This powerful 50-card deck of Creative Thinking Cards will provide hours of inspiration for individual and classroom activities. Included with the deck is a 42-page instructional booklet with dozens of ideas about how to use the cards, from simply forming groups to incorporating randomness to complex combinations that will spark the imagination. This card deck is incredibly useful for all artistic endeavors, especially creative writing, poetry, journaling, and storytelling. Teachers will find them particularly useful since they were designed by a teacher with classroom activities in mind.
Interpretations of creative expressions are always interesting. Just ask a dozen people about a painting or a song and you'll get a dozen perspectives -- or more! This is because an interpretation is part of an entire process. Just think: there's the artist, the inspiration, the medium of the art, the art piece itself, the context in which it was created, the interpreter, the interpreter's background and experiences, and the circumstances in which the art is being seen or experienced. All of these influence the overall interpretation of what that piece of art "means" -- at least, to that interpreter on that occasion. As a teacher, I don't think the important aspect of all this is whether students get an interpretation "right" or not. There are always multiple "right" answers, but I want my students to be able to justify their ideas, share their explanations, and come to understand that other people can see or experience the same exact thing but come to a very different interpretation. And that's fine! Encouraged even! It's what makes us different and provides us with opportunities for empathy and greater shared understandings.
A great many outlier ideas seem disconnected from the classroom process or dialogue. This is often because creative ideas appear "out of nowhere" without logical, sequential antecedent steps. When this happens, make sure to ask questions that will connect the current ideas to the process, so that everyone can follow the relevance: "Where did that idea come from?" or "Where in the text did you get that idea?" or "Walk us backward, how does that connect to what we've been saying?"
Although there are arguably many types of thinking, (like Bloom's Taxonomy, Webb's Depth of Knowledge, Gardner's Multiple Intelligences), I often consider these two to be the most fundamental. Creative thinking expands options, and critical thinking reduces options.Creative thinking has no rules, while critical thinking applies rules. Both are needed, especially "in the real world." This is because, on the one hand, we want to create something entirely new, but on the other, it has to appeal to an audience and be marketable. We want to break barriers, but might need to follow some of the conventions. Often people are very good at one or the other, which is why, for example, a lot of authors have to hire editors. Both can be practiced and improved.
Most students do no have a lot of practice asking questions. Just ask students to write 12 questions about a paragraph or short poem and many can't generate a dozen questions, let alone questions that are useful. I've even asked teachers to pair up and write 30 questions about a tree and only one group completed the task. The others quit early. What this means is that we need to give students more opportunities to practice curiosity and wonder. A great activity is to have students generate a list of questions and then to write questions about their questions. Not all questions are created equally, and students will develop a sense of different types of questions and what they are really asking.
These two styles of thinking can be easily appreciated by thinking about the writing process. In the beginning, we focus on creative processes, such as brainstorming, pre-writing, ideating, and drafting. Towards the end of the process, we focus on editing and revising. The early process calls more for generating and creating, the later process for refining and correcting.
Do You Have 21st-Century Skills to Help Your Students Succeed? Do Your Students Have 21st-Century Skills to Think for Themselves? The Power of the Socratic Classroom has the answers you are looking for—answers that will supply the strategies to show students how to succeed into the future. A future that has unknown products, unidentified jobs, and unanticipated challenges. In Socratic Seminar, teachers shift to the role of facilitator, where they help their students develop the collaborative interpersonal skills, the critical and creative thinking skills, and the speaking and listening skills to face the upcoming challenges of the 21st century.
Socratic Seminars are often very exciting and engaging. All too often students and teachers get deeply involved in the conversations and keep on going, sometimes right up to the end of class. Although it is tremendously exciting to have such energy in the classroom, groups do need a post-seminar of some kind to at least debrief and hopefully set both personal and group goals. When conversations are unstoppably amazing, teachers should still set aside at least a few minutes to check in and debrief with the students and, when there is time for it, they can always choose to continue the conversation next class period. The reflective process is one of the keys to help improve the group dynamics. What did the group do well? What needs improvement? How could conversation become better balanced? I once heard "You never really know something until you've reflected on it" and if there is any truth to this, then the post-seminar is not just good practice—it's absolutely essential!
It's easy to focus on the benefits of Socratic Seminar for the students, such as developing close reading skills, critical and creative thinking, collaboration, and many more. And many teachers recognize that the students become more engaged and energized when they are able to make their own decisions, which then leads to more excitement for the teacher. But there is also another benefit to this cycle. Old material becomes refreshed and reinvigorated. New students have new interpretations, new vernacular, and new updates to describe things. Even when the ideas are very much the same, the novel subtleties and nuances keep the classroom engaging and exciting.
What's important for facilitators to remember is that the first two stages, forming and storming, will basically happen automatically. People will naturally come together in some awkwardness and then begin to develop their group roles through vying for attention and power. But the next two stages, norming and performing, must be earned and worked toward. Some groups can probably succeed somewhat accidentally, but most groups need to establish norms, hold members accountable, set goals, and then work to improve.
I have facilitated over two thousand Socratic Seminars and observed many more. One thing has become abundantly clear to me: when seminars don't go well, when the conversation is flat, when students don't participate, when only a few dominate the dialogue, the main culprit underlying everything is the pre-seminar. There are many reasons why a seminar conversation might not work very well, but it starts with not having enough things to talk about. Students need multiple entry points into the text so that they all can begin the thinking process. The pre-seminar's job is to activate curiosity, to get students engaged in wondering, to get them to notice things. The dialogue then is for the students to put disparate pieces together into a meaningful understanding.
Especially after students begin to take control of the seminars, it's tempting to think about making notes while listening and observing. But the issue becomes that no matter how good the students are at facilitating themselves, the group could always use the teacher's wisdom and experience as an equal participant. Many seminar facilitators like to take themselves out of the process, for one reason or another, but this means that they can't contribute to the group intelligence. So, trying to make notes can be useful for something like setting individual and group goals, but should be something to work away from.
Sometimes I get asked about the fishbowl variation for discussions, so I'd like to make my position clear. Firstly, any lively and engaging conversation is worthwhile. If the fishbowl works for you, then you might as well keep it going. The main problem I have seen and experienced is that the movement involved can be highly distracting and can take away from the flow of good conversation. Think about it: some conversations are hard enough to enter, to get the timing right. Add the need to get up and change seats before talking and some students simply won't be able to contribute effectively. The point here is simple: dialogue is already difficult enough, so anything that can possibly get in the way becomes a hindrance.
