Hands-on math! About the Advanced Math Program
Objectives
Approach
Class Format
Math Olympiad
Homeschooling Information

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.

OBJECTIVES

 The objectives of our advanced math program are as follows: (in the order of importance)
  1. To interest students in math! (Most important!)
  2. To provide a positive experience that shows the student and family that math can be fun.
  3. 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.
  4. To prepare elementary students for secondary school mathematics, science, and computer courses.
  5. To give students a 'leg up' on the WASL.
  6. To provide students an opportunity to compete well at the Washington State Math Council (WSMC) Math Olympiad, held in early May of each year.

APPROACH

 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.

CLASS FORMAT

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:
  1. (5 minutes) Mental math. 3 to 5 problems to get students warmed up.
  2. (5 minutes) Review two or three homework problems. Students solve problems on the board.
  3. (10 minutes) Explanation of new topic, with examples on the board and interaction with class.
  4. (40 minutes) Students work problems in class with coaches assistance. Homework is handed out when students successfully complete the in-class exercise.
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.

MATH OLYMPIAD

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:
  1. Number Sense (arithmetic, number theory, fractions, decimals, percentages, basic logic, word-problem solution, negative numbers, prime numbers, factoring)
  2. Measurement (Systems of measurement, dimensions, approximation; areas, perimeters, and circumferences of 2-dimensional figures--triangles, quadrilaterals, circles--and volumes of 3-dimensional figures)
  3. Geometric Sense (geometric relationships and shapes, including properties of 3-dimensional solids, Pythagorean theorem)
  4. Probability and Statistics (simple probability, mean, mode, median, range, combinations, permutations)
  5. Algebraic Sense (expression evaluation, equation solution, word-problem solution, exponents)
  6. Problem Solving Students solve a written problem, showing how they solved it and communicating their understanding of the problem and its solution.
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.

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:
  1. Get a committed teacher sponsor. This smoothes communication with school administration.
  2. 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.
  3. 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.
  4. 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 assistants.
  5. Our school district has a math/science coordinator. If yours does also, contact this person for help and access to additional materials and resources.
  6. Start small:
  7. Recruit an administrative helper, preferably a teacher, to coordinate with parents and school administration, and with Math Olympiad officials.