1. Identification and comparison of numbers: First-year students are just beginning to learn numbers, and it is easy to confuse the shape and size of numbers. For example, they may mistakenly think that the number 5 is greater than the number 3, or that the number 6 is less than the number 8.

2. Operation of addition and subtraction: First-year students are prone to make mistakes when learning addition and subtraction. For example, they may forget to carry or abdicate, resulting in wrong calculation results. In addition, they may confuse the symbols of addition and subtraction, for example, they will mistakenly write a plus sign as a minus sign.

3. The concept of quantity: First-year students are not clear about the concept of quantity, and it is easy to confuse some concepts. For example, they may mistake two identical projects for two different projects, resulting in incorrect calculation results.

4. Understanding and comparison of graphics: Freshmen are apt to confuse different shapes of graphics when learning graphics. For example, they may mistake a square for a rectangle or a circle for a triangle.

5. Understanding of time and date: First-year students are prone to make mistakes when learning time and date. For example, they may get the day or month wrong.

To help freshmen avoid these error-prone problems, teachers can take some measures. First of all, vivid and interesting teaching methods can be used to attract students' attention and improve their interest in learning. Secondly, some exercises can be designed to consolidate students' knowledge and help them get familiar with various types of problems. In addition, teachers can also encourage students to do more oral and mental arithmetic exercises to improve their computing ability. Finally, teachers can review tests regularly, find students' mistakes in time, and give guidance and correction. Through these methods, first-year students can be helped to overcome mistakes and improve their mathematics level.