I believe that cooperation is the future. Or actually, the future is cooperation. Either way, if we are going to solve the world's biggest problems, then we are going to need solutions created by teams of the world's experts all working together in harmony. Sounds good, sounds easy, right? Well, the issue is that when groups get together there are numerous problems: ego issues, politics, personal agendas, personality conflicts and other teamwork struggles. If we are going to prepare students for the cooperative future, then we need to provide opportunities for them to practice the skills needed to succeed for dialogue and problem-solving. Socratic Seminar is one of the techniques designed for this specific purpose. Education is preparation for the future, so let's give students the skills they need!
Coaching or facilitating is one of the harder jobs in teaching. It requires a lot flexibility and adaptability, pivoting and decision-making. It can be overwhelming trying to decide what to do and when, or how to prioritize. But the key is fairly simple: What does the group need in oder to improve? And if you're not sure, just ask the students!
It's the big ideas in life that are truly important: What's the meaning of life? What is my purpose within that? What are we as humans supposed to be doing? What is our place in the universe? How can we best support each other as friends and family members? How can I develop my own personal genius? These and other questions are vital to our success as individuals and members of society. Schooling is a lot to do with providing a platform of knowledge and skills -- and that is certainly valuable and needed. But to what end? Education should also provide opportunities to explore life's big ideas, not necessarily in search of answers, but to help students ask the right questions of themselves and their peers.
A lot of parents and teachers underestimate just how difficult speaking in class can be for certain students. What's the big deal? Just speak once! Just share one thing! Just ask a single question! But what people do not understand is that speaking even once in class can be an extremely difficult challenge, full of nausea, nerves and self-doubt. It only takes one parent, teacher or mentor to say something harsh at precisely the wrong moment in a child's life to make them associate speaking and sharing with pain and disappointment. Such students need to see and experience a very safe judgment-free environment where it's clear they can actually speak and share and be appreciated. Getting some students to share even once can be a months-long process. Stay with it and understand that it's a long-term commitment.
Using texts that contradict each other, or at least seem to, are fantastic for Socratic Seminar. This is especially true if there is time in the curriculum to explore the ideas, issues, or values thoroughly. One amazing model for this is to combine seminars with debates, providing students with the opportunity to engage with the material on deep levels in both cooperative and competitive environments. Contradictory texts are also useful for students to see and understand that there are different ways of viewing the same issue and both or all viewpoints might be valid.
This is one of my favorite models for Socratic Seminar. Most teachers are familiar with using seminars as culminating activities, but they can also be used at the front end of a unit to then anchor subsequent conversations and understandings. For this to work in the best way, it is vital to hold the seminars when there are few or no absences—or at least record the seminar to allow everyone to have the shared understanding. As a conceptual scaffold or anchor, the seminar is used throughout the rest of the unit to hold everything together, to create enduring understandings. Using Socratic Seminar in this way is very similar to the function of Essential Questions.
There are many reasons why people become poor listeners, but creating bad listening habits is probably the top of the list. In my experience, early elementary students are taught about how to listening, often including "whole-body listening." Then as the curriculum gets more intense, listening takes a backseat to all of the "important" standards. Yet, students have to use their listening skills for all those other classes. Those skills tend to erode, however, as students furiously try to take notes and otherwise retain information. The irony, of course, is that if they could listen better, take fewer notes and engage in class, they would actually retain more.
I don't generally recommend taking many notes during a Socratic Seminar because it distracts from active listening and asking follow-up questions. There are times, however, where taking notes can be useful: before IEP meetings, for creating report card comments, writing student recommendations and so on. I worked at a school that used narrative report cards for many years, and my Socratic Seminar notes were a valuable resource for me to think about each student.
I often get asked about why NOT raising hands is important for Socratic Seminar. The answer is relatively straightforward. Raising hands negatively affects active listening. When we raise our hands to speak next, we often end up focusing on what we will be saying, not on what is currently being spoken. This means that participants in a seminar wouldn't be building on what the previous speakers said, so the conversation ends up being flat and unproductive.
As someone who loves language, I often anagram or rearrange the letters of words to see what creative insights I can discover. It's a tremendously powerful creative thinking tool that I would recommend to anyone. The word 'mistakes' has some fantastic anagrams that provide insights into how we can think about making them. For starters, 'mistakes' anagrams to 'As Kismet,' meaning we are destined to make them. It's so simple that we may forget we are always making mistakes... but how we deal with them is up to us. 'Mistakes' also anagrams to 'Ask Times,' meaning that mistakes are simply times where we need to formulate questions. That's it. Instead of getting frustrated we can simply shift into questioner mode and get curious. Another fun anagram is 'Team K.I.S.S.' This has all sorts of possibilities because of the acronym, but I would suggest: "Team Keep It Simple and Serendipitous." Teach students that mistakes are great teachers that can put us in the right mindset to truly learn what we were just struggling with.
Inquiry and asking questions is always worth revisiting. Questions tend to be the realm of the teacher and the textbook, so students do not usually have enough practice asking questions. They need to be taught how to activate their curiosity, what types of questions they could be asking, and they need to be given time to practice with all kinds of texts and activities. We can't expect students to be curious and engaged if they aren't given the opportunities to discover what they are actually curious about. It's simple and obvious, but time needs to be devoted to practice asking questions!
Mini-lessons are vital if a group is going to perform better. Sometimes mini-lessons can be planned ahead of time, especially around topics such as Active Listening or How to Cite a Text. But the best mini-lessons often emerge as a specific need, something that is holding the group back from functioning as a cohesive team. Most of the time, a simple question can provide the next mini-lesson topic: "What do we need to do better next time?" One area of note is definitely Active Listening. Groups often can't proceed until the participants truly know how to listen. This includes how to disagree with someone in a useful manner. We can't know if students are actually listening, but we can expect and look for the ingredients: maintaining eye contact, nodding, having fun, asking questions, and so on.
I often get asked how to ask better questions. Should you use Bloom's Taxonomy? Webb's Depth of Knowledge? Multiple Intelligences? All of the above? The reality is that before even considering any system for generating questions, there is a much more important element to asking better questions, no matter how they are phrased. You simply MUST ask questions from genuine curiosity--your genuine curiosity. Without doing this, you will maintain the power structure in the inquiry process and students will spend more of their time and energy trying to answer FOR YOU, rather than for the question itself.
I heard a saying once that definitely applies to Socratic Seminar: "The person who does the work, does the learning."And another idea comes to mind related to this: "Who is working harder, you or the students?" Too often teachers are the ones worker harder and doing the work... which means they are the ones doing most of the learning. They are more active, while students are more passive. For students to truly learn, teachers need to reverse these roles. The first step is to shift to a seemingly more passive role of questioner. ONLY ask questions. This will immediately shift students into more active roles where they are doing the work of learning.
