When I think about teaching math, I think of it as very linear: Here’s a math problem, students. Solve it. The trouble with teaching this way is that we sell our math lessons short. When we tell our students what to do and how to do it, we eliminate any chance of student engagement. We close the door to higher-level thinking. We also eliminate any chance of independent exploration and skill acquisition. Sure, our students may stumble and struggle, but the idea of “doing” mathematics reminds me of the quote that the journey is more important than the destination. When my students struggle, I feel like I am not doing my job, because I am not “saving” them. However, when I allow my students to work through difficulties, I allow them to take control of their learning. They’re active learners instead of passive ones. This is a good thing.
Math tasks also ask teachers to step back. Again, the journey is more important than the destination. The teacher poses questions and/or tasks and lets students do the learning in a way that makes sense to them. No two students or groups may arrive at the same conclusion or answer in the same way, but that’s OK, and the teacher needs give students the freedom to figure out things on their own. This is where relationships are important. Students need to trust that the classroom is a safe place to explore, struggle, and make mistakes. Meanwhile, the teacher needs to know what will engage students. Tapping into students’ interests will create engaging inquiry questions. For example, when studying physics, horse-crazy students may ponder the physics of equestrian show jumping (http://www.arthurstinner.com/stinner/pdfs/2014-tpt.pdf) and BMXers may consider the physics of a curved wall ride (http://bmx.transworld.net/features/the-physics-of-a-curved-wallride/#DxzaHJSZjeiYLfku.97). Many students find math difficult. If teachers make it enjoyable and allow students to explore it in a way that makes sense to them, they may not see it as hard and painful work.
As an English Language Arts major, I was excited to read about the literature links. (Far more excited than reading about the van Hiele Levels of Geometric Thought, I admit.) Linking literature to math makes sense to me. If “doing” math is about making connections and accessing prior knowledge, then it makes sense to seek out cross-curricular opportunities. Of course, the stars have to perfectly align and my ELA literature has to coincide with my math SLOs for this to work. This may be easier to do in elementary classrooms than middle schools where English and math are taught by separate teachers. I see the cross-curricular connections making math more meaningful to students. It shows them that math is not just a subject that is studied between, say, recess and lunch, but appears in all facets of life. The hand-shaking example in the textbook could extend to a health class: If one person in a room of six people wipes their nose with their hand and everyone shakes hands, how many people have you directly and indirectly infected with your cold virus? This cross-curricular approach to math also helps students form the habit of thinking mathematically more often than in that dedicated 60-minute block between recess and lunch.