NJCCCS FOR MATHEMATICS
Content Area Summary:
STANDARD 4.1 (NUMBER AND NUMERICAL OPERATIONS)
•Students must know that there are different types of numbers that can be used to represent quantities.
•Students will be able to perform the operations of addition, subtraction, multiplication, and division, as well as estimate values.
STANDARD 4.2 (GEOMETRY AND MEASUREMENT)
•Students must know that there are different units used for different measurements, and that there are certain qualities that define different geometric shapes.
•Students will be able to transform geometric shapes to form new ones and measure the length, area, volume, and angles of those shapes.
STANDARD 4.3 (PATTERNS AND ALGEBRA)
•Students must know that there are patterns in mathematics and that graphs can be used to give a picture of those patterns.
•Students will organize data in tables, charts, and graphs, and solve for variables in algebraic equations.
STANDARD 4.4 (DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS)
•Students must know that outcomes can be predicted based on the theory of probability.
•Students will be able to collect data and analyze it in order to determine the probabilities of outcomes of events.
STANDARD 4.5 (MATHEMATICAL PROCESSES)
•Students must know that mathematics is the language for many other disciplines in education.
•Students will be able to solve problems and communicate mathematical ideas by making connections, reasoning, representing data and ideas, and using technology.
Desired Dispositions:
In order for students to understand the importance of mathematics and how they can use it, curriculum must be developed so that students are active in hands-on problem solving. Students need to have access to the technology used in mathematics, such as computers and calculators. Teachers need to set high expectations for all students and must encourage them to strive for understanding beyond the standards in order to be prepared for college mathematics courses.
Strengths and Weaknesses:
The NJCCCS for Mathematics were revised and changed in 2008 from their previous version in 1996. The most obvious change is the reduction of standards: from 16 to 5 (with many subdivisions). This reduction is a definite evolution because “the new standards are more specific and clearer than the previous standards”. Another positive change which fosters curriculum development (because it helps to understand what to teach at many different stages and how/when to do assessments) is the fact that now expectations are set not only for grades 4, 8, and 12, but also for grades 2,3,5,6, and 7. If there is a weakness here is in the fact that the expectations for the high school years are limited only to the time when students graduate.
The strength of the new standards is in the awareness of how much is needed at every level and grade in order to make Mathematics both meaningful and connected to real life, especially at high school level (of course beyond the simple math of going to buy a gallon of milk or 2 pounds of oranges). And an additional strength is in “the vision of excellent mathematical education [which] is based on the twin premises that all students can learn mathematics and that all students need to learn mathematics”. Paradoxically, the biggest weakness of the NJCCCS is shown in the same area: by reading the 47 pages of standards one does not get the feeling that they go beyond the theory, with very minimal connection with reality and real-life use of mathematics.
The vision of the NJCCCS is very articulated and tries to go beyond the old stereotype about math and about the typical students who excel in it. The wording of the vision is very important: “students excited about math”, “learning math concepts rather than memorizing procedures”, “students working together”, “teachers with high expectation for ALL students”, “providing opportunities for success”, and so on.
Connection to Curriculum:
•Purposes of the standards are to gear the teaching methods towards student understanding of specific topics within the curriculum.
•The standards focus on getting students to understand and demonstrate specific mathematics concepts that are taught.
A foundation of mathematical ideas and applications that will prepare them for the workplace or for college.
•Initially, the standards might seem that they are meant to be followed in order and build on each other. After further review, the standards may be used simultaneously for certain lessons. It is possible to integrate algebra and geometry.
This provides the students with an opportunity to learn in different ways and apply what they have learned to specific tasks.
•Teaching of mathematics is objective and not subjective. There is a clear right and wrong.
•The standards gear students to acquire specific knowledge of certain concepts and skills.
•Mathematics curriculum is more of a scaffolding of prior concepts and knowledge
•HSPA clusters are aligned to the CCCS.
•You will probably touch upon every standard in a math course.
•At the moment, there is integrated math, which consists of a mixture of standards in each chapter.
When writing the curriculum, teachers try to include various standards in each chapter and in each lesson.
•Students build on what they know and apply that knowledge in later lessons and activities.
•I do feel that math standards and curriculum leaves less room for teacher and student creativity. It targets the student’s ability to memorize and understand rather than their creative and analytical ability.