There is a strong caution about trying Socratic Seminars occasionally without trying to build better group cohesion. The main reason is that groups go through predictable stages, and without goals and norms, many groups stay in a frustrating stage called Storming. This is the phase of group development where participants remain unsure of their roles and many vie for power and attention by dominating the conversation. Others stay remarkably quiet, frustrated that there is no space to talk into. Besides simply having more seminars more consistently, teachers can at least help the group stay connected to individual and group goals. In the pre-seminar make sure to revisit the goals and in the post-seminar debrief about how things went. Set new goals and post them in the classroom so the group knows where it is headed next seminar no matter how far away it is.
There are a lot of potential issues if a group "finishes" an opening question fairly quickly. The first is likely to do with inadequate preparation during the pre-seminar. In this stage, students must generate multiple talking points through annotating and generating questions. The next likely culprit, assuming the students are actually participating, is a lack of following-up questions. Socratic Seminar is meant to be an opportunity for deep conversation about complex issues, ideas, and values, and to get there requires a lot of follow-up questioning.
One of the under-appreciated benefits to Socratic Seminar is the data collection and reflection time built into the structure. Since students are gradually given more responsibilities, teachers can shift to the role of researcher. When harnessed properly, this "action research" can help improve practice and can become excellent professional development. After many years of trial and error, I slowly learned what practices were truly effective for Socratic Seminar.
We often focus attention on what the students should be learning, but for Socratic Seminar, there is probably nothing more important than the teacher practicing active listening and demonstrating true curiosity and wonder. I might even argue that shifting from teacher-lecturer to facilitator is not even possible without a journey to better listening skills. This is why it is common practice for teachers to sit outside of the seminar circle, taking notes and recording observations. But what is sometimes missed or under-appreciated, is that the teacher has a perfect opportunity to practice active listening. And there is actually an added problem: the students don't get to see the teacher actively listening, so they are missing the opportunity to see active listening modeled for them.
A lot of teachers hesitate to try Socratic Seminar because of a few main reasons: they worry about losing control, they can't connect the seminar to the standards, or they feel they don't have the time. To the first point about control, I would say that if you have established procedures and rapport with your students, then you will be fine. Just create a few additional expectations and the students will engage in the process. If you still fear losing control... well, who should be in control of their learning anyway? To the second point, Socratic Seminar can always connect to speaking and listening standards! To the third point about time, seminars are an amazing tool to review for tests, finalize written drafts, and otherwise synthesize learning. In terms of sharing and generating ideas, they are actually highly efficient and provide clues to the teacher such as checks for understanding.
Since Socratic Seminar is about the gradual release of responsibility, students should be invited to participate in the decision-making process as soon as possible. Draw a conversation map or use an app like Equity Maps to collect data about participation and debrief with the class about how the seating may have influenced the conversation. Set personal and group goals for improvement to work out any issues.When things go well, reflect on what seemed to help. Remember, conversations should flow naturally and smoothly, spiraling upward into collective insight.
Teachers are obviously in positions of power in their classrooms. They are professionals, empowered by certifications, degrees, age, reputation, professional standards and much more. This is a power dynamic from authority to the student, from the expert to the learner, from the experienced to the inexperienced, from the Jedi to the Padawan. In many ways this is normal and probably should be the case. However, if we want students to become critical thinkers, investigators and innovators who are liberated to the freedoms of their own thinking, then we have to create situations where they can practice the underlying skills. This is why the gradual release of responsibility is so vital. Shifting the power dynamic and making space for students to do their own thinking allows students to develop HOW to think rather than WHAT to think.
The general advice for close reading and annotating in Socratic Seminar is to have students annotate directly in the text or to use sticky notes. There are also a couple of effective alternatives: have students place their book in the middle of a file folder or large construction paper and annotate around the perimeter, or have students place a copy of a text in a plastic sleeve to annotate on that. But in the virtual world where students may not even have access to the texts, the classroom, or the teacher, what might you do? The strategy I would recommend is the DRTA. The text is slowly revealed to students with three main questions. Stop periodically and keep asking the same three questions. Students will adjust their reading habits with enough practice and will become stronger, more detail-oriented readers.
One amazing way to help students understand what is expected of them in Socratic Seminar is to have a seminar about a seminar. This is truly a metacognitive approach, a meta-seminar. One way to do this is to collect seminar data by using an app like Equity Maps or by keeping a dialogue map or even simple tracking data like tally marks in various categories. The meta-seminar would have students examine the data, make connections, draw conclusions, and set personal and group goals. Another way to do this is to have students watch a recording of another seminar to make observations and create understandings of how to work better as a group. A third way is to have students watch something like 12 Angry Men (there are several versions), which demonstrates group dynamics and decision-making. In any event, a seminar about a seminar only needs to occur once a year to help clarify understandings of the dialogue process and to anchor those insights for the future.
Not all questions are created equally. Some ask for specific facts or details, others for opinions, and still others call for speculation. Leading questions have implied expectations and answers within them. Many teachers ask polarized questions, which only have two possible choices presented in them. What we are searching for in Socratic Seminar are interpretive questions -- questions that have multiple right answers that are justifiable with evidence. These types of questions usually must be planned and strategized for. Perhaps the most important type of question for Socratic Seminar is one that is asked from genuine curiosity and wonder.
The best benefit of Socratic Seminar is that students actually have the time and space to practice their thinking skills in a structured and formalized setting. As with developing any set of skills, students need to have Socratic seminars on a fairly regular basis. Weekly if possible, but not less than every two weeks. Otherwise, students will not have enough continuity to build on their skills. Weekly often seems impossible for a lot of school schedules, but is easily managed if the core subject teachers each have a seminar about once a month.
I remember how nervous I was when I first decided to take a leap in my professional journey by trying out Socratic Seminar. I was nervous that the students wouldn't respond well. I was scared that they would erupt in chaos and that I wouldn't know how to respond. I was worried that they wouldn't be able to understand the text. But I knew what we were attempting was valuable. There was an underlying principle for me, which at the time I would have described as: "teachers need to make themselves increasingly obsolete." Now I prefer "gradual release of responsibility" since it sounds a lot more positive. Looking back, I completely overcompensated my shift to student-led discussion and put everything in their court, with hardly anything from me besides questions, shoulder shrugs and a stoic poker face. Here's the important part, though. The students rose to the challenge - just as in all my other experiences in over twenty years of teaching. The students can always rise to the challenge, though they may need some guidance along the way. Trust the process. They can do this. You can do this.
