RUcore: Rutgers University Community Repository
B63, Madison Project: Robert B. Davis Introducing Integers With Pebbles in the Bag (Presentation & classroom view), Grade 3-5, 1950s_1960s, Clip
Descriptive
TitleInfo
Title
B63, Madison Project: Robert B. Davis Introducing Integers With Pebbles in the Bag (Presentation & classroom view), Grade 3-5, 1950s_1960s, Clip
TypeOfResource
MovingImage
Genre
(authority = RURes_Genre)
Research data
Genre
(authority = RURes_dataGenre)
Observational data
Genre
(authority = RURes_dataLifecycle)
Raw data
Genre
(authority = RURes_qualitativeMethod)
Educational interventions (large group)
Genre
(authority = RURes_researchDataType)
Longitudinal data
Genre
(authority = RURes_researchMethodology)
Qualitative research
Genre
(authority = RURes_dataCollectionSetting)
School
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Barbara
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Vicky
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Greg
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Charlotte
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Ian
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Gary
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Sandy
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Nancy
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Todd
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Nora
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Paul
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Bruce
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Brett
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Gray
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Laurie
Subject
Name
(authority = RBDIL_corporate)
NamePart
(type = corporate)
Madison Project
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Jeff
Subject
(authority = Grade range)
Topic
3-5
Subject
(authority = LCSH)
Topic
Mathematics education
Subject
(authority = LCSH)
Topic
Manipulatives (Education)--Case studies
Subject
(authority = LCSH)
Topic
Learning, Psychology of--Case studies
Subject
(authority = NCTM Content)
Topic
Algebra
Subject
(authority = NCTM Process)
Topic
Problem solving
Subject
(authority = NCTM Process)
Topic
Communication
Subject
(authority = NCTM Process)
Topic
Representation
Subject
(authority = NCTM Process)
Topic
Connections
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Counting
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Additive reasoning
Subject
(authority = rbdil_mathProblem)
Topic
Pebbles in the bag
Subject
(authority = rbdil_mathStrand)
Topic
Algebra
Subject
(authority = rbdil_mathTools)
Topic
Colored stones
Subject
(authority = rbdil_representations)
Topic
Equations
Subject
(authority = rbdil_schoolType)
Topic
Public school
Subject
(authority = rbdil_setting)
Topic
Classroom
Subject
(authority = rbdil_studentEthnicity)
Topic
White
Subject
(authority = rbdil_studentGender)
Topic
Mixed
Subject
(authority = rbdil_topic)
Topic
Positive and negative integers
Subject
(authority = RURes_subjectOfStudy)
Topic
Sample of human subjects
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Direct reasoning
Subject
(authority = rbdil_cameraView)
Topic
Presentation view
Subject
(authority = rbdil_cameraView)
Topic
Classroom view
Abstract
(type = summary)
In this 8 minutes whole class discussion about early algebra ideas (specifically with regards to integers), Researcher Robert B. Davis models adding positive and negative integers to a class of elementary school students by having the students add and remove stones from a bag. The actions involve one student giving a command “Go” and then a second student proposes the number of stones to be added or subtracted. Davis then responds to the children’s directions from the class by either adding or removing a specific number of stones to the bag based on the directions. Davis and the students describe each action with symbolic equations that designates addition as “adding more pebbles,” which they symbolize as ‘+’, and subtraction as “take away,” which they symbolize by ‘-‘ before the numeral to designate a negative number. Examples of the equations that the students construct to represent pebble actions are:
3-3=0
5-6=-1
4-1=+3
Toward the end of the session, using pebble actions, Davis leads the class to discuss the meaning of -3 and +3 using the expression 2-5. The whole class agrees that +3 means 3 more pebbles. The camera view focuses on the teacher and whole class.
3-3=0
5-6=-1
4-1=+3
Toward the end of the session, using pebble actions, Davis leads the class to discuss the meaning of -3 and +3 using the expression 2-5. The whole class agrees that +3 means 3 more pebbles. The camera view focuses on the teacher and whole class.
