PART III: The Four Mistaken Goals of the Discouraged Child

 2. A Struggle For Power

Misunderstanding unpacked: "I only have value if I prove my own value by refusing to cooperate with the teacher and/or the classroom and its norms." 

 

Teachers who frame classroom management in terms of compliance/non-compliance are inviting a failure of classroom community. For one thing, there are 36 of them and only one of me. But more importantly, it is a missed opportunity to create the context in which a discouraged child can come to view herself as a community member.

 

As Dreikurs says, 

It is a grave mistake to try to overpower a power-drunk child. It is also futile. In the ensuing battle, which becomes chronic, the child merely develops greater skill in using [their] power and finds greater reason to feel worthless unless [they] can demonstrate it.  (Dreikurs, page 61)

 

Most teachers have heard that they shouldn't engage in a power struggle, but side-stepping the challenge to a power struggle activates reactions that run deep. In addition, if the child's intention is to assert power, any "attempts to make [them] stop only intensify [their] disturbing behavior." (Dreikurs, page 62). Resistance is easier said that done.

 

What I have found most effective is to build the habit of noticing within myself whenever a student is trying to engage me in a power contest. The secret is to notice the internal trigger, name it, and refrain from reacting with the conditioned habit they are trying to generate. 

 

It takes practice. I find myself mentally chanting, Notice... and refrain... notice... and refrain. 

 

And it works. This is the fastest way I know to defuse the power struggle most of the time.

 

A couple of notes. The first is, this doesn't mean there are no natural or logical consequences. There definitely are. And one of the things our students are learning is how to function in society. 

 

For example, one always has the power to not do one's tax returns, but then there are consequences. Some of those consequences are serious. But teachers should always avoid making the mistake of believing that we have to be the personal, immediate, and traceable agent of every consequence a student will ever encounter. That's just not sustainable, and teachers need to be in this work for the long haul.

 

If a student doesn't submit an assignment that is due, I simple place a zero in the gradebook with a comment that late work is always accepted, but is subject to a one-point late fee. Zeroes are erasable. Basically, it's the same as doing your taxes. Shit happens, and sometimes you have to turn things in late. If you learn to plan ahead, there's no late fee. The point is for the student to learn how to meet their deadlines and manage their life's competing obligations. Don't make it into a big deal. Think of yourself as the government agency in charge of tracking and reflecting students' work.

 

This year I encountered a weird new manifestation of this power struggle. Along with all the teachers at my school, I use Google Classroom as my CMS (Classroom Management System). My policy on homework is to simply check it in as the basic routine step. I ask students to turn in their homework by uploading a photo of the first page of their handwritten work. This is the honor system. Most students most of the time turn in a photo of their own detailed handwritten work as evidence of their effort. Since homework for me is only a record of deliberate practice with metacognitive self-reflection, this is enough. I can tell from students' Burning Questions the next day how deeply they have engaged with the work, and this gives me the formative assessment info I need to adapt my instruction.

 

Only later -- if there's a problem -- or occasionally -- as a spot check -- do I go through students' homework submissions in more detail.

 

But this year, I got a surprise at the end of the spring semester.

 

I noticed that one student had turned in a photo of a cheeseburger with fries in place of his homework for that day. In accordance with my policy, I put a zero into the points field and typed into the comments field, "This is a picture of a cheeseburger with fries. Please upload a photo of this assignment to receive credit, minus a one-point late fee."

 

No reaction. No emotion. I just switched into functioning as the conduit of natural and logical consequences for a decision that was made.

 

Of course, this experience encouraged me to look at his other submissions for the semester. And sure enough, I had missed some other cheeseburger submissions as well. Because I am acting as a neutral agency in this regard, I changed all of the scores for those assignments to zeros and copied and pasted my same neutral instructions into the comments field. There were also photos of a sneaker, a bicycle, and photos of somebody else's homework with their name printed at the top. I modified all scores for these and copied my neutral instructions into the comments field. Zero, zero, zero. 

 

Naturally, the student's grade started dropping precipitously, which finally prompted them to come up to me and apologize for the huge clerical mistake they had made. They asked if they could resubmit these homeworks. "Of course!" I told them. "That's the whole idea!"

 

In this case, the natural consequence of having to redo all those homework assignments was the need to spend time redoing them all -- knowing that I would look them over far more carefully than I might have done before, and also that I might discover even more phony assignments. 

 

A valuable lesson was received and integrated with far less conflict and more face-saving than if I had become emotionally activated. The lesson for me was, Don't bite the hook.

 

There were other students who had done the same thing as well, and I treated everybody who had done so with the most consistent standard of fairness I know. One student, who actually submitted photos of a table mate's work was horrified to learn that I'd sent that table mate and their parents an email notifying them that somebody else had been submitting photos of their work and that in California, this is considered academic cheating under the Education Code and would be a serious offense. Then the student learned that I'd sent an email to them and to their parents as well about the situation. 

 

Most students are good people. But they are also adolescents and they make ridiculous choices and mistakes. The horror for those two students of being caught out and unmasked for their parents was far more powerful than any rage-based consequence I could have meted out in the heat of emotion. And these two students both digested powerful lessons about the consequences of not living up to their own responsibilities. They each apologized to me personally and it was clear that they're not going to do this again. They were also grateful for the grace they were shown. 

 

Never argue with a power-drunk teenager. Find ways to notice and name the power move that don't jeopardize the underlying relationship between you unless you have absolutely no other option.

 

Our job is to support students in learning to rise to the occasion.

