As teachers, we all know what it feels like to grade a pile of tests and discover the unsettling truth that our students did not perform as well as we had hoped or predicted. For instance, after three of four weeks of teaching the Pythagorean Theorem, we find out that most of our students can't consistently identify the hypotenuse of a right triangle.
For years this was a frustration while teaching high school Algebra and Geometry. Adopting daily exit tickets to assess more frequently only solved some of my problems. I still needed to more deeply understand my students' misconceptions, and I wanted students to be in the habit of explaining what they were thinking.
Lessons from the Mathematics Assessment Project (MAP) turned out to be the perfect way for me to check for understanding in my Geometry class. Two-thirds of the way through a unit, I will spend about 90 minutes working with my students on a Formative Assessment Lesson (FAL). FALs are excellent pre-written lessons on different mathematical topics for grades 7-12, with materials included. Find the website here. Ninety-minute lessons can be found under the "Lessons" tab. There are shorter formative assessments under the "Tasks" tab. Every FAL requires students to work on rigorous problems with a partner who is equally matched for that skill. There is very little teacher talk time on FAL day. During that time, I'll listen to students debating with their partners, and collect data from their written work. After the FAL is complete, I adjust my teaching for the remainder of the unit based on what I learned: I can increase the rigor to ensure I am challenging them, and I can address their misunderstandings.
Not only do the FALs address Common Core standards, but also the Mathematical Practices, especially these two: "Make sense of problems and persevere in solving them," and "Construct viable arguments and critique the reasoning of others." My students love Formative Assessment Day, because at the end they always feel smarter. They succeed at pushing through rigorous problems that they previously would have been intimidated by. Most importantly, I get a chance to see exactly what students understand and what I need to do in the coming days.
Formative assessment lessons can be challenging to implement for the first time. Here are some tips to get you started:
It's important to group students with someone who performed just as well as they did on the pre-assessment. Trust me. You will be amazed at how well all of your struggling students perform when they must rise to the challenge of doing all of the thinking!
Your goal is to figure out what students know and understand, not the right answer. As teachers, we tend to ask leading questions. "What should you do next? It's not division, it's…" Instead, we need to ask open ended questions. "Great work. Why did you decide to multiply there?"
Take time to really get to know each lesson before you teach it. Though the lessons are planned for you, you will need as much time as a regular day to prepare to teach each lesson. Try to practice the lesson with a colleague.
The right lesson for your class may be labeled under a different grade level. Since many of our students were not in Common Core-aligned classrooms a few years ago, younger grade level lessons may be appropriate for them.
Because of the deep understanding I gain about student thinking from each FAL, each one I complete with my students pushes me to re-examine the rigor level of my classroom. I hope they do the same for you and your students!