HARLEM CHILDREN SOCIETY AUTUMN 2008 AFTER-SCHOOL PROGRAM
Biostatistics and Linear Algebra

As part of Harlem Children Society’s commitment to ongoing educational
initiatives, two after-school workshops were offered in autumn 2008 over a
six-week period (November 6 to December 18, 2008). HCS students who had
begun or continued their internships in the summer 2008 program were
invited to participate in these courses, which were complementary
educational opportunities. While 23 HCS students actually took advantage
of the New York City classroom experience, the workshops were also
videotaped for HCS students globally and made available to them via the
HCS website.

HCS staff members, Alejandro Naranjo and Irina Katz, spearheaded the
workshops. They both designed and taught courses for the entire period,
which met once a week at the New York Public Library branch on East 68th
Street in Manhattan. The workshops consisted of two modules: Introductory
Biostatistics and Linear Algebra. The course content was designed not only
to enrich HCS students’ science and math skills, but also to prepare them
for their 2009 summer internships, with particular focus on
bioinformatics.


Biostatistics Module

Irina Katz, HCS intern (BS in microbiology from University of Maryland,
MPH in epidemiology from Columbia University) taught the biostatistics
workshop, which was the first of the two workshops each week of the
course. She designed the workshop as a broad introductory experience, and
operated under the assumption that students knew absolutely nothing about
the topic.

As a point of departure, Irina distributed a nutritional survey derived
from NHANES (National Health and Nutrition Examination Survey) for the
students to complete. She then asked students to form hypotheses based on
the questions in the survey, and briefly went into the concepts of
dependent and independent variables. The students then exchanged papers
and were asked to describe their reactions to these hypotheses in writing.
Irina designed this effective exercise to illustrate the data collection
and analysis process in a Meta way.
In subsequent weeks, Irina routinely began each session with a review of
material covered in the prior class in the form of a brief quiz, followed
by answer review. The purpose of the quiz was to engage students in
thinking about key concepts and to prompt class discussion. Irina
reported the majority of the class regularly participated in these
discussions following the quiz “warm up” activity. She then devoted the
remainder of the session to introducing new topics, supplementing her
discussion with handout materials (worksheets, tables, etc.), and
assigning problems to be solved on the spot. The session routinely
concluded with students working as teams to solve assigned problems.
  By the end of the term, Irina’s students had developed an understanding
of the concept of biostatistics, basic data description and analysis.
The course concluded with an exam targeted to measuring students’
progress in understanding these key concepts.


Linear Algebra Module

Alejandro Naranjo, HCS intern (BS in electrical engineering with a
concentration in communication and information processing from Rensselaer
Polytechnic Institute, and MS candidate at Columbia University in
electrical engineering), followed the biostatics module with his linear
algebra workshop. He selected the subject matter based on its extensive
applications in the natural and social sciences. According to Alejandro,
“Linear simplicities are used in biology, chemistry, mathematics, and
engineering to solve a vast number of problems.” Developing the course
using MIT’s Open Course Ware in combination with his knowledge of the
subject, Alejandro designed preliminary layouts, PowerPoint presentations,
and accompanying worksheets to reinforce concepts introduced in each
session. The worksheets served dual purposes: as both class work and
homework for individual and group study.

In terms of content, the course followed a progression beginning with the
basics of linear equations, solution sets, scalars, variables, fields,
vectors, and vector properties. Matrices and their properties were then
introduced, followed by row echelon, Gauss-Jordan Elimination, Matrix
Properties, and vector and matrix addition and multiplication.

Alejandro routinely opened each session with a review of material covered
in the prior class before advancing to new topics. After presenting new
material, Alejandro concluded each session with cooperative problem
solving using the worksheet series he had crafted. He facilitated this
group activity, circulating through the room to monitor progress and
answer questions in the event students were unable to solve problems
themselves. Alejandro had designed the group activity for several
purposes: to reinforce new concepts, to prompt students to actively engage
in thinking, discussing, and formulating questions about the material, and
to empower students to complete their assignments at home. The students
then submitted the worksheets for grading when they returned to class, and
received problem solutions via email from the instructor.

By the end of the term, Alejandro’s students had developed a foundation in
the basics of linear algebra. Owing to the subject’s complexity, HCS plans
to offer After-School Continuing Linear Algebra in spring 2009, which
Alejandro will also teach. In conjunction, HCS plans to offer After-School
Continuing Biostatistics in spring 2009, which Irina will again teach.

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