PART II: The Four Mistaken Goals of the Discouraged Child

 The Four Mistaken Goals of the Discouraged Child

 What I love most about Dreikurs' psychology is his clarity about boundaries -- both the parent's and the child's. By putting courage and encouragement at the center of his framework, he centers the child's development and the adult's cultivation of strengths and belongingness, not of weaknesses or deficits and punishment. As he says, 

Parental love is best demonstrated through constant encouragement toward independence. We need to start this at birth and to maintain it all through childhood. It is made manifest by our faith and confidence in the child as he is at each moment. It is an attitude which guides us through all the daily problems and situations of childhood. Our children need courage. Let us help them to develop and keep it. (Dreikurs, p. 55)

This framework applies just as much to the teacher's role in the classroom as it does to the parent's role at home. Applying his framework to my classroom management has been a lifesaver and an opportunity to generate meaningful connections.

 The centrality of courage in Dreikurs' model reframes misbehaviors in a constructive and workable way. For Dreikurs, it is important for adults to understand that the child who is misbehaving or not cooperating in some fundamentally important way is the opposite of encouraged -- this child is discouraged. In Dreikurs' framing, misbehavior is the manifestation of discouragement. The genius of this insight cannot be overstated. Discouragement is a workable condition -- one from which a child can heal and reconnect with the social fabric of belonging. 

For this reason, Dreikurs invested an enormous amount of energy in his research into understanding what it means for a discouraged child to be discouraged. Through this research, he identified what he called the "four mistaken goals" of the discouraged child. Understanding these mistaken goals makes it possible for an adult to learn appropriate, insightful, and very creative methods of responding that will redirect the discouraged child into a more productive approach to finding belongingness.

The four mistaken goals of the discouraged child can be summed up as follows:

1.     undue or excessive attention-seeking

2.     a struggle for power

3.     escalation of the power struggle into the pursuit of revenge and retaliation

4.     shutting down and giving up as a form of self-protection against further discouragement

Even though these are dysfunctional strategies for dealing with discouragement, they deserve acknowledgment for how brilliant and resourceful they are. But they are dysfunctional and we can help students to do better, both for themselves and for the whole classroom community. And this is where the framework of the four mistaken goals of the discouraged child offers highly effective ways of helping students find their way back into healthy belonging and connection.

I want to emphasize that understanding these categories isn't a panacea. Nothing will be instantaneous. But Dreikurs' methods provide a sane, bounded, and healthy lens through which to understand what is going on with these students and to reflect on meaningful ways to address it.

Here's how I experience these in my math classroom.

1. Undue Attention-Seeking

Misunderstanding unpacked: "I only have value if I receive individual one-on-one -- and often immediate -- attention from the teacher." This can take a few different forms. 

During collaborative mathematical group work (using Complex Instruction or other approaches), the student who insists on turning away from their table group and receiving help directly from the instructor is seeking undue attention. This is the reason why we keep returning to the Complex Instruction rule of "only whole-group questions" to the instructor. Part of what students are learning during mathematical group work is self-reliance and peer-reciprocal-reliance. Students are also building their capacities for executive function, self-regulation, and impulse control. Our goal for students is to help them become self-confident, independent, and self-directed learners. They are learning how to look inward to construct their own answers using the best tools and ideas they know, and to engage in positive, pro-social, and interdependent analyses and investigations when they run out of their own personal knowledge. We want them to learn how to exhaust their team's collective resources first before reaching out to the teacher because this is how healthy adults function in the outer world. This is a very different approach to authority than younger children take, because students' self-actualization learning goals are as important as their mathematical learning goals.

The purpose of the "only whole-group questions to the teacher" rule is to build a healthy student fluency in independent thinking, problem-solving, and self-regulation

Another way I encounter undue attention-seeking is during unstructured group work or classwork. When students run out of runway, I encourage them to come up and ask their questions. Over the years, I have become a master at asking questions that elicit the student's thinking and at crafting the tiniest possible hint I can provide. My goal is to help them access the framework they have and to give them a little boost that can help them break through their stuckness and get them moving to the next level. 

There are healthier and less healthy ways that students try to use this kind of access. The unhealthy ways of approaching this that spill over into undue attention-seeking occur when a student plops themselves down and tries and monopolize as much time and attention as they can access from me. This is where gentle redirection is so important. I tell them I will only dispense one hint or piece of help at a time, but I invite them to come back with their next stuck point as many times as they need to. I reinforce that they're welcome to come back with their next question if they need it. 

I try not to allow any one student to monopolize access to me as a classroom resource. This is part of building trust and also of building classroom community and positive interdependence. In my 7th block class this past spring, a new piece of classroom culture emerged, in which students talked openly about "sharing the wealth." The student who had come over to ask for help on, say, problem 11, became a kind of shared community resource. Another table would call this person over to ask for guidance and they would confer and share insights -- never simply doing the problem for each other. 

This was far and away the greatest high point of my teaching year.

Belongingness Comes First: Classroom Management through a Harm-Reducing Lens -- PART 1

 

This is a post that has been rattling around in my mind for a long time, but this has been the year when colleagues younger and older have asked me to please write this down. It's the first of a series of posts I'm going to do this summer, mostly to help myself remember what I need to know when I have forgotten what works. May it be of benefit to others as well.

NOTE: The book of Rudolf Dreikurs that has most deeply influenced my work is from 1964 and is called Children: The Challenge. While every cultural reference in this book may feel cringe-worthy and embarrassing to you, don't let that put you off. Dreikurs was a true master, and his framework and insights on every page ring as clear and true as the most finely tuned bell. It just happens to come from a different age. Don't be tossed away. Dreikurs' psychological methods and insights have a clarity you will not find elsewhere. Take what is beneficial to you and release what does not serve your needs.

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Belongingness Comes First

In the child's mind, belonging is a life-or-death question.

 

The fundamental insight of Adlerian child psychology -- and of Adler's disciple Rudolf Dreikurs, who originated so many of the parenting concepts we now take to be obvious -- is that every child is driven to seek out belonging. The behaviors a kid manifests are designed to achieve their survival goal of secure belonging. 

