Striving for Authentic Learning

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By Cory Sheldahl, MN Region 2 Director

In this post COVID-19 year, it seems that learning for students is strange and somewhat difficult considering the stress and strain suffered from the previous year. I knew our traditional form of education was going to experience a similar strain at the high school I teach math.

My first sense at the beginning of the year for my pre-calculus students, was to find a curriculum that would help acclimate them to the material without overwhelming them with rigor since the textbook on-hand was very high-end. I searched for a curriculum for several days until I found one on Teacherspayteachers.com that was an interactive notebook. The students seemed to like it right away except for the fact that I would have to generate examples and/or extra practice for them to get used to the concepts presented. As I was scrambling to get organized, I did not provide enough practice and they started to feel lost. I did transition my focus to CK12.org and used a pre-calculus online e-book published there, but also provided resources and adaptable practice.  This alone did not suffice because the students preferred something more tangible to look at and did not feel they could navigate without some type of training.

This ultimately led me back to go to the interactive notebook again, except this time I would interchange practice from ck12.org with deltamath.com. Currently, I am also looking to find relevant projects to help tie their learning with trigonometry concepts to application so it’s not just pencil and paper skill building.

This is also the year I decided to change the curriculum for our eighth grade, because we typically push our eighth graders into Algebra 1, with a text that normally supports Minnesota ninth grade standards. I talked my principal into purchasing the Envisions Algebra 1 book set, in the hopes that the students would be able to work into high-end thinking (see Savvas.com, 2021). I did not think very much about designing learning activities, and since I only received the books and not the support materials, that meant I had to form everything on my own.

In a book I have been reading, Disruptive Thinking in our Classrooms (2020), Eric Sheninger writes that an important element of cognitive flexibility includes to “design learning activities to support divergent thinking where learners demonstrate understanding and creative and nonconventional ways.” As I was reading the issue of NCTM’s Mathematics Teacher: Learning and Teaching PK-12 (2021), it included an article geared towards providing students with a real-life problem to contemplate, specifically, The Great Pacific Garbage Patch. I used an article from Newsela.com to provide the proverbial carrot. Since they were working in the Envisions Algebra 1 (Pearson, 2018) book on system of equations and inequalities, I saw this as a great opportunity to provide the students with a project as an assessment to use inequalities to form fences around the garbage patch zones.

At first the students struggled to get a start; of why it was important to use an inequality instead of an equation, or in just drawing around the zone itself. I shared with him what it meant to have a shade or a barrier to the graph and what the shaded part of the graph meant from the inequality I put in Desmos. Right away they got very picky with my choice of inequality and started providing suggestions to change it and that’s why I said OK is your turn to form a better any quality and to come up with 6 to 8 possible solutions to contain the garbage patch area. I could see that after the second day they were starting to get the idea and some students were very proud of their maps that were superimposed into Desmos with their inequalities.

It seems if one keeps trying to make something more relevant and change it from a boring worksheet task, many times the students will surprise you. Even though now I created layers of grading for myself, I’m excited to see what level of learning they accomplished by doing their GPGP projects

Citations

Mathematics Teacher: Learning and Teaching PK-12 114, 11; 10.5951/MTLT.2020.0369

Savvas.com. 2021. enVisionmath AGA Algebra I, Geometry, Algebra 2 Common Core Program | Savvas High School Math Curriculum. [online] Available at: <https://www.savvas.com/index.cfm/k12cms/index.cfm?locator=PS3b2k&PMDBSOLUTIONID=6724&PMDBSITEID=2781&PMDBCATEGORYID=806&PMDBSUBSOLUTIONID=&PMDBSUBJECTAREAID=&PMDBSUBCATEGORYID=&PMDbProgramID=148986> [Accessed 18 December 2021].

Sheninger, E. (2021). Disruptive Thinking in Our Classrooms: Preparing Learners for Their Future. United States: ConnectEDD.