Reflections on Blogging

I have blogged before using blogger, but this was my first experience into blogging about a professional topic. Blogging about personal experiences is easier because you don’t have to look further than yourself for content or references. However, I enjoyed blogging about my topic “Thinking Outside the Math Textbook” as it is something I am passionate about. The more I searched for material, the more pages I added to my education Pinterest board. The most time-consuming aspect of this assignment was narrowing down my blog topics. There are so many activities available to apply math topics to fun and engaging activities that go well beyond worksheets. The more activities I sampled, the more I want to teach a computational thinking centered math class. I don’t know if I’ll continue to blog, at this time, but I will definitely continue to follow the multiple educational bloggers I found that appeal to my “thinking outside the math textbook” concept.

Within my future math classroom, I can definitely see using a blog to keep students and parents up to date with day to day classroom happenings. The blogs would likely include vodcasts I make demonstrating how to solve homework problems, or postings of notes made during class using the SmartBoard. A blog is a great way to save this information and reference it from year to year, adding more every year with each new class. Soon students will have a great resource full of information from their class and past classes. I like the idea of using a blog to compile this information more than using google drive or an online learning space because often the information shared within those storage spaces pertains only to one class and doesn’t offer much historical information to search and reference. If an Algebra II student needs to reference past notes they remember from my Algebra I class, it will be possible by searching the blog for past content. My future classroom will definitely have some type of online presence, organized for the benefit of all my students in all classes.

Using Card Tricks in Algebra

Incorporating short programming projects into high school math can be difficult as upper level math classes include more abstract concepts that do not always transfer well to short programming projects. I did not find any good Hour of Code or CodeHS programs that can be used to apply higher level math concepts and don't require extensive coding background knowledge. Without teaching full programming courses, I believe fun computational thinking exercises can still be emphasized and included in higher level math classes. 

Teaching London Computing created many activities that combine computational thinking and mathematics (https://teachinglondoncomputing.org/interdisciplinary-computational-thinking/computer-science-and-maths/). I evaluated their activity Red Black Mind Meld for the usefulness in an algebra classroom. I think this activity is a winner for high school algebra students. It is an unplugged activity, so no technology is required. It’s engaging, thought-provoking, requires substantial computational thinking, knowledge of algorithms, and also incorporates that dreaded word “proofs!”. It does all this by using a card trick that is sure to initially blow your students’ minds and hook them for the rest of the class period. The step by step instructions for performing the card trick can be found here (*.pdf), but be aware that those instructions also contain the answer. If using this in my classroom, I would provide the instructions for performing the card trick and remove the answers. Encourage students to figure out why the card trick works on their own, providing hints about setting up algebra equations, as necessary. After all, figuring out how it works requires an algebraic proof of the algorithm. It might be helpful to provide some pre-teaching about the words abstraction, algorithm, and computational thinking as these words are referenced multiple times in the Mind Meld instructions. I think this activity is also fabulous for TAG math students as you can easily expand upon it and require students to come up with variations to the algebra that will still provide an algorithm for a new self-working card trick. 

When it's time to reveal the answer, Teaching London Computing has a PowerPoint presentation you can download to explain the card trick. The algebra behind this algorithm is really slick and not too difficult to understand once students create the first basic equation. This activity clearly hits on multiple Iowa HS algebra math standards (2010), including: 

• A-CED-A.2: Create equations in 2 or more variables
• A-CED-A.4: Rearrange formulas to highlight a quantity of interest
• A-REI-A: Understand solving equations as a process of reasoning and explain the reasoning
• A-REI-C: Solving systems of equations
• MP1: Make sense of problems and persevere in solving them 
• MP2: Reason abstractly and quantitatively
• MP4: Model with mathematics

Teaching London Computing, while focused on spreading computer science and computational thinking throughout England, is also a great resource for math teachers in the United States to encourage "thinking outside the math textbook". 

References
Iowa State BOEE (2010) Iowa core mathematics. Retrieved from https://iowacore.gov/sites/default/files/k-12_mathematics_0.pdf

Teaching London Computer. (n.d.) The red black mind meld activity. Retrieved from https://teachinglondoncomputing.org/resources/inspiring-unplugged-classroom-activities/the-red-black-mind-meld-activity/

Learning Algebra Using the Bootstrap Curriculum

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