 

How can this be used in the classroom? Well, if a child enters a new situation and immediately experiences a sense of belonging, then things will tend to run smoothly. The child will read the room, unconsciously relax, and dive into the stream of seamless and happy participation.

 

Sounds easy, right? :)

 

In practice, it can be challenging to foreground belongingness in the classroom -- and to keep it in the foreground. It took me years to let go of my first teacher impulse to talk first and engage second. The way I've found best to implement belongingness is by consistently using a non-spoken daily structure that is impossible to ignore. When students walk into my classroom, the first thing they see projected on the screen is a "Welcome to Geometry!" slide with the instructions for the day. The very moment that class begins, I press "play" on my slide and the thundering drum fill from the Hawaii Five-O opening theme music crashes over the room. I have an ancient Bose speaker that amplifies the music. 

 

It's impossible to ignore. But just in case students manage to ignore it, when it fades out, I start yelling. "Instructions are on the board! Read them and follow them! Let's go! Let's GO!"

 

It's important that the first time they hear my voice, it is in service to our shared collaborative mission. This establishes the ground rules of belongingness in my classroom. WE have a job to do together. I'm just here to encourage that along.

 

As we move into the heart of the first week, I use this structure to train students on how to work with Burning Questions. A Burning Question is a question about the previous day's work that students can't answer for themselves. THAT is the proper use of the teacher. So the first segment of every class' instructions is to prepare for the Burning Questions segment of class. I'll take every BQ students have, but I don't accept the answer "all of them." That's lazy and threatens belongingness.

 

Once we've assembled our list of Burning Questions, we walk through worked examples, but the way I do worked examples is very different from what I've observed in other teachers' classrooms.

 

As Rudolf Dreikurs says, "We must observe the result of our... program and repeatedly ask ourselves, 'What is this method doing to my child's self-concept?" (Dreikurs, p. 39). As teachers we are always faced with the choice of encouraging independence, self-respect, and sense of accomplishment or undermining it. A huge part of what children are learning to develop through productive struggle -- psychologically speaking -- is a healthy ability to tolerate and manage frustrations. Obstacles are a critical fact of adult life. We need to support children in developing the courage to see productive struggle as another texture of adult life they can learn how to face and overcome. As Dreikurs puts it, encouragement -- not praise -- plays a crucial role in helping students develop the "self-respect and sense of accomplishment" they will need to find their place in our world. (Dreikurs, p. 39)

 

Burning Questions is a Narrated Thought Process

The key to encouraging students' courage during Burning Questions is not to do any part of the problem that students can do for themselves. Burning Questions is a profoundly interactive segment of class.

 

In practical terms, this means that demonstrating worked solutions requires modeling the metacognitive questions I would ask myself as a learner when I encounter a math problem of this type and find myself stumped. Modeling courage is essential. Students always already know something. And since what they know is the best thing they know, I use my understanding of their ZPD (Zone of Proximal Development) to find a simpler starting-point question that they can answer. This is usually a question about identifying the situation at hand in the problem. What kind of triangle do we have here? Do we have parallel lines? What kind of angle pair are angles 1 and 8 in the diagram? Do we have an altitude-to-the-hypotenuse situation here?

 

Encouraging students to name -- and use names for -- different mathematical situations is a critical part of my pedagogy. It enables me to ask them dozens or even hundreds of times whether we can spot one of our familiar important mathematical situations

 

I  break down and ask the questions; if the students don't provide the answers to my much-simpler questions, then we simply don't progress. My wait time game is strong. I can sit silently, blinking, for three whole minutes, if need be. 

 

Belongingness dictates students' need to collaborate to find answers. I name and narrate behaviors that I see which are positive and constructive learning behaviors which everyone in the room can do. "I see some people flipping back through their notes, looking up different situations. That seems like a good idea to me." More pages start getting flipped. Quiet conversation ensues at different tables. Students point out possibly relevant parts of their previous days' notes.

 

Eventually somebody brave will pipe up with an idea. I will repeat the idea for the whole class and ask if that makes sense to them. I will often take a vote. I am not some deified source of right and wrong answers. I am actively trying to encourage them to rely on courage and on each other. We'll take a vote. Only then will I confirm whether or not this makes sense.

 

Wrong answers are fine and we honor them by interrogating them and passing by quickly. They give me an opening to ask more clarifying and refining questions about key properties and distinctions. I tell students that spotting known mathematical situations is like bird-watching. You need a field guide and practice identifying the distinguishing characteristics of different situations. This is how people learn.

 

This is my process for modeling courage and resourcefulness during productive struggle. Mine might work for you, or you might need to find your own on-ramp.

 

Students get a lot faster at this interactive process. At the beginning of the school year, I may have to wait minutes before moving on. Within a few weeks, it will only take a matter of seconds for students to pipe up with answers for each questions.

 

"What kind of situation do we have here?"

"Altitude to the hypotenuse situation."

"Good. What pieces of the situation do we know? Which lengths do we have? Which lengths do we need to find?"

 

Never answer a question that the students can answer for themselves or for each other. This is how we cultivate courage and endurance for productive struggle.

 

Piece by piece, question by question, we walk through the problem together. Belongingness is non-negotiable. Whole-class segments not only teach participation and collaboration skills; they enact belongingness. Even if you are totally off-task, absorbed in texting, or feeling heartbroken over your relationship break-up or something even worse, during whole-class segments, you still belong.

 

As Dreikurs puts it, "All comparisons are harmful." (Dreikurs, p. 44)  Whole-class segments are not the time to yell at a kid for being glued to their phone. If you have to have that conversation with a kid, do it in private. "Her abilities will increase only if her confidence is restored." (Dreikurs, p. 44). The ultimate larger goal is to encourage each student to reach "the point where [they] will enjoy learning... and may find out how much more capable [they] are than [they] have thought till now." (Dreikurs, p. 45)

 

The Enemy of Belongingness is Discouragement

 

But if a child has become discouraged, their focus will shift from participational and cooperative behaviors toward less constructive behaviors that are unconsciously designed as defense mechanisms to protect them against their perceived failure to achieve belonging.

