Sample Elementary School Curriculum
Investigations in Number, Data, and Space: Turtle Paths

While standard elementary school math curricula generally do not cover computer programming in any significant way, the recent Investigations in Number, Data, and Space series published by Pearson Scott Foresman approaches basic geometry using Logo to supplement paper-and-pencil exercises. Here, we examine the "Turtle Paths" unit in the Investigations third grade curriculum as an example of the integration of programming into pre-existing course material.

Jointly developed by Pearson Scott Foresman and TERC (a non-profit organization originally named Technical Education Research Centers), the Investigations series does not have an independent programming unit at the third grade level but rather introduces students to programming as part of a unit on angles and distances. Specifically, the "Turtle Paths" unit teaches a variant of the Logo programming language entitled Geo-Logo to introduce "rotation and reflection, coordinate geometry, the propeties of 2-D shapes, and angles" (I-9). The teacher's guide for this unit explains that the curriculum is based on studies indicating that children learn geometry by action rather than visualization. For this reason, watching the Logo turtle move, as well as participating in kinesthetic activities, supports the more traditional lesson plans and appeals to different learning styles. TERC presents a series of studies confirming the effectiveness of the teaching strategies employed in the Investigations series.

Additional advantages of using Geo-Logo, according to the teacher's guide, include:

• While hand-drawn diagrams can be difficult to evaluate, a series of Logo commands are less ambiguous, allowing teachers to more easily identify "differences in students' conceptions" (19)
• Geo-Logo appeals to students interested more in art than science, since they are directing the turtle to draw.
• Students must be able to "verbalize" their commands, rather than having only an intuitive understanding of the geometry they are studying.
• Geo-Logo emphasizes construction over recognition.

Programming exercises in this curriculum designed to appeal to younger students include the following:

• A student is asked to "come to the front and be a robot," physically acting out the steps that the Logo turtle eventually will follow (7). This activity, variations on which are used in several curricula for computer science at all levels of instruction, helps students conceptualize the level of detail required to write programs. Additionally, it provides an example of the type of kinesthetic learning encouraged by the Investigations curriculum.
• In the "Commanding the Turtle" exercise, students direct the Logo turtle to retrieve a toy from a simple maze and bring it back to the center of the maze. This exercise motivates learning the syntax of Logo with a more concrete goal than constructing some geometric figure.
• Students expand their knowledge by starting with simple 90-degree turtle turns and progressing to more angles when they discover that it is not possible to draw a triangle using only these turns.

Other interesting components of the Investigations curriculum pertaining to early computer science education include:

• Special attention is directed toward appealing to a "linguistically diverse classroom" consisting of both native and non-native English speakers. The concept of a "command" in Logo is generalized to the formation of commands in the English language, providing a short supplementary English lesson.
• Instructions are provided for teachers with limited computing resources; effective methods are explained for dealing with classrooms with only a few computers as opposed to a lab.
• A detailed instruction manual for teachers using Geo-Logo is provided for teachers less experienced with computer programming.

Overall, the Investigations provides a simple introduction to the algorithmic thought process with little emphasis on programming syntax or methods. Such a curriculum could be useful for schools seeking to use programming to supplement pre-existing lesson plans rather than teach computer science as its own subject area. These activities support computer science curricula indirectly, since they instill confidence in students hesitant to learn more complex programming techniques by starting with a relatively simple language. On the other hand, however, Investigations' lack of focus on programming techniques implies that it does little to directly support the introduction of more complex programming languages in later years.