Research documents the powerful impact the inclusion of effective formative assessment has on student learning. I contend that by incorporating formative assessment strategies as a component of our instructional practices, we will almost naturally foster the inclusion of the Mathematical Practices. Both formative assessments and the Mathematical Practices are processes that will foster better teaching and provide evidence that students are learning. They can and must be included in each and every mathematics lesson as we strive to improve our students’ interaction with mathematics. After all, we are seeking better outcomes for all our students.

So, what does this all look like? Every class should begin with posing a

*range question*designed to assess prior student knowledge. Think about the students who demonstrated proficiency in prior mathematics: Do they really need to review what they already know and are able to do, or should they be challenged to apply that knowledge to a more rigorous problem? By posing the range question you will be able to inform your instructional decisions which may require you to tier your instruction or the problems you assign so those students needing more support receive that support and those who need more of a challenge get that opportunity to deepen their understanding.

The inclusion of a

*conjecture board*in every mathematics class (a hypothesis board in science class) not only allows students to make conjectures and analyze the reasoning of others (MP3), but more importantly allows you, the instructor, to identify student misconceptions. This conjecture board seamlessly fits into most lessons and does not need to be added on to other protocols you may use. Once conjectures are made, students work to prove or disprove those conjectures using multiple representations and appropriate manipulatives (MP 1, MP 4). As soon as one counterexample or negation is identified, the conjecture is erased, as it is not a mathematical truth. Students as young as kindergarten and first grade are able to and do make conjectures that are appropriate for their level of cognitive development.

One of the most important tenets of formative assessment is providing immediate feedback to students. This feedback may be oral, as students work through the problem solving process (MP 1), or written on work that students pass in. Either way, the feedback should address the strengths of the student’s thinking, and also raise questions about whether the procedure used will always work. Feedback should include, “Will that always work?” or “Can you convince me that is true?” or “ What would happen if…?”

The inclusion of these formative assessment strategies not only will provide you the time you need to observe, listen, and gather evidence about what the students know and are able to do, but also will empower your students to self-reflect on their own assumptions, misconceptions, and understandings.

Anne