We had a Math Institute at my school which took place the first week of our summer vacation. (So, yeah, that sucked, but my goal is to BE POSITIVE and so I shuffled some things around and went.) For several years now, my school has focused on Whole Class Processing, finding ways to get all students thinking and participating. Now we want to find ways to go further, and get students to start reflecting on their own thought processes (metacognition).
Our department head had taken an online course through the University of San Diego called “Math is Not Just Numbers” that she recommends as a way to start facilitating classroom discussion. Now, of course, in order to have effective classroom discussion, there must also be effective and consistent classroom management, but that is a discussion for another day.
The articles that we studied came from the National Council of Teachers of Mathematics (NCTM) .
Lesson planning goals:
Goal #1: Building Lessons
Creating lessons that focus on exploration rather than lecturing and that encourage students to visualize and discuss larger concepts.
Goal # 2: Modes of Response
Teaching students how you want them to think about things and encouraging group or partner discussion.
Goal #3: How You’re Asking for the Answer
Types of questions to ask students: Explain your reasoning: how did you get there? Can you model it? Can you explain it?
Goal #4: Student Discourse
Engaging students in discussion and getting them to critique each other’s reasoning, encouraging them to look for counterexamples.
Some other ideas for encouraging students to think critically:
“Socratic Survivor.” Points are given for each question level, and there are two groups of students arranged in a “fishbowl” design, where the inner group discusses, and the outer group evaluates the discussion.
A,B,C level responses on homework assignments
C level: Do the problem; give the answer
B level: Show what formula or theorem is used. Show all work.
A level: Justify each step. Explain how you got the answer.
This allows small and simple assignments that encourage whole class participation, while rewarding students who put in extra thought and effort.
Building the knowledge base of fundamentals so that the students have the working ability for higher-level thinking. This can be done by introducing these higher-level thinking concepts with lower-level mathematics.
Resource for effective questioning: Developing Mathematical Thinking With Effective Questioning
Resource for interactive lesson plans: http://geogebrawiki.wikispaces.com
Resources for test writing: Smarter Balanced Assessments
Humble Pi 