 

This is the most important insight a teacher can integrate into their classroom management orientation. 

 

These are not deliberate strategies. These are observed and catalogued patterns of behavior that arise when a child fails to achieve successful belonging. 

 

This is good news for classroom teachers. If you can make sense of and spot these behaviors, you can generally find solutions for redirecting them into pro-social behaviors that will be more satisfying for everybody involved, including both you and the child.

 

When I first read Dreikurs' analysis of the four mistaken goals of the discouraged child, I had a breakthrough in my understanding of students' misdirected behaviors. I'm writing this down because I want other teachers to be able to make sense of this too.  It's so much easier to deal with when you have a validated framework for making sense of what's going on.

 

Here is Dreikurs' 30,000-foot perspective, with one modern update from me in brackets:

 

Children want desperately to belong. If all goes well and the child maintains his courage, he presents few problems. He does what the situation requires and gets a sense of belonging through his [success] and participation. But if he becomes discouraged, his sense of belonging is restricted. His interest turns from participation in the group to a desperate attempt at self-realization through others. All his attention is turned toward this end, be it through pleasant or disturbing behavior, for, one way or another, he has to find a place. There are four recognized "mistaken goals" that such a child can pursue. It is essential to understand these mistaken goals if we hope to redirect the child into a constructive approach to social integration. (Dreikurs, p. 58)

 

Once I started understanding student misbehaviors as falling into one of the four mistaken goals of a discouraged child, it became much easier to find appropriate and effective methods for redirecting student energies in healthier and more constructive ways. 

 

I want to emphasize that there are two important elements to healthy classroom management here. One belongs to the teacher, keeping a clear understanding of the situation, not allowing oneself to get triggered, refraining from reacting to the triggering behavior, and maintaining healthy boundaries to preserve your own sanity. The other belongs to the student who is suffering and acting out in one of the four mistaken ways. The student needs to feel seen, understood, appreciated, and guided in a healthier way. 

 

But because the student is still developmentally a child -- with a child's incompletely formed sense of judgment and executive function -- plus whatever other factors are at play in the child's outside life situation, this is one of the most important situations in which to understand that telling is not teaching. This is the real genius of Dreikurs' approach. He understands that the language of actions is the only way in which the adult can successfully reach the child with these messages. It has to take place at an unconscious level. And it is by taking this approach and following it all the way through that a teacher can reach and encourage the student to follow the better, more effective and healthier path.

 

To put it another way, we have to use psychodynamic wisdom in order to achieve psychological goals.

Week 3 — Talking Points — Desert Island Thinking #MTBoSBlaugust

When I arrived at Princeton, I had been placed with three other roommates in a Gothic dorm suite. I was proud of the things I had accomplished so far. I'd been tied for valedictorian at a huge and competitive public high school, I'd been a soloist at the All-State choral and orchestral concert, and I'd been president of and/or varsity lettered in all my extracurriculars.

So as I discovered that everybody I met had also been valedictorian, editor of the school newspaper, an All-State varsity athlete or musician, etc., I had quite an adjustment. I had to learn how to stay present with my own inner experience and on what was in front of me directly.

I've been thinking about that experience these past two weeks as I have been watched my incoming 9th graders at Lowell adjust to the shock of discovering what it means to arrive at the next level.

The classes are much, much more demanding than they are used to, even at the strongest middle schools. And in addition, as every visitor can see at the front entrance of our school, there is a board that celebrates accomplishments of many of our Lowell graduates since our founding in 1856. There are three Nobel laureates, Pulitzer Prize winners, Broadway and Hollywood stars, admirals and generals and and politicians and world leaders. There are sports legends and pop culture icons, civil rights heroes, the founder of The Gap, and friggin' Lemony Snicket, among others.

Every race, ethnic background, and gender seems to be well-represented.

No wonder my poor kids are freaking out.

Now I try to imagine what it must be like to be one of the very few African-American students in our school. Some of them appear to be doing just fine, but I imagine it is a very strange and disorienting experience to find yourself in what must seem like an endless ocean of whiteness.

We are trying to be intentional in how we are supporting these students and transforming our school culture. We are following best practices and reflecting critically on how we are doing and how we can support their experience. I wish that I could magically airlift in a larger number of faculty of color so that they felt more reflected in the adult community they see all around them. But that is not how public education works. And we have no time to indulge in magical thinking.

So this is the point at which I am introducing some Talking Points on what I like to call desert island thinking. It is the best way I have found to help students to cope with their own feelings of imposter syndrome and the need to be their own best supporters as they enter a completely new territory.

I call it desert island thinking because it is what helped me to cope when I felt overwhelmed and alone as a freshman at Princeton. I reminded myself over and over that, if I were stuck on a desert island, I would want to be with other smart and motivated and hopefully good-hearted people because that would give us our best chances to survive and thrive.

In my teaching life, I think of this as Otter Nation. Our motto is, Hold hands and stick together. When sea otters sleep, they hold hands so they don't drift apart from their tribe. The same is true of us math teachers. We hold hands through the #MTBoS and through #educolor , through Twitter and blogs, and through every social media-based method we can find.

We hold our students in our hearts and try to give them every possible support and advantage we can provide.

For me, a part of that involves helping them to become metacognitively aware and and self-reflective about what they are experiencing and how they can cope with it, how they are brave and well-equipped and the advantages of holding hands and sticking together.

