alice in summerland

learning and teaching math in alice

Planting the seeds of computational thinking: An introduction to programming suitable for inclusion in STEM curricula

pdf Eric Freudenthal, Art Duval,  Alexandria N. Ogrey,  Kien Lim, Sarah Hug,  Catherine Tabor, and Rebeca Q. Gonzalez, Alan Siegel, Proc. FIE, 2011.

Because of insufficient math preparation, many capable students do not pursue or succeed in Science, Technology, Engineering, and Mathematics (STEM) academic programs. To solve this problem, there exists a family of courses entitled Media Propelled Computational Thinking (iMPaCT). iMPaCT stresses learning about and developing calculator programs during math courses so that participating students can better understand fundamental math concepts through visualization and programming experience.

These calculator programs are obviously simpler than coding in more advanced programming languages, but they still teach fundamental concepts of programming. A program entitled “Direct Algebraic,” for instance, draws a line of points using a simple code. The program starts by initiating variables x, b, and m as 10, -15, and 2, respectively. While x is less than 20, do the provided function “set-pt” for variables x, m*x+b, since the equation for a line is y=mx+b. End.

A key observation is that students tend to focus too much on memorization and not enough on truly understanding fundamental concepts: “Students are invested in their ability to memorize procedures to manipulate algebraic and graphic representations and are uninterested in examining underlying principles, which are essential for success in advanced STEM coursework and careers.”

A simple raster-based graphic output of students’ programs has shown to be enough to engage students in conceptual aspects opposed to memorization. Apparently, instructors have reported that college students have “literally squealed with delight as they discovered the simple principles underlying familiar but opaque algebraic formulae they had memorized how to manipulate.”

This observation is extremely important to this Alice project this summer. Often when writing my programs, I need to decide whether I want a certain algorithm to be elegant using variables and parameters, or if I want to use explicit numbers so that the kids have to calculate the answers while they are writing their programs. Variables win in terms of flexibility and legibility, and basically every other category other than requiring students to practice problems while writing code. The expressed need for fundamental understanding opposed to useless memorization helps the case that using variables are actually better. This will be key in convincing teachers to incorporate Alice into their lesson plans. If Professor Rodger and the other girls agree that using parameters and variables is the right way to go, then I think I am going to stick to that for my other programs.

There are three expectations for students who attend iMPaCT:

  1. Increased competency and confidence at computational thinking tasks.
  2. Relevant experiences applying math towards problems that include computational thinking early enough to affect choices regarding major and career.
  3. Greater success in subsequent coursework that includes mathematics or quantitative reasoning.

The calculator program resonated very positively among participating students in the pilot program. One student said, “We sometimes used mathematics to make a graph. This class requires more thinking and analysis to make things work and in math we just have to memorize and understand equations to solve a problem.”

According to the statistically significant results of this study, students were much more engaged in problem solving and attendance dramatically improved. Additionally, incorporating computation into high school math classes can drastically increase the number of students, especially women, who choose to study computation.

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