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Math teachers understand that these basic operations are the foundations of more **advanced math** topics, and show **their students** how the topics they learn at the beginning of high school transfer to later grades, and more **advanced math** classes.

Certification also tests future educators on their knowledge of the properties of prime numbers, even and odd numbers, and multiples. They should be able to express these numbers using algebraic expressions, formulas, and equations to demonstrate an understanding of number theory.

Potential teachers who want to pass certification must be able to analyze precision, accuracy, and errors in measurement situations. For example, when solving problems between relationships in geometric shapes, teachers must understand concepts of approximation.

The certification process necessitates teachers understand basic transformations, such as the reflections, translations, and rotations that underlie concepts of geometry. Teachers must have an understanding of the basic geometric constructions, such as cubes, rectangles, rhombuses, and trapezoids.

Statistics knowledge allows math teachers to interpret and draw conclusions from data sets, and use these conclusions to reach decisions in complex problems. Teachers who pass certification tests demonstrate how finding the mode, median, and mean contribute to statistical reasoning.

Teachers must also understand statistical limits, such as false generalizations about populations. Teachers organize the statistical data they interpret into algebraic functions and formulas, necessitating a thorough understanding of more complex math topics, such as calculus.

Certification in mathematics shows that a teacher has worked hard to meet the standards set by state certification exams. If you’re interested in a career in teaching high school math, you can learn more about your state’s certification process here. Improving Mathematical Learning

According to “Five Ideas for 21st Century Math Classrooms,” published in American Secondary Education, studies show that students from many Asian countries excel in math, and that by adopting some of these teaching strategies, American math scores would improve.

In the article, Kenneth W. Gasser notes that U.S. classrooms must shift focus to “problem-based instruction.” Gasser writes that many math teachers might say they already use problem-based instruction, but in reality, most students don’t care that “27 heads and 78 legs in a barn equates to 12 cows and 15 chickens.”

To make math more applicable to __their students__, teachers should provide questions that are more meaningful to **their students**‘ lives. For example, students who work on problems such as how much gas they can buy with a set amount of money would show a greater understanding of the subject matter.

Gasser also says that too often, a teacher is leading an uninterested class of students who don’t feel as if they are actively participating in the learning process. Math teachers should **allow students** to attempt problems without being lectured, leading to greater discovery and student-led solutions.

Teachers should *allow students* to attempt new problems with the best of their knowledge. This allows students to discover solutions on their own, dynamically solving problems with experience. After *students attempt* to solve problems, only then should teachers show students the correct steps and the right approach.

This leads to another valuable trait of learning Gasser says is often missing in the U.S. classroom: failure. Gasser notes that failure should be seen as part of life and the learning process. Students must become less apprehensive of failure, and teachers must produce an environment where failure should not be shameful.

Lightening the classroom mood by making failure normal naturally makes the classroom environment less stressful as well. Students who are having more fun and who are less stressed while learning are also more likely to retain complex concepts of math year-to-year.