About the Advanced Math Program
ABOUT THE ADVANCED MATH PROGRAM
The Advanced Math Program is a math enrichment program for
students in grades 5, 6 and 7. This program was developed by
parent volunteers, working with educators, in the
Highline School District #401, Seattle, WA. It began
with 12 students in 1990 and has
grown to include more than 300 students in 15
public and private schools around Puget Sound.
Each school has one or more volunteer coaches (parent or educator)
using the materials provided at this site.
The schedule is specific to the Highline School District,
but serves as a template to deliver these same concepts
to any student in any school, including home-school.
The objectives of our advanced math program are as follows: (in the order of importance)
- To interest students in math! (Most important!)
- To provide a positive experience that shows the
student and family that math can be fun.
- To provide math enrichment for highly
capable and highly motivated students. This includes kids
of average ability that are willing to work at math. Your child doesn't have to be a 'math whiz' to succeed at this.
- To prepare elementary students for secondary school
mathematics, science, and computer courses.
- To give students a 'leg up' on the WASL.
- To provide students an opportunity to compete well at the Washington State Math Council (WSMC)
Math Olympiad, held in early May of each year.
This program has evolved from a program offered to gifted sixth grade students at a single elementary
school into one offered to any fifth and sixth grade student in the
Highline School District who is willing to invest the required
effort and who has a math coach. The course is normally
offered as a before school (period 0) or after school elective starting in late
September and going through early May (approximately 7.5 months). It
introduces subject matter normally encountered in seventh and eighth
grades. However the approach is different and the topics are not
covered in the depth that middle school math receives. Our
approach builds upon skills mastered in grades K-4 to teach advanced
math concepts. For example, to solve the equation: X - 4 = 10 we use
the “fill in the blank” technique students were taught in the second and
third grades: __ - 4 = 10 rather than the “perform the same operation
to both sides of the equation” technique taught in algebra. This
gives the intermediate level student an introduction to algebra without the rigorous techniques that will come later. In fact, we
have discovered that, by and large, intermediate
students are not developmentally ready for rigorous techniques.
Similar simplifying techniques are used to teach geometry and
probability concepts. We avoid memorization of formulas and equations.
This is basically a concepts course that introduces the student to the
richness of math and its wide application in the larger world.
We attempt to follow the
standards set forth by the National Council of
Teachers of Mathematics (NCTM) in our course.
It is our experience and our continuing hope that the students' exposure
to this wide exposition of math concepts will spark an interest in math
and engender confidence in their math abilities that will follow them
through middle and high school and into a career. The
principal reason that participation in the Washington State Math Olympiad
is included as an objective is the focus that this event provides, and
the strong feeling of accomplishment that students get from competing in
an academic event. When asked at the end of the year what their
favorite part of the program was, most students mention this
competition. A caveat is in order here. While competition is an objective, winning is not. Our first year program is not
sufficiently intensive or deep to train a student to win the state
competitions. That level of preparation would restrict our program to a
few gifted students and would violate objective #3. Students in the top
two or three percentile will find these lessons easy. They are not our
target student population. Many of the students participate in a second
year of this program to increase mastery of concepts and to refine
problem solving techniques, and they traditionally compete at a higher
level. A major benefit for
offering a math concepts course to this age group is that girls in this
age group generally have not lost interest in math. It is our goal to
expose girls to these advanced concepts at an early age so that their
interest and confidence will follow them through the rest of their
school years and into careers that utilize math. Frequently we see
math teams in which girls outnumber boys.
This course is designed to be taught in a one hour session once a week.
Beginning with lesson #9, additional practice competition materials for
a second hour long session are provided. The one hour lessons generally
follow this format:
Notice that only 10 minutes of the hour are devoted to “chalkboard lecture.” For the largest part of the hour students are actively working independently or in groups. One of the main ways our program has improved over the years is to
include more hands-on problem solving and less lecture. We have found
that this format achieves better results.
The one hour practice competition offered in a second class session each week
after lesson#9 consists of two quizzes in two selected Math Olympiad subjects and never
covers new material. Students are organized into teams of three or four
for these practice competitions. We hand out small prizes for high
scoring teams. Students find these practice competitions to be
enormously fun. They learn to work as teams and to allocate work among
team members. Each team requires a captain to coordinate problem solutions.
- (5 minutes) Mental math. 3 to 5 problems to get students warmed up.
- (5 minutes) Review two or three homework problems. Students
solve problems on the board.
- (10 minutes) Explanation of new topic, with examples on the board
and interaction with class.
- (40 minutes) Students work problems in class with coaches
assistance. Homework is handed out when students successfully complete
the in-class exercise.
The Washington State Math Olympiad covers mathematical material
consistent with the
Washington State Essential Learning Requirements and also with
standards published by the National Council of
Teachers of Mathematics (NCTM). Math Olympiad competition is open to fifth through eighth grades in a team-format competition. Teams consist of 3-4 students who compete in the following areas:
Each subject area test (algebraic sense, probability and statistics, geometric sense, number sense and measurement) consists of five problems. Students are expected to assign problems among their team members based on individual abilities and time. This requires a fair amount of teamwork and organizational ability within the team, as one team member
could not possibly solve all problems in 20 minutes. The team submits
one paper for a team score. Identity of who solved which problem is
known only among the team members themselves. This helps build teaming skills.
- Number Sense (arithmetic, number theory, fractions, decimals, percentages, basic logic, word-problem solution, negative numbers, prime numbers, factoring)
- Measurement (Systems of measurement, dimensions, approximation; areas, perimeters, and circumferences of 2-dimensional figures--triangles, quadrilaterals, circles--and volumes of 3-dimensional figures)
- Geometric Sense (geometric relationships and shapes, including properties of 3-dimensional solids, Pythagorean theorem)
- Probability and Statistics (simple probability, mean, mode, median, range,
- Algebraic Sense (expression evaluation, equation solution, word-problem solution, exponents)
- Problem Solving Students solve a written problem, showing how they solved it
and communicating their understanding of the problem and its solution.
In addition, each team is required to solve a "significant problem" and to respond in a written paper that is scored with a scoring guide (rubric). The "significant problem" may involve several or all of the Essential Learnings, including logical reasoning, connecting math to applications, and communication of understanding. See our problems page for examples of these.
RECOMMENDATIONS FOR IMPLEMENTATION
With this brief historical sketch in mind, we make the following suggestions
for any parent group contemplating a similar program:
- Get a committed teacher sponsor. This smoothes communication with
- Involve the community by soliciting parent support through the PTA.
There are nominal costs of approximately $300-$400 for this program. These include purchase of notebooks, 4-function calculators, registration of teams, and T-shirts if you decide to go to the Olympiad.
Your PTA may want to help out.
- Coordinate your program with the middle schools that students will
later attend. Take a look at the middle school curriculum and be prepared to advise in the placement of students who are exiting this program.
- Solicit help from the parents of your students. They are motivated
to ensure that your program is a success. Some may volunteer to help as
- Our school district has a math/science coordinator. If yours does
also, contact this person for help and access to additional materials and resources.
- Start small:
- Only one instructor?: One grade, 10 students max.
- One instructor and a non-teaching helper?: One grade 14 students max.
- 2 instructors?: One grade, 18 students max.
- Recruit an administrative helper, preferably a teacher, to
coordinate with parents and school administration, and with Math Olympiad