Suggested readings:
Hyde, A. (2007, November). Mathematics and Cognition. Educational Leadership.
Jones, A. (2001, February). Welcome to Standardsville. Phi Delta Kappan. Vol. 82, No. 6, pp. 462-464.
Loewenberg, D. (1996, December). Reform by the Book: What Is: Or Might Be: The Role of Curriculum Materials in Teacher Learning and Instructional Reform? Educational Researcher. Vol. 25, No. 9, pp. 6-14.
Reys, B. (1999, February). Mathematics Curricula Based on Rigorous National Standards: What, Why, and How? Phi Delta Kappan. Vol. 80, pp. 454-56.
Steen, L. (2007, November). How Mathematics Count. Educational Leadership.
Usiskin, Z. (2007, November). Do We Need National Standards with Teeth? Educational Leadership.
Wednesday, May 14, 2008
Science vs. Math CCCS
Andrew J. Wells
Principles of Curriculum Development
Spring 2008
Dr. Goldstein
CCCS Individual Paper
The primary purpose of education in New Jersey, as outlined by the state Core Content Curriculum Standards (CCCS), is to improve student achievement by clearly summarizing what all students should know and be able to do at the end of their public school education. The primary principle of education in our state is that all students can achieve these standards, regardless of their career goals, native language, disabilities, or socioeconomic background. The standards provide classroom teachers and curriculum designers with sample teaching strategies, adaptations, and background information relevant to each of the content areas. Supposedly, the statewide assessments were aligned to the Core Curriculum Content Standards. The NJCCCS are not meant to serve as a statewide curriculum guide. They are just an outline of the expectations to be met if we are to ensure that all students receive a thorough and efficient education, as promised by our state constitution. Individual school districts must use the standards to develop curriculum to ensure that students achieve the expectations. The NJCCCS show a vision of the skills and understandings all of New Jersey’s children need to be successful in their careers and daily lives. These standards provide useful framework to help us identify teaching and learning priorities and guide our design of curriculum and assessments (Wiggins, 2005).
The CCCS group project really helped me to understand the nuts and bolts of each content area’s standards, which will be very useful to me when I am an administrator. However, I am most thankful that I now have a better understanding of the Science standards. I have dreaded, in the past, when my supervisor tells our department that we must include standards on our lesson plans. The reason being, just like I felt at the start of the project, the thick document was too overbearing. Having the nuts and bolts outline improves my understanding and ability to site standards in my lesson plans. Likewise, my understanding of backward design will guide me to plan activities based on the standards rather than find which standards my activities fall under.
As I stated in my group presentation, Math is the language of Science so there are some similarities in the two content areas and their standards. Both state the importance of technology in their fields and both stress the importance of problem-solving skills and analytical thinking. The standards for the two content areas also have some differences. The most obvious difference is the number of standards. Math has five, while Science has ten. While there are benchmarks for all five Math standards extended over grades 2 through 8 and grade 12, the first four Science standards have benchmarks for grades 4, 8, and 12 while the rest have benchmarks for grades 2, 4, 6, 8, and 12. When looking at the Math standards, it seems feasible to accomplish the goals for all grade levels. The standards for science have just too broad of a range to be able to cover all at any one grade level. Science is comprised of just too many branches. In Math, you could explore numerical operations, geometry, measurement, patterns, algebra, data analysis, probability, and processes at almost any grade level. In Science, it seems impossible in a single year to cover processes, history, math concepts, technology, Biology, Chemistry, Physics, Earth Science, Astronomy, Space Science, and Environmental Science.
