NOW I get it!

I finally get it.

I have never understood the assumed necessity of having and using some big publisher’s packaged curriculum. You know the one, 15 pound student textbooks with a teacher’s guide painstakingly chosen by a committee every X years (or not, depending on the budget cuz they’re damn expensive). It seemed so Old-School-ish to me:  curriculum = ultra traditional textbooks = lesson plans, Day 1, Lesson 1, Page 1. Here’s how you do it kids, practice it 5000 times, the test is next Thursday. Repeat ad nauseam. Yuck (with smug eye-roll). As a teacher, I rarely used the school’s textbooks except as an occasional resource. I already know what I have to teach, isn’t that the point of having standards? How I teach is up to me (thank goodness), and I chose to work towards constructing understanding via student-centered learning via worthwhile tasks. Prioritized student reasoning and valid arguments, focused students more on Why than How.

At least, that’s what I always aimed for. What a rebel. Consequently, I spent hours and hours (because I did not know about MTBoS yet!) developing my own curriculum, planning my own lessons, agonizing over details.  H.O.U.R.S. Constantly creating, reflecting, refining. Continuously making shit up, learning from my mistakes (plenty of those!), trying again. The long hours and effort probably contributed to my early burnout, do ya think?

What I realized today is that I did not see any need to rely on a packaged curriculum because I had never met one I liked, one that I believed in, one that rang true for me, impressed and inspired me, one that I could follow without hesitation or makeovers or by sacrificing my convictions.

Until now.

I seriously cannot say enough good things about Illustrative Math and Open Up Resources.  OMG, this brand-spankin’-new 6-8 curriculum really delivers.  It aligns so beautifully with my beliefs about teaching a learning mathematics that I could actually do Day 1, Lesson 1 without any qualms whatsoever. None, I’m not kidding. I get chills (they’re multiplyin’) just thinking about the implications.

NOW I get what you mean,  Sadie Estrella (Math Nerd) when you insightfully advise us to rely on our good curriculums so we can put our precious time and energy into knowing our students and meeting their needs.  I GET IT!  Only now do I see and believe that it’s possible, because finally finally and oh joy of joys, here is a worthy curriculum that is going to hold me up when I lean hard on it. More than good.  Glorious.

Plus, FREE is a very good price.  Check it out NOW!



Out of the Woods

UPDATE 1/20/27:  Difficulties concentrating today, so I am submitting this already published post for the MTBoS 2017 Blogging Initiative, Week 3, “Read and Share”.  Looking foward to some feedback!

I am struggling to write this post, and I am not sure why. I want to offer a thorough response to a blog post as evidence of my growth, but am battling (maybe?) feeling underqualified and lacking in credibility. And strangely vulnerable.

I could describe my eight little years of teaching as a classic case of not being able to see the forest for the trees. Its like I downloaded the awesome constuctivist app I really wanted, but never thought to or knew how to update it. My current situation allows me to finally view the forest, a chance to look around and consider the bigger picture. This perspective has helped me recognize and understand my shortcomings and offers me insights for moving forward. MTBoS is helping me update my app, and essentially, I want to test it out to see if I’m understanding how to use it. Consider it a formative assessment.

The inspiration for these musings comes from Justin Aion  . Actually, I mentioned him (and This Post) the last time I blogged, so thank you, Justin, for the two-fer.

It would be best for you to read his whole post, of course.  He leads with a brief description of his school’s current math textbook:

Each section begins with an introductory activity that is frequently hands-on.

The task is this:

Justin Aion’s Photo

Draw a pentagon with extended sides.
Label the external angles.
Cut out the external angles.
Put the external angles together and make and observation.
Repeat with a hexagon and an octagon

Seems straight forward enough, right?  But what happened was this:

It didn’t go as I would have hoped.

Apparently, even mostly on-task groups did not get done, in spite of the fact that they had just done the same thing with internal angles. I know EXACTLY the feeling. Been there, by golly, many, many times. Loads of empathy here. Too much precious time spent on a hands-on activity and no learning taking place. In fact, it would not surprise me that this is the #1 Reason for Avoiding These Kinds of Tasks.

He also writes,

(Students) are much more attentive to the tasks when they are working individually or when I’m giving direct instruction.

I suspect that means it’s a larger issue than just these kids in this class.