Our Latin Club has hoodies with one of my favorite lines from Virgil's Aeneid emblazoned on the back: forsan et haec olim meminisse iuvabit, which I would loosely translate as, "Perhaps some day we will laugh about this."   This is pretty much where many of my students — and especially my students of color — find themselves at the start of Week 3 too. At this point in Aeneid I, Aeneas and his troops have been driven from their homeland in Troy and find themselves on storm-tossed seas, wondering how they are going to survive.

A growth mindset, and some desert island thinking, along with Talking Points about it, are the best support I can offer them.

The concept of betweenness

I am coming to believe that, much like the concept of substitution, developing a deep understanding of the idea of betweenness is a huge part of the psychological and conceptual work of Algebra 1.

I have been dissatisfied for years now with the fact that we tell students about the geometric interpretation of absolute value, but we don't really get them to live it. And yet that idea of the "distance from zero" on the real number line is not something we give students time to really marinate in.

And you know what? That feels dumb to me.

So this week and part of the next, my students and I are really wallowing in that idea.

I've taken a page from my studies as a young piano student. In the study of the piano, there are certain studies of technique that really force you to slow down and take apart the finger movements. There are specific figures that you have to practice over and over and over so that they become part of your finger memory. How they feel in your fingers is how you come to relate to them.

This is not just about developing automaticity, although that is a side benefit. This is about learning to feel these foundational figures in your bones. In your body. They become so fundamental that as you learn and grow as a musician, you come to feel them when you see them coming up in a new score you are studying.

The technique does not replace musicianship. The technique supports the musicianship.

I've been noticing lately how my own experience of absolute value is about noticing boundary points at the periphery of my mathematical perception. I see them out of the corner of my mathematical mind's eye. And how an inequality is said to relate to them defines how I relate to those boundary points.

So I am taking the risk of sharing this mathematical experience with my students.

As with young piano students, we take this slowly. One figure at a time. Right now we are only dealing with the case of an absolute value being less than a nonnegative quantity. We are dealing with situations of betweenness, where an inequality presents us with a figural situation that is going to wind up with a quantity being between two boundary points.

That is all. And that is enough.

I see the effort in their faces and in their fingers as they rewrite, revise, calculate, solve, and sketch graphs. I see them noticing and wondering whether they need to use a closed dot or and open dot.

And I hear them developing the confidence that comes from experience in developing a relationship with these quantities.

They are not following rules. They are listening to their own deeper wisdom. Everybody knows something about the situation of being "between" other things. Betweenness is one of the most elemental human ideas.

They are making friends with mathematics.

TMC #14 Group Work Working Group Morning Session – Annotated References & Framework

I'm having a lot of fun planning the Group Work Working Group morning session for Twitter Math Camp 2014, and it's time to start sharing.

Here is the background material I'm using for developing the group work morning sessions. Please note that this is NOT required reading!  Recreational reading only! So please don't freak out!  :)

I wanted to give people a sense of the framework and background I'd like us to start from so attendees can decide whether this morning session will be right for them. I also wanted to provide links and titles to valuable materials.

These are listed in order of relevance to the Group Work Working Group morning session — they are not in formal bibliographical form.

National Academies Press, How People Learn (downloadable PDF here)
This amazing free book provides the framework within which we'll consider the use of group work. I am especially keen for us to explore how we can develop and implement tasks that fit within their (approximately) four-stage cycle for optimizing learning with understanding while also fitting with our own individual school and district requirements. In a nutshell, the four stages are as follows:

STAGE 1 - a hands-on introductory task designed to uncover & organize prior knowledge (in which collaboration cultivates exploratory talk to uncover and organize existing knowledge)

STAGE 2 - initial provision of a new expert model (with scaffolding & metacognitive practices) to help students organize, scaffold, & develop new knowledge (in which collaboration provides a setting to externalize mental processes and to negotiate understanding)

STAGE 3 - what HPL refers to as "'deliberate practice' with metacognitive self-monitoring" (in which collaboration provides a context for advancing through the 3 stages of fluency with metacognitive practices)

STAGE 4 - transfer tasks to extend and apply this new knowledge & understanding in new and unfamiliar non-routine contexts

Malcolm Swan, "Collaborative Learning in Mathematics" (downloadable PDF here)
A short and highly readable summary of Swan's instructional design strategy for collaborative tasks, including notes on his five types of mathematical activities that constitute the bulk of the Shell Centre's formative assessment MAP tasks and lessons.

Malcolm Swan, Improving learning in mathematics: challenges and strategies (downloadable PDF here)
An in-depth introduction to Swan's approach to designing and using the kind of rich tasks offered by the Shell Centre and the MARS and MAP tasks.

Chris Bills, Liz Bills, Anne Watson, & John Mason, Thinkers (can be purchased from ATM here)
The richest source book imaginable for ideas for activities to stimulate mathematical thinking. Often credited by Malcolm Swan and Dylan Wiliam.

Anne Watson & John Mason, Questions and Prompts for Mathematical Thinking (can be purchased from ATM here)
The richest source book imaginable for variations on questioning and prompting strategies.

Dylan Wiliam, Embedded Formative Assessment
This book is a gold mine. Don't leave home without it.

Substitution with stars

This one is for Max, who asked about it on Twitter, and for Ashli, who interviewed me for her Infinite Tangents podcasts.

As Ashli and I were talking about some of the struggles we see as young adolescents make the transition from concrete thinking to abstraction, I mentioned substitution.

For many learners, there comes a point in their journey when abstraction shows up as a very polite ladder to be scaled. But for others (and I count myself among this number), abstraction showed up as the edge of a cliff looking out over a giant canyon chasm. A chasm without a bridge.

This chasm appears whenever students need to apply the substitution property of equality — namely, the principle that if one algebraic expression is equivalent to another, then that equivalence will be durable enough to withstand the seismic shift that might occur if one were asked to make it in order to solve a system of equations.

Here is how I have tinkered with the concept and procedures.