Most teachers begin the school year by asserting pre-made classroom rules and expectations. Socratic Seminar facilitators start the dialogue process by establishing norms or agreements with the group. Notice the vital difference in language. Some facilitators even like to co-create the norms with the students so that there is little or no top-down feeling to the agreements made within the group. I have done this on many occasions and students always rise to the challenge when they are trusted to make such important decisions.
Socratic Seminar is the single most powerful classroom technique that I have encountered. Because of the gradual release of responsibility, students are actually able to practice important skills of all kinds. If practice makes perfect, as they say, then Socratic Seminar is the perfect technique!
In this era of distance learning, something as simple as a good turn-and-talk or think-pair-share seems out of reach. But a few adjustments can make them at least somewhat possible. The most obvious is to use some variation of breakout rooms, but many schools don't allow them without adult supervision. So a few other ideas can still get pairs working together. Pair up the students ahead of time and have them chat privately to each other. It's not talking, but at least it's interaction. Or set up a Google Doc or Slide ahead of time, put the link in chat and have students interact that way. Or set up a Padlet and have students interact there. They could even record short videos responses to each other.
The single most important step for teachers who love to talk and be the "sage on the stage" is to ask questions that do not have specifically clear answers. This often requires carefully selecting a rich text that has layers of complexity embedded in it. The questions, then, can unlock multiple right answers that are justifiable in the text. This allows participants to create different viable viewpoints instead of arriving at a singular answer.
The first shifts into the unknown are understandably the hardest. Many teachers are skeptical or afraid of handing over responsibility to their students. In some cases, apprehensions are understandable. Theoretically, quite a few things could go wrong. But a lot will go right. Many teachers are embracing the growth mindset concept, so there's no better place to begin with than ourselves as the role-models. Taking a risk is a fantastic way to experience a little discomfort and put yourself in a growth mindset. The main mistake that teachers make is that they release too much responsibility too quickly, almost certainly resulting in chaos as the students are suddenly unclear on what they are expected to do. The key is the gradual release of responsibility, where everyone can be successful.
On many occasions, we agree to disagree because of a lack of time. This is especially true in school where we must follow predetermined schedules. But realize that agreeing to disagree can often be an easy way out, a way of not really listening to the other side(s). If time allows, it is definitely worthwhile to continue the dialogue. The main exception is the principled impasse, where people are disagreeing based on firm principles. Many people are willing to change their minds, but few are willing to change their core beliefs or principles. When an impasse is reached at the level of principles, it is safe to agree to disagree unless you happen to have an extraordinary amount of time to spare.
"We do not learn from experience... we learn from reflecting on experience." John Dewey. I remember reading that quote years ago and... reflecting on it. I struggled with the notion for a few years before really seeing the value of his words. Our experiences are often too fast to make sense of at the time and we find ourselves grasping the deeper meanings only later when we have a chance to step away from them. Dialogue is no different. Many conversations are fast moving and require participants to pivot and make choices in the heat of the moment. We might say words we don't mean or disagree with something that is incomplete or misinterpreted. Often we need to gather our thoughts before synthesizing understanding. This is why every seminar should have at least a small debrief at the end, and ideally a more thorough reflection process.
In over 20 years as a teacher and administrator, I have yet to come across a single technique that is as powerful as Socratic Seminar. That's not to say that other techniques or approaches aren't useful — it's simply that dialogue accomplishes many things simultaneously. Many of my former students who are now adults don't remember a lot from middle school, but they definitely remember Socratic Seminars and how much they learned from each other.
I often get asked what to do about students who dominate the conversation. It's a double-edged sword at first. On the one hand, talkative students are at least talking. After all, the whole idea behind seminars is to pass responsibility over to the students. So dominant talkers can at first seem like a good thing. However, they need to be reined in fairly quickly because they are taking up conversation space. Many students need time and space to speak into. They often need dialogue to be slower and calmer. Talkative students will habitually take that space if we let them, to the point where they will talk for the sake of talking. Breakthrough ideas rarely come from the big talkers; they often come from the shy students, the thinkers, the ponderers. So we must make space for them. Besides, the big talkers need to work on their listening skills!
When a Socratic Seminar does not go well, the usual suspect is the pre-seminar. Without enough preparation time in this stage, the ensuing conversations will often be dull and lifeless. Most teachers do not spend enough time preparing a text for dialogue, which usually involves annotations of one kind or another. I usually have students prepare the text the day before the Socratic Seminar so that they can begin the thinking process ahead of time. The single most important way to get students more engaged is to have them generate their own questions. This will hopefully activate their curiosity and wonder to forge relevance.
Many students recently experienced online discussions in one form or another - most of the experiences I heard about were through Zoom. Some groups experienced quite a bit of success with online discussions, but likely quickly noticed that they fall far short of classroom dialogues. But the weakest part is often the follow-through blogs or forums or chat rooms where teachers hope the students will continue the conversation. Many teachers have discovered what I have encountered on many occasions: that the written follow-up "conversation" is often remarkably shallow and unproductive. There are many reasons for this. Text message and Tweet-length thoughts rarely build upon each other in significant ways. The biggest single culprit is the lack of follow-up questions. Without them, discussion boards and the like will remain shallow. Any system that wants to promote deeper thinking must address this issue and somehow build in live, dynamic ways to include follow-up questions.
Mini-lessons are an important part of Socratic Seminars. Groups are like people in that they need a focus to grow and develop. Mini-lessons are a great way to move groups along the continuum from Forming to through Storming to Norming and hopefully to Performing and beyond.
Yes, more than ever! When I started my teaching career moe than 20 years ago, I thought students desperately needed critical thinking skills. Now, in the fake news era, they need them more than ever. Exponentially more. Painstakingly more. It's how we might try to help students develop these skills that worries me. There are no easy solutions. Worksheets won't produce good thinkers, just as writing prompts don't get a novel written. Occasional practice won't work either - just choose a sports analogy. What students need is extended structured practice time with thinking skills. What schools and teachers need is Socratic Seminar.
Any start is a great start! There is a learning curve for all things and facilitating is no different. It can be scary to release responsibility to the students, but trust the process. Once you get started, you will likely enjoy seminars and you will be amazed when the students rise to the challenge!
The first one, how many students changed their minds, is a great test for a good seminar. Just think about how many things would have to happen for students to change their minds. They would need to listen carefully, consider new evidence, weigh it against the old evidence, and be open-minded enough to be willing to change their minds. A quick way to gather this information is to have the students write their answers to the seminar question before and after the seminar.