Justin works hard to see the forest while standing in the trees; in my opinion, his suspicions are spot on.

What I see is a chance for me to check my understanding.

First, I connected his final comments to my recent reflecting on teaching and learning. That was my last post, and my hypothesis is that students are passive learners because they are put in the passive role. School happens to them.

Wait, this was an “age/grade appropriate” task, though. Hands-on! Engaging! Student-centered! Everything a constructivist teacher’s heart would desire!

What I am beginning to understand is that “engagement” is more complex than providing something for students to do. That not all tasks are created equal, and implementation matters.  I’m not talking about comparing mindless worksheets to learning in groups; I’m talking about those activities and tasks the look great on the surface, when in fact they do not genuinely engage because they are not designed to.   These pseudo-engaging activities are easy to miss, and I did, many times over.  Here’s what I noticed about the lesson from Justin’s textbook:

  • From the students’ perspective, the need to explore external angles is non-existent (other than compliance), so there is no intrinsic motivation.*
  • Also missing: student-generated observations and questions. No perplexity, no curiosity, no ownership.
  • The method to explore external angles does not come from students but from a textbook (and the teacher). No exploring, no creativity, no problem-solving.
  • Student role is passive: they are merely following directions. In an attempt to keep students “on task”, teachers often model step by step directions, keeping their grip on the active role. “Engaged” means “looking busy”.
  • The low cognitive demand throughout the task actually frees them up to socialize. Hence the fun (for students) and frustration (for teachers). Some may even want to prolong this “easy” part to avoid what feels more challenging: making an observation. Coping via procrastination.
  • There’s no intrinsic reason to finish, either; experience has shown these students that whatever they are ‘supposed to learn’ from this hands-on busy work will be stated for them, anyways, by the teacher (or by the “smart” kids).

I am not yet knowledgeable/confident enough to play  “What Can You Do With This?”  although I have ideas brewing. For now, what I do have to offer is this:
Assuming you want to empower students to be productive, active learners, consider developing the habit of regularly running lessons, activities, and tasks through the role-lens. All of them– your creations, the textbook’s (especially these), something gleaned from the internet– as often as you are able. Examine closely what students will be doing and keep tweaking** until you think the active role has switched to them, where it belongs more often than not. Take a risk and trust them to rise to the challenge. Be vigilant, be intentional.

What can you let go of and turn over to students?

Will they be asking and answering their own questions?

Will they notice patterns and make conjectures without you prompting them?

Will they be curious and driven to make sense of something, even if that something is math?

Will they own the learning and all the work it took to get there, together?

Anyway, that’s what I would try to do, were I feeling a bit lost in the woods.

*Which also perpetuates the perception/myth that math is a Random Bunch of Useless Stuff No One Really Cares About.

**Here are some practical ideas and resources for tweaking from a couple of Experts that are not overwhelming. The ideas, that is, although Dan Meyer and Kate Nowak are probably also not overwhelming. They are two of many that have been instrumental to updating my app me.

From Dan Meyer:

Makeover Monday .  His MM summary is here.

His delightful  video on relevance ,  also located here.

From Kate Nowak :

Make Them Figure Something Out

Plan a Killer Lesson Today


Yesterday, being Tuesday, I volunteered all day in Jackie’s 7th grade math classes. Last night, being me, I started reflecting on what took place– what we did or did not do, what students did or did not do– in terms of the conversation she and I had at the end of the school day. Today, being unusually snowy (for NW Oregon) and stay-at-home-y, I’m gathering my thoughts here.

My sister’s backyard.

Let me first say that Jackie, like many other teachers including me, wants to teach in a way that student learning moves forward. Neither one of us know exactly how to pull that off, so in some many ways, its the blind leading the blind.

She was willing to spend weeks (weeks!) on making sense of integer addition, but was, well, flabbergasted when she asked them to write in their journals (in their own words) what it means to add and, with the exception of one student (out of about 100), students wrote basically this: adding means to put numbers together to go up to a bigger number. The use of “bigger” notwithstanding, what prevented these students from writing something like this?? Adding means to combine. Sometimes when you add, you increase to a higher value, sometimes you decrease to a lower value. It leaves us wondering what in the world it takes for students to internalize concepts well enough to build on them, to move along.

