety of areas such as these. Also, I question the appropriateness of the mathematics for the age of the child. In 2nd, 3rd and 4th grade standards I didn’t find too many inappropriate standards that students may not be ready to learn, but I did in kindergarten and first. I can see that the CCS are trying to build upon ideas as each grade gets higher, but are they expecting too much at some grades and concepts and too little in others? I think we can speculate what our children will know and what gaps they will have, but we won’t really know until we test these Common Core Standards out.
Sources:
Common Core Standards Document (www.corestandards.org)
CCSD Power Standards (Grades 2-4)
Observation of Standards
Looking at the Common Core Standards (CCS), I noticed through the grade levels the standards do build upon each other. For example, in measurement for second grade students are required to read time to the nearest 5 minutes and in third grade they are to know it to the nearest minute. This shows that the writers are developing skills based on the previous grades knowledge. Of course, this is not completely consistent throughout the document, but overall there is a continuous building of skills. I also took note of the examples that were provided for many of the standards. These ideas help clarify what a teacher is to teach, but the examples can also be limiting for a teacher to think that is all they have to teach (that one example). The Nevada Standards and CCSD are very long in comparison to the CCS, but they are very thorough in showing teachers what is expected to be taught.
Comparing NV/CCSD Standards to CCS
As I mentioned before, the CCS are limited in their number of topics covered and explanation of what is expected as compared to our CCSD Standards. However, there are some similarities and differences among our standards and CCS.
Similarities
The CCS has a strong emphasis on Operations and Algebraic Thinking and Number and Operation in Base Ten. CCSD has a similar approach by focusing on these areas in the Power Standards. In addition in these areas, the expectation of student learning is similar. In CCS second grade students are supposed to work with numbers up to the 1000s, third grade they work with numbers in the 1000s and in fourth grade up to and into the millions. This strongly correlates with the CCSD standards. In addition when it comes to operation, second grade students are expected to add and subtract with numbers within 100, third grade students move to multiplication and division within 100 and fourth grade students develop multiplication and division further. These standards match quite similarly.
Differences
There are several similarities, but unfortunately there are a lot more differences. In the CCS, there is a strong focus on the topics mentioned above, but limited on measurement, data and geometry, especially in grades 2 and 3. For example, in grade 2 students are only expected to focus on drawing shapes. They only focus on 2D shapes and the cube. In CCSD standards, grade 2 students are expected to work with 2D and 3D shapes. In third grade, students are expected to identify the attributes of shapes, which match CCSD standards, but are not expected to discuss lines and angles. In fact, only in 4th grade in CCS are students expected to discuss lines, rays, angles, and symmetry. This seems to be a little late to expect students to develop all this knowledge in one grade level. CCSD standards gradually develop the concepts in geometry. The CCS seems to limit the information until higher intermediate grades.
Overall View
The CCS have positive points, as well as negative points. Looking at them as a teacher, they are definitely more focused and would probably be easier to teach than my current CCSD standards. There are not as many standards and within the standards the strands limit what I can teach. In addition, the examples are provided to help guide my instruction, which can be helpful when trying to decode the language of the standards. Looking at the CCS from a mathematics approach, I question the strength and effectiveness they will have on student learning. The CCS have a strong emphasis on number, but little on geometry, data and measurement. This is concerning since students need to apply their knowledge of number to a variety of areas such as these. Also, I question the appropriateness of the mathematics for the age of the child. In 2nd, 3rd and 4th grade standards I didn’t find too many inappropriate standards that students may not be ready to learn, but I did in kindergarten and first. I can see that the CCS are trying to build upon ideas as each grade gets higher, but are they expecting too much at some grades and concepts and too little in others? I think we can speculate what our children will know and what gaps they will have, but we won’t really know until we test these Common Core Standards out.
Sources:
Common Core Standards Document (www.corestandards.org)
CCSD Power Standards (Grades 2-4)
Tuesday, August 31, 2010
Common Core Standards Reflection
The Common Core Standards document is well organized where teachers can clearly determine what needs to be taught. Each grade level lists several domains with the standard and a cluster of explanations describing exactly what needs to be taught. As the introduction states, “These Standards do not dictate curriculum or teaching methods” (Common Core, p. 5). This shows that these standards are exactly like our current Curriculum Essentials Framework in the sense that they are to guide teaching topics, but not determine how topics are taught. However, the Common Core Standards does provide a recommended list of Mathematical Practices that a teacher can follow to provide effective instruction. These practices were taken from NCTMs Process Standards and the National Council’s Research report Adding it Up (Common Core, p. 6). From reviewing these parts, it seems as if the Common Core Standards created a clear format for teachers to use and used some current research to support its ideas in best practices.
After reviewing the introduction, I began to look at kindergarten, first, second and third grade standards in the domain of Number and Operations. Looking at these standards I began to notice a strong difference between the current Nevada Standards and the Common Core Standards. First, in kindergarten students are expected to compose and decompose numbers 11-19 into tens ones and some further ones. In the Nevada state standard, there is no mention of place value. For first, the common core continues to build on kindergarten by expecting first graders to identify the ones and tens place and compare numbers by their place value position. This does match the Nevada state standards to some degree, but Nevada students are currently expected to do less with their place value knowledge. By second grade, Common Core Standards require students to use place value in the hundreds and thousands, which Nevada standards again requires students to go up into the thousands, but students are expected to do less.
Looking at this information, I understand that we are trying to make a nation of successful learners, but did the writers of this document truly look at the developmental abilities of the students at each grade level. I fear, especially for kindergarten, the writers made assumptions about student ability and at home preparation of students. Also, I am wondering what is going to happen when students get behind and do not master the core standards. Each level seems to build on each other rapidly. There is no room for students to review previously taught concepts like the current Nevada Standards have. Again, I have only closely looked at this domain in these grade levels and it may be different. I need to investigate more to find out.
Source: http://www.corestandards.org/
After reviewing the introduction, I began to look at kindergarten, first, second and third grade standards in the domain of Number and Operations. Looking at these standards I began to notice a strong difference between the current Nevada Standards and the Common Core Standards. First, in kindergarten students are expected to compose and decompose numbers 11-19 into tens ones and some further ones. In the Nevada state standard, there is no mention of place value. For first, the common core continues to build on kindergarten by expecting first graders to identify the ones and tens place and compare numbers by their place value position. This does match the Nevada state standards to some degree, but Nevada students are currently expected to do less with their place value knowledge. By second grade, Common Core Standards require students to use place value in the hundreds and thousands, which Nevada standards again requires students to go up into the thousands, but students are expected to do less.
Looking at this information, I understand that we are trying to make a nation of successful learners, but did the writers of this document truly look at the developmental abilities of the students at each grade level. I fear, especially for kindergarten, the writers made assumptions about student ability and at home preparation of students. Also, I am wondering what is going to happen when students get behind and do not master the core standards. Each level seems to build on each other rapidly. There is no room for students to review previously taught concepts like the current Nevada Standards have. Again, I have only closely looked at this domain in these grade levels and it may be different. I need to investigate more to find out.
Source: http://www.corestandards.org/
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