Does comparison support transfer of knowledge investigating student learning of algebra l.jpg
This presentation is the property of its rightful owner.
Sponsored Links
1 / 24

Does Comparison Support Transfer of Knowledge? Investigating Student Learning of Algebra PowerPoint PPT Presentation


  • 116 Views
  • Uploaded on
  • Presentation posted in: General

Does Comparison Support Transfer of Knowledge? Investigating Student Learning of Algebra. Jon R. Star Michigan State University (Harvard University, as of July 2007) Bethany Rittle-Johnson Vanderbilt University. Acknowledgements.

Download Presentation

Does Comparison Support Transfer of Knowledge? Investigating Student Learning of Algebra

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Does comparison support transfer of knowledge investigating student learning of algebra l.jpg

Does Comparison Support Transfer of Knowledge? Investigating Student Learning of Algebra

Jon R. Star

Michigan State University

(Harvard University, as of July 2007)

Bethany Rittle-Johnson

Vanderbilt University


Acknowledgements l.jpg

Acknowledgements

  • Funded by a grant from the Institute for Education Sciences, US Department of Education, to Michigan State University

  • Thanks also to research assistants at Michigan State:

    • Kosze Lee, Kuo-Liang Chang, Howard Glasser, Andrea Francis, and Tharanga Wijetunge

  • And at Vanderbilt:

    • Holly Harris, Jen Samson, Anna Krueger, Heena Ali, Sallie Baxter, Amy Goodman, Adam Porter, and John Murphy

AERA Presentation, Chicago


Comparison l.jpg

Comparison...

  • Is a fundamental learning mechanism

  • Lots of evidence from cognitive science

    • Identifying similarities and differences in multiple examples appears to be a critical pathway to flexible, transferable knowledge

  • Mostly laboratory studies

  • Not done with school-age children or in mathematics

(Gentner, Loewenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001; Loewenstein & Gentner, 2001; Namy & Gentner, 2002; Oakes & Ribar, 2005; Schwartz & Bransford, 1998)

AERA Presentation, Chicago


Central tenet of math reforms l.jpg

Central tenet of math reforms

  • Students benefit from sharing and comparing of solution methods

  • “nearly axiomatic”, “with broad general endorsement” (Silver et al., 2005)

  • Noted feature of ‘expert’ math instruction

  • Present in high performing countries such as Japan and Hong Kong

(Ball, 1993; Fraivillig, Murphy, & Fuson, 1999; Huffred-Ackles, Fuson, & Sherin Gamoran, 2004; Lampert, 1990; Silver et al., 2005; NCTM, 1989, 2000; Stigler & Hiebert, 1999)

AERA Presentation, Chicago


Comparison support transfer l.jpg

Comparison support transfer?

  • Experimental studies of learning and transfer in academic domains and settings largely absent

  • Goal of present work

    • Investigate whether comparison can support transfer with student learning of algebra

    • Experimental studies in real-life classrooms

AERA Presentation, Chicago


Why algebra l.jpg

Why algebra?

  • Students’ first exposure to abstraction and symbolism of mathematics

  • Area of weakness for US students (Blume & Heckman, 1997; Schmidt et al., 1999)

  • Critical gatekeeper course

  • Particular focus:

    • Linear equation solving

      3(x + 1) = 15

  • Multiple strategies for solving equations

    • Some are better than others

    • Students tend to memorize only one method

AERA Presentation, Chicago


Solving 3 x 1 15 l.jpg

Solving 3(x + 1) = 15

Strategy #1:

3(x + 1) = 15

3x + 3 = 15

3x = 12

x = 4

Strategy #2:

3(x + 1) = 15

x + 1 = 5

x = 4

AERA Presentation, Chicago


Current studies l.jpg

Current studies

  • Comparison condition

    • compare and contrast alternative solution methods

  • Sequential condition

    • study same solution methods sequentially

AERA Presentation, Chicago


Comparison condition l.jpg

Comparison condition

AERA Presentation, Chicago


Sequential condition l.jpg

next page

next page

next page

Sequential condition

AERA Presentation, Chicago


Predicted outcome l.jpg

Predicted outcome

  • Students in the comparison condition will make greater procedural knowledge gains, familiar and transfer problems

  • By the way, there were other outcomes of interest in these studies, but the focus of this talk is on procedural knowledge, especially transfer.