Now, I don’t think at all that zero learning has taken placement but, c’mon. Nor am I going to say these kids are lazy or don’t care or don’t try hard enough. Quite the contrary; these kids are normal, but they are for the most part passive learners. It makes me wonder what’s going on here (and it went on in my classes, too) that needs addressing. Plenty, I’m sure.

Allow me to digress a bit.

(I may never get over how amazing it is that you can be pondering a particular problem or question and *ding*, the MTBoS sends you a pertinent post from a total stranger.  Its cosmic.)

This morning my inbox contained  a post from Justin Aion. One of the reasons I follow his blog is because he is so candid in his daily reflections and I can easily relate. If I understand him correctly, there’s a conflict between teaching the way he wants to teach (for deep and lasting conceptual understanding) and teaching in a way students expect him to teach (direct instruction), and feels a more than a little guilty when he gives in.

Which brings be back to some questions I have percolating*.

  • Are students ‘passive learners’ because that is the role given to them, over and over, the active role belonging to the teacher?
  • If a teacher strives to develop a thriving, student-centered learning community and struggles to make it a reality, is it (in part) because these roles have not sufficiently switched?
  • What are some obstacles to switching roles and how do you think they can be overcome?
  • If so, what can one do, alter, and even not do to make the switch and make it last?

What do you think? What do the roles look like in your classroom?  What recommendations do you have for switching the active role to the students?

*My fairly confident answer for 1) is YES and 2) is It’s worth considering.   My answers for 3) and 4)  are a bit more tenuous and lengthy, so I’d like to make them  another post.

Week 2, With Time to Spare!

My solution for missing the deadline for Week 1 of the MTBoS 2017 Blogging Initiative was to write a belated post (see below).  Not wanting miss this opportunity again, I am already posting for Week 2! The focus: soft skills.  That is, the part of teaching that is more about raising children, the crucial part you don’t realize about teaching until after you are standing in front of a room full of students.

Unfortunately, the more I reflect on my set of soft skills, the more I realize that, in SBG terms, they are in the “getting there” stage, and I don’t have really much more to offer other than it is primarily about building relationships. Those more proficient, experienced, and successful than me in the relationship-building arena will have oodles to share, I am sure. In fact, a lot has been written about soft skills already, as evidenced by the 2010  Soft Skills Virtual Conference recommended by Sam Shah.

On his advice, I read (and in several cases, re-read) most of the contributions to the conference. Fabulous, all. What I want to share here are two related excerpts that stood out rather significantly for me. As in, holy shit!

From  Shawn Cornally, whose writing I could read all day long:

He would sit with me for 15 minutes stints, explaining things that I should have learned in high school, because he realized something that every teacher should: teach them where they’re at, not where you wish they were. You can only do that if you manage to somehow care more about the kids than your list of standards.

(Emphasis is mine.)

From Riley Lark, organizer and curator of the SSVC:

These roles [facilitator, resource manager, task manager, recorder/reporter] make me more comfortable with my guilty admission: I don’t care very much if the kids learn math. I mean, I’ll teach them some math, and when they leave they’re going to see more of its beauty and be equipped to use it in society. But which is more important, vector addition or working in a team? Factoring or formulating questions? Integrating or leading peers? Obviously, obviously, the math comes second. It’s just lucky that learning math provides so many opportunities for learning the more important things.

(FYI, the emphasis on that second ‘obviously’ is not mine.)

Talking Points!  For each, decide if you agree, disagree, or are sitting on the fence, and include WHY. It’s OK to change your mind after listening to another’s points of view, or to restate your mind and strengthen your argument.

  1.  Obviously, obviously, the content comes second.
  2. Standards are required, I must be sure to get through them all.
  3. Virtual Conferences are a fabulous idea.
  4. The MTBoS would benefit from more input from elementary teachers.
  5. To meet each student ‘where they are at’, we need leveled and remedial classes.
  6. (Insert a related Talking Point of your choice here.)


UPDATE: Serendipity: Liz Mastalio’s Week 2 post “Honestly, the Math is Secondary”.

A Duh Moment

The penny finally dropped.

I blogged on March 1 of last year about the apparent inconsistencies between coordinates and tables organized in one order (x, y) and rate/slope in another, as y/x.   I played around a bit with writing slope as x/y (which feels more intuitive to students) and found that when graphing, you get the same graph as long as you keep the change in x horizontal.  This post is a lengthy update to that one.

