Opening the Door to My Classroom
When Cathy started teaching mathematics, she thought it focused on what?
Arithmetic, that teaching math was about showing methods, and that learning math meant carefully following procedures.
What was Ms. Humphreys writing project from her master's paper?
Algebraic representations
____, is one of the most rapidly growing areas of mathematics and scientific research.
Visualization
What is the difference between instrumental and relational understanding?
Instrumental (what to do)
Relational (What to do and why)
What manipulatives did Ms. Humphrey use in her sequence-linked lessons for students to use for their investigation?
Cubes, tiles, toothpicks, pattern blocks, and Cuisenaire Rods.
What four different representations were planned to be introduced to students thought a series of lessons?
Geometric, numeric, verbal and algebraic
In the article by Alan Schoenfeld, what did he say about students who have mastered procedures without mastering the underlying substance?
"Being able to perform the appropriate algorithmic procedures, although important, does not necessarily indicate any depth of understanding."
What is task implementation?
The decisions teachers make when they present tasks to the classroom.
As Ms. Humphrey walked around during small group work, her goal was not to correct students' errors or to put them on the right track but to_____?
Ask questions and find out how they are thinking. To keep students responsible for their thinking.
When Cathy and her team watched the classroom videos, what were they looking for?
Interesting, unexpected, and sometimes difficult moments that occurred during ordinary lessons.
Without talking or writing, calculate the number of colored squares in the border.
10+9+9+8
10+10+8+8
(10x10)-(8x8)
4x9
What idea causes students to engage in cognitive conflict that promotes learning?
Competing Ideas or Passive Reception Ideas
Competing Ideas, because research tells us that students learn a lot when they consider ideas, even when some of them are wrong.
What themes emerged for the team as they were watching the mathematical videos?
Grappling with making connections among mathematical ideas, representations, or models or with real-world context.
Name three out of the nine types of teacher questions that are used to build an understanding of algebraic representation.
1. Gathering information, checking for a method, and leading students through a method.
2. Inserting terminology
3. Exploring mathematical meanings and relationships
4. Probing; getting students to explain their thinking
5. Generating discussion
6. Linking and applying
7. Extending thinking
8. Orienting and focusing
9. Establishing context