The CCCS presents a variety of challenges for teachers, many of which may be arguable, and there is also the added pressure of No Child Left Behind (NCLB). The most prominent challenge is that we are constantly told to use multiple forms of assessment, yet the measure of progress in education basically relies upon standardized tests. The NJCCCS are divided into nine content areas, yet the High School Proficiency Assessment (HSPA) only tests two of those areas- Math and Language Arts. They have been attempting to add science to the HSPA for the past few years, but have recently abandoned the idea for a year-end exit exam. So, how can we assure that our students are receiving a thorough and efficient education when our schools are forced to justify their existence on a two-subject standardized test? What I really don’t understand are the writing components on the HSPA. My understanding is that the writing component is supposed to get away from a strictly multiple-guess (choice) test and assess higher-level thinking. Well, I just can’t see how those picture prompts assess any kind of intelligence. My final point on assessment refers back to the year-end Biology exit exam that is being implemented this year. The test covers the topics of Biology and Environmental Science. Both of those topics have their own one-year course. This exam has had Science Departments everywhere scrambling to change their curricula to fit the test. In Science, we require lots of time to develop inquiry-based lessons. Because of the more open-ended nature of these activities compared to traditional science lessons, implementing Standards-based inquiry activities concordant with NCLB poses a major challenge—how do we assure that academic standards are met during student-centered, inquiry-based investigations? (Hendrickson, 2006). As stated earlier, there are some other challenges for our schools in regards to CCCS and NCLB. The biggest problem in my eyes is effect that standardized testing will have on our curriculum development. The more pressure we receive to score well on standardized tests, the more CCCS become our curriculum guide instead of the framework to help us design our curriculum and assessments.
Reference:
Hendrickson, S. (2006). Backward Approach to Inquiry. Science Scope. Vol. 29, No. 4,
pp. 30-33
Wiggins, G. & McTighe, J. (2005). Understanding by Design (2nd Ed.). Alexandria, VA:
Association for Supervision and Curriculum Development.
Principles of Curriculum Development
Spring 2008
Dr. Goldstein
CCCS Individual Paper
The primary purpose of education in New Jersey, as outlined by the state Core Content Curriculum Standards (CCCS), is to improve student achievement by clearly summarizing what all students should know and be able to do at the end of their public school education. The primary principle of education in our state is that all students can achieve these standards, regardless of their career goals, native language, disabilities, or socioeconomic background. The standards provide classroom teachers and curriculum designers with sample teaching strategies, adaptations, and background information relevant to each of the content areas. Supposedly, the statewide assessments were aligned to the Core Curriculum Content Standards. The NJCCCS are not meant to serve as a statewide curriculum guide. They are just an outline of the expectations to be met if we are to ensure that all students receive a thorough and efficient education, as promised by our state constitution. Individual school districts must use the standards to develop curriculum to ensure that students achieve the expectations. The NJCCCS show a vision of the skills and understandings all of New Jersey’s children need to be successful in their careers and daily lives. These standards provide useful framework to help us identify teaching and learning priorities and guide our design of curriculum and assessments (Wiggins, 2005).
The CCCS group project really helped me to understand the nuts and bolts of each content area’s standards, which will be very useful to me when I am an administrator. However, I am most thankful that I now have a better understanding of the Science standards. I have dreaded, in the past, when my supervisor tells our department that we must include standards on our lesson plans. The reason being, just like I felt at the start of the project, the thick document was too overbearing. Having the nuts and bolts outline improves my understanding and ability to site standards in my lesson plans. Likewise, my understanding of backward design will guide me to plan activities based on the standards rather than find which standards my activities fall under.
As I stated in my group presentation, Math is the language of Science so there are some similarities in the two content areas and their standards. Both state the importance of technology in their fields and both stress the importance of problem-solving skills and analytical thinking. The standards for the two content areas also have some differences. The most obvious difference is the number of standards. Math has five, while Science has ten. While there are benchmarks for all five Math standards extended over grades 2 through 8 and grade 12, the first four Science standards have benchmarks for grades 4, 8, and 12 while the rest have benchmarks for grades 2, 4, 6, 8, and 12. When looking at the Math standards, it seems feasible to accomplish the goals for all grade levels. The standards for science have just too broad of a range to be able to cover all at any one grade level. Science is comprised of just too many branches. In Math, you could explore numerical operations, geometry, measurement, patterns, algebra, data analysis, probability, and processes at almost any grade level. In Science, it seems impossible in a single year to cover processes, history, math concepts, technology, Biology, Chemistry, Physics, Earth Science, Astronomy, Space Science, and Environmental Science.
