Module 5, Unit 4, Activity 1: Pre-Assessment for Differentiation

Pre-assessment in a Mathematics Class (11^th grade)

In order to assess my students before beginning a new topic, I’m going to apply a quiz at the end of the class. This quiz will have 5 questions:

-1 question asking them what they know about the next subject,

-2 simple questions regarding the following topic, for example a very basic problem,
-2 questions that require mastery of the following topic.

For mathematics, I think quizzes are a very straightforward way to discover what students know or don’t know. It’s not only effective and provides the required information, but it’s also quick, so not a lot of time of instruction is lost.

With the information gathered from the quizzes, I will be able to identify 3 groups of students:

1. the students who answered all, including at least 1 of most difficult questions of the pre-assessment questions correctly
2. the students who have some knowledge about the topic as shown in their score, but need to develop higher order thinking skills. These students were able to answer the first 2 or 3 questions but were unable to solve the problem that required mastery of the topic
3. the students who appear to have limited knowledge about the topic, answering less than questions accurately.

For ELL students and students with special needs, they can answer questions to the quiz by drawing the solution when appropriate. For students with special needs, they can email me the quiz later that day.

A sample of this quiz would be the following:

The topic for the next class is derivatives

ELL students or students with special needs can draw what a derivative represents if they struggle finding the words to define it.
 

Example of answers with drawings:

1.

Now that I have gathered the information from the quizzes and that I have distinguished 3 groups of students as described above, this is the plan for the next class:

  

All of the students will receive the same instruction in class during the first 20 minutes: I will explain with many examples the concept and use of derivative, where it comes from and how does it look in a graph. After this, I will explain how to solve problems with the “I do, we do, you do it together, you do it alone” technique.  I will solve simple problems and then problems of medium complexity, then to continue solving problems I will ask for the participation of the students (“we do it together” part) when solving the second set of problems. After this, I will divide the classroom in 3 groups, for the “you do it together” part. The groups will be as follows:

- Students who have answered all of the questions of the quiz correctly, or at least 4 of them, clearly know how to find derivatives, they will be solving more complex problems on IXL.com, after solving problems and therefore reinforcing their knowledge, they  watch a short video that explains how to find derivatives of rational functions such as

The transition from finding derivatives of complex polynomials to finding derivatives of rational functions is very natural and students that have proven to understand how to find the derivatives of complex polynomials will see that they can express the given rational functions as polynomials, and therefore, finding the derivatives should be very easy for them. With the help of IXL.com they will solve simple exercises of this kind.

The next class, I will give a larger introduction on finding derivatives of rational functions, and these students can assist me on helping their classmates to solve these kind of problems when the time to solve problems comes (for this class I will also employ the “I do it, we do it, you do it together” method).

- Students in group 2 will focus on reinforcing the knowledge learned in class by solving exercises pertinent to them. They can form small groups of 3 students each and help each other solve problems. To each group I will give several exercises to solve, and when everyone is done, one group will grade the exercises of one group, and so on.

- I, the teacher, will be with students in group 3, I will explain the topic again in a brief way and using more drawings and graphs to better illustrate the topic.  And then I will employ the “I do, we do together, you do it alone” technique for solving problems. For the last part of the class, they will again solve the quiz and other exercises.

Since all the 3 groups will be solving exercises, besides helping them reinforce they knowledge it will help me assess the students as well. For this unit, since being able to find derivatives requires practice, I will be employing the “I do it, we do it, you do it together, you do it alone” method. This method will also help me assess the students throughout the unit.

Alternative pre-assessment: Another option is to give a brief introduction to the new topic the day before the new topic is introduced and ask them to fill out a KWL chart, where K denotes what they already know, W denotes what they want to learn, and L denotes what they’ve learned, as the introduction would be very brief (less than 5 minutes), there won’t be much material for them to write in the L section, but at least they would be able to remember what topic is the one that we will be addressing next class and hopefully (with the right encouragement) be excited about learning the new topic.

With the information I gather from the KWL charts, I can find interesting ways to present the new topic to the students and will also be able to identify the 3 groups I mentioned previously with the help of the “what I know” part of the chart.