In a predominately DI classroom where students are shown How and expected to memorize processes, they tend to not raise questions about Why.  I certainly never did.  Like others, I might’ve notice the inconsistency and accepted it because, well, math is just confusing and you have to just memorize and follow rules in order to pass a test to get an A and look/feel smart.  Many practices in education not only encourage this approach but also award those who can use it well.

I started wondering about the Why of (x, y) vs y/x  last year when I started regularly volunteering in an 8th grade classroom.  Students were being show a whole lot of How, with plenty of examples to copy, and then given HW to practice.  When I heard one student mumble mostly to himself, a little to me, about why you move horizontally first when graphing coordinates and vertically first when determining slope from a graph, I was delighted by him yet frustrated with me because I had no response for him other than I was wondering about that, too.

Which bugged me, so I kept picking at it.  I even got brave and posted my musings.  I really hoped I would figure it out and get back to that curious student.  I let him down.

Fast foward ten months to yesterday.  I woke up early, and for some reason, it popped into my head WHY rate is written y to x and not the other way around. Isn’t that weird? I suspect seeing this  “Silent Solution” video the previous day on writing rate from a table lit up that part of my brain again.

It was in front of me all along, I already knew this, so it was my Duh moment.

If there is relationship between two things that co-vary, then you can see a pattern and develop generalized equations.  The three equations you can write for a proportional relationship are:

Dependent Variable = rate • Independent Variable

IV = DV / Rate

Rate = DV / IV <<<——Whomp, there it is!   Why (algebriacly) m = y/x and not the other way around.  (I still am leaning toward convention as to the order of coordinates.  I does feel more intuitive to list the IV first.)

Students should be empowered to explore ideas like rate and slope in such a way that they do the sense-making.  I am confident that they are fully capable of understanding Why, that the How can emerge from them and be owned by them.  And it will be glorious.

What do opportunities for student-generated sense-making look like in your classrooms?  What do you do to nurture curiousity and facilitate learning?  What do you struggle with?


PS.  I am also pondering the duality of the way rate is represented.  As a ratio, it is a comparison of two values, a quantitative description of a c0-varying relationship.  A change of two in This for every change of three in That.  We even need two number lines to graphically represent This and That’s relationship.  When rate gets put into a proportional or linear equation, it suddenly behaves like a single value, locateable on a single number line:  two-thirds.  What’s with that?

AHA #3. If it’s broken, throw it out.

I’ve been reading Alfie Kohn’s book The Schools Our Children Deserve; it is part of the required reading for a course I’m taking. Just before summer got crazy busy with Other Stuff, I had read through Part 1: “Tougher Standards versus Better Education”. I admit I do not feel intrinsically motivated to write thoughtful any reflections on Chapter 5 (Getting School Reform Wrong) or Chapter 6 (Getting Improvement Wrong); while they contain additional compelling evidence for what is currently amiss in eduction and with ed reform, I am already long on board. In fact, even though I took a un-planned break from the course, I’ve continued to think/read/journal/blog/reflect in order to keep moving myself towards insights about teaching and learning.

Recently, I decided to take up Kohn’s book again, looking forward to “Part 2”, in which Pooh Kohn offers solutions. Chapter 7: Starting From Scratch.

Well, beam me up Scottie if this chapter isn’t fully in sync with my current thinking and wondering.  Suddenly, I feel motivated. Huh.

What I’ve been wondering about in recent weeks stems from a conversation I had with Jackie, a middle school math teacher friend. I volunteer regularly in her room and we meet to talk almost as regularly about pedagogy and moving student learning forward and other Important Things. My role in part is to support her implementation of several strategies that are intended to create an active learning culture in which students make sense of math.

She noticed that in spite of the on-going, long term math PD that has been invested in K-12 teachers in her district and in spite of her efforts to increase student talk and focus on student reasoning, learning remains for the most part passive and feels glacially slow. Mindsets cling to answer-getting, compliance, and performance, about speed and status. In many ways, what she wants happening in her classroom differs from what is actually happening.

Been there, done that.

