> Y[X#` @'bjbj\.\. 4L>D>D&jjj8<T}+>>TTTTTT*******$-h/"+!TT!!"+TT7+$$$!|TT*$!*$$'(T2``i5wjG"d')M+0}+',90"90(90(T$$TTT"+"+$^TTT}+!!!!$ &D&LA VILLITA: THE RETURN TRIP FROM NORMAL TO INFINITY
Nerida F. Ellerton and M. A. (Ken) Clements
Illinois State University
This is a story about the developing relationship between Infinity High School one of four high schools that began, in 2005, in a single complex within La Villita on the southwest side of Chicago and Illinois State University, which is located in the city of Normal, two hours south of Chicago. Over the past three years, the authors, who work in the Department of Mathematics at Illinois State University, have developed links with the Principal and the mathematics teachers, at Infinity High School. On many occasions we have driven from Normal to Infinity, and then back to Normal, quite comfortably, in a single day!
La Villita: Background Factors
Socio-Demographic Background Factors
Demographic data for Chicagos Little Village (called La Villita by its residents) point to a challenging educational environment. Recent census data indicate that La Villitas population is almost 100,000 people, with 83% being Latino and 13% African-American (see Table 1). Like most parents, La Villita parents want the best for their children, and that is why they went on a hunger strike to put pressure on Chicago Public School officials to provide them with high quality, modern, educational facilities. Unlike most other schools close to La Villita, the four schools making up the composite Little Village High School now occupy a magnificent, modern structure. From experience we know that the teachers, support staff, and equipment at the La Villita schools are equally impressive.
Table 1
La Villita Statistics
Indicator (U.S. Census Bureau, 2000)NeighborhoodUnited StatesPercent Latino population83%13%Renter-occupied housing units79%34%High school graduate or higher17%80%Foreign-born37%11%Speaks a language other than English at home63%18%Families below poverty level42%9%
The mean family incomes and educational levels of the parents of Little Village High School students are low and crime and gang membership within La Villita are high. According to recent Office of Population Research statistics, La Villita is the third largest Mexican community in the United States. The Foreign Born entries in Table 1 do not take account of many foreign-born undocumented residents in La Villita. Over one-half of La Villita families with children live in poverty, and based on Census data, over one-half of La Villita families have a grandparent as the main caregiver.
Educational Background Factors
Three important indicators low academic performance of students, high enrolment of economically disadvantaged students, and low high school completion rates draw attention to the education challenges associated with schools within La Villita. Approximately 15,000 elementary/middle level students attend 17 public schools in the Little Village area, with15 of the 17 area schools falling below standards on their yearly testing scores. According to the Illinois State Governments Report Card for 2005, up to 66% of students in La Villita elementary schools met the state standards for reading, but mathematics results for these same elementary schools were much lower. Only 24% of students met mathematics standards set for entry into high school.
Problem-Based Learning at Infinity High School
Before Infinity High School opened in 2005, its Principal-elect expressed a desire to collaborate with Illinois State University on curriculum development, teaching and evaluation. Because of the well-documented low-performance patterns of students from the La Villita area in mathematics, it was agreed that Illinois State University would liaise with Infinity High School with respect to its mathematics program. The two authors offered their assistance in that regard.
In August 2005, Infinity High School opened its doors to its 100 foundation students who were all in Grade 9 (and aged between 13 and 15 years). There were two full-time mathematics teachers. We met with the teachers and with the Principal and were determined to support the school in its implementation of whatever school mathematics program it chose. The teachers and the Principal committed themselves to developing a problem-based mathematics curriculum that did not depend on any single commercial textbook series. The other three high schools in the Little Village High School complex decided to adopt a well-known Standards-based textbook series to support their mathematics programs.
Between 2005 and 2008, we have met with the Infinity High School Principal and the Schools mathematics teachers on a regular basis. We have been participant observers in the Schools mathematics classrooms on numerous occasions. We also accepted the Principals invitation to conduct a series of number sense and algebra classes for incoming Grade 9 students and for continuing students about to start Grade 11, during the summer vacation in August 2007. These classes occupied a total of 15 hours.
The Principal asked us to evaluate the effectiveness of the schools problem-based mathematics program. The term problem-based was interpreted by the school as providing a set of culturally and locally relevant experiences that would enable the students to learn the key areas of the mathematics curriculum as defined by Chicagos Public School authority. It was vitally important for the school that students would be as well prepared as possible for the State-wide mathematics tests taken by students in Grade 11. The Schools results on these tests would clearly be carefully scrutinised by a wide range of stake-holders including students, teachers, parents, and District and State system authorities.
Infinity High Schools mathematics curriculum was largely developed by the mathematics teachers themselves. For example, the topic of graphs of linear functions, with associated sub-topics like units, gradient, and rate of change, was related to the Chicago Marathon. One of the teachers actually ran the marathon, and that generated many graphs showing, for example, the teachers speeds over different sections of the marathon. These graphs were drawn by the students, and the whole exercise was celebrated with wonderful displays all over the mathematics room. Students who developed a graph had to explain what it was all about to the other students.
Home-Run Pizza Inn has been based in La Villita for many years, so the teachers invited the local area manager to come to outline Home Run Inns need to expand its range of products and associated profit margins. Students were asked to develop possible marketing strategies with a view to maximising profits. The main mathematical objective of this exercise was to help students learn and apply percentage and percentage-gain concepts.
When learning about trigonometric ratios, students took rise and run measurements on the schools staircases, and then determined how steep the staircase was. They also used these measurements to build cardboard models, and to consider the practicalities of different rise-over-run ratios.
In the paper we will discuss some of the program evaluation instruments we developed, and the data generated. Briefly, the students acquisition of problem-solving skills was impressive. They enjoyed investigating the problem situations. Analyses revealed, however, that there are still concerns with their acquisition of basic skills of the kind needed for the State-wide testing regime.
We are confident that Infinity High School students have been well prepared for engaging in problem-based scenarios in the future. We also expect Infinity High School students to perform at an educationally significant higher level than students from surrounding high schools on the state-wide tests. Indeed, we expect to be teaching some of these students when they enter Illinois State University and study Mathematics in the not-too-distant future.
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