As a sixth grade math teacher who relies heavily on NCTM standards and lessons, I wanted to see how much Common Core State Standards aligned with NCTM's Principles and Standards for School Mathematics. The comparison is not as easy to make, because the CCSS are not divided between the same strands as NCTM. NCTM divides their content between between 5 content standards: Number & Operations, Algebra, Geometry, Measurement, and Data Analysis & Probability. CCSS content is divided between Ratio & Proportional Relationships, The Number System, Expressions & Equations, Geometry, and Statistics and Probability. This leads to some deficiencies and confusion.
For example, standards from the measurement strand for NCTM have been placed in other strands or deleted altogether in CCSS because there is no measurement strand in CCSS. Standards covered under Measurement for NCTM include conversions between metric and customary systems, area, perimeter, surface area and volume, formulas for finding areas of geometric shapes, and using scales to develop ratios and proportions. In CCSS, converting measurements is covered under the Ratio & Proportional Relationships Strand number 3, Use ratio and rate reasoning to solve real-world and mathematical problems. Area and volume are covered under the Geometry strand in CCSS.
However, the data Analysis and Probability strand in NCTM is fairly close to the Statistics and Probabilty srand of the CCSS. NCTM's standards are designed around collecting data and describing it as well as discussing probabilty of events. CCSS discuss the same items, yet it seems to be a bit more vague. NCTM provideds specific content to teach (ie. - formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population). Compared with the standard in CCSS (recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers), teacher will find that the NCTM standards are more specific and easier to follow. CCSS is too vague leaving room for error.
Overall, within the middle grades, I would say that because the CCSS are more vaguely written than the NCTM standards, many of NCTM standards can fit within the CCSS, just under a different strand than the strands all educators are used to.
Tuesday, September 28, 2010
Thursday, September 16, 2010
Professional Development with the CCSS
Professional Development will be vital to the life and success of the Common Core Standards. Teachers who are exposed and trained in the right way will be more willing to implement the standards and be supportive. If teachers are not trained right, or the standards are just pushed upon them, there may be some harsh backlash.
Dream Scenario:
I am currently working in the middle school setting, where professional development may look very different than at the elementary school setting. But, my underlying point remains the same - teachers need time to absorb these standards. The CCSS should not be thown out to them the few days before school starts or at the end of the year with the expectation that teachers will implement them immediately.
I would recommend having someone from the State Department of Education of CCSD present an introduction of the CCSS standards and reasons for the switch in a staff meeting at the beginning of the school year, one year BEFORE the standards are implemented. With the idea of professional development for a middle school math department, the CCSS should be rolled out one strand at a time. For example, the 5 strands of standards for 6th grade math are Ratios & Proportional Relationships, The Number System, Expressions & Equations, Geometry, and Statistics and Probabilty. The math department should be presented with the Ratios & Proportional Relationships strand in January of the year before implementation. The department should meet and discuss the standards, look for similarities in the current standards(if possible, align them with the current standards), and look for where that standard is supported in the current curriculum. In February, teachers would receive the Number System strand, and so on. By May, teachers will have thoroughly investigated the new standards and will hopefully feel comfortable implementing them in the coming fall. Ideally, teachers should be given staff development time to review the standards, and also be paid for afterschool or Saturday meetings. Also, teachers need to be able to ask questions about the standards with people in the Department of Education directly. In turn, the State Department of Ed should also be asking for feedback and willing to take suggestions about implementation.
Reality:
CCSD will inform the administration that they are working on a professional development plan and are working with the State Department of Education to roll one into place. About 4-6 months before the implementation date, administrators will be informed that it will be their responsibility to inform the staff and to provide professional development how they see fit. Administration will go back and forth trying to develop a plan. But ultimately, teachers will receive a fullday training of all of the standards all at once on the first staff development day of the new school year. (One of those 3 days before students arrive.) The next day, teachers will be able to develop lesson plans with these standards in grade-level or subject-level teams. The third day will be more of the same, and the teachers will be unhappy about the lack of time they have for setting up their room. Teachers will have questions that administration won't be prepared to answer. But administration will gladly do some research to answer those questions or concerns during the first staff development meeting after the students arrive.
Dream Scenario:
I am currently working in the middle school setting, where professional development may look very different than at the elementary school setting. But, my underlying point remains the same - teachers need time to absorb these standards. The CCSS should not be thown out to them the few days before school starts or at the end of the year with the expectation that teachers will implement them immediately.
I would recommend having someone from the State Department of Education of CCSD present an introduction of the CCSS standards and reasons for the switch in a staff meeting at the beginning of the school year, one year BEFORE the standards are implemented. With the idea of professional development for a middle school math department, the CCSS should be rolled out one strand at a time. For example, the 5 strands of standards for 6th grade math are Ratios & Proportional Relationships, The Number System, Expressions & Equations, Geometry, and Statistics and Probabilty. The math department should be presented with the Ratios & Proportional Relationships strand in January of the year before implementation. The department should meet and discuss the standards, look for similarities in the current standards(if possible, align them with the current standards), and look for where that standard is supported in the current curriculum. In February, teachers would receive the Number System strand, and so on. By May, teachers will have thoroughly investigated the new standards and will hopefully feel comfortable implementing them in the coming fall. Ideally, teachers should be given staff development time to review the standards, and also be paid for afterschool or Saturday meetings. Also, teachers need to be able to ask questions about the standards with people in the Department of Education directly. In turn, the State Department of Ed should also be asking for feedback and willing to take suggestions about implementation.
