Peter Liljedahl on...Building Thinking Classrooms: Conditions for Problem-Solving

Thursday, December 20, 2018

Peter Liljedahl is a professor of Mathematics in the Faculty of Education and an associate member in the Department of Mathematics at Simon Fraser University.  The following is an excerpt from his 2016 article on building thinking classrooms in order to create conditions for problem-solving.  This article was originally published here:

Liljedahl, P. (2016). Building thinking classrooms: Conditions for problem solving. In P. Felmer, J. Kilpatrick, & E. Pekhonen (eds.) Posing and Solving Mathematical Problems: Advances and New Perspectives. New York, NY: Springer. [ResearchGate, Academia]

In this chapter I first introduce the notion of a thinking classroom and then present the results of over ten years of research done on the development and maintenance of thinking classrooms. Using a narrative style I tell the story of how a series of failed experiences in promoting problem solving in the classroom led first to the notion of a thinking classroom and then to a research project designed to find ways to help teacher build such a classroom. Results indicate that there are a number of relatively easy to implement teaching practices that can bypass the normative behaviours of almost any classroom and begin the process of developing a thinking classroom.

MOTIVATION

My work on this paper began over 10 years ago with my research on the AHA! experience and the profound effects that these experiences have on students’ beliefs and self-efficacy about mathematics (Liljedahl, 2005 ). That research showed that even one AHA! experience, on the heels of extended efforts at solving a problem or trying to learn some mathematics, was able to transform the way a student felt about mathematics as well as his or her ability to do mathematics. These were descriptive results. My inclination, however, was to try to find a way to make them prescriptive. The most obvious way to do this was to find a collection of problems that provided enough of a challenge that students would get stuck, and then have a solution, or solution path, appear in a flash of illumination. In hindsight, this approach was overly simplistic. Nonetheless, I implemented a number of these problems in a grade 7 (12–13 year olds) class. 

The teacher I was working with, Ms. Ahn, did the teaching and delivery of problems and I observed. Despite her best intentions the results were abysmal. The students did get stuck, but not, as I had hoped, after a prolonged effort. Instead, they gave up almost as soon as the problem was presented to them and they resisted any effort and encouragement to persist. After three days of constant struggle, Ms. Ahn and I both agreed that it was time to abandon these efforts. Wanting to better understand why our well-intentioned efforts had failed, I decided to observe Ms. Ahn teach her class using her regular style of instruction.

That the students were lacking in effort was immediately obvious, but what took time to manifest was the realization that what was missing in this classroom was that the students were not thinking. More alarming was that Ms. Ahn’s teaching was predicated on an assumption that the students either could not or would not think. The classroom norms (Yackel & Rasmussen, 2002 ) that had been established had resulted in, what I now refer to as, a non-thinking classroom. Once I realized this, I proceeded to visit other mathematics classes—first in the same school and then in other schools. In each class, I saw the same basic behaviour—an assumption, implicit in the teaching, that the students either could not or would not think. Under such conditions, it was unreasonable to expect that students were going to spontaneously engage in problem-solving enough to get stuck and then persist through being stuck enough to have an AHA! experience.

What was missing for these students, and their teachers, was a central focus in mathematics on thinking. The realization that this was absent in so many classrooms that I visited motivated me to find a way to build, within these same classrooms, a culture of thinking, both for the student and the teachers. I wanted to build, what I now call, a thinking classroom —a classroom that is not only conducive to thinking but also occasions thinking, a space that is inhabited by thinking individuals as well as individuals thinking collectively, learning together and constructing knowledge and understanding through activity and discussion.

EARLY EFFORTS

A thinking classroom must have something to think about. In mathematics, the obvious choice for this is a problem-solving task. Thus, my early efforts to build thinking classrooms were oriented around problem-solving. This is a subtle departure from my earlier efforts in Ms. Ahn’s classroom. Illumination-inducing tasks were, as I had learned, too ambitious a step. I needed to begin with students simply engaging in problem-solving. So, I designed and delivered a three session workshop for middle school teachers (ages 10–14) interested in bringing problem-solving into their classrooms. This was not a difficult thing to attract teachers to. At that time, there was increasing focus on problem-solving in both the curriculum and the textbooks. The research on the role of problem-solving as both an end unto itself and as a tool for learning was beginning to creep into the professional discourse of teachers in the region.

Interested to read more? Find the rest of the article HERE

Posted by Meghan Burns at 9:20 AM – 1 Comments

Three Ways Garfield Gini-Newman Has Helped Me Re-Think My Teaching

Monday, December 10, 2018

The best thing that I learned at Garfield Gini-Newman’s Creating Thinking Classrooms workshop is that I don’t have to throw out everything I am already doing to create a community of critical thinkers in the classroom. This was a huge relief to a new teacher in the “create-as-I-go” stage of my career, and who has worked hard to amass the few resources that I do have. Rather, Mr. Gini-Newman suggests tweaking what is already happening in classrooms to foster environments that encourage both critical thinking and creativity. Simple changes in what I am doing that will lead to big changes in my students’ learning? Sounds like an idea I can get behind! Here are my top three takeaways from Garfield Gini-Newman’s two recent Manitoba ASCD events.

