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C109 Instructional Strategies
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Terms in this set (26)
What is "relational understanding"?
It is when the student knows what to do and why
What are three strategies for developing relational understanding?
Problem-based learning
Promote discourse
Effective questioning
Instrumental understanding
Know what to do, but not why
I.e.: memorizing math facts
It is the goal of math understanding, able to make connections
What are some examples of effective questioning?
1. "What did you do that helped you understand the problem?"
2. "Was there something in this problem that reminded you of another problem you've done?"
3. "Did you find any numbers or information you didn't need?"
4. "How did you know that information wasn't important?"
5. "How did you decide what to do?"
Name some verbs that are used during effective questioning in order to promote higher/deeper thinking.
Construct, Develop, Explain
Explore, Formulate, Predict
Solve, Represent, Verify
Name 5 ways to promote discourse
Revoicing
Rephrasing
Reasoning
Elaborating
Waiting
Describe "revoicing"
Restating a statement as a question in order to clarify, apply appropriate language, and involve more students. Its important to reinforce language and enhance comprehension.
Describe "rephrasing"
Asking students to restate someone else's ideas in their own words will ensure that ideas are stated in a variety of ways and encourage students to listen to each other
Describe "reasoning"
This move asks what they think of the idea proposed by another student
Justify their response
Describe "elaborating"
Challenge, add on, elaborate, give an example.
It is intended to get more participation from students, deepen student understanding and provide extensions
Describe "waiting"
Not talking
Quiet time, gives students time to think
3-5 seconds is an adequate wait time
Cognitive Constructivism
Students build in prior knowledge and experiences. Allows them to make connections.
(PIAGET)
Social cultural theory (aka Social Constructivism)
Students working together and teaching each other (Vygotsky)
Learning is dependent on the new knowledge falling within the ZPD of the learner (who must have access to the assistance), and occurs through interactions that are influenced by tools of mediation (words, pictures, etc.) and the culture within and beyond the classroom
Tools for mathematical concept
Object, picture, or drawing that represents the concepts or onto which the relationship for that concept can be imposed.
Illustrates a concept
Strategies for teaching mathematics
Build new knowledge from prior knowledge
Provide opportunities to talk about mathematics
Build opportunities for reflective thought
Encourage multiple approaches
Engage students in productive struggle
Treat errors as opportunities for learning
Scaffold new content
Conceptual Understanding
Knowledge about relationships or ideas of a topic
Comprehension of math concepts, operations, and relations
How is conceptual understanding beneficial to students when learning mathematics?
It allows the student to apply mathematical principles in different contexts.
5 strands of mathematical proficency
Conceptual understanding
Strategic competence
Procedural fluency
Adaptive reasoning
Productive disposition
Procedural fluency
Knowledge and use of rules and procedures used in math.
Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
Strategic Competence
Ability to formulate, represent, and solve math problems
Need to be able to switch strategies and figure out how to solve problems
Adaptive Reasoning
Capacity for logical thought, reflection, explanation, and justification
Reflect on own work, evaluate it, and adapt as needed.
Productive disposition
Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with belief in diligence and one's own efficacy.
"Can do" attitude
reflective thought
The effort to connect existing ideas to new information
What are the two ways reflective thought occurs?
This can happen in two ways—assimilation and accommodation
describe what happens in assimilation
It occurs when a new concept "fits" with prior knowledge and the new information expands an existing network.
describe what happens in accommodation.
It takes place when the new concept does not "fit" with the existing network (causing what Piaget called disequilibrium), so the brain revamps or replaces the existing schema
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