Most kids understand the idea that a dollar is worth one hundred cents and that one hundred cents is equivalent to the value of one dollar. I would characterize this as a robust conceptual understanding of the ideas of substitution and of equivalence.

One dime is equivalent to ten cents. Seventy-five pennies are equivalent to three quarters. You get the idea.

We play a game. "I have in my hand a dollar bill. Here are the rules. When George's face is up, it's worth one dollar. When George is face down, it's worth one hundred cents. Now, here's my question."

I pause.

"Do you care which side is facing up when I hand it to you?"

No one has yet told me they care.

"OK. So now, let's say that I take this little green paper star I have here on the document camera. Everybody take a little paper star in whatever color you like."

Autonomy and choice are important. I have a student pass around a bowl of brightly colored little paper stars I made using a Martha Stewart shape punch I got at Michael's.

Everybody chooses a star and wonders what kind of crazy thing I am going to have them do next.

We consider a system of equations which I have them write down in their INB (on a right-hand-side page):

We use some noticing and wondering on this little gem, and eventually we identify that y is, in fact, equivalent to 11x – 16.

On one side of our little paper star, we write "y" while on the other side, we write "11x-16":

I think this becomes a tangible metaphor for the process we are considering. The important thing seems to be, we are all taking a step out over the edge of the cliff together.

We flip our little stars over on our desks several times. This seems to give everybody a chance to get comfortable with things. One side up displays "y." The other side up displays "11x–16." Over and over and over. The more students handle their tools, the more comfortable they get with the concepts and ideas they represent.

Then we rewrite equation #1 on our INB page a little bigger and with a properly labeled blank where the "y" lived just a few short moments ago:

"Hey, look!" somebody usually says. "It looks like a Mad Lib!"

Exactly. It looks like a Mad Lib. Gauss probably starts spinning in his grave.

"Can we play Mad Libs?" "I love Mad Libs!" "We did Mad Libs in fifth grade!" "We have a lot of Mad Libs at my house!" "I'll bring in my Mad Libs books!" "No, mine!"

It usually takes a few minutes to calm the people down. This is middle school.

I now ask students to place their star y-side-up in the blank staring back at us.

Then it's time to ask everybody to buckle up. "Are you ready?"

When everybody can assure me that they are ready, we flip the star. Flip it! For good measure, we tape it down with Scotch tape. Very satisfying.

A little distributive property action, a little combining of like terms, and our usual fancy footwork to finish solving for x.

Some students stick with substitution stars for every single problem they encounter for a week. Maybe two. I let them use the stars for as long as they want. I consider them a form of algebraic training wheels, like all good manipulatives. But eventually, everybody gets comfortable making the shift to abstraction and the Ziploc bag of little stars goes back into my rolling backpack for another year.

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I'd like to thank the Academy and Martha Stewart for my fabulous star puncher, without which, this idea would never have arisen.

I wore out my first star puncher, so I've added a link above for my new paper punch that works much better for making substitution stars. Only eight bucks at Amazon. What's not to like? :)

What We Actively Value, Versus What We Tell Students We Value

Lately I've become acutely aware of what I actively value in my classroom, which has entailed an uncomfortable amount of noticing the conditioned habits of my teacher personality. I don't collect and stamp homework assignments. I don't have each day's agenda and objective for the day neatly written on the whiteboard by the time the first bell rings. My classroom is pretty messy most of the time. I don't have a good system for filing away those last three copies of every handout for future use. I took great permission from @mgolding's system of daily handouts using her Container Store hanging file system: basically, the handouts migrate downward one pocket until there are no pockets left, at which point they go into the recycling bin.

I've made my peace with these tradeoffs because I discovered early on that if I was allotting attention to those things, then that was attention I wasn't allotting to the things I actually do value.

I adopted an SBG assessment system because it aligns my grading/scoring system with the things I actually value: mastery, effort, and perseverance. And also presence — being fully present with the activity we are doing that I actually care about. And as I've noticed that, I have noticed something else I feel good about in my classroom: my kids know that those are the things I value. Which that means they don't waste valuable life-energy bullshitting me about the small stuff we all know I don't really care about.

This has led to a lot of interesting progress with students I didn't expect to make progress with. Less successful students who don't feel shamed stick around to ask questions and engage in meaningful academic inquiry. They come to my room during their study hall periods to follow up, get help on missed or misunderstood assignments, or ask for additional work they can do to improve their understanding.

Not their grade -- their understanding. Their performance.

I am not used to this, and it causes me a lot of inconvenience. 

Students who have a reputation for giving up and giving in ask me if they can write another draft, reassess their missed algebra skills/concepts questions, and take greater ownership of their learning in my classroom. My ego would like to think this is because I'm such a highly effective teacher, but in actuality, I think it's more that my walk is becoming more aligned with my talk. I care about mastery and effort and perseverance, which means that those are the things I respond to.

What I did not realize until this afternoon is that this also means that I don't respond to things that are NOT those things. Which means that my kids are not expending any effort pretending to care about things around me that they really don't care about either. There is a focus on the work, and there is not a focus on things that are not the work. This may sound obvious, but actually it's not -- or at least, it wasn't for me. It took me years to discover that I'd been walking around in a consensual trance all my life.

This kind of awareness is challenging, to be sure, but it is also incredibly freeing. Students spend a huge part of every school day pretending to care about things that don't actually matter to them. Fitting in, pleasing teachers, winning points. Some of it is necessary but much of it they know to be complete and utter crap.

Ten, fifteen, forty, or fifty minutes of being authentically engaged in something that matters to somebody is a huge thing. Ten, fifteen, forty, or fifty minutes of authentic interaction with someone who is trying to focus as sincerely as possible on what actually matters in this life is even bigger.