The CCCS presents a variety of challenges for teachers, many of which may be arguable, and there is also the added pressure of No Child Left Behind (NCLB). The most prominent challenge is that we are constantly told to use multiple forms of assessment, yet the measure of progress in education basically relies upon standardized tests. The NJCCCS are divided into nine content areas, yet the High School Proficiency Assessment (HSPA) only tests two of those areas- Math and Language Arts. They have been attempting to add science to the HSPA for the past few years, but have recently abandoned the idea for a year-end exit exam. So, how can we assure that our students are receiving a thorough and efficient education when our schools are forced to justify their existence on a two-subject standardized test? What I really don’t understand are the writing components on the HSPA. My understanding is that the writing component is supposed to get away from a strictly multiple-guess (choice) test and assess higher-level thinking. Well, I just can’t see how those picture prompts assess any kind of intelligence. My final point on assessment refers back to the year-end Biology exit exam that is being implemented this year. The test covers the topics of Biology and Environmental Science. Both of those topics have their own one-year course. This exam has had Science Departments everywhere scrambling to change their curricula to fit the test. In Science, we require lots of time to develop inquiry-based lessons. Because of the more open-ended nature of these activities compared to traditional science lessons, implementing Standards-based inquiry activities concordant with NCLB poses a major challenge—how do we assure that academic standards are met during student-centered, inquiry-based investigations? (Hendrickson, 2006). As stated earlier, there are some other challenges for our schools in regards to CCCS and NCLB. The biggest problem in my eyes is effect that standardized testing will have on our curriculum development. The more pressure we receive to score well on standardized tests, the more CCCS become our curriculum guide instead of the framework to help us design our curriculum and assessments.
Reference:
Hendrickson, S. (2006). Backward Approach to Inquiry. Science Scope. Vol. 29, No. 4,
pp. 30-33
Wiggins, G. & McTighe, J. (2005). Understanding by Design (2nd Ed.). Alexandria, VA:
Association for Supervision and Curriculum Development.
Friday, May 9, 2008
What I learned about myself and curriculum planning
What I learned about myself is that I can change my ways. I am often be stubborn and set in my own ways. If something ain't broke, don't fix it. I am a good teacher and I realize that there is always room for improvement. But when I find something that works, I try to keep improving on it every year. I have my curriculum and try to fine tune it every year. After reading Understanding by Design, I realize that I was doing it all backwards, actually frontwards, but that is backwards of backwards design. I was an activity planner and I tried to see what standards fit into my activities. I should have been focusing on my goals and what proof I needed to see that those goals were being achieved, then planning my activities to achieve those goals. It will take a lot of work and I will often feel like a new teacher again, but I need to totally rethink and rework the way I design my lessons. I am glad that I finally found out what curriculum was. I have always had an idea, but not an understanding. I am very tempted to jump at the next opportunity to rewrite our science curriculum for our school or district.
Thursday, May 1, 2008
Reflecting on new teacher curriculum development process
As always, trying something new feels uncomfortable. UbD seems like a great idea when reading about it, but when you actually attempt to do it, backwards curriculum development is tough. You can't teach an old dog new tricks. Even though I never believed in that adage, I kept thinking of it as we developed our curriculum. It was fun and a good experience to go through. Every Spring, I hear about Summer opportunities for writing curriculum and I always wondered what it would be like. I felt that I wasn't ready, but then I heard that usually a couple of people worked together on writing the curriculum. So, that must be a lot easier. Well, working in our group was quite the experience. We had people from different subjects, grade levels, demographic areas, and roles in education. it was a challenge to meld our ideas together when we were all used to developing curricula in different ways. Also, when we got near deadlines and we needed to rely on others to get their part done it got quite interesting. Overall, it was a very positive experience. I look forward to completing it and am very glad that we had to go through the uncomfortable feeling of doing something new.
Asessing other groups' assessments
It was interesting to see how other groups' new teacher programs were shaping up. As we looked at the first groups, we realized that their project was totally different from ours. We wondered if we were doing something wrong. Then we saw the next group's and it too was different from ours as well as from the first group's we saw. As we went along from group to group, we saw that all of the groups seemed to interpret different aspects of the project differently. It was also interesting to see how different groups had different priorities and assessment ideas for their new teachers. Dr. G said that she wanted us to feel uncomfortable. It was very uncomfortable trying make curriculum in a new way. There were many times when there were feelings of uncertainty. It was reassuring to be able to see other groups' work and be able to compare ours to their's.
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