Term
5 features of qualitative research 

Definition
Bogdan and Biklin
Never Mind I Don't Care
Naturalistic
Meaning
Inductive
Descriptive
Concern with Process 


Term
5 mathematical representations 

Definition
Clement
Pretty Soon Women Rule Men
Pictures
Spoken Language
Written Language
Relevant Situations
Manipulatives 


Term
Strands of Mathematical Proficiency 

Definition
Adding It Up
SuPer CAP
Strategic Competence
Procedural Fluency
Conceptual Understanding
Adaptive Reasoning
Productive Disposition 


Term

Definition
Relational Understanding (understanding reasons)
vs.
Instrumental understanding (rules w/o reason) 


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Calculational vs. Conceptual 


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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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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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supporting/extending moves 


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Discourse (talk moves): revoicing, wait time, students apply their own reasoning 


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Algebrafy existing materials 


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= means 'same as'
creating t/f statements to explore equality understanding  led to variable use lessons with student created problems 


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even/odd study with 2nd grade 


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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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multidigit 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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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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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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validity  study measures what it claims
reliability  results are consistent 


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surveys
open ended vs. forced choice 


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two views on teaching (to child's interests vs. what the curriculum dictates) don't have to be mutually exclusive 