I have often made the mistake of giving students jobs to do during seminar if they were simply enthusiastic enough. It always seems like a good idea at the time. However, enthusiastic students without enough direction and focus can seriously derail Socratic Seminar conversations. Eventually, I appreciated that "slow and steady wins the race." It is much more effective to gradually release responsibility. Now, I often train one student to do a particular job and then have that student teach someone else. In the meantime, I can be teaching someone else a new job. In this way, the integrity and quality of the seminars can be upheld.
My students have truly enjoyed seeing the data presented, particularly from the amazing app for iPad called Equity Maps. In the beginning of the year, when I first start tracking seminars, the students get curious about what I am doing and then they quickly want to see more about how they are contributing to the quality of the seminars. They want to know - and more importantly, they want to improve! Sharing data is powerful, a lot more powerful than many teachers even suppose. Give it a try, even if it's a static screen shot from the end of the seminar.
I remember when I first heard the expression, "Those who do the work do the learning." And I thought nowhere is this more true than in the development of skills. It's obvious, really, that students (or anyone) can't develop skills without practice. They need to work and try and fail and try again. They need to embrace uncertainty and confusion until they create meaning within themselves. Only then will they truly learn. Socratic Seminar is the perfect classroom technique to gradually release responsibility to the students.
The area I get asked the most about is how to get shy students to participate. It's painful sometimes to watch weeks go by and some students haven't spoken up in class. Obviously, some students speak a lot and others don't. But observe many of the shy students and you will notice that they speak a lot outside of class. What's going on? It's an important question because helping shy students find their voices is vitally important. After years of facilitating seminars and working with shy students, the main issue is with the speed of conversation. Many discussions simply move too quickly for the shy students and they can't find ways into the conversation. The single best method to help is to ask a new question, use a turn-and-talk and follow with "I'd like to hear from someone who hasn't spoken yet." This alone will work 90% of the time.
A leading question has the answer implied in it. Students don't have to think own their own if they can simply infer the answer already from the question. If you find yourself asking leading questions, simply rephrase them as statements and ask new questions. Stay with what you are genuinely curious about. If possible, plan your major questions ahead of time and make sure they have multiple right answers that are justifiable. This shift away from leading questions will make a huge difference for the thinking dispositions of the students!
There are a lot of considerations for the reflection process, such as the complexity of the text, the initial opening question, the maturity and experience of the students and so on. I always found it useful to focus on the text and the question because those can be easily changed for future lessons. My ability to facilitate a group of students is much harder to control since every group is so different and my actions change so drastically. So I use the same text but ask different questions each class period and then make a note of the most productive questions for future use.
I have seen a lot of systems for grading seminars or discussions and many of them are based on some kind of point system. The trouble is that many students will then talk for the sake of a grade instead of the actual conversation. What tends to happen is a lot of talking but little or none of it is truly relevant and working toward a group goal. I have rarely seen any of these systems generate a quality conversation. If you do want to continue with a point system, make sure to add a group grade to help steer conversation into more productive directions.
I often get asked how to generate useful questions for visual arts. There are numerous techniques, but the one I like to share shows how the right approach can make the questioning process fairly easy. Remember, that the opening question for a seminar should have multiple right answers justifiable in the text. So, for any visual art, one technique is to divide the piece into nine parts by superimposing a tic-tac-toe grid. Then generate questions using the grid squares. Here are some examples: Which square is most important for understanding this piece? Which square is least interesting? Which one best shows the artist's techniques?
Students need practice! Luckily, curiosity and wonder can be developed about anything at all. Quality follows quantity.
The problem with these is easy to understand: Someone else's generic, universal curriculum questions are unlikely to spark your curiosity and wonder. Fixed questions lack context and specificity. They are often anachronistic, or at least not fully relevant. They can be a great place to begin, but they can never replace genuine curiosity and wonder in the teacher and the students.
Curiosity and wonder are important elements in helping students stay engaged in seminars and school. To be blunt, many students and teachers are not nearly curious enough to maintain their connections to learning. The result is that many people - students and teachers - completely disconnect from the learning process. School then becomes a chore instead of a joy, a mandate instead of a wonderful option.
When I speak to teachers about failed Socratic Seminars, there is almost always a lack of work in the pre-seminar stage. This component is absolutely vital to a quality conversation, since this stage mainly involves activating curiosity and wonder. Without these two components from the students, the inquiry exercise is mainly driven by the teacher - and is, in addition, often agenda-driven. If we want our students to be engaged in curiosity and wonder, then we have to give them opportunities to practice engaging organically with complex texts.
This always sounds good in theory, but it really does not produce quality dialogue. If we agree to disagree then both of walk away from the conversation with disagreement. If this is done early in a dialogue, then participants miss out on the vital process of establishing understanding. Effective dialogue should seek similarities and points of agreement with the goal of empathy. I may disagree, but at least I understand your position and your beliefs. But if we agree to disagree to early, then we will never achieve empathy and understanding.
Since a "text" is just an anchor for dialogue, they can be nearly anything. In fact, the greater the variety, the more the students' skills will develop. They will begin to see that the approach to almost any text is remarkably similar, and that annotating and generating questions will always be a useful strategy toward understanding.
Obviously, conversations are complex and arriving at a grade is not easy - but it can be done. I recommend in my workshops that teachers use triangulation, that is, that they use at least 3 grades that make up the overall grade for the students involved in the conversation. For me, this is most often: a grade for the annotations that a student submits; a grade for their individual participation; and a grade for the entire group. I often leave the weights for the students to decide. Once students have been taught how to mark up a text, annotations are graded against anchor papers. For the individual grade, I often use "threshold grading," where a student receives full or partial credit for participation. The group grade can be determined by a rubric or through the use of exit tickets. A student's grade might then be 40% annotations, 40% contributions, and 20% group grade.
In addition to the narrative from my book, the best insights and my favorite ideas have most often come from the fringe students. They are the ones who, to use a cliché, "think outside the box." They are the rare students who are not afraid to propose unusual ideas that may seem alien at first pass. All the power to them! They are the people who will move the world and shake the Earth!
It's important to realize that norms or agreements are much more in keeping with Socratic Seminar. Because a teacher is trying to pass authority and ownership to the students, "rules" is the wrong approach. A rule is a top-down authority move. Now, a classroom might need rules, especially in situations where there are school-wide ones that must be posted in every classroom. And there may be some rules that need are non-negotiable Otherwise, norms or agreements are much more in fitting with a democratic process. I have asked numerous seminar groups over the years what would be needed to have productive dialogues, and they generally all come up with the same essential concepts. The language is different each time, of course, but the need to listen to and respect each other, patience and taking turns and so on. Trust the process. The students want to have quality conversations.
