Staff View
Beginning to Understand Linear Functions: Guess My Rule

## Descriptive

TypeOfResource
Text
TitleInfo
Title
Beginning to Understand Linear Functions: Guess My Rule
Identifier (type = doi)
doi:10.7282/t3-ng5r-4008
Abstract
The purpose of this analytic is to show how mathematics learning occurs when children are encouraged to "create their own way of understanding" [RB Davis, 1992]. The patience and guidance exhibited by Teacher/Researcher in this analytic is a pedagogic model for teachers. The way the students explore and struggle with the first "guess my rule question", and the way they explore with success that excites them on the second problem, provide a rich model of student math learning.

This analytic shows 6 boys: Ariel, Duwad, Brandon, Christian, Yonny and James, learning about linear functions through a game called â€œGuess My Ruleâ€ . In this game, the students are given points on a line and asked to guess the equation. Points are expressed as ( box, triangle) pairs instead of the traditional (x,y) values. The rule they are guessing is a linear equation. Teacher/Researcher Arthur Powell uses a chart to show each pair of values:

| box |triangle |
| 5 | 13 |
| 3 | 7 |

The boys are told what the rule does to each â€œboxâ€ number, but they have to figure out how the rule works. The first rule they work on is y=3x -2 (or triangle = 3box - 2) . The boys begin to work on this rule by looking at the difference between the values. As they work, they begin to see a pattern, and Ariel is the student who figures out that if we add 8 to 5, and 10 to 6, then we would add 12 to 7 (not shown in the video) and 14 to 8.

This is a recursive solution that is not clearly articulated or used by all of the boys. Once Powell puts zero in the box (or x) column, even Ariel is not sure of his recursive solution. (0, -2) is what the rule tells them.

Note that Powell always asks them if they know the rule - but he doesnâ€™t tell them the answer even though they are struggling. Instead, Powell decides they should move on to another rule.

The second rule was created by Yonny, one of the 6 boys. Yonny charts the information and the boys start out by giving Yonny the number 1. Yonny puts (1, 15) on the chart. With this second rule the boys are energized and quickly call out answers, incomplete and with errors at first, but quickly they figure out that the rule is y=10x+5.

It is notable that they first express the rule as a concatenation of symbols: 1-> 15, 2-> 25, 3-> 35. Christian says to take the number (box) and put a 5 at the end to produce the triangle value. Powell has to tell them to express the rule as a (mathematical) operation.

This game was pioneered by Dr. Robert B. Davis, and adapted for use by Dr. Arthur Powell for this study.

The boys in the source videos for this analytic were part of a group of 7th graders in the Frank J. Hubbard Middle School in Plainfield who participated in an after school, 3 year NSF study called IML (Informal Mathematics Learning, Award REC-0309062).

References
Davis, R.B., (1992). Understanding Understanding, Journal of Mathematical Behavior 11, 225-241
Genre (authority = RULIB)
Effective teaching
Genre (authority = RULIB)
Professional development activity
Genre (authority = RULIB)
Student engagement
Genre (authority = RULIB)
Reasoning
Genre (authority = RULIB)
Representation
RelatedItem (type = host)
TitleInfo
Title
RBDIL Analytics
Identifier (type = local)
rucore00000002136
Name (id = NAME-1); (type = personal)
NamePart (type = family)
Leslie
NamePart (type = given)
Joyce
DisplayForm
Joyce Leslie
Role
RoleTerm (authority = marcrelator); (type = text)
Creator
Affiliation
Rutgers University
Name (id = NAME-2); (type = personal)
NamePart (type = family)
Maher
NamePart (type = given)
Carolyn
DisplayForm
Carolyn Maher
Role
RoleTerm (authority = marcrelator); (type = text)
Publisher
Affiliation
Rutgers University
OriginInfo
DateCreated (qualifier = exact)
2016-06-29T08:38:42-0400
OriginInfo
DateOther (qualifier = exact); (type = modified)
2016-06-29T09:09:06-0400
OriginInfo
DateOther (qualifier = exact); (type = published)
2019-08-05T11:11:27-0400
Back to the top

## Rights

RightsDeclaration (AUTHORITY = RULIB); (ID = rulibRdec0007)
The author owns the copyright to this work.
Status
Availability
Status
Open
Reason
Note
RightsHolder
Name (TYPE = personal); (ID = R-NAME_0001)
Joyce Leslie
Role
Author
ContactInformation
ContactInformationDate
2019-08-02T06:04:43-0400
Back to the top

## Technical

ContentModel
Analytic
PreservationLevel
full
Generation
born digital source
MimeType (TYPE = file)
application/xml
FileSize (UNIT = bytes)
19199
CreatingApplication
CreatingApplicationName
RUanalytic
CreatingApplicationVersion
2.4 (summer 2017)
CreatingApplicationDateCreated
2019-08-05T11:11:27-0400
Note
Generated using the RUanalytic tool export function.
Back to the top
Version 8.5.2