A few months ago I informally asked a group of elementary students what they think of when they hear the word math. I heard many responses from the students. First and second graders focused on the words adding, subtraction, shapes and money. Upper elementary students emphasized multiplication, division, money (again!) and fractions. Often, the student responses were directly related to the last few units that were taught.
I find that the perspective of math changes as kids move grade levels. My own perspective of math has changed over time. I used to dread talking about fractions when I was in middle school. My perspective switched gears when I started to see the different uses of fractions outside of the classroom. When I started to see fractions as less abstract, my notion that they were evil started to dissipate. Events similar to this affected me and my teaching style during my first few years of teaching.
My first teaching job out of college started in an empty fourth grade classroom. I was placed on a team with a two veteran teachers. I remember being given a curriculum guide and told to teach math in specified units that were often separated into math concepts. I don’t believe there’s anything specifically wrong with this, but wonder now if the idea could use some tweaking. This type of unit lesson planning lasted throughout the year. During those units, the lessons were directly related to a particular standard and didn’t deviate much from that path. My team was extremely supportive, although we didn’t question the sequence or the curriculum. Once students took the unit test, the class moved to the next unit of study, which was generally a different math strand. For example, fractions were out and division was in. This process was repeated throughout the school year without revisiting past strands. Of course there was review, but the units didn’t seem connected in any way. As students moved through the units they often had a challenging time applying skills taught earlier in the year. The gap between the content in the units seemed to widen as the year progressed.
I bring this up because it relates to a book that I’m reading. Over the past month I’ve been participating in a math books study with some amazing educators. We’ve been discussing this book over GHO every other week. One of the passages that peaked my interest came from page. 74
“Structuring units – and – lessons within the units – around broad mathematical themes or approaches, rather than lists of specific skills, creates coherences that provides students with the foundational knowledge for more robust and meaningful learning of mathematics.”
As math educators plan units I feel as though the above is sometimes a missing component. Planning opportunities for students to discover how math concepts are connected can be a powerful learning tool. It also shows students that math is not defined as a checklist of singular concepts or “I can” statements. As students switch their mathematical lenses, they see the connected aspects of math, as I read on page 76.
“When they teach the sequence of lessons that they have prepared as a team, the teachers will continually ask students to switch the lenses that they use – from looking at a situation algebraically to exploring how it connects with geometry that they have been studying.”
This year I’m more intentional in planning lessons and activities that connect math strands. I follow the curriculum, but in addition to that I’m finding that activities and lessons that blend math strands gives students more opportunities to cement their mathematical understanding. Problem-based learning projects often lend themselves well to these types of lessons. Even showing students the sequence of the curriculum can prove beneficial as students see where they are starting and the expected finish. It also helps students to be able to view math beyond the abstract. That connectedness can bring a new appreciation and possibly a renewed math perspective.