Problematize Everything

I was struck by how easy it is to implement Mr. Gini-Newman’s ideas. He argues that we should create problems as learning experiences in our classrooms to get students thinking. Isn’t the best kind of PD the one you can take back to your classroom on Monday morning? To create problems in everything students do in the classroom, I simply need to shift my planning mindset. For students to think critically, there needs to be a problem for them to solve. Seems simple, right? As I move forward planning the rest of the school year, I am trying to find the clarity of where my students are and where they should be going. Once I accomplish this, I can make thoughtful choices to provide my students with a problem that will become the vehicle for a unit of study. I must always consider the learning that I am trying to advance.

It's The Adjective That Matters

Launch Learning with Meaningful and Authentic Challenges

Okay, so now I have my problems and I’m ready for my students to solve them, but if I am not piquing my students’ interest from day one with something meaningful and authentic, how will they be invested in solving these thoughtfully created problems? Mr. Gini-Newman argues that to have a thinking classroom, thinking needs to be happening every day. I can’t plan on going into the classroom and teaching for a week, and then once I am finished expecting students to magically start thinking. By changing the order of my unit, I can engage students from the very beginning with thoughtfully created problems. These problems will serve as anchors for how content is delivered and provide opportunities for daily thinking.

Classrooms Need to be Set Up for Thinking and Creativity

In our grade five classroom, my students and myself spend a lot of time at the beginning of the year setting up routines and expectations. We use these throughout the year and we revisit them when things need tweaking. Why am I not considering the need for thinking and creativity as we co-construct our expectations? If I am changing the way that I approach teaching, I need to also consider how the classroom runs. Am I cultivating a safe space where students know it is okay to take risks, fail and persevere? Am I encouraging student curiosity and giving students the freedom to solve problems in their own ways? This third takeaway has resonated with me the most. I still have more questions than answers, but if I can expect daily thinking even in the most minute of ways, I think I am on the right track. My hope is to create an environment where students are curious and are not afraid to take risks. In this case, students will be allowed to fail early and will hopefully come to see failures as learning experiences.

Six Forms Of Critical Thinking Tasks

Potential Classroom Plans

Mr. Gini-Newman says, “a thinking classroom is a classroom where students think to learn and learn to think. It is a classroom where students are invited to think critically, creatively, and collaboratively.” I think with a little work, I can start to create a thinking classroom. Of course, I couldn’t help but leave both sessions with my mind buzzing with ideas. Here are two ways that I think I can get more critical and creative thinking happening in my classroom.

Overhaul the Design Process

I love Grade 5 science. We learn about neat topics and have so many opportunities for hands-on authentic learning experiences. Why have I been saving the design process for the end of units? Instead of having my students evaluate food products and decide which ones to bring for a healthy lunch at the END of learning about nutrition, I plan on giving them the choice from day one. Once they make their initial choices using prior knowledge, they can continually re-evaluate and change those choices as they learn more about different nutrients and healthy eating habits.

Curation

One form that creative thinking can take is curation. In this task, students gather together sections of works - poems, paintings, artifacts etc. To complete this task, one must understand what makes a specific type of work “good” and worthy of the collection. In the new year, I want to have my students curate different French texts. Sometimes, I find that teaching in a second language can limit a student’s ability to express their creativity. Vocabulary and syntax place constraints – has anyone ever mentioned how difficult French is to master? On the other hand, if students can recognize what a great French text looks like and justify their choices, they think critically about French texts, understand the criteria and components, and then have the opportunity to demonstrate those skills in a creative way.


Finally, as I head off with all my big ideas, I still have so many questions. What about my kids who are “good” at school? If I cease to give them a right answer, will they be uncomfortable for possibly the first time in their school career? This is excellent but definitely overwhelming. How do I help them change their mindset and stay engaged? And as always, the age old new teacher question. How? How do I make sure they actually learn? What if I have great problems and ideas, but fail to guide my students appropriately? How do I deliver content in critical ways? I have my big ideas and questions, but now how do I tackle day to day thinking? I want to make sure that I am teaching the necessary content in ways that encourage critical thinking, but I’m still stuck on the “how”.

I feel very strongly that teaching should be a collaborative effort and invite you along on my journey. Do you have answers to my questions? New ideas or questions that I haven’t even considered? I’d love to hear your thoughts and suggestions on how to incorporate critical and creative thinking into our classrooms. 


Meghan BurnsAbout the Author

Meghan Burns is a second year Grade 5 French Immersion Teacher at École Charleswood School. She is passionate about collaboration, dedicated to continued growth as an educator and is always looking for ways to get students hooked on learning! You can find her on twitter @madameburns

Posted by Meghan Burns at 12:53 PM – 4 Comments