AERA Presentation, Chicago


Procedural knowledge measures l.jpg

Procedural knowledge measures

  • Intervention equations

    1/3(x + 1) = 15

    5(y + 1) = 3(y + 1) + 8

  • Familiar equations

    -1/4(x - 3) = 10

    5(y - 12) = 3(y - 12) + 20

  • Transfer equation

    0.25(t + 3) = 0.5

    -3(x + 5 + 3x) - 5(x + 5 + 3x) = 24

AERA Presentation, Chicago


A tale of two studies l.jpg

A tale of two studies...

  • Study 1

    • Rittle-Johnson, B. & Star, J.R. (in press). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology.

  • Study 2

    • not yet written up

AERA Presentation, Chicago


Study 1 method l.jpg

Study 1: Method

  • Participants: 70 7th grade students

  • Design

    • Pretest - Intervention - Posttest

    • Intervention during 3 math classes

    • Random assignment of student pairs to condition

    • Studied worked examples with partner

    • Solved practice problems on own

    • No whole class discussion

AERA Presentation, Chicago


Study 1 results l.jpg

Study 1: Results

  • Comparison students were more accurate equation solvers for all problems

    • almost significant when looking at transfer problems by themselves

Gain scores post - pre;*p < .05 ~ p = .08

AERA Presentation, Chicago


Study 1 strategy use l.jpg

Study 1 Strategy use

  • Comparison students more likely to use non-standard methods and somewhat less likely to use the conventional method

Solution Method at Posttest (Proportion of problems)

~p = .06; * p < .05

AERA Presentation, Chicago


Study 2 method l.jpg

Study 2: Method

  • Participants: 76 students in 4 classes

  • Design:

    • Same as Study 1, except

    • Random assignment at class level

    • Minor adjustments to packets and assessments

    • Whole class discussions of partner work each day

AERA Presentation, Chicago


Study 2 results l.jpg

Study 2 Results

  • No condition difference in equation solving accuracy, on familiar or transfer problems

Gain scores post - pre

AERA Presentation, Chicago


Study 2 strategy use l.jpg

Study 2 Strategy use

  • Comparison students less likely to use conventional methods

  • No difference in use of non-standard methods

Solution Method at Posttest (Proportion of problems)

* p < .05 ; +After controlling for pretest variables, the estimated marginal mean gains were .67 and .55, respectively, and there was no little of condition (p = .12)

AERA Presentation, Chicago


In study 2 l.jpg

In Study 2

  • Advantage for comparison group on problem solving accuracy disappears

    • Condition effect on transfer problems disappears

  • Use of non-standard methods equivalent across conditions

    • Sequential students much more likely to use non-standard approaches in Study 2 than in Study 1

  • Why?

AERA Presentation, Chicago


Our hypothesis l.jpg

Our hypothesis

  • Recall that in Study 2:

    • Assignment to condition by class

  • Whole class discussion

AERA Presentation, Chicago


Discussion comparison l.jpg

Discussion  comparison

  • Multiple methods came up during whole class discussion

  • Sequential students benefited from comparison of methods

    • Even though teacher never explicitly compared these methods in sequential classes

  • Legitimized use of non-standard solution methods

    • As evidence by their greater use in Study 2 in both conditions, but especially sequential

AERA Presentation, Chicago


Closing thoughts l.jpg

Closing thoughts

  • Studies provide empirical support for benefits of comparison in classrooms for learning equation solving

  • Whole class discussion, which inadvertently or implicitly promoted comparison, led to greater use of non-standard methods and also eliminated condition effects for procedural knowledge gain

AERA Presentation, Chicago


Thanks l.jpg

Thanks!

You can download this presentation and other related papers and talks at www.msu.edu/~jonstar

Jon Star

[email protected]

Bethany Rittle-Johnson

[email protected]


  • Login