Quite simply, students do not have enough practice asking their own questions. Ask many of them to jot down even a short a list of questions and they can't do it. In my experience, even adults begin to falter after trying to jot down more than 7 questions about something specific. Much of this has to do with curiosity and wonder. Most students don't have much of it. Neil Postman once quipped that children go to school as question marks but return as periods. We need to do more to help students develop curiosity and wonder - and helping them formulate questions is a great place to start.
When a text has a moral at the end, especially one that is a succinct summary, then it may take away from the thinking process. I often take the morals off texts and have students create their own morals. I don't usually share the original moral unless specific students ask about it. I find that students judge themselves on how well their morals seem to be in line with the original. It can ruin their thinking skills and their confidence, especially when they have crafted a viable moral, but reject it once they compare it with what the author wrote. This comparison ruins the general idea that there should be multiple right answers to any complex thinking process.
I have often said over the years that shifting to the role of facilitator is some of the best professional development. It's probably more true now than ever. This is because teachers can create that all-important reflective thinking work that will improve their practices. Most often this is in the form of reflecting with students after each seminar and getting crucial feedback. What worked well? What could we improve? With several classes answering those questions, teachers can begin to pull together the "wisdom of crowds" in order to make the processes better for everyone.
Because Socratic Seminar is meant to be dialogue, not debate, heated topics do not work well. There is nothing wrong with debates. but polarizing topics simply do not facilitate cooperative learning, where everyone is meant to add to a cumulative process. Certainly students can debate on common topics like the death penalty, but those should simply be done in a debate format instead of a seminar format.
Socratic Seminar as a Course of Study is BY FAR my favorite model. When students have consistent practice developing their seminar skills, then they truly reach amazing levels of performance. A visitor once came to observe a middle school seminar and he commented that the dialogue sounded like his graduate school classes. This is the power of continued practice! It really shouldn't surprise anyone that students would get really good at the things that they practice, in the case of seminar skills: active listening, building ideas, asking questions, citing the text, composing arguments, thinking critically, creativity, and many more.
The so-called "soft skills" continuously make the list of desired workforce skills that employers are looking for. Choose any of these lists and you will find that all or nearly all of them get practiced and honed in a seminar environment. It might seem hard to believe, but the simple answer is that the students are doing the thinking.
Although I have many phrases that I like, "Do you want some help or do you want more time?" is definitely one of my favorites. One reason is that it gives students a choice. They still feel empowered to make a decision, even though they are currently stuck. Another reason is that students almost always choose to have help, meaning that they can call on someone. Reliably, they will call on someone whose hand shoots up and clearly knows at least part of the answer. Time-wise this strategy is quite efficient. A third reason is that students will quickly learn that "I don't know" is not an acceptable opt-out answer. Eventually, with older students at least, you will begin to hear, "I'm not sure, but maybe someone can help me." This is vastly better!
Many teachers are afraid to release power. They fear what they think will be the inevitable uncontrolled chaos. They may also have concerns that the students will not be able to get the right answer. The first fear is understandable, since most students haven't been taught how to participate in group discussions. They need practice and guidance! The second concern is also understandable, but we want students to become thinkers. We want them to become historians and scientists, careful readers and mathematicians, and so on. Again, students need to practice. They'll may draw illogical conclusions and arrive at unusual answers, but mistakes are part of learning!
Mini-lessons are are great way to help individuals and groups improve. Students can set personal goals and groups can work toward specific group goals. Mini-lessons work well in block scheduling, but can be taught modeled and practiced in other class periods. One of the first places to start: Active Listening! Most groups will not improve without working on listening skills.
Many teachers who try Socratic Seminar first sit outside the dialogue circle in an attempt to very purposefully shift power to the students. But many of these teachers forget to reinsert themselves into the process once the students have become a high-achieving group. In my mind, this is a mistake, since the most experienced person in the room is not participating!
I think consistency is the answer to all of these questions. Whether a two-part answer is really two contributions or one episode of talking can be determined by you as the facilitator. Just stay consistent so that any data collected remains valid across different classes and even school years. Track anything and everything that you value as a teacher, and/or what the group needs in order to improve, and/or what the students suggest.
The post-seminar often takes two different forms. Either there is a debrief of how things went (process), or there is an extension of the ideas, issues and values from the seminar (product or text). A debrief of the process should always aim to make the group better. An extension activity either deepens the thinking, applies the ideas in a new context, promotes new iterations, etc. The post-seminar can be as quick as: "What did we do well today and what needs improvement?" Or it can involve entire projects that spiral out of the conversation.
Deep thinking takes time. A lot of it! It's not unusual for a genuine thought breakthrough to take 70 minutes or more. If we want students to generate new thoughts, new ideas and innovations, then we must give them the necessary processing time. Although many teachers find it difficult to set aside so much time, Socratic Seminars produce excellent results in terms of creating essential frameworks for thinking.
I struggled to name this level - I just knew that there was a level of "listening" in between basic hearing and more active, more conscious listening. I settled on Assumed Listening because after a while it was an obvious choice. We probably all know people who believe themselves to be good listeners. The reality, however, is that they show the classic signs of not truly listening: distracted mind, verbal discontinuities, physical mismatches and so on. Luckily, there are simple solutions!
If the students even think that you know the answers to your questions, then the conversation really becomes a guessing game, not a thinking exercise. This is where being too much of an expert can be a bad thing. Mortimer Adler and others have even suggested that teachers should facilitate seminars outside their area of expertise in order to help shed that authority. It can be intimidating to facilitate an academic conversation around something unfamiliar, but then your questions will be genuine! Have a colleague pick a text you have never seen before and give it a try.
Intermittent Socratic Seminars are generally not ideal. Collaborative skills, such as active listening, paraphrasing, and elaborating, take time to practice - just like all skills. Having a seminar only occasionally, such as only at the end of a unit, will leave most groups in the Storming stage of development. In this stage, students are usually vying for talk time and struggle to actually work together as a collaborative team. However, groups can develop further into Norming and Performing stages. Students should have Socratic Seminar, or some collaborative process, at least every two weeks. I recommend once a week, which is possible if teachers in core subjects each had a seminar at least once a month.
