# Hands On Mathematics

*“Struggling in mathematics is not the enemy, any more than sweating is the enemy in basketball; it is part of the process, and a clear sign of being in the game.”*—*Suzanne Sutton*

This quote has hung in my classroom for six years, defining how I approach teaching mathematics. Math—and every other subject—should be accessible to every learner, and facilitated by a master learner. I’m a teacher, but above all I’m a learner who embraces struggle and creates opportunities for students to positively wrestle with problem solving by providing learners a context and reason for learning. In my classroom we focus on defining, modeling, and applying mathematics. These are skills necessary in math, but they can be translated across disciplines.

**Defining:** Students at any level need to have a way to connect learning to background knowledge. Defining mathematical terms in light of a familiar context is one way to do this. In a classroom setting, I use bell work to elicit memory from yesterday’s material or their long-lost basic algebra days. In addition, I connect material to situations within the parameters of my students’ world (i.e., Intro to Algebra and basic financial literacy with addition and subtraction; Geometry with house design; Algebra 2 with modeling business projections using systems of equations). It is also effective to define terms by what they are not, and to discuss the biconditional nature[1] of definitions within mathematics. The more specific we can be in defining terms and notation, the more articulate the math conversation can be. In the last year, I have connected math concepts to grocery shopping, mindcraft, video game programing, theme parks, art, sports, cooking, engineering, and physics. Get creative and collaborate with your students and colleagues to find connections that work for your students.

**Modeling:** *Design it. Draw it. Build it.* These are the mantras I live by in the classroom. No matter how old your students, these ideals facilitate learning for all modalities and encourage student problem solving. My classes design mathematics in groups as we collaborate and research possibilities. We draw math situations with crayons, colored pencils, graph paper, compasses, protractors, and graphing calculators. Remember the phrase, “If you build it, they will come”? We build math with Legos, manipulatives, Wikki Stix, string, toothpicks, and recyclables. There is absolutely a place for technology, but it should never be a replacement for student-teacher interaction and conversations about mathematics[2].

**Applying:** Modeling is the first step in applying. The visual shows the application; however, I never exit a unit without connecting it to past units and previewing what is next. Part of application is explaining how the puzzle pieces of our learning fit together. We call it the “story of math.” In this story, we must understand positive and negative numbers before we can understand balancing equations. We must understand linear functions before we can understand parabolic functions. Project-based learning is ideal for this type of application, but it can be challenging given school parameters. I advocate for mini-projects and consistently require written components that allow students to articulate math in words. After all, the ultimate goal is for students to be math literate and able to construct arguments and critique the reasoning of others. As an added bonus, this type of application addresses the standards for mathematical practice dictated by the NCTM.[3]

Just try it! Don’t be afraid to challenge your own classroom norms. As I change schools this year, I am feeling like a new teacher all over again, and developing a fresh perspective on my methods right along with you! I am embarking on the adventure of flipping my classroom with video lectures/notes at home to allow for more guided application in my classroom. In order to make sense of mathematics it is my goal to provide learners with different entry points to the curriculum by clearly defining, actively modeling, and articulately applying concepts into the larger “story of math.”

**Alaina Shelton**

Associate Consultant—Mathematics

TeachBeyond

[1] Biconditional definition is where both the conditional and the converse are true: Example-Definition of parallel. Conditional: If two lines are parallel, then the lines have the same slope. Converse: If two lines have the same slope, then the lines are parallel. Biconditional: Two lines are parallel if and only if both lines have the same slope.

[2]Resources: http://illuminations.nctm.org; https://www.ted.com/talks/tom_wujec_build_a_tower—best team building exercise I’ve ever done!; https://www.teachengineering.org

[3] National Council of Teachers of Mathematics whose standards correlate with both the Common Core State Standards (US) and Canadian Mathematics Curricula (Ontario Curriculum, Quebec Curriculum, and WNCP-based curricula). See here for a chart outlining the correlation of these standards.

**Photo Credits**: *Algebra. *World Bank Photo Collection Flickr via Compfight cc, *Angles*. Alana Shelton.

**Alaina Shelton** is a Kansas math teacher and TeachBeyond associate member who has 6 years’ experience specializing in Algebra 2 and below. She’s most passionate about Geometry and designing hands-on curriculum. This school year, she is reinventing her craft by digging deep into blended learning and the flipped classroom model!