Summer 2004
JiM commenced with a three-week summer institute, held June 5 - June 24, 2004. The institute was comprised of
two 600-level courses. The first course was entitled "Problem Solving". The intent of this course was to teach ways to
approach a math problem using a variety of techniques such as drawing a picture, making a chart, or constructing a
model. We introduced a variety of games and manipulative activities to explore concepts in mathematics appropriate
for use in the classroom.
The second course, "Numeration and Operation," dealt with the historic construction of our current number system
and ways to perform operations such as addition, subtraction, multiplication, and division of fractions, decimals, and
whole numbers. We explored these concepts using different representations and manipulatives. We also
highlighted historical figures and stories to add interest and context into mathematics.
The funding for this grant payed for tuition, books, and lunch. The grant will payed travel and housing costs
for participants from Lake and Peninsula School District. Funding was available for all successful participants to
spend on mathematical manipulatives or supplies of their choosing for their classrooms. Each participating school
received funds to spend on mathematical library materials. Additionally, ten of the successful participants
received funding to attend an NCTM summer workshop of their choosing.
We intended for future Summer Institutes to feature courses in geometry and measurement, data analysis and probability, algebra,
an introduction to the concepts of calculus, and a capstone.
Summer 2005
The Summer 2005 JiM institute consisted of two master's-level, three-
credit courses. ED 684 examines concepts of elementary algebra and
pre-algebra; ED 680 considers strategies to develop understanding
of geometry and measurement skills in K-8 students. Both courses are
filled with activities that are research-based, hands-on, and aligned
with state and national standards. Instructors this year include
master teachers Alison Mall, Alison Vail, Sandy Schoff, and Jim Seitz
and UAA professors Claudette Engblom-Bradley, Cora Neal, and Debbie
Narang.
Summer 2006
The final JiM summer institute was held June 12th to June 30th, 2006. The participants met for approximately 115 hours of instruction over a three-week period. The institute consisted of three three-credit graduate-level courses, Calculus and Trigonometry: Concepts for K-8 Teachers, Data Analysis and Probability: Content and Pedagogy for K-8 Teachers, and Capstone: Advanced Topics in Mathematics for the K-8 Teacher.
These courses complete the requirements for the recently established K-8 mathematics endorsement and are aligned to state and NCTM standards.
Participants in the calculus and trigonometry course, taught by Deborah Narang from the UAA Mathematical Sciences Department with Claudette Engblom-Bradley of the UAA College of Education and Ruth Mount from the Anchorage School District, discovered the basic ideas behind the derivative, the integral, and the trigonometric functions. As in the algebra class, they modeled real-life situations using variables, and created, analyzed, and transferred among concrete, visual, pictorial, graphical, and symbolic representations. They learned how the derivative describes the rate of change of a function, how to use the derivative to describe the graph of a function, and how to compute derivatives of polynomial functions. They learned the relationship between integral and area under a curve, how to compute definite integrals of polynomial functions, and made conjectures of a simple form of the Fundamental Theorem of Calculus.
The teaching team for the data analysis and probability course was comprised of Dr. Cora Neal from the UAA Mathematical Sciences Department, Sandra Schoff, Penny Williams and Sunny Mall from the Anchorage School District. Participants constructed an assortment of graphs, explored visual interpretations of means, medians, modes, and standard deviations and computed regression lines. These concepts were further investigated through the use of TinkerPlots, a statistical software package designed for use by middle school students. Probability was explored through a variety of hands-on activities where students simulated random events to compare empirical results to theoretical calculations.
The capstone course consisted of three modules highlighting advanced mathematical topics: group theory, knot theory, and discrete mathematics and a seminar in teacher leadership. During the daily leadership sessions led by Sandy Schoff, teachers studied and discussed two books, Leadership Capacity for Lasting School Improvement by Linda Lambert and Teacher Leadership That Strengthens Professional Practice by Charlotte Danielson. Cora Neal taught sessions on discrete mathematics, including counting arguments and the famous Traveling Salesman and Four Color Problems. Debbie Narang shared the basic ideas of group theory with the participants, focusing on properties of operations, the definitions of group, order, and subgroup. Neil Portnoy, Assistant Professor and Director of Mathematics Education at Stony Brook University of New York, taught knot theory to our participants in the second week of the capstone, sharing his expertise developed through his NSF grant Knot Theory for Preservice and Practicing Secondary Mathematics Teachers. Teachers learned about knot projections and knot invariants such as crossing number, linking number, and tricolorability used to classify knots. All three instructors used simple, hands-on exercises to illuminate the concepts and gave the teachers a chance to see mathematics with a much different perspective than that of typical lower division college courses.
