“Real world application” -- the three words I seriously dread as an educator. I am a learner who did what I was told because I was told, and I honestly enjoyed the academia. I did not need (nor care) when or why I had to learn something. As a result, I feel woefully inadequate, especially as a math teacher, to create “real world” scenarios and lessons. However, I understand some students truly need these frames in order to engage in learning.
As an English teacher, I always felt comfortable creating (and justifying) lessons as pertinent and important for all students. However, math has always been harder. I struggle because it isn’t my strength, and I struggle with how to find meaningful activities within students’ skill sets. In recent years, more material has become available, but it is still a struggle to find the right activities.
Math is a pervasive subject, despite what many people think, yet the kinds of math all people do every day isn’t directly what we teach (per the standards) in high school. In looking at the Bureau of Labor Statistics “Occupational Outlook Handbook,” only 4 careers appear under “math.” Carpentry, sales, engineering, and farming are not listed, and I know these careers are math-heavy which makes the data a bit misleading. The website predicts 28% growth in mathematics careers, especially data handling. The one thing all these careers do have in common, and the direction I believe math is heading, is more focused on inquiry and problem-solving. We will still be teaching geometry and algebra, but within those concepts, I hope to see more focus on the broader skills needed for many careers. When I look through the lists of most desired skills as published by National Association of Colleges and Employers and the American Management Association, I see math as a critical practice field for developing all the top skills: critical thinking, problem solving, collaboration, and communication. If we work to change even our practice of teaching to focus on these skills and math as a means to gain them, we will still be preparing our students well for the future.
One concern with “real world” problems is that we could actually make things worse by creating contrived and/or overly-simplified problems. Just using a real set of data doesn’t necessarily make the learning authentic, which is what I think we really mean when we say “real world.” For example, in his article posted on NCTE in 2014, Matt Felton notes the classic candy in a bag problem as being real but not authentic. As he suggests, this could provide a stepping stone or concrete example of a concept, but being able to generalize knowledge and learning is a well-documented problem for students. While being “real” this example still asks students to generalize the learning to future situations which they may or may not be able to do, so by including this example have we really done a better job teaching? Felton goes on to suggest a more “authentic” approach, such as asking students how unequal is wealth distribution in the US? I would go one step further and ask why that matters or how it could be fixed or what implications this has on society? (But that might be the English teacher in me talking in math class!)
Another facet of this real-world application dilemma is what will constitute “real world” (and meaningful) for our students? It is well-documented that 50-70% of the jobs our students will hold do not even exist, so to what context do we even address problems? Maybe this isn’t the issue, but knowing how hard it is for students to generalize and then wondering if my “great” real world problem will even be relevant in 2 years is a bit daunting.
In looking into “real world math,” many of the tasks lean toward a project-based learning frame. This is a great frame, but not currently one that is compatible with our system, or even standards. Our courses are tightly aligned to the state standards, and we try to prepare students for college entrance exams and state assessments. PBL takes a significant amount of time, and I wonder how teachers are able to guarantee that standards are covered if students are truly following their passions. While we shouldn’t look for or accept roadblocks, we do have to live within the rules (even while we try to change them). If I am responsible to teach a certain set of standards, I must balance that with “add-ons.” When there is only so much time, additions must be carefully considered-adding more to an already full course can undermine any good that could come from the addition because students are overwhelmed.
All the concerns aside, two good resourcesI found that I plan to try to use this year are Illuminations (http://illuminations.nctm.org/) and NRICH (http://nrich.maths.org). While maybe not the perfect answer to including more authentic math, I think it is a good step to engage students in the process and understanding of math--to move away from drill and kill and completely abstracted math work. I hope to expand on these tasks as I determine which ones resonate best with students and connect the learning. In looking at the NRICH site, I already created a list of not only potential ideas for different math courses, I also found many that would lend themselves to paired readings. This creates both that authenticity and relevance and reinforces content area reading skills.
American Management Association. (2012). Critical skills survey. Retrieved from http://www.amanet.org/uploaded/2012-Critical-Skills-Survey.pdf.
Bureau of Labor Statistics. (2015, 17 December). Math occupations. Retrieved from http://www.bls.gov/ooh/math/home.htm.
Felton, M. (2014, 7 July). Mathematics and the real world. National Council of Teachers of Mathematics. Retrieved from: http://www.nctm.org/Publications/Mathematics-Teaching-in-Middle-School/Blog/Mathematics-and-the-Real-World/.
National Association of Colleges and Employers. (2015, November 8). Job Outlook 2016: Attributes Employers Want to See on New College Graduates' Resumes. Retrieved from http://www.naceweb.org/s11182015/employers-look-for-in-new-hires.aspx#sthash.2vw7Z5VN.dpuf.