Geometry, Measurement, & Reasoning

All students of the 21st century must be mathematically literate to perform in the workplace, be lifelong learners, and be confident problem solvers. Our changing society demands a working knowledge of patterns, functions, algebra, spatial relationships, geometry, measurement, data analysis, probability, and competent use of technology. As our society and technology changes, so too does the mathematics which is accessible to students and the way in which it is taught and learned.

Traditional topics of algebra and geometry remain important components of the secondary school mathematics curriculum. The core learning goals call for a shift in emphasis from memorization of isolated facts and procedures and proficiency with paper-pencil skills to emphasis on conceptual understandings, multiple representations and connections, mathematical modeling, and mathematical problem solving. The integration of ideas from algebra and geometry is particularly strong, with graphical representation playing an important connecting role. Reference is made in the expectations to the use of current technology which includes computers and calculators as appropriate. In addition, topics from data analysis and probability are elevated to a more central position in the core learning goals for all students.

The elements of this core content, compiled to drive mathematics instruction in the high school, are not meant to be separate mathematical courses taught in any particular sequence. This content assumes mathematical preparation at the K-8 level consistent with Maryland Voluntary State Curriculum. Processes such as problem solving, communication, reasoning, and connections should be embedded throughout the content. Real-world applications are the backbone of this content and show students the inherent value and power of mathematics.

Technology is vital to the study of mathematics. While today that technology takes the form of computers and graphing calculators, it is essential that technologies continue to reflect current standards. With the change in technologies, the mathematical processes change.

All students will have equal access to this highly challenging, 21st century mathematics content. All students are expected to demonstrate the ability to apply mathematical knowledge and problem-solving strategies to numerous activities through high school mathematics.

Comments

The following comments are applicable to every expectation:

• The use of " and," "and/or", and "or" should be interpreted for instructional purposes to mean that all of the mathematics included in a goal, expectation, or indicator should be part of the instruction. For assessment purposes, however, it is unlikely that an item will include all of the mathematics included in a goal, expectation, or indicator.
• Instruction at all levels should include opportunities for students to read, interpret, and apply mathematics in context from textbooks and appropriate materials in a variety of ways. Assignments that require students to read mathematics and respond both orally and in writing to questions based on their reading should be an integral part of the mathematics program.
• Multiple approaches to attain the indicators are encouraged.
• Units of measurement can be metric or customary.
• In the Goal 2 statement:
  • 'Justify conclusions' means the student will use mathematical principles to support the reasoning used to solve the problem or to demonstrate that the solution is correct. This could include the appropriate definitions, postulates, and theorems.
  • 'Explain the processes used' means the student will use the language of mathematics to communicate how the student arrived at the solution.