Don't just provide answers to the students. Show them example problems in their textbook and then ask them to walk through them on their own. This allows students to think on their own and figure out the paths needed to solve the math problems. The more students think about solving these problems, the faster they can arrive at the solution.
Provide students with guidance. Ask them probing, leading questions that are designed to aid them in their thinking. Questions such as "What do we do next?" or "Can you tell me which equation we use to solve this?" engages students and helps them arrive at the correct answer. Also engage students by relating mathematical concepts to real-life examples. This realistic interpretation of math can aid the learning process.
Taking notes is a vital skill for students in every subject, including math. Many types of math require the memorization of various equations and formulas. Write these on the class whiteboard or another surface where they are visible to all students. Instruct the students to copy these down. Note-taking reinforces the formulas in their mind and provides an easy reference for when students are studying at home.
Be aware that not all students are the same. No one type of learning works for everybody. Note taking may be beneficial to many students but not all. Try to identify which students are struggling more than their peers with specific sections of your curriculum. Engage them one-on-one to help aid their critical thinking. They may need to discuss the problems further or see more examples written by you.
Calculators are a helpful addition to any math classroom. Many schools require math students to purchase and bring their own calculators, while some may provide calculators to the students. Allow the use of calculators during normal class lectures and study sessions. Ask the students to attempt the problem without using a calculator and then use the calculator to verify their answer. This can help students feel more confident in their critical thinking abilities, or it can show them where they went wrong with their manual calculations so they can improve their skills.
Put your students in groups to bolster their thinking abilities. By putting their heads together, students can come to conclusions faster and help correct each other. This fosters a social atmosphere that can be beneficial to the classroom, as well as allowing the teacher to drift from group to group to provide focused instruction to several students at once. Ideally, the various strengths and weaknesses of the group members compliment each other, and critical thinking improves.
Tests and quizzes are effective ways to assess the abilities of each student. Take a look at each student's scores and test answers to see which areas of the curriculum are causing the student to struggle. This can show you what to focus on during one-on-one and group-based teaching sessions. Math-based competitions also can greatly improve critical thinking. In competitions, students are forced to react quickly and efficiently to compete successfully. This increase in mathematical acuity can translate into better critical thinking skills during normal class time.