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Paper-and-Pencil Activities

Below are a few (in some cases shorted or paraphrased) examples of elementary-level algorithmics problems proposed in the Michael Fellows paper, which explored the possibility of teaching algorithms to elementary and middle school students. The importance of the algorithmic component of the early computer science education curriculum is not to find the right answers to every question or to rediscover algorithms taught in the corresponding undergraduate course, but rather to be actively engaged in trying to solve non-trivial computer science problems. The goal is to have students figure out the main components of optimal/correct algorithms and defend them intelligently. It is possible to have the students collaborate especially challenging problems, thus bringing an additional component of team development to the lesson plan. Additionally, these "algorithmic lab" activities do not require computer resources, and thus could be used as an alternate activity for students who do not have access to computers.

  • Muddy City: Minimum Weight Spanning Trees (MST's)
    To explore MST's in the classroom, students will be given the map on the right, accompanied with the following setup: "Citizens of Muddy City want to pave enough roads so that anyone can get anywhere. They want to keep the cost down, and don't mind if the traveling distances on the paved roads are long." Then, the students are asked to choose a set of roads that satisfy the criteria laid out by the citizens of Muddy City. When he used this activity, Fellows found that the classroom "exploded with activity" and that there was "a tremendous range of response." After the initial attempts of the students, Kruskal's algorithm, which is relatively simple and intuitive, could be introduced in an informal sense; students could then apply the algorithm to find the optimal answer.

  • Map Coloring
    This archetypical computer science/mathematics problem can easily be introduced to young students by passing out uncolored maps and markers and having the students try to find the minimum number of colors needed to make sure that no two adjacent countries have the same color. While they may not be able to prove the Four-Color Theorem, the certainly can discover the difficulty mathematicians faced in fully understanding graph coloring and even some of the basic "greedy" algorithms for coloring graphs.

Professor Fellows also suggests other engaging topics in computer science that can be examined away from the keyboard. These include sorting algorithms, logical and mathematic puzzles, planning the route of the traveling salesman, and devising one-way street assignments.


Early Acquisition of Computer Science · ©2008 Justin Solomon and Peter Rusev