EDUC A300 McMurtrie

Content standards are the actual skills that teachers aim to impart to their students. They change as students age, becoming more complex. The National Council of Teachers of Mathematics (NCTM) divides K-12 mathematics educational standards into five categories, which evolve throughout elementary, middle, and high school.

• Number and Operations: Students understand numbers (including fractions, decimals, and percentages), their relationships to one another, and their uses in the real world, as well as the properties of number systems.
• Algebra: Algebra entails recognizing number patterns, though this standard also includes the introduction of variables and the use of graphs beginning in middle school. High school students move on to functions, exponents, polynomials, and more.
• Geometry: Kindergarteners and first-graders learn basic shapes, while high school students analyze the properties of three-dimensional shapes, learn trigonometry, and examine the relationships between shapes and objects.
• Measurement: Younger students learn how to use a ruler or scale. As they advance, they learn different systems of measurement (e.g., metric) and calculate complex equations that include different units.
• Data analysis and probability: In their introduction to data analysis and probability, students gather data about their immediate surroundings and situate it in charts and graphs. Eventually, they analyze the relationships between variables and learn to determine randomization and the applicability of statistical studies and surveys.

Process standards are rooted in the methods that students are taught to use as they approach math problems. They are foundational and can be applied to different kinds of math problems throughout a student’s academic career. The Common Core and the NCTM use five different process standards:

• Problem-solving: No matter what they’re learning, students should solve problems in math class, including both abstract and real-life ones. This forces them to apply the concepts they’ve learned within specific parameters to come up with the answer.
• Reasoning and proof: Students should understand why mathematical proofs are important to the field, since this helps them understand the theory behind the math and the reason why things work the way they do.
• Communication: Students need to be able to communicate mathematical ideas to each other, reinforcing key concepts in the process. They can also effectively analyze the ideas and concepts of mathematicians and other students.
• Connections: Students should understand how mathematical concepts relate to one another and apply those connections in different contexts, both inside and outside of the classroom. Strong communication fosters connections.
• Representation: Students should be able to come up with scenarios and models that illustrate mathematical concepts, demonstrating that they can apply those concepts in any situation.