Dialogue and discussion are not the same, though they can appear similar in the classroom. Discussions are often for eliciting opinions and engaging students. But they are also typically funneled through the teacher. Students in discussions rarely build on each other's thoughts. In dialogue, though, the goal is to build ideas in order to explore text complexities and nuances. Students respond to each other in order to achieve deeper thinking. Teachers must establish specific classroom norms in order to elevate a discussion into a collaborative dialogue.
The most genuine way to "talk aloud" through a text is to read and annotate a brand new text. Have a colleague choose a text for you to work through for the first time in front of your students. This will actually simulate their reading experiences, which are almost always based in first readings. Modeling like this takes some bravery, but it is totally worth the effort!
In one form or another, this is the question that I get asked the most: How do I get students to participate? Although there are many techniques to try, teachers must take a serious look at the ecology or culture of the classroom. A simple thing like sarcasm may be stopping several students from participating, not only in seminars but in class in general. Most students want to share their thoughts and ideas. Just watch those same quiet students at lunch and they are likely talking a lot. So one important approach is: Why aren't students participating?
We all know about the importance of wait time for general discussions and class engagement: more wait time means more participation. Thinking questions go well beyond the standard thinking time in order to give students time for a complete thought process. As a teacher, wait until the uncomfortable silence. Wait for the awkwardness to settle in and you will likely hear a brand new idea.
I once heard that you really don't know something until you have reflected upon it. If this is even partly true, then the post-seminar component of Socratic Seminar is a vital part of improving group dynamics and abilities. Seminars often get very exciting, so it can be hard to stop several minutes before class is supposed to end, but the reflection time will pay off in the long run.
Teachers sometimes get stressed about crafting questions using Webb's DOK or Bloom's taxonomy, but the best questions come from genuine curiosity and wonder. The best Opening Questions have multiple right answers that are justifiable in the text.
Keep in mind that speaking once is a monumental achievement for some students. Large conversations are extremely intimidating to some participants, so even once can be challenging. The goal is to help students find their voices, to help them face brave conversations where they can solve problems, ask questions, and advocate for themselves. These are skills they will need in almost any circumstance.
I vastly prefer printed texts for seminar over digital texts. My students have been much more engaged and focused when we use printed texts. If teachers want to incorporate technology, then I would recommend adding to the seminar experience using an app or website such as Padlet.com where students can collaboratively share their ideas, questions and annotations.
For Socratic Seminars, it is vital to have a good dictionary available in order to make sure that all participants have a baseline understanding of the words that are important to the text. I always deal with definitions in the pre-seminar stage so that the actual seminar dialogue can be in creating greater understanding about the text.
By listening more, teachers have the opportunity to truly build relationships with their students. If the teacher does all the talking, then the students only know about the teacher and his or her stories and interests. The teacher will not be able to learn about the students and their lives. Perhaps more importantly, the students won't have the chance to learn about each other. Listening is the key! Teachers need to create classroom environments where listening is a priority for everyone. This is one of the first steps in building relationships.
I was very relieved when I first learned about group stages. It suddenly explained to me why I had to facilitate in certain ways with EVERY group, even when I had students for multiple years. It also explained to me why some teachers quit doing Socratic Seminars since those groups, for whatever reason, couldn't break out of the storming stage.
There are two strong signs that a seminar went well. The first is if students continue talking about the subject out into the hallways. The more the talk, the better. The second is how many students changed their minds during the dialogue. The more, the better. A changed mind means that someone listened effectively, weighed evidence, and bought into the new idea.
Quite simply, presenting students with two contradictory texts is a fantastic way to get them thinking! The one caution is that texts around political ideas will often result in debates where students adhere to pre-conceived belief, rather than objective discussions of the texts.
Overall, I I have found that there are seven levels to listening, though only five really show up in seminar. The sixth level is Appreciative Listening, which goes beyond empathy into true understanding. The seventh level is Deep Listening, that kind of listening that blends into meditation and mindfulness. These can all be taught and practiced by students!
After facilitating a few seminars, make a list of the actions you took: asking questions, redirecting students, suggesting a turn-and-talk, and so on. Begin handing those tasks over to the students so that you can move on to more complex tasks, such as paraphrasing or adding academic language..
I have found that a little bit of ceremony makes a huge difference with students. A small change in routine for something like Socratic Seminar creates a whole other level of seriousness and focus
Preparing the text for dialogue during pre-seminar is the single best way to increase student participation. Another reliable technique is to ask a new question, use a turn-and-talk, and then ask to hear from someone who hasn't spoken yet. Truly quiet students need personal help to find their voices. I often meet with them outside of class and make a plan for what they could say in the next discussion.
Let's face it: teacher burnout is very real, especially at the end of April when teachers and students are fatigued. What most people don't realize is that when a teacher transitions to the role of facilitator, new and exciting things happen that can re-energize and revitalize teaching and learning. The teachers gets the benefit of listening to asking new questions and listening to fresh ideas. The students get the benefit of taking control of the conversation and sharing their best, most creative ideas. Everyone wins!
A "text" for seminar can be nearly anything that invites complex dialogue. Many teachers feel that seminars mostly belong to the humanities, but this is certainly not the case. One of my favorite conversations happened when one day I noticed a new hole in the school fence. I took the students outside and asked, "What happened here?" The students began investigating, CSI-style, and we had an intriguing conversation - and a hole in the fence was the seminar text!
It's important to remember that seminars are meant to produce dialogue - not debate or discussion.With numerous companies stressing "soft skills" these days, dialogue is definitely the best way to practice.
Many people ask what exactly a Socratic Seminar really is. To me, the question is huge and nuanced, but a simple answer is that a Socratic Seminar is basically a discussion where the students take ownership. The teacher gradually releases responsibility to to the students so that they can become more self-sufficient.
This is always an important shift in the classroom. Students are often very trained to raise their hands, but when we move to a seminar situation, we want students to assume greater responsibilities. This includes and often starts with figuring out how to take turns. This is often hit-or-miss, trial-and-error, but the the students often appreciate the endeavor. A lot of teachers shift to use a talking stick, talking chips, or other external turn-taking strategy, but I have rarely found that these work well. Often the focus seems to shift from the conversation about the text, to the use and misuse of the talking device.
When I follow up with teachers who have had a disastrous Socratic Seminar experience, the culprit is almost always consistency. These disasters frequently occur when teachers only have a few seminars per semester, so there is not a clear end in mind for the students. The group often stays in the storming stage of development where individuals compete for attention instead of working together as a team. Teams need time for cohesion and seminar groups are the same way. If a team only practiced eight times a year, you wouldn't expect a lot of growth. Socratic Seminar groups are the same way. Consistency is key.