Reality:
CCSD will inform the administration that they are working on a professional development plan and are working with the State Department of Education to roll one into place. About 4-6 months before the implementation date, administrators will be informed that it will be their responsibility to inform the staff and to provide professional development how they see fit. Administration will go back and forth trying to develop a plan. But ultimately, teachers will receive a fullday training of all of the standards all at once on the first staff development day of the new school year. (One of those 3 days before students arrive.) The next day, teachers will be able to develop lesson plans with these standards in grade-level or subject-level teams. The third day will be more of the same, and the teachers will be unhappy about the lack of time they have for setting up their room. Teachers will have questions that administration won't be prepared to answer. But administration will gladly do some research to answer those questions or concerns during the first staff development meeting after the students arrive.
Tuesday, September 7, 2010
The Progression of Standards in Common Core
As a sixth grade math teacher, I have been spending my time familiarizing myself with the sixth grade Common Core standards. I wanted to see what the standards looked like in fifth grade, and also, what will they look like in seventh grade. With Common Core, it is not as easy to see a progression between the elementary and middle schools - it is a bit of a jump. For example, in elementary, standards are given for the following five areas: Operations & Algebraic Thinking, Number & Operations in Base Ten, Number & Operations - Fractions, Measurement & Data, and Geometry. However, in middle school, the standards are presented in the following five areas: Ratios & Proportional Relationships, The Number System, Expressions & Equations, Geometry, and Statistics & Probability. With the different categories, it is more difficult to find the progression. Since Geometry is presented in both elementary and middle school, I will evaluate the progression of standards within the Geometry strand.
In fifth grade for Geometry, students should be able to recognize an x- and y-axis and plot points on the first quadrant of a coordinate plane, identify attributes of two-dimensional figures, as well as identify the hierarchy of two-dimensional figures. I am surprised that there is no mention of three-dimensional figures in fifth grade. I taught three-dimensional shapes when I was teaching third grade.
When students get to sixth grade for Geometry, students are responsible for finding the areas of polygons using other shapes, use formulas to find the volume of given three-dimensional shapes, draw two-dimensional shapes on a coordinate plane, and use nets to find the surface area of three-dimensional shapes. I am surprized that students are expected to use formulas to find volume and surface area of three-dimensional shapes when this is the first exposure to 3-D in the Common Core standards. There also is no mention of whether students are only responsible for plotting points in the first quadrant of the coordinate plane or all four quadrants. In seventh grade, students will be working with finding actual lengths from scale drawings and vice versa, draw triangles with given angle measures, describe relationships between two- and three-dimensional figures, use circumference to solve problems, find volume and area using formulas, and use facts about angles to solve equations to find unknown angles. Using formulas to find volume progressed nicely from the students' exposure in sixth grade. I did notice that there is no mention of angles in sixth grade, so the curriculum in seveth grade must be filled with angles if students are expected to be able to find measurements of unknown angles.
Overall, there does not seem to be nearly enough geometry in the elementary grades. In middle school, the Common Core standards emphasis on Geometry increases each year. Some standards are progress from previous standards and some are brand new concepts.
In fifth grade for Geometry, students should be able to recognize an x- and y-axis and plot points on the first quadrant of a coordinate plane, identify attributes of two-dimensional figures, as well as identify the hierarchy of two-dimensional figures. I am surprised that there is no mention of three-dimensional figures in fifth grade. I taught three-dimensional shapes when I was teaching third grade.
When students get to sixth grade for Geometry, students are responsible for finding the areas of polygons using other shapes, use formulas to find the volume of given three-dimensional shapes, draw two-dimensional shapes on a coordinate plane, and use nets to find the surface area of three-dimensional shapes. I am surprized that students are expected to use formulas to find volume and surface area of three-dimensional shapes when this is the first exposure to 3-D in the Common Core standards. There also is no mention of whether students are only responsible for plotting points in the first quadrant of the coordinate plane or all four quadrants. In seventh grade, students will be working with finding actual lengths from scale drawings and vice versa, draw triangles with given angle measures, describe relationships between two- and three-dimensional figures, use circumference to solve problems, find volume and area using formulas, and use facts about angles to solve equations to find unknown angles. Using formulas to find volume progressed nicely from the students' exposure in sixth grade. I did notice that there is no mention of angles in sixth grade, so the curriculum in seveth grade must be filled with angles if students are expected to be able to find measurements of unknown angles.
Overall, there does not seem to be nearly enough geometry in the elementary grades. In middle school, the Common Core standards emphasis on Geometry increases each year. Some standards are progress from previous standards and some are brand new concepts.
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