Term
| 5 features of qualitative research |
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Definition
Bogdan and Biklin
Never Mind I Don't Care
Naturalistic
Meaning
Inductive
Descriptive
Concern with Process |
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Term
| 5 mathematical representations |
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Definition
Clement
Pretty Soon Women Rule Men
Pictures
Spoken Language
Written Language
Relevant Situations
Manipulatives |
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Term
| Strands of Mathematical Proficiency |
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Definition
Adding It Up
SuPer CAP
Strategic Competence
Procedural Fluency
Conceptual Understanding
Adaptive Reasoning
Productive Disposition |
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Definition
Relational Understanding (understanding reasons)
vs.
Instrumental understanding (rules w/o reason) |
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Definition
| Calculational vs. Conceptual |
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Definition
| Conceptual understanding needs to come first |
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| Rachel video paper - conceptual understanding needs to come first |
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| students follow the action in the story so solve problems |
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Definition
teachers must have a flexible mind to understand and appreciate studetn's thinking
also, all things constructivist |
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Direct Modeling -> Counting -> Derived Facts
Problem Types - SCU, JRU, etc. |
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Definition
| supporting/extending moves |
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Definition
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| Discourse (talk moves): revoicing, wait time, students apply their own reasoning |
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Definition
| Algebrafy existing materials |
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Definition
= means 'same as'
creating t/f statements to explore equality understanding - led to variable use lessons with student created problems |
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Definition
| even/odd study with 2nd grade |
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Definition
teaching +/- algorithm often makes kids lose sense of place value
students naturally move towards more efficient strategies and can understand concepts |
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Definition
multi-digit multiplication - algorithm mistakes made with addition and multiplication
invented strategies move from concrete (repeated addition) to abstract (partitioning and simple/complex doubling) |
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| 6th/7th graders lack number sense, improved when instruction involved estimation and reasonableness |
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| 5th/6th graders - fractions without algorithms - students constructed knowledge about abstract concepts |
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| experiment w/4th graders rational number development - began by teaching percentage first |
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| fractional multipliers and quantities, fraction problem types |
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Term
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Definition
discuss ways to do qualititative research including:
ethnography, case study, action research
data collection: field notes and transcripts with audio/video recordings
triangulation
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Definition
focus on data analysis methods including:
microanalysis, open coding, axial coding, memos and diagrams
grounded theory
research process should start with a good question |
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| conversation vs. formal ethnographic interview |
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| all about clinical interview |
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Definition
validity - study measures what it claims
reliability - results are consistent |
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surveys
open ended vs. forced choice |
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Definition
| two views on teaching (to child's interests vs. what the curriculum dictates) don't have to be mutually exclusive |
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