PhysicalDescription
Extent
(unit = digital file(s))
1
InternetMediaType
video/mpeg4
Form
(authority = gmd)
TargetAudience
(authority = RURes_discipline)
Social science
TargetAudience
(authority = RURes_domain)
Mathematics education
Name
(type = personal)
NamePart
(type = family)
Davis
NamePart
(type = given)
Robert B. (Robert Benjamin)
NamePart
(type = date)
1926-1997
Affiliation
Rutgers, the State University of New Jersey
Role
RoleTerm
(type = text);
(authority = marcrelator)
Researcher
Classification
(authority = RUresearch);
(edition = Data)
Location
PhysicalLocation
(authority = marcorg);
(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
OriginInfo
Place
PlaceTerm
(type = text)
New Brunswick, NJ
DateIssued
(point = start);
(encoding = w3cdtf);
(qualifier = approximate);
(keyDate = yes)
1957
CopyrightDate
(point = start);
(encoding = w3cdtf);
(qualifier = approximate);
(keyDate = no)
1957
Subject
HierarchicalGeographic
Country
UNITED STATES
RelatedItem
(type = constituent)
TitleInfo
Title
Early algebra ideas involving one variable, Clip 2 of 11: Introducing integers with pebbles in the bag
Identifier
(type = doi)
https://doi.org/doi:10.7282/T32J69R3
RelatedItem
(type = references)
TitleInfo
Title
Davis, Robert B. The Madison Project: a Brief Introduction to Materials and Activities. 1965. ED028948
Identifier
(type = url)
http://library.webster.edu/archives/findingaids/madison/
Identifier
(type = rbdil)
B63-1950-1960-MADPR-PCV-CLASS-GR3-5-ALG-PIB-CLIP
Note
(type = APA citation)
Robert B. Davis Institute for Learning. (1957). B63, Madison Project: Robert B. Davis Introducing Integers With Pebbles in the Bag (presentation & classroom view), Grade 3-5, 1957_1969, Clip. [video]. Retrieved from
Note
(type = supplementary materials)
Transcript is also available
Note
(type = supplementary materials)
Students work not available
RelatedItem
(type = host)
TitleInfo
Title
Robert B. Davis Institute for Learning Mathematics Education Collection
Identifier
(type = local)
rucore00000001201
Location
PhysicalLocation
(authority = marcorg);
(displayLabel = Rutgers University. Libraries)
NjR
Identifier
(type = doi)
doi:10.7282/T3GQ71Z9
Back to the top
Rights
RightsDeclaration
(AUTHORITY = rbdil1_v1);
(TYPE = [rbdil1_v1] statement #1);
(ID = rbdil1_v1)
The video is protected by copyright. It is available for reviewing and use within the Video Mosaic Collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.
RightsHolder
(type = corporate)
Name
Robert B. Davis Institute for Learning
Role
Copyright holder
Telephone
732-932-8848
Address
Rutgers Graduate School of Education
10 Seminary Place
New Brunswick, NJ 08901-1183
10 Seminary Place
New Brunswick, NJ 08901-1183
RightsEvent
Type
Permission or license
Label
Non-exclusive licence to share the video presentation via RUcore
Detail
Non-exclusive license to digitize and make openly available the videos and other collection resources of the institute is on file in the office of the Rucore Collections Manager
AssociatedEntity
Role
Licensor
Name
Maher, Carolyn A.
Affiliation
Director, Robert B. Davis Institute for Learning, Rutgers Graduate School of Education
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
Publication
Status
Unpublished
Back to the top
Source
SourceTechnical
SourceType
Videotape
AnalogDigitalFlag
(authority = AES)
Duration
00:07:49
Back to the top
Technical
RULTechMD
(ID = TECHNICAL1)
ContentModel
MovingImage
Duration
00:07:49
BitRateReduction
Codec
CodecName
MPEG-4 Visual
DataRate
6 554 Kbps
Frame
Width
864 pixels
Height
486 pixels
AspectRatio
16:9
Rate
23.976 (23976/1000) fps
Structure
Progressive
FormatColors
YUV
Sound
AudioDataEncoding
twos
Channels
NumberOfChannels
2 channels
Sampling
SamplingRate
44.1 KHz
Back to the top
Statistical Profile