Pre-assessments, formative assessments, and summative assessments are all methods of assessing, monitoring, and evaluating student learning. Pre-assessments give the teacher insight on each student’s ability or level of understanding prior to starting a lesson. This allows the teacher to make any necessary changes to his/her lesson in to adapt to the learning needs of the students. In mathematics at the high school level, pre-assessments are usually implemented by assigning the students a problem on the board to solve. The students work through the problem on their individual white boards and show the teacher their answer. Another way that this may be implemented is by asking students to analyze any errors in a worked out example to assess their ability to critique the reasoning of others. Depending on the lesson following the pre-assessment, it may be administered the day before to give the teacher the opportunity to address any misconceptions in the upcoming lesson the next day. One way to accommodate the pre-assessment is to have students explain to their partners what the activity is and what they need to do before attempting it. This will help address any misunderstanding they may have about the activity.
Formative assessments monitor student learning by providing the teacher with ongoing feedback. Instead of waiting until the end of a lesson sequence, the teacher monitors his/her students’ learning throughout the entire process of the learning sequence. They are not only a way of monitoring student progress from the teacher’s perspective, but a way for teachers to guide their students’ learning through reflection. In mathematics at the high school level, formative assessments take place in a variety of ways. For example, the teacher may use the time that students are working with their partners to circulate around the classroom and engage each of the groups. The teacher may periodically have the students use their individual white boards to work on a particular problem. Other forms of formative assessments may be a little more extensive. For example, the teacher could engage the students in a performance-based assessment task or a project-based learning activity. Both of these could last a little longer than a class period, but the level of student engagement and participation provides the teacher with a wealth of information regarding the students’ current level of understanding. One way to accommodate this type of assessment is by grouping particular students with other students who are willing to provide extra help during the assessment. This will allow those students to get the support they need from their peers as they work through the assessment.
Summative assessments are usually given to evaluate student learning at the end of a learning sequence, limiting the teacher’s ability to monitor his/her students’ progress throughout the lesson sequence. Summative assessments that are used more periodically allow a teacher to reflect on the results of those assessments and gauge their teaching appropriately. In mathematics at the high school level, these usually come in the form of a chapter test, but not always. They can also come in the form of weekly quizzes and mid-chapter quizzes. The format of the assessment varies according to the material being covered. One way to accommodate summative assessments is by providing students with a menu of questions, allowing them to choose the questions that they feel more confident answering.