Tag Archives: Embedding Formative Assessment

Changing Our Practice, Slowly

I am enjoying our slow book chat on Dylan Wiliam’s Embedding Formative Assessment. (You can download the first chapter here, if you are interested.)

Chapter 2 is Your Professional Learning.

Wiliam says, “A far more likely reason for the slowness of teacher change is that it is genuinely difficult.” (page 17)

I second this with a resounding yes!

How many professional development sessions have you attended where the goal of the presenter was to “save the teacher”?

The presenter has all of the answers for how teachers should be teaching students mathematics, and those still in the classroom have none of the answers.

When are we going to believe that those teachers who are still sitting around the table have the best interest of students’ learning at heart?

When are we going to realize that over the past few years teachers have been making efforts to change their classroom instruction from students “sitting and getting” to students actively engaging in the mathematics?

And that changing our practice is good, hard, slow work.

We certainly aren’t completely “there” yet, but we are closer than we were a few years ago, and we need to acknowledge that progress instead of pretending that it’s nonexistent.

Wiliam says, “…we have to accept that teacher learning is slow. In particular, for changes in practice – as opposed to knowledge – to be lasting, it must be integrated into a teacher’s existing routines, and this takes time.” (page 18)

Most of the teachers I know are doing good work.

Even so, “All teachers need to improve their practice; not because they are not good enough, but because they can be better.” (page 20)

Can we, as PD presenters teachers of teachers, recognize that it’s not our job to “save” the teachers in our care?

Can we, as PD participants lifelong learners, recognize that we can all improve our practice?

Is there something you’ve wanted to do differently in your classroom but haven’t had the time to try it yet? Do you keep meaning to give your students a challenge from Estimation 180 or Which One Doesn’t Belong but just haven’t [yet] taken the time? Do you keep meaning to have your students tweet what they are learning? Do you want to incorporate short-cycle formative assessment into your lessons?

A new semester has started (or will start soon, depending on your school calendar). Matt Cutts suggests that we should try something new for 30 days to help make it a habit.

Wiliam suggests teachers need to take small steps as we change our practice. We need accountability, and we need support.

What practice will you change for the next 30 days? Who will serve as your “supportive accountability” partner?

Together, we can do even better work to effect student learning and understanding of mathematics.


Cross posted on The Slow Math Movement.

Wiliam, Dylan, and Siobhán Leahy. Embedding Formative Assessment: Practical Techniques for F-12 Classrooms. West Palm Beach, FL: Learning Sciences, 2015. Print.


Posted by on January 11, 2016 in Professional Learning & Pedagogy


Tags: ,

Short Cycle Formative Assessment: 45-45-90 Triangles

I am enjoying our slow book chat on Dylan Wiliam’s Embedding Formative Assessment. (You can download the first chapter here, if you are interested.)

Chapter 1 is Why Formative Assessment Should Be a Priority for Every Teacher. Wiliam convinced me of this in Embedded Formative Assessment, but I still learned plenty from this chapter. My sentence/phrase/word reflection was actually a paragraph:

Formative assessment emphasizes decision-driven data collection instead of data-driven decision making.

As I planned our Special Right Triangles lesson for Wednesday, I decided what questions to ask based on what was essential to learn.

Level 4: I can use the Pythagorean Theorem & special right triangle relationships to solve right triangles in applied problems.

Level 3: I can solve special right triangles.

Level 2: I can use the Pythagorean Theorem.

Level 1: I can perform calculations with squaring and square rooting.

We started class with a Quick Poll.

I was surprised at how long it took students to get started. I hadn’t planned it purposefully, but the way the triangle was given forced them to make more connections than if the two legs had been marked congruent.


Eventually, everyone got a correct answer (and the opportunity to learn more about using the square root template) using the Pythagorean Theorem.

I asked them to determine the hypotenuse of a 45˚-45˚-90˚ triangle with a leg of 10 next. As soon as they got their answer, they announced “there’s a pattern”.

3 Screenshot 2016-01-06 08.40.44

They conjectured what would happen for legs of 12 and 7.

4 Screenshot 2016-01-06 08.40.49

I asked them to select a number between 20 and 100 for the leg and convince themselves that the pattern worked for that number, too.

I loved, though, that the first student whose work I saw had to convince himself that it worked for a side length of x before he tried a number between 20 and 100. I took a picture of his work and let him share it later in the class.

5 IMG_0663

Students shared their results with the whole class, and then I sent another poll.

6 Screenshot 2016-01-06 08.45.03

Which led us to reverse the question using the incorrect answer. If √6 is the hypotenuse, what is the leg?

And then a poll to determine the leg given the hypotenuse.

And another poll to determine the leg given the hypotenuse.

I set the timer for 2 minutes and asked students to Doodle what they had learned, using words, pictures, and numbers. And I was pleased that more than the majority took their doodles with them when class was over.

Wiliam says, “But the biggest impact happens with ‘short-cycle’ formative assessment, which takes place not every six to ten weeks but every six to ten minutes, or even every six to ten seconds.” (page 9)

I sent this poll first thing on Friday.

17_1 Screen Shot 2016-01-09 at 2.16.10 PM

Students gave these responses after working alone for 1-2 minutes.

I didn’t show the results, and got these responses after students collaborated with a partner for next minute or two.

When I gave a similar question a previous year, allowing collaboration, the success rate was informative but abysmal.

23 Screen Shot 2016-01-09 at 2.20.51 PM

And so the journey continues … focusing on decision-driven data collection, giving my students and me the opportunity to decide what do next based on “short-cycle” formative assessment.


Wiliam, Dylan, and Siobhán Leahy. Embedding Formative Assessment: Practical Techniques for F-12 Classrooms. West Palm Beach, FL: Learning Sciences, 2015. Print.


Posted by on January 9, 2016 in Geometry, Right Triangles


Tags: , , , , , ,