Education ∪ Math ∪ Technology

This is part two of a three part series on formative assessment. This post deals with some things you can do between individual lessons based on formative assessment and during a lesson. You can read part one here.

Introduction

The objective of this post is to describe two possible procedures teachers can use for ongoing, day-to-day formative assessment. The first of these procedures is easier to implement, but gives teachers less information on what students understand. Remember that a primary objective of formative assessment is to create a feedback loop for both teachers and students into the teaching and learning process.

Example 1

At the end of your last class you gave an exit slip. One strategy, which is not too time-consuming, is to take the exit slip and first sort it into No/Yes piles, and then sort these piles into 3-4 solution pathway piles, essentially organizing all of the student work by whether or not it is correct and what strategy students used. It may be useful to have an other group, with students whose strategy which are unable to decode.

These groups of student can be used to decide on student groups (recommendation: group by different strategy) for the following day, decide if you need to try a different strategy for tomorrow, and/or find examples of student work to present to students. It can also be used to decide on re-engagement strategies1 for the lesson from the previous day, or just decide that you can move onto the next topic in your unit sequence.

Example 2

An exit slip is not the only kind of formative assessment you can do2. The most important feature of formative assessment is coming to understand what students are thinking. You can do this by conferring3 with individual students during your lesson and asking them questions to elicit their thinking. Of course, this assumes you have given students an assignment which requires them to think!

Imagine students are working on a rich math task4 and that you start by initially observing students and see if they are able to get started on the task without your intervention. As the students begin to work, you begin walking around the classroom, and observing them working, and listening to their discussions about the task. Your objective at this time is to gather evidence of what students are thinking about while they do the task.

The three main problems you may have to solve during this time are; students who are unable to get started on their own, students who are going in the completely wrong direction on the task, and students who have completed the task. One of the early tasks during your observation of students working is to figure out which students are in which group. Note that there is a fourth group; students who are not done the task, who may be struggling a little bit, but are making progress. Do not intervene with this group of students!

When you are confused about what students are talking about, or what they are writing, you spend some time clarifying your understanding of what they are thinking, so that you feel completely clear. Now, you choose an intervention5 for the student, such that the student is left to do the mathematical thinking of the task, and you do not lower the cognitive demand of the task. During the entire time students are working on the task, you collect information6 on what the students do during the task.

Conclusion:

In the next post in this series, I will discuss more of the overall objectives of formative assessment, and discuss how the feedback loops created by the process of formative assessment can improve the effectiveness of teaching and learning in classrooms.

Information:

1. Re-engagement is an alternative to reviewing material with students. It can be done during any time the unit when you want to consolidate student understand.

2.  For other examples of formative assessment, see this presentation that I curated. It has 54 different possible formative assessment strategies in it, some of which are more appropriate for a class focused on literacy skills, and some of which are useful for a mathematics classroom.

3.  This document describes the process of conferring.

4. A rich math task allows for students to demonstrate mathematical reasoning, is often open-ended, and allows for multiple solution paths. These kinds of tasks generally take students some time to complete.

5. The intervention you choose should not lower the demands of the task you have set the student. You could ask them a question to prompt their thinking, or suggest a way they can interact with one of their peers (do not assume your students know how to collaborate, they may need a prompt to help them orient to each other’s work and thinking).

6. It is useful to have anticipated student responses before the task, and solved the task yourself a couple of different ways. Finally, having a template to collect information during the lesson would be critical. Here are two such template designed by my colleague Sara Toguchi: Descriptive information, Specific criteria information