Neither she nor I are implying that their previous teachers are at fault! Nor are we blaming the students! (I just heard again today that The Reason students don’t learn is that they “just don’t try hard enough”.  I disagree.  I may need to blog about that.) At this point, this is merely an observation that her desired change seems too minimal. Its frustrating. We know there is more work to do, more than we anticipated.  Persevere.


Every worthwhile observation should be followed by a genuine question. It’s how we learn, how we find solutions.  What I wonder is, exactly what is going on in schools and classrooms (including mine) that impedes or prevents moving from a performance culture to a learning culture?

If we only make changes- even great ones– to some of the things we do while maintaining others, the “old-school” culture prevails. This is a big AHA for me.  Most teachers seeking to improve practice consider what to do differently or what to add in, but it is equally important is to identify what needs to be (gasp) thrown out.  In October 19’s post, I listed several widely accepted, rarely scrutinized practices that I believe undermine honest efforts to transform teaching and learning. Alfie Kohn provides a similar list and includes justification.  For both of us, grades top the list. Teachers, administrators, parents, even students, should make their own lists. This is where conversations need to begin; this is where priorities get identified, appropriate long-term goals get made, resources located, and plans developed . This is where meaningful change- change that moves education forward–stands a chance.

I recommend reading Kohn’s book. In the meantime, here’s some of my additional take-aways from Chapter 7:

  • You can’t make people want to do something, like learn. You might offer rewards and threaten punishments (grades, points, stickers, perks, honor roll, a different track, detention, praise, admonishments, etc.) but you get compliance or defiance, not motivation. Being extrinsically motivated to get the reward or avoid the punishment is not the same as being intrinsically motivated to learn. Intrinsic motivation comes naturally and heightens engagement, but can be extinguished or nourished, depending on what takes place in the learning environment.
  • The purpose of school, the reasons for educating people, tend to be debated in rather polarized terms. This or that.  Kohn writes, “It’s more a continuum than an either-or, but the point on that continuum we identify as ideal makes all the difference.”  A lot of this and a little that.  For individual educators, teams, schools, and communities, identifying where that point is located will help clarify which practices support or impede genuine learning.
  • In “traditional” school cultures, there is a disconnect between long term goals (those ideals shared by most educators and parents) and short term goals (those skills, mandated and tested) and practices within classrooms. We say we want one thing, and we do and/or allow something else. (Is that the problem Jackie and I are facing??) If our long term goals are for students to be curious, to be intrinsically motivated, active learners, to listen empathetically, to construct viable arguments and critique the reasoning of others, to persevere, to make sense of complicated ideas, and so on (all valuable life skills, by the way), but we put more energy into short term goals like being sure they can correctly add and subtract rational numbers, then it is possible– even probable— that the long term goals will never be met.
  • If, on the other hand, we first identify that ideal place on the continuum, clarify our long-term goals, and then teach in such a way that always supports these goals, then both long and short term goals will be met. Frequently meeting and reflecting on our long term goals and evaluating what is happening in our learning communities is a must.  Remember, some practices may need to be updated, included, or even discarded to be sure long term goals are supported.
  • Achievement should not ever be a long term goal. Low achievement is not the real issue (although it is popular to say so), disengagement is. Its not that students are not “trying” hard enough; they just don’t see the point.  We should be wondering why.  The performance/compliance/accountability culture that is touted as the “solution” is actually a massive obstacle to achievement; focusing on grades and points and data and test scores in order to improve learning simply backfires.  John Nichols said, “Teaching requires the consent of the students, and discontent will not be chased away by the exercise of power.”  (That quote is in Kohn’s book.)
  •  In contrast, high achievement results naturally when both long and short term goals are met by capitalizing on intrinsic motivation and student interest. Common sense tells us that all people learn best when they are interested in what they are learning about; schools can and should be putting their efforts into creating and sustaining learning environments for students and their teachers.

If you have not already done so, please check out  MARK CHUBB’S informative post about how his district set and went about meeting long term learningculture goals and what happened to student achievement.

Where is the “ideal” place on the continuum?  For you, for your school, for your students.  Why?

What practices and policies do you use or see used in your school or district that are intended to create and sustain an active learning culture? How effective are they?

What else is going on that undermines these efforts and perpetuates fixed mindsets, passive learning, and disengagement?

What’s on your list? Why?  Who will you share it with?