Different assessments

Many assessments are very useful in helping teachers to check students' understanding for the learning materials. In my student teaching math class, three often used assessments are monitoring the students' homework corrections and providing explanations for the questions that they have difficulties to solve, asking questions during instructions to check their understanding for the new content study, and  giving short daily quiz to check if the students grasp the new learning materials. These assessments are very effective for finding students' weaknesses or confusions, so teacher can give appropriate help immediately. Through homework corrections, teacher can know exactly which concepts and math skills that students haven't grasped, so she or he can give instructions or modelings to clarify the problems. The teacher can also provide more exercises for students to practice. Asking questions are also an effective way to know whether  students are ready to move to next instruction. By daily quiz, teacher can clearly know the status of students' understanding of the new contents, so she or he can make decision on the teaching pace for re-teaching or moving on the next content learning.
For ELL or student with special needs, the teacher may need to modify the assessments. The teacher may use individual tutor for ELL instead of asking ELL questions publicly because of the language difficulties of the student. The teacher may use more mathematical expressions and less talking to help the student to understand the math concepts and skills. For the student with special needs, besides the teacher should often check the student' understanding privately, she or he can pair the student with a gifted student so that the partner can give the student learning help. Also, the teacher should communicate with the resource teacher of the student and learn the status of the student's study, and the teacher can also provide the student more time for finishing exercise and quiz so that the student can complete his or her task with less time pressure.
The assessment discussed in the Tomlison textbook is the way to assess students' knowledge by linking the content study with students' interest and their real lives. "One of the pleasures of teaching is the chance to introduce students to q world full of ideas and opportunities they've not yet discovered. Interest-based instruction can not only draw on and expand already existing student interests, but can help them discover new interest as well." (Tomlison, p 54). I feel like to use projects to connect the learning contents with students real world. For example, when I teach the knowledge of Exponential Functions, I can assign a project to let my students to search the data of world population in different period of time, analyze the data, and draw the conclusion to see whether the population growth is exponential from the human history. Through the project, students will feel useful of their math learning and have more interests for their future studies as well as making connections with different learning fields (math and human growth).

 Reference:
Tomlinson, C.A. (2001).  How to differentiate instruction in mixed-ability classroom.