Developing the “Why” for Middle Grades Math
By Christian Polizzi
As they transition from elementary school into the middle grades, students start asking those hard questions, like why is Joe buying 5 crates of watermelon each holding 8 watermelons? Young adolescents want you to be real with them and they want the truth: Why should math matter to me?
Many standards are abstract and do not divulge the importance of the skill or why this is relevant to them as students. As a math teacher or an educational leader, you should remedy this, not just move on. Taking time to incorporate real life examples, asking students for examples in their lives, and having students create their own math problems will not only impart the “why” but will help them grow their math knowledge.
Adding Real Life Examples
Sometimes adding real life examples is easier said than done. Taking an abstract standard, such as Common Core standard 7.G.A.1 (Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale) and framing this standard to make sense to students can seem difficult.
Reflecting on your personal life and how you would use this standard in the real world and sharing your reflection with your students should be your first approach.
For standard 7.G.A.1, this might include pulling up a map showing two cities on the smartboard or projector and zooming out, revealing that the cities might have moved closer, but their distance apart has not changed.
Or show the students a blueprint for a house. Is the house going to be the size of the piece of paper? No, it is drawn to scale. Not only will the students see the concept in a new light, but they will also understand why this is relevant to them.
Examples in Student’s Lives
Culturally relevant pedagogy is not talked about in math enough – in part because teachers sometimes struggle to find examples that make sense to adults, let alone students. This step is usually the hardest as it requires you to know your students, the community, and how to make connections with their worlds.
When you reference places in the community your students shop or eat at, sports or games they play, or their personal interests and tie it to a mathematical “why,” students will better understand the relevance. Sometimes, asking kids the simple question about where they see this skill or standard in their lives elicits a student generated “why.” Other times you will need to dig deeper into “why” the topic is relevant.
Teaching a math lesson to students in an international community where the game of (team) handball is valued, I taught ratios in the amount of steps you could take between each dribble (3:1) or by looking at pictures and finding ratios of the red team members versus the blue team members.
By Kuebi – CC BY-SA 3.0
This can spur the group to look at more complicated ratios such as shots taken by each team, or saves by the goalie, or passes made. Students’ prior knowledge of the sport came in handy as they were able to better frame their understanding of the math concept. Given this example, students were able to make deeper connections with the concept and standard. Teachers in various countries can duplicate this idea using popular national sports.
Student Developed Problems
Creating is at the pinnacle of the Revised Bloom’s Taxonomy and an excellent example of what a math classroom should strive to be. Not only should your students create examples at this step, but in addition they should create their own personal “why.”
What “why” would they incorporate into one-variable equations? What lens should they view linear equations through? Creating problems and delineating a connection to their life show mastery of the skill.
Likewise, in the process of creating these types of problems, students who are struggling can learn from peers who successfully navigated the problem and have found their personal “why.” Students teaching students is an approach that can benefit students at both higher and lower levels of mastery as they continue to master the skill. Similarly, students will be excited to share their “why” because it will be personal, giving them an opportunity to learn to love the content.
Establishing the “Why” Takes Time
Taking time out of math instruction to explain a “why” that is relevant to your students and providing time for students to develop their own problems with their own “why” can seem overwhelming.
Start small and grow the “why” for each unit, then standard, and eventually each of your lessons will provide access to the content your students didn’t previously have. Finally, pushing your students to advocate for their own personal “why” will open the door for mastery for all students.
But before any of this can happen, you need to take your time and find your “why.” Take time to understand “why” math is important, and “why” you teach middle grades math.
Christian Polizzi is Academic Coordinator and Curriculum Lead at Washington Global Public Charter, a middle school in Washington DC. He has experience teaching social studies, ELA and math, and working as a special education teacher, at both public schools and private international schools abroad. He is continuously seeking ways to provide support and equitable access to education for all students across the globe, and is continuing to grow by pursuing his Educational Doctorate.