December 5, 2023

Formative Fridays

Formative Friday finishes off the week of antiracist interventions. Students take a formative assessment, as a team one week and as individuals the next week. Both assessments use a unique three read graphic organizer that helps students focus as much on the process of solving problems as much as getting the right answer. Each assessment consists of two or three high cognitive demand, Depth of Knowledge three or four problems. Each problem’s solution is broken up into four parts. The first part “What do we want?” is where students identify what solution the problem is actually asking for. The second part “What do we got?” ask students to identify all of the numbers (quantities), units, formulas, rules and tools that they have at their disposal that they may need to solve the problem. Part three “How are we going to get it?” asks students to describe their step by step plan for solving the problem in writing. Lastly, the “Solution” section asks students to actually solve the problem mathematically. Each section is worth the same number of points which is intended to help shift the student’s mindset from answer getting to problem solving. This allows every student to engage in every problem at multiple levels and see themselves a member of the mathematics community (Boaler & Staples, 2008; Boaler, 2016; Langer-Osuna, 2015; Walton et al, 2012). For both individual and team assessments students are allowed to use computers, calculators and notes. Phones are not allowed only in an effort to reduce distractions. With 15 minutes left in class, students are asked to clear their desks of everything but their test paper and a color marker which is given to them. A rubric is then displayed on various large screens around the room where students evaluate their own answers.  It is important to note that students are instructed that if they have an answer that isn’t the same as the one in the rubric they can ask for the teacher’s immediate evaluation. This is another important element of the assessment because it allows students to give themselves immediate feedback which is critical to making the assessment a tool of growth as opposed to just a ranking device (William, 2018, p.123). This also helps give the student agency over their own learning which research has shown leads to greater mathematical growth for students (Boaler, 2003). The final part of the antiracist formative assessment process comes with the individual assessment. Once students have evaluated their own assessment, handed it in and the scores are recorded they can come back in before school, during lunch or after school (Saturday school also when available) to redo every part they lost points on for full credit. This is designed to reinforce that this is a tool of growth, not judgment, help them take ownership and agency over their learning and achieve mastery of the concept. Research shows that this type of scaffolded response is the most effective (Day & Gordon, 1993). Because of the structure of the three read system it is easier for students to assess at what part of the problem-solving process they are struggling the most with. When the students come back in to work on their tests it is with the teacher’s assistance which allows for individually tailored productive struggle toward mastery (Day & Gordon, 1993).

Supplies: 3 Read Test paper, 3 Read Rubric, a class set of a single colored marker

Mathematical Practices

  • Make sense of problems and persevere in solving them: 
  • Reason abstractly and quantitatively
  • Construct viable arguments and critique the reasoning of others
  • Look for and make use of structure

21st Century Skills

  • Critical thinking
  • Collaboration
  • Adaptability and Flexibility
  • Emotional Intelligence (EQ)
  • Judgment and Complex Decision Making


  1. Instruct students that they can use their computers, desmos etc but they can’t use their phones. Also make sure they know if this is a team or individual test.
  2. Pass out the test paper and instruct them to get started. (Students will figure out the process without too much instruction. Make the first one you give a TeaTest and really curve it)
  3. With 15 minutes left in class give them all a unique color marker and have them clear their desks of everything but that marker and their test.
  4. Go through the rubric slide by slide explaining what a 5, 3 or 1 point answer looks like. As they become more familiar with the process they really take ownership of what they award themselves.
  5. Have students add up their scores and collect the test papers and markers.

THE ART OF TEACHING: Picking/writing three rich multistep, low floor, high ceiling problems that make it easy for this process to work is a bit of an art form. I generally end up writing my own. Making the rubric is also a bit of an art form but the more you do it the easier it will become. As time passes you will be amazed at how students appreciate the process and take ownership of it. Rarely have I had a student give themselves more points than I would have in fact usually the opposite is true. Now instead of spending hours grading papers you can invest that time in creating high quality problems and rubrics.