A Middle Grade Teacher’s Guide to Model Eliciting Activities

Abstract

This Teacher’s Guide of implementation strategies for Model Eliciting Activities (MEAs) was developed through a collaboration between an 8th grade mathematics teacher and a university partner who served as one of the “clients” during four week-long MEAs in the 2006–2007 school year. The guide provides principles which may be useful to teachers and researchers who wish to conduct investigations of students’ or teachers’ actions during modeling activities in middle grades or other contexts. Neither the mathematics teacher nor this Guide’s collaborator had had prior experience with MEAs. Thirty-two 8th grade students from a magnet school in an urban U.S. district took part in these activities. They were combined from two classes: one regular mathematics class and one special education class. The heart of this Guide comes from reflections by the regular mathematics teacher explored during a May, 2007 interview with the first author who was also one of the university partners. From these experiences, four strategic categories emerged: (1) Group composition, (2) Relevant MEA selection, (3) Teachers’ roles during group work, and, (4) Culminating group presentations and individual written work. During the activities, both the regular and special education teacher observed active engagement by several students who previously rarely participated in mathematics class.

Appendices

Appendix 1 Fun on the Field: Model Eliciting Activity

Problem:	Student	100 Meter Run	800 Meter Run	High jump	Fitness test
Use the data here to develop a method to split the	Betsy	17.3 s	3 min 38 s	5’3”	Pass
6th grade class into three equal teams. Write a	Caroline	16.0 s	3 min 1 s	3’5”	Fail
letter to the Organizers of the Fitness Field Day	Daniel	19.89 s	2 min 42 s	5’5”	Pass
explaining the method you used to divide the	Dick	18.52 s	2 min 55 s	4’4”	Pass
class. The Organizers will use your method for	Jason	16.48 s	2 min 55 s	3’9”	Pass
other grade levels and for the annual local-level	Judi	17.2 s	3 min 22 s	3’6”	Fail
competition among all district schools, where	Lupita	20.2 s	4 min 0 s	5’0”	Pass
they will need to divide a large number of players	Mack	18.25 s	3 min 16 s	5’6”	Pass
into equal teams.	Manuel	17.1 s	3 min Iis	4’2”	Fail
	Margret	20.32 s	2 min 51 s	5’7”	Pass
	Michelle	16.44 s	2 min 45 s	4’5”	Fail
	Rob	19.2 s	3 min 12 s	4’10”	Fail
	Sandra	17.34 s	3 min 50 s	5’ 1’	Fail
	Scott	17.0 s	3 min 30 s	4’ii”	Pass
	Susan	18.3 s	3 min 0 s	5’3”	Pass

*Students either passed or failed the fitness test, which included 30 push ups, 50 jumping jacks, and 20 sit-ups

Appendix 2 Paper Airplane Model Eliciting Activity

Beginner competition problem	Straight path
In past competitions, the judges have had problems deciding how to select a winner for each of the four awards (Most Accurate, Best Floater, Best Boomerang, and Best Overall).	Team	Amount of time Length of throw Distance from in air (seconds) (meters) target (meters)
The judges don’t know which measurements to consider from	Team 1	3.1	11	1.8
each path to determine who wins each award. Your team is		0.1	1.5	8.7
being asked to consider how to use the measurements for the		2.7	7.6	4.5
Beginner Competition only. Recall that the Beginner	Team 2	3.8	10.9	1.7
Competition involves only a straight throw; so Best Boomerang		4.2	13.1	5.4
is not an option. Some sample data from last year will be		1.7	3.4	8.1
provided. Write a memo to the judges of the contest. In your	Team 3	4.2	12.6	4.5
memo include procedures to determine Most Accurate. Best		5.1	14.9	6.7
Floater. and Best Overall. Within the procedure. clearly State		3.7	11.3	3.9
the reason for each step. heuristic (i.e. rule). or consideration in	Team 4	2.3	7.3	3.3
your procedure. Use your procedure and the sample data		2.7	9.1	4.9
provided to determine the winners in each category. Make a		0.2	1.6	9.1
note of the winners but do not include this in your memo.	Team 5	4.9	7.9	2.8
		2.5	10.8	1.7
		5.1	12.8	5.7

Sample data table for beginner competition

Appendix 3 The “Big Foot” Model Eliciting Activity

Monrovia Someone who lives in this small rural Illinois town just outside of Chicago cares about the town’s children. While most residents will do anything for the children, from volunteering for tutoring at the elementary school to umpiring the children’s baseball league, one resident went beyond the call of duty by fixing and repainting the playground equipment. Where there is no problem in making sure the equipment is in good shape, the problem is finding out which resident took the time and resources to fix the equipment. Park District Superintendent Ruth Spears would like to thank the person. Spears said the park district would like to thank the person who replaced the chains on the swings, repaired missing or loose boards on the merry-go-round and repainted the monkey bars and swings. “They didn’t have to do that, but we thank them and we would like to honor them,” Spears said.

Monrovia town marshal Samuel Rose first noticed the new park equipment when he and police officer Reggie Perkins were called to the town park around 11 p.m. on Monday when neighboring residents reported funny noises, such as rattling chains, nailing of wood and other sounds associated with repairs. “We saw the subject’s shadow as he was leaving the park,” said Rose. “We did not get a clear look at the person, so we have no idea what the person looked like.” Officer Perkins, upon further investigation of the repaired and repainted equipment, noticed footprints around the swings, the merry-go-round and the monkey bars. “That is really the only clue we have to go by at this point in the identification process,” said Perkins. Rose, along with Spears, said that no charges would be filed against the Good Samaritan. “We’re just happy we have a resident who is willing to help the community,” said Rose. “I just wish we knew who they were.”

Readiness questions:

What is the problem in Monrovia?

Who is Ruth Spears?

Why does Ruth Spears want to contact this mysterious person?

Who first noticed the new park equipment?

What evidence did the mysterious person leave behind?

How can Ruth Spears identify this person?

The Problem: Sometime late last night, some nice person rebuilt the old brick drinking fountain in the park. The mayor wants to thank the person who did it. But nobody saw who it was. All the police could find were lots of footprints. One of the footprints is shown here. [Note: Students were given a cutout of a 22 inch footprint]

The person who made this footprint seems to be very big. But, to find this person, we need to figure out how big he or she probably is. Your job is to make a “HOW TO” direction sheet (i.e., a set of step-by-step directions) that the police can use to figure out how big people are just by looking at their footprints. Your direction sheet should work for footprints like the one that is shown here, but it also should work for other footprints.

Appendix 4

Photograph accompanying Tom Thumb Gardens Model Eliciting Activity