7.11 - Mathematics Policy

SERIES 7 - EDUCATIONAL PROGRAM

What we want to find out is whether [the study of mathematics] is on the whole one which, when taken further, has the effect of making it easier to see the form of the good. And that, we say, is the tendency of everything which compels the mind to turn to the region of ultimate blessedness which it must spurn no effort to see. —Plato

Principles for Teaching Elementary Mathematics:
Historically in the United States, mathematics has been taught procedurally. With the procedural approach students are taught “cookbook steps” for solving problems Studies show that students are able to extract simple concepts from procedural teaching in the
early grades, but in later years, as concepts become more difficult, understanding is lost, and students retain less knowledge.

Liberty utilizes a conceptual approach to teaching mathematics. With the conceptual approach, it is not enough to assert something is true; instead teachers (and students) must be able to prove why something is true every step of the way, based on concepts the students already know and understand. Once students understand why something works, they can apply the concept to other situations.

New knowledge builds on old knowledge. To be successful, students need to thoroughly master a math concept before moving on to the next.

As students progress along the Thinking Framework, they should recognize multiple ways to solve a problem, be able to evaluate each approach, and determine which would be the most reasonable to use.

The Singapore National Math Curriculum is a conceptual math curriculum which supports these principles and has been approved for math instruction in kindergarten through 6^th grade at Liberty Common School.

Principles for Teaching Junior High And High School Mathematics:
Many junior high schools in the United States employ an integrated approach to math that attempts to spread the material from Algebra 1, Geometry, and Algebra 2 over the course of three years. The math material is sometimes diluted with social studies and science to solve “real world” problems. This curriculum is inconsistent with conceptual mathematics because in many cases the math concepts are presented in a fragmented way so that mastery is not developed and thus student understanding is reduced.

At Liberty Algebra 1, Geometry, and Algebra II with Trigonometry are purposefully taught as distinct year-long courses.
 

• A fundamentally sound understanding of Algebra is critical to further studies in math and science.
• The study of Geometry/Trigonometry develops logic and thinking skills necessary for higher level mathematics, science, mature writing composition, philosophy, and general research.

Through an in-depth study of Algebra and Geometry, students become very familiar with multiple approaches to solving the same problem and develop the thought process (reasoning) involved in identifying the “best” option for a given problem.

The goal is for all Liberty graduates to be ready for college-level mathematics courses, including but not limited to calculus and statistics courses.
 

Skill Development
Skills and understanding are heavily intertwined. Teachers must combine the approved math curriculum with proper emphasis on automation of skills

Automaticity, the ability for students to immediately recognize math facts, takes practice. Automaticity allows students to focus their mental energies on the demands of more difficult math concepts. Teachers will establish expectations for math fact automaticity at each grade level.

Fluency in executing basic math skills is essential for students to progress to the next level. Once concepts are taught, students should be assigned sufficient practice problems to develop fluency of the math operations.

Calculators
Calculators prevent automaticity and are not to be used for math in grades K-6. Calculators may be used in junior high and high school math, science, and economics courses only after students have developed automaticity and mastery of the math concepts being used. Junior high and high school teachers may develop additional policies and procedures for the use of calculators, as appropriate.

Curriculum Considerations

• The approved curricula may not sequentially cover all math content in the Core Knowledge Sequence. In accordance with the school’s Educational Priorities policy, teachers should follow the timeline in the approved math curriculum rather than the Core Knowledge Sequence. Teachers should verify, however, that the Core Knowledge math content for their grade level is covered at some grade level in the approved curriculum. Any gaps in the approved curriculum should be documented by the teacher and provided to the Principal.
   
• Teachers must review the current Colorado standards and ensure students have covered the requirements.
   

Supporting References

• Knowing and Teaching Elementary Math by Liping Ma
   
• Basic Skills Versus Conceptual Understanding, by H. Wu, American Educator, Fall 1999
   
• A Review of an Integrated High School Mathematics Program by Diane Fogler, mathematicallycorrect.com

Adopted: 11-18-04
Amended: 12-03-2011
Amended: 02-27-2020