The SPOSA Model for problem-based teaching
By Larry Copes
This step is often unnecessary. Occasionally you'll want to remind students of the context in which they've been working, or tell them where you got the problem.
It's a problem that you haven't told them how to solve. Someone should read it aloud, perhaps a student in each group, for the more aurally-oriented students. Clarify any non-mathematical words that studentsespecially ELL/ESL studentsdon't understand.
Observe without saying much. Students may be working in groups(with subsequent presentations) or as a class. Play the ITM role.
Summarize (perhaps with students' help) the mathematical ideas that have arisen. Tell students common terms for the ideas they've just encountered. Use complete sentences: not "percentages" but "Percents are a common way of talking about hundredths" or "To calculate a percent from a fraction you convert the fraction to a decimal and move the decimal place two places to the right." If not all ideas have arisen that you wanted to teach, it probably won't do any good to insert them at this point unless the links are clear.
Students assess their own learning, perhaps through one-minute papers answering questions such as "What did you learn and what are you confused about" or through journaling or through staring on their homework. You make quick notes about how well the teaching went, what you might do differently next time, and observations you made about individual students while they worked. ("Chris showed good critical thinking for the first time.")
Institute for Studies in Educational Mathematics