Recently, I visited with some of our seventh-grade students whose goal it was to envision and redesign classroom spaces to reflect a more contemporary learning environment. Since this project was an assignment in their pre-algebra class, they were expected to use math as a tool to help them design scale models of these contemporary educational spaces. I was encouraged to see these students integrating quantitative methodologies, such as ratios and proportions, with the spatial qualities associated with design thinking. The qualitative considerations that come into play when designing a classroom space include, “transparency, flexibility, dispersed technology, soft seating, adaptability, variety, indoor-outdoor connectivity (Jacobs, 2017).”
What fascinated me the most was how well the students were able to take this open-ended requirement and generate ideas that were bounded only by their own imaginations. How we group students for the purposes of math instruction plays a significant role in educational outcomes and expectations (Pritchard, 2012). Traditional schooling systems encouraged students to work alone effectively and rewarded the “diligent solitary scholar (Jacobs, 2017).” That sort of “classical” or “antiquated” system limits the possibilities that can be generated by grouping students according to interests or a “felt need” rather than initial perceived ability levels. Contemporary instructional grouping permits the free-flow of ideas that are needed in a global society that places a premium on innovation.
A very special “THANK YOU” to the 7th-grade math teachers, Ms. Reilly and Ms. Abrahamsen, for this lesson. The “21st Century Classroom Redesign Project” encouraged students to solve real-world, relevant problems using an array of techniques and ideas in a collaborative fashion. What better way to learn algebra than by “doing” algebra – in this case, by scaling down the classroom into a working model.
From my own personal experience, here’s a problem that recently required me to “do” algebra that sounds almost like a seventh-grade math exam question:
My brother Dan and I took an airplane trip to Florida to visit our father. Dan bought two round-trip airline tickets for $425 and I paid for the car rental at $120. If Dan and I agreed to split the total costs evenly, how much did I owe Dan? I like to think that I have a basic understanding of algebra (or in this instance, the “mathematics of equality”) so I wrote the following equation:
let x = the amount of money that I owe Dan (in US dollars) where:
425 – X = 120 + X
2X = 305
X = 152.50
I owed him $152.50 (we figured that the airport parking that I paid was a wash for the night he took me and our dad out for dinner). My point to this whole story is that when we use algebra, we’re not solving math-problems, we’re solving life-problems. Algebra is a math tool that helps us find equality, balance, and proportionality in our lives. More importantly, these quantitative tools, when combined with a qualitative analysis of the world around us, will allow us to find innovative solutions to all sorts of problems that have yet to be solved.
References:
Jacobs, H. (2017). Bold Moves for Schools. ASCD. Alexandria, VA
Pritchard, R. (2012). “The Influence of Ability Grouping on Math Achievement in a Rural Middle School” unpublished dissertation. Seton Hall. University Dissertations and Theses (ETDs). 1817.