Mathematics isn’t just knowing that one plus one equals two. It means understanding why that’s true. To mathematicians –– and those in related fields, such as engineering and computer science –– numbers and equations contain a lot of meaning that those with untrained eyes might not be able to see.
There are those who believe that our ability to process and understand math is innate; some of us are “math people,” and others are not. However, the way that elementary, middle and high school educators teach mathematics can make a difference in students’ ability to understand and process math. Teaching mathematics effectively involves incorporating process and content standards into daily lessons. What is the difference between content standards and process standards for math? Continue reading to find out.
Teaching Math in the 21st Century
As of 2019, 41 states and the District of Columbia adhere to the Common Core standards, which the National Governors Association and Council of Chief State School Officers implemented in 2010. Though not legally binding, they offer benchmarks for each grade level in different subjects, setting a national standard for educational development.
The Common Core website notes, “Mathematics education in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country.” To help U.S. students improve their math abilities and keep the country among the world leaders in STEM (science, technology, engineering, and math), the Common Core implemented content and process standards for teachers to administer and students to meet.
Understanding Content Standards vs. Process Standards
Mathematics education is about ensuring students understand the process behind the content they’re learning. In turn, they become high-level problem-solvers rather than machines who arrive at the correct answer without necessarily understanding the rules and theorems that underlie the equation. Educators should make sure that not only are their students able to arrive at the right answer but that they thoroughly understand the line of thinking that gets them there. Process standards and content standards are developed by state and local educational boards, and both should be used in the classroom to ensure a comprehensive understanding of the topic.
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.
Learning to Teach Math with Maryville University
Mathematics teachers make it their duty to foster a love of mathematics in their students, which can become a lifelong pursuit. Many students discover a passion for mathematics during elementary, middle, and high school education, wherein content and process standards are reinforced. Those who hope to become educators, incorporating powerful learning strategies in the classroom, can benefit from Maryville University’s online Bachelor of Science in Mathematics. Find out more about how this degree can help you instill your love of math in the next generation of students.