Mathematics

Introduction
 The Diocese of Trenton Mathematics Curriculum Guidelines is the culmination of work developed over a period of one to two years by the Diocesan Mathematics Curriculum Committee.
 
The document, Diocese of Trenton Mathematcs Curriculum Guidelines is based on the investigation and research of numerous documents:

• National Standards and Benchmarks for Effective Catholic Elementary and Secondary Schools, 2012
• New Jersey Student Learning Standards, 2014
• National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics, 1989
• New Jersey Department of Education, Core Curriculum Content Standards, 2008 & 2010
• New Jersey Council of Catholic School Superintendents, Mathematics Curriculum Guidelines, For the Catholic Schools in the State of New Jersey, 2000
• Diocese of Trenton, Mathematics Curriculum Committee, Mathematics Curriculum Calendar Mapping, Grades K – 8, 2004.

               
In 1989, mathematicians projected the following concepts to be developed for the 21st century:

“Today's students will live and work in the twenty-first century, in an era dominated by computers, by world-wide communication, and by a global economy. Jobs that contribute to this economy will require workers who are prepared to absorb new ideas, to perceive patterns, and to solve unconventional problems.

Mathematics is the key to opportunity for these jobs. Through mathematics, we learn to make sense of things around us. As technology has mathematicized the workplace, and as statistics has permeated the arena of public policy debate, the mathematical sciences have moved from being a requirement only for future scientists to being an essential ingredient in the education of all Americans.” [“Teaching Mathematics for Tomorrow’s World”, Lynn Arthur Steen, St. Olaf College, Educational Leadership, 47:1 (September 1989) 18-22.]

In an article written by the president of the NCTM in 2010, he stated the following:
“To instill positive and productive attitudes toward mathematics lies within our own hands—in our teaching. No standards on earth—be they state or national—no testing or assessment procedures, no Race to the Top or mandates from above can make as much of a difference as we can every day through our own instructional practices.” [It’s Time to Stamp Out the Phrase “I’m Bad at Math” by NCTM President J. Michael Shaughnessy, NCTM Summing Up, October 2010]

Developing challenging, ambitious expectations for student learning in mathematics is imperative if we are to prepare students to compete in a global economy in the 21 st Century.   Preparing students and teachers in the 21 st century demands that all students and teachers become immersed in the concepts of mathematics as well as connecting mathematics concepts to literacy in language, economics, communication and new technology as it emerges.
 
In addition to the Core Content Standards in Mathematics, contained within this document, there is also a set of Mathematical Practice Standards to incorporate the content standards and apply them to other disciplines and real life applications. These Mathematical Practice Standards are summarized as follows from the Common Core Mathematical Standards, 2010.

1.   Make sense of problems and persevere in solving them.

• Students make conjectures about the form and meaning of the solution and plan a solution pathway.
• Students monitor and evaluate their process and change course if necessary.
• Younger students might rely on using concrete objects or pictures to help conceptualize or solve a problem.
• Older students might transform algebraic expressions to get the information they need to solve a problem.
• Students check their answers to problems, possibly using a different method, to determine if the solution makes sense.
• Students can understand the approaches of others and recognize the commonality and differences between solutions.

2.   Reason abstractly and quantitatively.

• Students make sense of quantities and their relationships in problem situations.
• Students develop the ability to abstract a given situation and represent it symbolically and be able to manipulate the symbols independently of the problem.
• Students should be able to reason quantitatively creating a coherent representation of the problem, considering the units of measure necessary in the problem solution.

3.   Construct viable arguments and critique the reasoning of others.

• Students understand and use stated assumptions, definitions, and previously established results in constructing arguments.
• Students make conjectures and build a logical progression of statements to explore the truth of the conjecture.
• Students should be able to analyze a solution and recognize and use counterexamples.
• Students should be able to justify conclusions and communicate them to others.
• Students should be able to compare the effectiveness of two or more plausible arguments and recognize flawed arguments and explain the flaw(s).

4.   Model with mathematics.

• Students should use a variety of methods to solve problems, including
  • Geometry
  • Use of functions to describe how two quantities are related
  • Making assumptions and approximations
  • Graphing
  • Flowcharts
  • Formulas

5.   Use appropriate tools strategically.

• Students should choose proper tools when solving a problem. The tools could include
  • Paper and pencil
  • Concrete models
  • Ruler, compass, protractor
  • Calculator
  • Spreadsheet
  • Computer software
  • Estimation

6.   Attend to precision.

• Students should be able to communicate mathematical thought precisely to others
  • Using clear definitions
  • Stating the meaning of symbols used
  • Being careful about specifying correct units of measure
  • Labeling axes on a graph
  • Calculating accurately and efficiently with precision

7.   Look for and make use of structure.

• Students should discuss patterns and structure
• Students should use commutative, associative and distributive properties
• Students should be able to see complicated tasks as a series of simpler structures

8.   Look for and express regularity in repeated reasoning.

• Students should notice repetition in specific calculations
  • Changing fraction to a decimal (repeated decimal digit(s))
  • Using slope to check whether a point is on a line
  • Recognizing specific products in algebra
• Students should maintain oversight of a process while attending to details
• Students should recognize the reasonableness ofanswers as attending to detail (thinking about thinking)

The Standards of Mathematical Practice indicate ways in which students ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout their formative years. Educators should attend to the need of connecting mathematical practice with mathematical content. It is imperative that mathematical practice be developed so that students will not rely too heavily on procedural methods only. Without a flexible base from which to work students may not be able to develop alternate methods of solution or accept a comparable argument developed by others.

Diocesan Curriculum Goals in the Teaching of Mathematics are the following:

Students will:

• experience a rigorous mathematical education that teaches them to develop into reflective, creative, collaborative and global citizens that reflect the values and concepts of the Catholic Faith.
• learn Catholic ethics that influence analyzing and comparing mathematical statistics
• become mathematical problem solvers and critical thinkers, confident in their understanding and abilities in mathematics.
• become problem solvers, transferring mathematical content to real-life applications.
• be able to communicate mathematic concepts, verbally and with written  expression.
• demonstrate mathematical applications in various disciplines.
• use appropriate forms of technology to demonstrate and communicate application of mathematical concepts.
• be assessed and evaluated in diverse ways so that each student will achieve their potential in mathematical education.
• develop an in depth comprehension of the mathematical concept that is being taught.
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