Understanding and Doing Mathematics
How Do Children Learn?
Teaching for Understanding
Mathematics Classrooms that Promote Understanding
MISC.
100
The NCTM identifies which process standards that children should engage in when learning mathematical content.
What are problem solving, reasoning and proof, representation, communication, and connections?
100
The notion that learners are not blank slates, but rather creators.
What is Constructivism?
100
In this type of classroom teachers begin where the children are, and with the children's ideas.
What is a learner-centered classroom?
100
The three most common types of teaching.
What are direct instruction, facilitative methods, and coaching?
100
You should encourage children who use the same tool or strategy every time to do this. (Teaching Tip)
What is take risks to try new tools and strategies?
200
Ability to formulate, represent, and solve mathematical problems.
What is "Strategic competence"?
200
A primary goal of teaching for understanding is to help children develop this.
What is relational understanding of mathematical ideas?
200
Example: When the teacher introduces only one way to solve multidigit addition problems-by modeling how to add numbers using base-ten materials.
What is "teaching toward instrumental understanding?"
200
Besides the students, who else a learner in the classroom?
Who is the teacher?
200
As you listen to children talk about what they are thinking and doing, you should avoid doing this.(Teaching Tip)
What is imposing your ideas onto their ideas?
300
These individuals said, "An understanding can never be covered if it is to be understood."
Who is Wiggins and McTighe?
300
The zone in which the best learning for any given child occur.
What is the zone of proximal development?
300
What can children do when they have more choice in determining which strategies to use.
What is learn more content and make more connections?
300
Teachers should refrain from responding in these ways.
What is "Yes that is correct" and "No that is wrong"?
300
The figure that shows the continuum of understanding.
What is Figure 1.3?
400
Children who look for a pattern or a structure can experience a shift in their perspective or understanding.
What is "look for and make use of structure."
400
The theory that suggests that the learner can be assisted by working with others who are "more knowledgeable."
What is Sociocultural Theory?
400
This type of teaching allows math to be personalized.
What is "teaching toward relational understanding"?
400
Children must come to what understanding to be successful in math.
What is that mathematics makes sense?
400
The strand that talks about comprehension of mathematics in Figure 1.1.
What is conceptual understanding?
500
Conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, productive disposition.
What are the five strands of mathematical proficiency?
500
Making connections can happen in these two ways.
What is assimilation and accommodation?
500
This type of teaching does not allow learners to observe strategies that are more efficient than their own.
What is "teaching toward instrumental understanding"?
500
The teacher should NOT be doing this in the classroom.
What is the thinking, reasoning, and connection building?
500
The title of this chapter.
What is "Teaching Mathematics for Understanding"?
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