Saturday, November 2, 2013
Connect by Asking, "Why?"
Post by Marty Beck: Marty is in her 13th year of teaching math, the last seven at Bettendorf High School. She currently serves as our district's lead facilitator/trainer of College Preparatory Math (CPM).
Not so long ago, I was behind a young family checking out at Target. A young preschool-aged boy peppered his mom with questions; the most common one being, “Why?” Eavesdropping on their exchange both warmed my heart and made me sad. I loved witnessing that unbridled curiosity and it brought back fond memories of my own children. The sadness, though, comes from the realization that, at some point, many children lose that sense of wonder and the desire to know “why”, especially in my math classroom.
So recently, I've been doing a great deal of reflecting and asking “why”. You see, I've been on a journey. The journey started some 10 years ago when my youngest child entered kindergarten and I decided to go back to teaching. Soon I was standing in front of the class, talking to students and explaining how to do the examples that were just like the homework problems I would assign that night. This was the way I was taught to teach math and the way I was taught math, from grade school through college. It felt familiar, but yet, somehow wrong. There were bored looks from disengaged students staring back at me. Some dutifully took notes, others wrote notes to their friends instead (pre-portable technology). When students came in for help, they wanted to practice procedures, but it became obvious that many did not understand why the procedures worked or when to use them if a problem didn't look exactly like an example I’d done on the board.
This wasn't what I aspired to be…a talking head in front of a class. I wanted my students to be engaged, to make connections, and to be able to use what they were learning outside the classroom.
A conversation with an English teacher friend who professed to be terrible at math (though her mental math is faster and better than mine) provided me a spark to get me started on my journey. In her junior year of high school, she had to take a low level math class. During that class, she struggled with her multiplication facts. One day, the teacher she was working with explained that if she couldn't remember the fact 6 x 7, she could add the number 6 seven times. She was dumbfounded! At no time before had anyone explained to her that multiplication is a short cut for repeatedly adding the same amount. A light bulb moment for her then, and for me as she related the story!
You see, I was a memorizer as a student. With a really good memory, math was easy for me, as long as I had seen the same type of problem before, I could usually do another. Despite all those credits of college math, I would have never thought of explaining that multiplication is repeated addition to a student who was struggling. I memorized, but I hadn't really understood. How many other students memorized, or tried to memorize, the math they needed to get through the next test?
When my school adopted the Discovering Algebra curriculum, the next door on my journey opened. I was given the opportunity to see and feel what it was like for students to develop an understanding of concepts instead of just memorizing. The investigations in the text engaged students. Through the investigations, I saw teamwork and camaraderie develop. I saw curiosity emerge. Not to say there was never a lecture, but the atmosphere on investigation days was invigorating. Students were genuinely engaged and I, well I enjoyed being the guide/facilitator in the classroom. Sometimes we even learned together. Graphing calculator technology was new to me, but the students helped me through. It was so rewarding to see what students could do on their own when given the opportunity.
When I moved to my current school where a traditional math curriculum was used, I missed the energy and engagement of the investigation days. I tried to recreate it by using some of the lessons I had brought with me, and by searching out other activities to supplement our traditional text. To say this was hard would be an understatement. Not only did it take time to find, tweak and implement these activities, it was hard for the students too! I was asking them to understand “why” instead of just “how”. They weren't used to that! They had been conditioned by years of being “spoon-fed” their math. They seemed to truly believe that when I asked them to do activities, look for patterns and use their reasoning skills, that I was NOT teaching them. They thought that I should be standing at the board, writing notes for them to copy, demonstrating my knowledge by doing examples of problems that would later be in their homework and that somehow, by me doing all this work, they would amazingly learn the procedures. I swear some students believed that osmosis would work!! That they could learn by just watching me and never practicing themselves.
Enter 2010 and the adoption of the Common Core State Standards by Iowa. “The Core” contains standards for both math content and math practices like reasoning abstractly, looking for repeated reasoning, constructing viable arguments and critiquing the reasoning of others. After professional discussions with colleagues, conferences and more reading, consensus began to build that we needed to change how we were teaching math. We already knew that what we were doing in the classroom didn't work for many students. The laments about students not being able to apply what they’d learned and not retaining the content from one class to another were common, both in our math office and in disciplines where students needed to use math that they had previously been taught.
As part of the journey, many of us tried to write units of instruction for Algebra 1. It was really tough, and I’m not sure how effective. We knew what we wanted students to discover and the connections we wanted them to make through our instruction, but putting that together in a curriculum that others could use without reading our minds was much tougher than we imagined! We began looking for a curriculum that might meet our needs.
Many said to wait. Curriculum companies hadn't had time to catch up with the new standards. Their books were not necessarily aligned to the Common Core, even if they said so. We looked anyway. What we found was the “many” who said to wait were right. Many texts didn't change much except maybe to add some statistics and a couple of richer problems here and there to the “traditional” math text.
As we kept looking, I remembered sessions from the NCTM conferences I had attended; sessions that had helped me to make connections between the bits and pieces of knowledge that I had previously learned. If the activities and problems helped me to make connections, they would have to be good for students! The brain research I read definitely made the point that we are better able to remember information that we can connect to previous knowledge. I dug through the piles of handouts I had brought home from NCTM looking for an answer….where did that material that I liked so much come from? Finally, I found it…College Preparatory Mathematics (CPM). More research ensued. The CPM curriculum was written for teachers by teachers. It was based on research about learning and included collaborative inquiry, the math practice standards, (before they were officially known as that) and had been recently revised to meet the Common Core Math Content Standards. It seemed too good to be true!
Now two years into being a facilitator of learning using this curriculum, I can honestly say that my classroom feels “right” again. Not perfect, not by any means. I still have a lot to learn. It is hard to transition from being the “giver of knowledge” to the guide who questions, trying to lead students to see the patterns, the structure and the beauty of mathematics. Difficult, but rewarding! The engagement and energy are back. So is what can look like chaos, but it’s a controlled chaos. Students are discovering why the “short-cuts” and rules of math work. They are building an understanding and seeing how different ideas and concepts work for themselves. They don’t have to believe me. They get to prove it to themselves.
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