1. Make a double sided copy
2. Cut out the strips
3. Tape the two strips together into one long strip
4. Hold an end in each hand, twist, then tape together
5. Draw a line on one side of the paper.
What happened? The line never crossed an edge, but met up with its starting point! A Möbius strip is an object with only one side and no beginning or end.
I see it as a direct analogy for teaching and learning. Practice, instruction, assessment, and application are. These elements cannot be arranged into a definite pattern with a definite beginning or a definite end. Nor can they be teased out from one another without losing their effectiveness. Teaching and learning is a continuous loop with each aspect supporting and strengthening the other.
Keep picturing teaching and learning as a continuous loop. Now, consider how formative assessment is defined. Dylan Wiliam describes formative assessment as “the bridge between teaching and learning.” Marzano states, in the book Formative Assessment & Standards-Based Grading, that formative assessments are “used while instruction is occurring” and refers to Brookhart’s explanation that “formative assessment means information gathered and reported for use in the development of knowledge and skills[…]” The CCSSO defines formative assessment as “a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning.”
Now consider how formative assessment is implemented in many classrooms. Quizzes, exit slips, conferences, observations, dip sticks? Sure, most of us classify these as formative assessment strategies. But wait, make sure these strategies inform what comes next: instruction, practice, or application, and further assessment. Tests, essays, presentations, performances? Not so fast, these are end of learning assessment strategies. Or are they? When instruction, practice, assessment, and application are intimately entwined, all assessment is formative because everything is informing the next steps for both teachers and students. Sometimes the next steps are interventions. Sometimes the next steps are moving from building background knowledge to building relevance. Sometimes the next steps involve going deeper with reasoning levels with a particular target. Sometimes the next steps are new learning targets. It’s Merlin and Arthur. Take a look at that teaching and learning Möbius strip again.