The turn-and-talk strategy, where students essentially talk in pairs for a brief time, is a seriously underused strategy. I have found that asking a new question in class, then using a turn-and-talk is an amazing way to get conversation restarted. Add "I'd like to hear from someone who hasn't spoken yet" and you will get everyone to participate quite easily.
I first heard this concept at an International Listening Association conference and I immediately fell in love with the idea. I haven't found a more succinct way to communicate to students exactly what their most fundamental job is during a Socratic Seminar - or any class for that matter!
Students are always amazed when I point out that Listen and Silent are anagrams, that is, they use the exact same letters. They often respond with open mouths and wide eyes as they realize that this is somehow very profound. This mysterious connect between these words is tremendously powerful. When students aren't listening well, I often just tap my head and remind them that they must silence their minds in order to truly listen.
Follow-up questions are the single best way to drive inquiry deeper. Obviously, a good complex text, a provocative opening question, and curious students always help. But follow-up questions are what truly drive inquiry. Just think of a young child who repeatedly asks, "Why?" How long is it before you, as the adult, are stuck in the thinking process? Why is grass green? Chlorophyll. Why is chlorophyll green? Um... because it reflects green light... Why does it reflect green light? Uh... Make sure to ask quality follow-up questions whenever you want to drive inquiry deeper!
Because text selection is so difficult, I am always on the lookout for quality complex texts. I have a folder at school to collect stray texts that I get from other teachers. Sometimes I even find gems left on the copying machine! I also keep folders on my computer with lists of potential texts, such as TV shows. I have often found that science fiction shows like Star Trek or The Twilight Zone have excellent episodes that should promote quality dialogue. Text pairings are strong choices as well because they often promote at least two lines of thinking that can be supported in the texts.
Anchor papers are the single best way to clarify for students what is expected of them in the pre-seminar stage. Without properly preparing the text for dialogue, there will rarely be quality conversations. Students need numerous talking points in order to navigate complex texts and negotiate meaning together.
Seminar for synthesis is probably the most common form of Socratic Seminar. There are plenty of other ways to use seminars, though. Because of the shift to the role of facilitator, there is an excellent opportunity for teachers to collect data and make observations about their students. Using an app like Equity Maps allows teachers to then share data with their students, allowing them to further take ownership of their learning. This allows teachers to gradually release responsibility, which is one of the very many benefits of Socratic Seminar.
Straight-A students, who play the school "game" extremely well, often just regurgitate information. They are usually organized and take good notes. But many do not think for themselves. When confronted with the openness of a Socratic Seminar, straight-A students do not know what to say or think. The students who immediately make an impact are the students who have refused to play the school "game." Many of them are at-risk for failing, most often because they are thinkers! They are the ones who come up with solutions the teacher hasn't thought of. They are the ones who already think beyond the scope of the textbook. Those students thrive in seminar.
We are living at a time where technology is moving at an accelerated pace, so fast that we can no longer reliably see into the future. A new breakthrough could irrevocably change how we educate children. So, how are we supposed to equip students to be successful? It all comes down to "soft skills," that set of somewhat intangible skills that would allow a person to think through and negotiate a solution to a complex problem. Socratic Seminar is a classroom technique, a training ground, for these skills.
When high school senior Matt Forsythe discovers a weird computer and a secret door at school, a series of events unfolds where he and his friends solve one mathematical puzzle after another. After finding a teleportal, they travel to a strange world where numbers are actually alive! There they meet the mad scientist Maglio and the ghostly Fifty-Seven and discover that some of the numbers are mysteriously disappearing.
This challenge is a lot of fun! As a teacher, I have always liked to give students creative thinking challenges to see how they would solve them. This one was a lot of fun in my 6th grade math class!
Have some mathematical fun by trying to find different types of numbers. In this case, palindromic numbers that are the same forwards and backwards. Sure, it's easy to write them, but try finding them scavenger hunt style. It's not as easy as it seems!
Everything, absolutely everything is made up of opposites! A great classroom activity is to have students make lists of opposites and then to start categorizing those pairs. What kinds of opposites exist? What types of relationships are there between pairs of opposites? How many ways can something be an opposite? My middle school students have always loved this incredible thinking process!
One of the reasons I wrote Beyond Infinity was to get students more interested in numbers. Like anything else, numbers have stories behind them, histories full of cool facts and ideas. Students become more engaged when they can play with numbers and learn more about their connections to all things.
I wrote Beyond Infinity to help teach middle school students that there is more to math than repetitional arithmetic. Math is actually a vast domain of interesting and complex patterns. Beyond Infinity makes an excellent read-aloud for math teachers because it brings up recreational mathematics topics to help show students the realm of mathematical possibilities.
These are fun numbers to discover and play around with. Multiples of 7 create other interesting patterns for students to discover!
A little excerpt about the number 13, which seems to get a bad rap. But there are numerous positive aspects to the number as well.
This is one of the many fun puzzles I came across while researching material for the book. My target audience for Beyond Infinity is actually math teachers themselves—hoping that they would use it as a read aloud. When they come to puzzles like this one, they could stop and challenge the students, just like in the book.
One of the reasons I wrote this book is because I wanted to make mathematics more interesting for students. For many younger students, math just seems like repetitive arithmetic operations. Let's face it, there's not a lot of excitement there - though it might be necessary. The domain of mathematics is absolutely huge, though, and it's our job as teachers to at least show students more of the domain.
Playing around with numbers is something that students should do more often in school. Just as art teachers might have students freedraw or language arts teachers might use freewriting, math teachers can have students play around with numbers. This can be done as a warm-up activity at nearly any time.
I remember coming across this exact rearrangement with 17.5% and being blown away! I have wondered since how often students could solve complex problems if they only knew how to rearrange or reframe them.
I had fun writing this little excerpt. The main character, Matt, thinks about mathematics all the time, including things like types of infinity, expanding universes, and more. I wrote the book with math teachers in mind, hoping they would use it as a read aloud in math class. There are a huge number of talking points in the book that make for excellent class discussions - this being an example.
As a math teacher, I wanted my students to begin to understand that numbers have personalities. They have characteristics and traits beyond their numeric value that make them different. Throughout Beyond Infinity, the narrator pauses periodically to explore specific numbers using examples from everywhere. It is my hope that readers will get curious enough to start collecting their own examples.
As a teacher, I have always been fascinated by the power of curiosity. It is an underrated tool for most teachers. This excerpt is my book in a nutshell - an attempt at getting readers to think about the many numbers that exist around them. They are insignificant until we begin to ask questions and see patterns. For example: What is the meaning of the number seven?
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