Bootstrap is a research-based
curriculum designed for students in grades 6-12. Bootstrap's curriculum has been used
in math, computer science, physics, and other STEM related classes.
Specifically, I will be focusing on their algebra curriculum. Their curriculum
differs from other beginning programming curriculum because it explicitly focuses
on the math concepts and applies them within the programming framework. Scratch,
the most common block-based programming language, is great for teaching beginning
programming concepts if your focus is solely on programming and animation. But because I want to apply math topics to computer science, I chose to research
and test out Bootstrap’s nine algebra units.
Algebra is the gatekeeper to high school math. There are essential
elements within algebra that must be understood to reach mastery within the
subject. The main concepts learned within algebra that will be applied to
many different equations, scenarios, and classes in one’s future are the
coordinate system, order of operations, functions, and decoding word problems.
These big ideas create the basis for all future math classes, including
geometry, trigonometry, calculus, etc. Bootstrap incorporates all of these big
ideas into their algebra curriculum. Their algebra curriculum helps students
create a video game with players moving in two dimensions (x and y directions).
Functions are used to describe the movement between frames (ie: (define x ( x +
5)) describes a linear movement with a change of 5 spaces for each frame). Understanding
the correct mathematical order of operations is essential within programming in
order to correctly parse and evaluate an equation. Throughout all nine units, students
work through a “Design Recipe” packet that walks them through each step of
changing a word problem or equation into a coded function. Students can then
enter the function into their game to get immediate feedback on the
correctness. This is engaging for students and highlights misunderstandings for
the teacher and learner.
To
evaluate the effectiveness of Bootstrap within the classroom, Schanzer, Fisler, Krishnamurthi,and Felleisen (2015),
proposed the following hypotheses:
Hypothesis
1. Students who complete Bootstrap will improve in their performance on algebra
word problems and function composition problems.
Hypothesis
2. Students who complete Bootstrap will show more improvement in performance on
algebra word problems and function composition problems than students who did
not take Bootstrap.
Both
of these hypotheses were proven correct based on pre and post assessment of
students who either participated or did not participate in the Bootstrap
program. Ninety-five percent of the 101 teachers who were trained in and used Bootstrap
believed the program to be relevant to algebra (Schanzer, et al., 2015).
Research says this program works to engage students and
deepen their algebra knowledge, so I decided to try out the curriculum to form
my own opinions. I like that the Bootstrap game grows with the students. For
each new lesson, students add a new game feature, learn a new programming
construct to add the feature, and all of this relates to a new math concept. It keeps students wanting to learn more when they can visually see their progress within their computer game. The
Bootstrap curriculum does not require the teacher to have extensive programming
experience and is designed to be used in the math classroom, not the
programming classroom. As I mentioned in my previous blog, math needs to be
less about computations and more practical, conceptual, and engaging. I believe
Bootstrap meets these criteria. And the success stories from teachers and
students who used Bootstrap within their algebra classroom prove that when combining
programming and algebra concepts students learn more, have a better
understanding, and achieve higher test scores (if standardized testing is your
end goal… but THAT is a whole different topic for another blog post). Bootstrap is not
meant to be the end all be all of algebra. It is meant to be used as an
alternative, supporting curriculum to the regular math class. It does not cover
the entire algebra curriculum or all the math standards, but I believe it does
touch on the key elements of algebra and helps bring a deeper understanding of
those key elements, which will set students up for success in the rest of their
algebra class. One thing many students struggle with is decoding word problems into equations. Bootstrap could be a valuable tool to help students understand these types of problems and increase their mathematical literacy. Students will walk away with basic understanding of computer
science functions, variables, and programming syntax, which will give them an advantage within any future computer science classes they chose to take.
And now, to walk you through an overview of the Bootstrap algebra program I created:
References
Lee, R. (2013). Teaching algebra through functional programming:An analysis of the bootstrap curriculum
(Doctorate Dissertation). Retrieved from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4518&context=etd
Schanzer, E., Fisler, K., & Krishnamurthi, S. (2018) Assessing bootstrap: Algebra students on scaffolded and unscaffolded word problems. Retrieved from: http://cs.brown.edu/~sk/Publications/Papers/Published/sfk-bsa-scaff-unscaff-wp/paper.pdf
Schanzer, E., Fisler, K., Krishnamurthi, S., & Felleisen, M. (2015). Transferring skills at solving word problems from computing to algebra through bootstrap. Retrieved from: http://cs.brown.edu/~kfisler/Pubs/bootstrap-sigcse15.pdf
McClanahan, W., Pepper, S., & Polin, M. (2016). “I program my own videogames”: An evaluation of bootstrap. Retrieved from: http://www.bootstrapworld.org/impact/EvalReportDec2015Medium.pdf
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