Math CCCS Presentation

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.
o 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.
o 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.
o 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.

Curriculum Planning and Myself

There are a few areas in which I realized I needed more help. I begin with the lesson planning I have been for a few years. Designing lessons in the same way that we have learned in class will allow the students better opportunities to think critically and also think in the long term. It is a great way for them to connect the stages as they move along the school year. When it comes to curriculum planning, it is obvious now, that we are able to combine various disciplines. After listening to CCCS presentations, I realized how the standards have many things in common all across the different disciplines. Staying on the positive side, this has been a very helpful course. I have acquired new ideas and new skills in writing lessons and in writing curriculum. I have learned ways in which I can teach along with my colleagues from other subjects. I will be putting many of my new skills into practice and I am sure the students will appreciate it.