Thursday, December 1, 2016

Promoting Productive Struggle & Implementing Formative Assessment Lessons

We had an amazing meeting yesterday with our district's Math Design Collaborative yesterday for training on implementing FALs. One of the resources we went through was this article of 8 Teaching Habits that Block Productive Struggle in Math Students. It's kind of a what-not-to-do guide to teaching math. I also like that they paired it with this infographic poster of what to do instead. 

Our district is involved in a 3-year initiative with SREB, and I really couldn't possibly be more excited about this. Our best teachers have been selected (2 per school) to participate. We have teachers from every grade level 6-12, and from all types of schools. (Even our alternative school is participating!!)

During year 1, we have 8 days together as a group, and yesterday was Day 5. PD focuses on how to implement Formative Assessment Lessons (FALs), which are housed at

Now, when I was in the classroom, I was aware of this website, but hadn't implemented any of the lessons in their entirety. (To be REALLY REALLY honest, I had just stolen a few tasks and card sorts, and not used anything else.)

I had NO IDEA that all of the resources on this website are research based and are most effective (by far!) as complete lessons. 

Here's the basic idea, but you'll really get a better picture by reading through one of the scripted lessons. 

  • FALs are separated into 2 categories:
    • Concept Development (named based on content)
    • Problem Solving (name based on context)
  • Concept Development FALs are meant to be used one-half to two-thirds of the way through a unit. The goal is to figure out what kids know, what they don't know, and then use that to guide instruction (both through the remaining part of the unit, and to change how you teach that content next year). Sometimes these FALs also work at the beginning of a unit to review prerequisite content and guide the transition into new content. 
  • Problem Solving FALs can be used any time during a unit, and are structured around really great problems with plenty of arguing potential. ;)

Here's the basic process to go through a FAL (I'll use a concept development FAL as an example, because so far it's the one I've worked with the most)

The day before the FAL: 
  • Give the pre-assessment as an exit slip.
  • That afternoon, sort the pre-assessments into 1,2, & 3 point piles (1 - little to no understanding, 2 - demonstrates some understanding, 3 - demonstrates understanding). Then use these piles to create homogeneous pairs of students (so the top 2 kids are paired together, then the next highest 2, etc). This isn't a formal grading process. 
  • Once pairs are developed, and while the results on the pre-assessment are fresh in your mind, choose (or create) some feedback questions from the script. They should be based on the major misconceptions, obstacles, or gaps in learning you observed on the pre-assessments. 
  • Make sure you have all materials & cards prepped and ready.
Day of the FAL:
  • Follow the lesson script through the whole class intro, collaborative activity, sharing & whole class discussion, and then administer the post-assessment. 
    • Whole class intro: usually involves white boards and some powerpoint slides. During this portion, you're just reminding kids of the work they did on the pre-assessment, and not "teaching." Just ask them some guiding questions to get them to notice differences in each other's responses. 
    • Collaborative activity: when students work on activity (usually a card sort) in the pairs you designed based on their pre-assessment. Just give the time allotted in the script, and let go of the idea of completion. Just let each pair get as far as they can in the time given. During this time, project the feedback questions developed the day before.
    • Sharing/Whole Class Discussion: usually involves some time to combine/change groups and compare answers, then a return to the whiteboards to discuss as a class. 
    • Post-assessment is "graded" (but not really) the same way that the pre-assessment was, so that you can measure growth for each class.
My personal favorite FAL? Right now, it's Generating Polynomials from Patterns
Students use dot patterns to develop polynomial expressions for the white, black, and total dot patterns and WOW do they have to do some serious work with this one! It seriously challenges the advanced kiddos without being inaccessible for lower-achieving students.

Second runner up is Applying Properties of Exponents. I had a huge "AHA" moment with this one. How many times, when we're teaching laws of exponents, do we pretend like addition and subtraction of terms just cease to exist for a week or two? I'm definitely guilty. Here are the first few cards from this FAL so you can see what I'm talking about:

But if we choose not to shy away from types of problems that aren't immediately simplified using one application of one exponent property, our students are all the better for it. And this FAL does a phenomenal job of facing those obstacles, misconceptions, and gaps in learning square in the face.

Each of the FALs is designed to promote productive struggle in students. Each one is also designed to promote valuable, serious mathematical discourse. And that's something we should all strive to include more of in our classrooms.

And don't forget about the What-Not-To-Do and What-To-Do-Instead for Promoting Productive Struggle that I mentioned in the beginning of the post from the MIND Research Institute blog


  1. Teaching math is struggle indeed. It is like a battle that leaves no mercy to those who don’t appreciate its value in the knowledge-getting process. The tips teach the teachers how to praise creativity and witty mind rather than show off students who have already gained something. It shows that with the right approach even the students with low math scores will be motivated to try harder and try understanding math, thus leaving more time for other subjects and training other skills like how to buy an essay online for instance.

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