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FocusLast spring, I attended the most inspirational professional development sessions ever. Steve Leinwand, one of the lead authors of Principles to Actions, Ensuring Mathematical Success for All, spent the day in Iowa with the Statewide Mathematics Leadership Team. I left feeling reinvigorated and committed to make a small, yet significant, change to my teaching.

Steve’s challenge to us was to think about how we can encourage colleagues to implement the teaching practices for effective mathematics instruction. It has to start with our own practice. This made me wonder, “how am I working toward implementing the practices in my own instruction?”

One of Steve’s main points really resonated with me. He said that it is ineffective to expect to change everything all at once. Instead, Steve proposed to focus on one practice, do it really well, and then add another focus later. This seemed so simple because it is easier to focus on one thing rather than several. That’s a change from the past, when too often I have found myself leaving a professional development wanting to try everything. Then, I rarely continue any of them because I did not allow the time for those practices to become an innate part of my craft.

From the reflection of my own learning experiences in mathematics and permission from Steve to focus on just one practice, I committed to focusing on implementing tasks that promote reasoning and problem solving. According to Principles to Actions, implementing tasks that promote reasoning and problem solving means that “effectively teaching mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving, and allow multiple entry points, and varied solution strategies.”

This focus has helped me improve my instruction because I now encourage a variety of strategies for solving problems from my students. Creating a space for students to discuss how different methods are similar and different helps me know that they are engaged in the mathematics and are experiencing mathematical reasoning and problem solving.  

The students are willing to share their ideas and discuss with each other how to find the most efficient strategies. We often compare and contrast their solutions and, when someone comes up with a new or interesting method, we will give the student naming rights for the method. For example, a new method for factoring polynomials might be called the “Charles Method.” They feel pride in finding a strategy that helps their classmates understand how to solve a problem. 

Before I had a focus, I used to use a number of open-ended tasks that easily lent themselves to this type of group work and discussion. However, some students would struggle to interpret these more complex tasks. I would usually give students a handout with the task printed in paragraph form at the top of the page; then, the task would be followed by questions for the students to answer. We would read the problem together as a class and I would instruct them to work together in small groups to answer the questions. I knew that this was not working for many students because often students would not know what they were supposed to do or even what the problem was.

Steve helped me to see how to improve the equity of access to these tasks and introduced to me a new strategy to present tasks to my students. He suggested that instead of introducing all of the text at once, introduce the text one line at a time. Using this strategy, revealing each line of information with a pause for students to think, allows students the opportunity to reflect on what their background knowledge tells them about the situation. This gets the students engaged with the task, the reasoning, and the problem solving.

For example, consider the problem of calculating the amount of fertilizer needed to cover a specific area. First, I would first tell the students that Anne wants to purchase fertilizer. Now I would ask the students, “what do we know about Anne?” Some students might suggest she’s a farmer, some might say she runs a golf course. Already, they are curious about Anne, and curiosity is a powerful engager.  

As I introduce each line of information, the students are able to narrow down what they know about the situation and refine their beliefs about the problem. This is the point where the magic happens: After students have all the information they need about the task, I ask them, “What is the question?” Usually the question I was intending them to answer is one they most frequently suggest, but often the students suggest other questions that are more interesting and challenging to answer.  

Sometimes I let them choose which question they want to investigate or I will purposefully suggest which one they might want to start with first. Rarely are there questions about what they should be trying to find, and even when students are stuck, they can correctly tell me a lot about the context of the problem. Usually this is enough to get them engaged and ready to start even the most challenging tasks. 

Having a focus of one of the practices has made a significant difference to how my students experience mathematics, reasoning, and problem solving. Focusing on one thing has allowed me to implement and refine my practice and for it to become an innate part of my craft. I will purposefully pick a new focus for next year.

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Posted by : Mary Watson