Company Name

Pattern Growth

A rich set of pattern growth activities were developed to support students becoming articulate about the ways in which patterns can grow, scaffold the discussion of how simple local rules can create rich emergent patterns, and explore the conversation between object-based reasoning and aggregate analyses including graphs, difference tables and tables of ratios of successive terms. A number of the initial activities had students create their own patters that grew in "regular" ways on paper and then the calculator screen (see Figure below). These patterns were to grow in any way the students invented and students used tables and graphs to analyze their patterns' changes. In subsequent activities, students were asked to create patterns that had certain specifications (e.g. grow by two every iteration). The teacher called these "thinking backward" activities. For both the "thinking forward" initial activities and the "thinking backward" activities, some of the patterns had both positive and negative markers and this helped create a interesting set of oscillatory patterns and conversations about combining functions (one function for positive tiles and one for negative tiles combining to give the total value function).

Growth Patterns as Implemented on the Calculators and as Mirrored in StarLogoT

Interwoven with these pattern growth activities was the use of StarLogoT models that rendered and extended some of the patterns. While students did find it challenging articulate "local" ways of describing the growth of their patterns (as opposed to simply saying, "I just alternated adding two at the ends here…") we were encouraged by the depth and creativity of student engagement with these tasks. We also believe that over time these individually created and, eventually, interactively created patterns will held scaffold student engagement with object-based modeling related to pattern formation. Already significant issues of aggregate and object-based complementarity have developed. For example, students made important connections between adding two tiles each time and graph of the number tiles being linear. Oscillatory patterns and some quadratic patters and were also developed. In the future we expect to do more with exponential pattern growth.

Uri Wilensky
Northwestern University
Evanston, IL

Walter M. Stroup
The University of Texas
Austin, Texas


Pattern Growth

A rich set of pattern growth activities were developed to support students becoming articulate about the ways in which patterns can grow, scaffold the discussion of how simple local rules can create rich emergent patterns, and explore the conversation between object-based reasoning and aggregate analyses including graphs, difference tables and tables of ratios of successive terms. A number of the initial activities had students create their own patters that grew in "regular" ways on paper and then the calculator screen (see Figure below). These patterns were to grow in any way the students invented and students used tables and graphs to analyze their patterns' changes. In subsequent activities, students were asked to create patterns that had certain specifications (e.g. grow by two every iteration). The teacher called these "thinking backward" activities. For both the "thinking forward" initial activities and the "thinking backward" activities, some of the patterns had both positive and negative markers and this helped create a interesting set of oscillatory patterns and conversations about combining functions (one function for positive tiles and one for negative tiles combining to give the total value function).

Growth Patterns as Implemented on the Calculators and as Mirrored in StarLogoT
Interwoven with these pattern growth activities was the use of StarLogoT models that rendered and extended some of the patterns. While students did find it challenging articulate "local" ways of describing the growth of their patterns (as opposed to simply saying, "I just alternated adding two at the ends here…") we were encouraged by the depth and creativity of student engagement with these tasks. We also believe that over time these individually created and, eventually, interactively created patterns will held scaffold student engagement with object-based modeling related to pattern formation. Already significant issues of aggregate and object-based complementarity have developed. For example, students made important connections between adding two tiles each time and graph of the number tiles being linear. Oscillatory patterns and some quadratic patters and were also developed. In the future we expect to do more with exponential pattern growth.


Uri Wilensky Northwestern University Evanston, IL		Walter M. Stroup The University of Texas Austin, Texas