Manitoba ASCD Blog

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

Peter Liljedahl on...Flow: A Framework for Discussing Teaching

Wednesday, November 7, 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 using flow to talk about engagement in the mathematics classroom.  This article was originally published here:

Liljedahl, P. (2016). Flow: A Framework for Discussing Teaching. Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education, Szeged, Hungary.

In this paper I explore Mihály Csíkszentmihályi's notion of flow as a lens to analyse the teaching practices of two very different teachers. Results indicate that flow is not only a good theoretical framework for drawing attention to the differences in teaching style, but also for describing these differences in ways that is grounded in what we know about good learning. The possibility of shifting flow from a descriptive framework to a prescriptive one is also explored.

FLOW AND THE OPTIMAL EXPERIENCE

In the early 1970's Mihály Csíkszentmihályi became interested in studying, what he referred to as, the optimal experience (1998, 1996, 1990),

 “a state in which people are so involved in an activity that nothing else seems to matter; the experience is so enjoyable that people will continue to do it even at great cost, for the sheer sake of doing it.” (Csíkszentmihályi, 1990, p.4)

The optimal experience is something we are all familiar with. It is that moment where we are so focused and so absorbed in an activity that we lose all track of time, we are un-distractible, and we are consumed by the enjoyment of the activity. As educators we have glimpses of this in our teaching and value it when we see it. 

Csíkszentmihályi, in his pursuit to understand the optimal experience, studied this phenomenon across a wide and diverse set of contexts (1998, 1996, 1990).  In particular, he looked at the phenomenon among musicians, artists, mathematicians, scientists, and athletes.  Out of this research emerged a set of elements common to every such experience (Csíkszentmihályi, 1990):

  1. There are clear goals every step of the way.

  2. There is immediate feedback to one’s actions.

  3. There is a balance between challenges and skills.

  4. Action and awareness are merged.

  5. Distractions are excluded from consciousness.

  6. There is no worry of failure.Self-consciousness disappears.

  7. The sense of time becomes distorted.

  8. The activity becomes an end in itself.

The last six elements on this list are characteristics of the internal experience of the doer. That is, in describing an optimal experience a doer would claim that their sense of time had become distorted, that they were not easily distracted, and that they were not worried about failure.  They would also describe a state in which their awareness of their actions faded from their attention and, as such, they were not self-conscious about what they were doing. Finally, they would say that the value in the process was in the doing – that the activity becomes an end.

In contrast, the first three elements on this list can be seen as characteristics external to the doer, existing in the environment of the activity, and crucial to occasioning of the optimal experience. The doer must be in an environment wherein there are clear goals, immediate feedback, and there is a balance between the challenge of the activity and the abilities of the doer. 

This balance between challenge and ability is central to Csíkszentmihályi’s (1998, 1996, 1990) analysis of the optimal experience and comes into sharp focus when we consider the consequences of having an imbalance in this system. For example, if the challenge of the activity far exceeds a person's ability they are likely to experience a feeling of anxiety or frustration. Conversely, if their ability far exceeds the challenge offered by the activity they are apt to become bored. When there is a balance in this system a state of, what Csíkszentmihályi refers to as, flow is created (see fig. 1). Flow is, in brief, the term Csíkszentmihályi used to encapsulate the essence of optimal experience and the nine aforementioned elements into a single emotional-cognitive construct.

Figure 1: Graphical representation of the balance between challenge and skill

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


Posted by Meghan Burns at 10:14 AM – 0 Comments

Garfield Gini-Newman on...Creating Thinking Classrooms

Thursday, September 13, 2018

Garfield Gini-Newman and Roland Case have created an strategy packed book, loaded with stories, and examples to reinvigorate today’s schools. The following is an excerpt from the preface of Creating Thinking Classrooms: Leading Educational Change for This Century.

 

This book is for classroom, district, and university educators who are working to make schools effective institutions for developing all students’ capacity for rigours and imaginative thinking so that they can become healthy individuals, contributing global citizens, thoughtful consumers of media, and adaptable learners who can thrive in a rapidly changing world.

Our goal is to help educators at all levels to understand and respond thoughtfully to the diverse and sometimes overwhelming calls for school reform that currently dominate public and professional attention. These calls are noisy, confusing, and not entirely coherent. We hope to separate the rhetoric from the reality surrounding many of the popular buzzwords and vague claims associated with learning in the contemporary world. In addition, we seek to unpack the widely recommended goals, initiatives, and pedagogical practices that advocates of reform are championing. Finally we propose an approach supported with practical advice to educators in their efforts to navigate the substantial, often upsetting, challenges of educational change.

The most significant contribution of this book lies in its attempt to clarify and bring coherence to the current reform efforts. When distilled to its essentials, this movement represents a desire to shift the educational system in three important ways involving nine core ideas:

  • Shift 1: Reorient the foundational beliefs about teaching and learning from the mindset characteristic of a discovery or didactic classroom to that of a thinking classroom.

  • Shift 2: Refocus attention on more enriched versions of the three traditional educational goals, moving from fostering knowledge to deep understanding, from skills to real-life competencies, and from attitudes to genuine commitments.

  • Shift 3: Align teaching practices with five key principles of powerful learning. These guiding principles are to engage students, sustain inquiry, nurture self-regulated learners, create assessment-rich learning, and enhance learning through digital technology.

 

Interested to learn more? Click here for a sample first chapter of Creating Thinking Classrooms. Click here to purchase a copy of Creating Thinking Classrooms, or copies will be available on October 4th at the Manitoba ASCD workshop.

 

Posted by Meghan Burns at 8:42 PM – 0 Comments

Garfield Gini-Newman on...Critical Thinking

Wednesday, September 5, 2018

This article was originally published at https://arpdcresources.ca/resources/critical_thinking_with_garfield_gini_newman/#7

Teachers and 21st century curricula recognize critical thinking as one of the most important educational goals. Yet it can be challenging to embed in everyday teaching. Teachers ask, "What are practical and effective ways to invite critical thinking? How can I use technology to help my students develop critical thinking? How are creativity, entrepreneurial thinking and critical thinking related?" Join Garfield Gini-Newman, Senior National Consultant with The Critical Thinking Consortium, as he explores these questions and provides concrete examples of inviting critical thinking across Alberta programs of study.


Learn more with video clips here

Posted by Meghan Burns at 8:10 PM – 0 Comments