I learned this lesson from years of experience with my mentor and teacher, Dr. Fred Joseph Orr — mind to mind, and heart to heart, though it took years to digest, and quite frankly, I'm still digesting. I'll probably be digesting for the rest of my life. No one had ever paid that kind of focused, intensive, thoughtful, and bounded attention and awareness in my presence before. And it made me discover how it feels to feel alive. I only discovered how precious that kind of awareness was -- and still is -- once that chapter of my life ended and a new chapter had begun.

I was noticing all this today during a test in which some of my lowest-performing students were asking for "help" with certain problems. I noticed that each time I came over in response to their request, they were not so much asking for assistance as asking for a kind of authentic engagement and support that was neither judging nor doing for them but simply witnessing their effort with presence. What I noticed today inside myself — and what distinguished this from mere adolescent attention-seekig behavior — was my own felt sense of a embodied memory of seeking out this kind of authentic connection in my own work with Fred. And this felt sense gave me the motivation to allow that connection and that presence. I trusted something inside my own inherent, intelligent functioning that told me to allow the connection rather than to pull back and resist. It was a subtle and quiet movement inside me, and I'm still figuring out what exactly was going on.

How many times have I mistaken noise for the signal? Do discouraged students ask because they hang on to the sane and healthy hope that they can learn and connect and make progress? Fred always told me, "The organism moves toward health," and I grew to believe him. I wonder if this is what my discouraged students are really asking for when they ostensibly make a seemingly attention-seeking request for something called "help."

Intermezzo - summer reading seminar on The Curious Incident of the Dog in the Night-Time

One of the things I sometimes forget that I love about teaching English is the fact that I get to get adolescents talking and thinking about issues we all feel deeply about. The cool thing about sparking these conversations with young adolescents (by which I mean secondary students, as opposed to college students) is that most of them are just waking up to these issues for the first time in their lives, which means passions run deep. And that means they are ripe for thinking deeply about these issues — more deeply than we often give them credit for.

In my seminar this afternoon on The Curious Incident of the Dog in the Night-Time, I wanted to get students to develop for themselves a question that I think is fundamental to citizenship in a functioning democracy — specifically, who is it who, in different contexts, gets to decide what is to be considered "normal," and therefore acceptable?

The Curious Incident is an interesting reading choice for incoming 9th graders because the narrator, Christopher, is a young man on the autistic spectrum who easily qualifies in students' eyes as an outsider. In spite of extremely high math and science aptitude and achievement (preparing to take his maths A-levels at age 15), he is prevented from attending a mainstream secondary school. Instead, his social and emotional impairments have caused him to be marginalized into a special needs school where even he can see that most of the students are far less socially and emotionally functional than he is.

The students in my seminar are outgoing 8th graders I have known for a full year now. Because I teach both math and English, I have actually taught most of them for at least one period a day, and in many cases, for two periods a day. Which is to say, I know them unusually well for a casual summer reading seminar. I also know the ELA curriculum they have all just finished working through because I helped to develop some of it, and this gave me a lot of touchstones to draw on in our discussions. However, I would like to point out that this kind of lesson could work well with almost any group of students, since it centers on one of the main issues in adolescent life: namely, issues of fairness.

The activity I set up for today involved small groups doing "detective work" on five related thematic issues in the novel and then sharing out their findings with the rest of the group. The five thematic areas were:

• Belief systems: conventional religious beliefs versus Christopher's own unique belief system
• "Normal" behavior and how we judge differences in the behavior of others
• The nature of human memory: Christopher's beliefs about his own memory and other people's
• The significance of Christopher's dream in the novel
• The interrelated issues of truth, truthfulness, and trust

To get things started, I modeled the investigative process using issue #2 - what is considered "normal" behavior and who gets to decide whose behavior in a society will be considered "normal" and whose will be considered "deviant" (or sub-normal). Students needed a little more context on what autism is and how it can affect a young person socially, so we did a little quick internet-based research (thank you, iPhone!) on the autistic spectrum and what it means to be higher-functioning or less-high-functioning. Students zoomed in on the exact contradiction I had hoped — but have learned never to expect— they would target: the question of varying standards of "Behavior" that govern the judgment of and consequences for actions of adults (such as Christopher's father) and those of a kid like Christopher himself. Fairness is something that most adolescents feel strongly about, even when they are generally treated quite fairly, as most of these students usually are. [SPOILER ALERT: stop reading here if you haven't read the novel and don't want to know what happens as it progresses].

The kids were really quite exercised about the fact that while Christopher was the one labeled as having "Problem Behavior," his father committed a number of acts that we all agreed had to qualify as "Problem Behavior," including (a) killing an innocent dog, (b) lying to his son about the boy's mother being dead, and (c) hiding her letters to him to maintain the lie of her having died of an improbable illness. These were just the big issues.

So we circled around until we needed to land on a word they did not yet have in their vocabulary: arbitrary. Our dictionary manager looked the word up and read its several definitions to the group while we tried it on for size. "Arbitrary" definitely seemed to fit the contradictory categorizations of behavior of adults versus of Christopher in the novel. There was no way around the fact that the rules seemed both arbitrary and easily manipulated by the adults — far more easily than by Christopher himself. The notion that society's rules are subjective constructs, influenced by the personal beliefs and opinions of human beings, struck them as a significant new insight.

This part of the discussion led to a second insight I'd been hoping we might arrive at: the fact that whoever is in power gets to determine what will be considered normal. The idea of differences in power is something most of these students have not encountered much, except in the context of adults/parents versus adolescents/children. So for many of them, it was a new idea to think that these inequities could extend outside of families to other social relationships and interactions.

Their investigations and presentations were rich and quite thorough. To save time, I provided more scaffolding in the worksheets (chapter and/or page references) than I would have if we had been doing the project over several class periods. Still, I was pleased that they were able to reread their sections closely, draw on their annotations and notes, and quickly assemble arguments about each of these thematic areas that were supported by evidence from the text.

