Growing up I always enjoyed math. I felt that math was very black and white, I loved that there was a “right” and “wrong” answer to problems. The fact that you can go back and see your mistakes to learn from them made math that much more exciting for me. Math problems were a series of steps that you systematically followed then moved on to the next step to solve the answer, it was organized and concrete. It wasn’t until my Sophomore year of college where I took on a whole new perspective of math…
As an education major with a minor in math (I wanted to teach middle school math) I found myself working in the Math department as a tutor for a little extra “fun” money in college. I enjoyed my time in the department but found that the majority of my time was spent not tutoring, but rather as a glorified study hall for myself as rarely did students come in for tutoring. One day on a particularly slow day, one of the professors in the department presented me with a logic puzzle to challenge my mathematical abilities. Now, I don’t recall the exact problem but I will never forget the excitement and frustration I felt as I attempted to solve the problem! This was no ordinary math problem, there was no sequence of arithmetic, order of operations, etc. I honestly thought this problem was impossible to solve. To my dismay the professor told me the answer and how he came up with the answer – I was in shock. It was so easy yet I was unable to solve independently, maybe I wasn’t a mathlete after all!
Obviously this led to a lot of reflection and great dialogue with this professor. In my PreK-12th grade math experience, I was taught systems, numbers and operations, measurement, functions, etc., rarely was I asked to explain why something was the way it was – (except in geometry when solving proofs) nor was I asked to think critically about numbers and their relationships.
Clearly times are different now, I graduated High School almost 20 years ago, but I often wonder, how many opportunities are we giving our students to slow down and struggle to see patterns, relationships and solve math puzzles that require more critical thinking, using collaboration, communication and creativity?? Or Are we still just solving for X?
There are easy ways to shift how we, as educators, teach math and ensure we are incorporating the 4Cs into our math lessons, here are a few suggestions that are fun and can be adapted to any grade level:
- Explore value with virtual manipulatives – “As they see and play with different ways to formulate the same value, they build stronger number sense and a better conceptual understanding of factors. As students play with virtual manipulatives, they build cognitive models that teachers can actually see, allowing them to quickly perform formative assessments and identify misconceptions.” Creating a 21st Century Classroom – Combining the 3R’s and the 4C’s, Tech4Learning.
- Pattern play with Virtual Manipulatives – “As students participate in this type of play , they naturally sort, compare, match, and begin to create patterns, exactly the sort of mathematical thinking outlined in the Common Core State Standard for Mathematical Practice: 7. Look for and make use of structure.”Creating a 21st Century Classroom – Combining the 3R’s and the 4C’s, Tech4Learning.
- Connecting math to art – “Using art is a great way to help students see the beauty of math as well as help them connect math to the world around them.”Creating a 21st Century Classroom – Combining the 3R’s and the 4C’s, Tech4Learning.
Yes, it takes time for explorative, hands-on learning. But do we really want students graduating HS only knowing math as a series of rote memorized facts, a sequence of equations, and shapes? Or do we want students to see the mystery in math and be able to apply their mathematical problem solving skills to any scenario?
Katie Algrim – Director of Innovative Professional Learning