Having just come back from Twitter Math Camp, and still being immersed in rich dialogue about math pedagogy and equity, the conversation reminded me that every subject area in which we teach is a powerful opportunity to engage with students. At Twitter Math Camp, I loved being able to drop directly into the middle of an ongoing conversation I've been having with colleagues in the Math Twitterblogosphere for months or years in the virtual realm. In our seminar today, I loved being able to drop directly back into pretty advanced investigation with these students because I had already done so much formative assessment with them over the past year in this same kind of context.

These conversations are a gift of deep teaching and learning, and they are a reminder of what gets lost when policymakers become enchanted with the kind of magical thinking that allows them to chase the illusions of quick fixes and silver bullets such as plopping kids down in front of a giant library of videotaped lectures. Developing a library of tutorial videos may be a worthwhile archival goal, but it is no substitute for the magic that can happen when good and authentic teaching connects with a ready student.

On choosing sanity, and on modeling this choice for our students

I want to talk a bit about sanity — not because I think I'm an expert (I'm not; no one is) but because I have come to understand sanity as a choice we make moment by moment, and because, in so doing, I have seen how we either model — or do not model — it for our students in our classrooms and in our lives. And this is an enormous part of the social and emotional life training they either receive or do not receive in this crucial part of their lives.

I teach middle schoolers, or rather, I should confess that they teach me. Every student and every class is a mirror in which I can see what I am teaching them. Perhaps because their access to it is new, middle school students have a finely tuned hypocrisy detector. More so than any of the high school or university students I've ever taught, middle school students want to see who "walks their talk." Do so, I have learned, and they will follow you anywhere. Fail to do so at your own peril.

So a big part of this year's learning, for me, has been learning how to tune in to what I am actually doing and checking in on whether this is consistent with the social and emotional lessons on appropriate self-care I am trying to teach. Sometimes that has meant being the adult in their lives who tells them to stop the madness. The only way to stop the war is to stop fighting, stop struggling, stop efforting. There really are only so many hours of the day, and for middle schoolers, about eight of those need to be spent sleeping. That means every piece of homework can't always get done every day all the time. Sometimes a person has to choose sanity. So I try to understand that and allow for it, because learning to allow space for all of life is something they are going to have to learn if they are going to do better in running this world than we have done so far.

I've also had to learn how to trust my training and my gut. I was blessed to study for over ten years with a pioneer in integrating social and emotional intelligence and mindfulness into learning environments ranging from special education to mainstream classrooms to therapy situations. You probably haven't heard of him because he has spent his life being what I think of as a guerrilla bodhisattva — a pioneering educational psychologist and an undercover evangelist for social and emotional health in daily life. His name is Dr. Fred Joseph Orr, and I am blessed to count myself among his students. Actually, we think of ourselves as his disciples, though he would undoubtedly discourage that characterization. But it's a fair one. He taught us to integrate teachings from whatever sources might be beneficial to ourselves and our communities — teachings from Adlerian psychology, spiritual development, meditation, yoga, Buddhism, his own mischievous sense of humor and spirit of adventure, writing as a practice, the practice of joy and creativity in whatever form they might take, and environmental restoration and ecological rebalancing. I came to him as a writer, writing teacher, and longtime meditation practitioner, but I quickly became much more than that under his mentorship. And it was the kind of mentorship that is a true spiritual gift — the kind you can only repay by sharing it with others. In his life, he suffered in ways that most of us would find unimaginable, and yet he remains the most radiant and joyful person I have ever known. And although his active teaching practice has been cut short by a medical condition that has become the focus of his own personal life practice, his students carry on his great efforts, sharing the learning and the gifts we received from his teachings. His teaching of us was an investment in the future and a labor of love. I wake up every morning determined to be worthy of the effort, love, and energy he poured into teaching me.

There's an urban fable Fred used as a teaching tale. It's known as The Hundredth Monkey principle. It began in the 1950s as a call to end the escalating nuclear arms race, but Fred believes it has broader applicability as a model for how human awareness and sanity can be activated too, and I have come to believe this too. The idea is simple, yet profound: when a critical mass of individuals' consciousness gets raised, it inevitably triggers a paradigm shift in the dominant culture. So this turns out to be a more leveraged model for social change than the conventional wisdom tends to think, for when we direct the focus of our daily efforts on helping individuals and small groups to shift their energies, awareness, and attention, we are doing our part to put our culture on the path that leads toward greater sanity, in addition to greater achievement.

So what does all this squishy-sounding woo-woo stuff have to do with teaching and learning mathematics?

I believe it provides us with an on-ramp, a way to reach the hearts and minds of the students who are most discouraged and shut down in the math classroom. It's differentiated for the most capable students because most of them have never been given tools to cultivate self-awareness and other-awareness as a part of their learning. And by learning — and by teaching these discouraged students how — to cultivate their social and emotional intelligence in how they engage in mathematical practice in our classrooms, we can change their relationship with mathematical studies to one based on what the American Tibetan Buddhist teacher Pema Chodron describes as "unconditional friendliness."

Over the last couple of days, as I've begun my yearly summer rituals of cooking and storing school lunches in the freezer for days when I need the loving self-care of hand-made soup in the middle of my day, I have realized that this is the heart of my Twitter Math Camp talk. My topic is Dan Pink's book, Drive: The Surprising Truth About What Motivates Us, and how to use his ideas about intrinsic motivation to reach the discouraged math learners in our classrooms. I've begun to understand how Fred's work with me is an arrow that flies straight to the bullseye of this target, and it's given me some hopefully valuable insight into how to create the toughest of Pink's three pillars of intrinsic motivation. That pillar is autonomy, and I'll write more about it in an upcoming post as I flesh out my talk with ideas and activities.

In the meantime, I'm going to let my subconscious mind work on the problems while my conscious mind takes a nap.