Answer Getting & Resource Finding

I posted the following three tweets yesterday, which I need to elaborate:

“Answer-getting” sounds pejorative but it doesn’t have to be. Math is full of interesting answers to get. But what Phil Daro and others have criticized is our fixation on getting answers at the expense of understanding math. Ideally those answers (right or wrong) are means to the ends of understanding math, not the ends themselves.

In the same way, “resource-finding” isn’t necessarily pejorative. Classes need resources and we shouldn’t waste time recreating good ones. But a quick scan of a teacher’s Twitter timeline reveals lots of talk about resources that worked well for students and much less discussion overall about what it means for a resource to “work well.”

My preference here may just mean grad school has finally sunk its teeth into me but I’d rather fail trying to answer the question, “What makes a good resource good?” than succeed cribbing someone else’s good resource without understanding why it’s good.

Related

  • I felt the same way about sessions at Twitter Math Camp.
  • Kurt Lewin: “There is nothing so practical as a good theory.”
  • Without agreeing or disagreeing with these specific bullet points, everyone should have a bulleted list like this.

Featured Comment

Mr K:

This resonates strongly.

I shared a lesson with fellow teachers, and realized I had no good way to communicate what actually made the lesson powerful, and how charging in with the usual assumptions of being the explainer in chief could totally ruin it.

Really worthwhile comments from Grace Chen, Bowen Kerins, and Fawn Nguyen also.

Adrian Pumphrey:

Really, we need to literally go back to questions such as ‘Why am I teaching this?’ ‘Where does this fit into the students learning journey?’ and ‘How am I going to structure the learning so that the student wants to learn this?’ before we even think about where resources fit into our lesson. This takes a lot of time to think about and process. Time and space many teachers just don’t have.

Chris Hill:

Early on I would edit resources and end up reducing cognitive demand in the interest of making things clearer for students. Now I edit resources to remove material and increase cognitive demand. Or even more often, I’m taking bits and pieces because I have a learning goal, learning process goal and study skills goal that I have to meet with one lesson.

Kelly Stidham:

Great lessons in the context of learning around mindset and methods are the instruments we use to “do” our work. But the reflection and coaching conversations where we “learn” about our work are critical as well. Without them, we use scalpels like hammers.

But this work is much harder, much more personal, much more in the moment of the classroom. Can we harness the power of tech to share this work as well as we have to share the tools?

2014 Sep 8. Elissa Miller takes a swing at “what makes a good lesson good?” Whether or not I agree with her list is besides my point. My point is that her list is better than dozens of good resources. With a good list, she’ll find them eventually and she’ll have better odds of dodging lousy ones.

About 
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

27 Comments

  1. This resonates strongly.

    I shared a lesson with fellow teachers, and realized I had no good way to communicate what actually made the lesson powerful, and how charging in with the usual assumptions of being the explainer in chief could totally ruin it.

    More regularly, when discussing lessons during PD, I feel like the things I look for in lessons (what *are* the students thinking, what are they struggling with, and how will their resolution of that struggle on their own leave them prepared for what comes next) are not the same thing most other teachers look for.

    I’m used to awkward social disconnects – I used to be a software engineer. But on this, I often feel like I’m in a weird parallel universe.

    • That weird parallel universe thing – it happens at every school where there are #MTBoS members! And then, while you are trying to teach and listen for understanding they department chair wants every Alg II class to take the same summative multiple choice test that doesn’t test for any understandings being taught- aargh!

  2. The first thing I look for in a teaching resource is it’s connection to the other activities in my class. What hole is this filling, and does it tie naturally into the narrative? In the same way, there’s nothing wrong with ‘answer getting’ if it isn’t the end of the process. Let’s face it – math isn’t very satisfying for most people if they aren’t getting answers (and most math teachers are satisfied if their students can get answers.) Is there a cultural expectation that our students are tying those answers into a similar narrative? Expecting kids to create a consistent ‘story of math’ without getting answers first is unrealistic at best. The obvious follow-up question is: how do we create a culture where students see getting answers as an intermediate step to understanding math?

  3. Do you really think grad school has sunk its teeth into you or is it simply a matter of you applying your passion for design in a different area?

    It’s still Essence vs. Accident for me. We can be talking about resources today or photography (5 years ago) and it’s still the same conversation: Why is something good ?

    When we understand the essence of what makes something effective, the activity itself becomes secondary in that it can be adapted, adjusted or even replaced with something all together different.

  4. I think that this is a really, really interesting observation. It raises up all sorts of questions for me, each leading down a different path of inquiry:

    1. Twitter only lets you type 140 characters. Would there be more theory-talk on a different platform?

    2. Would more theory-talk about task design lead to less resource requesting? Don’t know if I believe it, but here’s the hypothesis: if teachers believe that task-design is complex, they’ll be more reluctant to ask the world for resources.

    3. Are we talking about criteria for task-design or criteria for task-selection? Or are they the same?

    4. You’re saying that certain twitter conversations are unproductive. Can you point to, or describe, some twitter discussions that are closer to the ideal? (Extension: Are there better and worse ways to use twitter?)

    5. What can teachers do to develop their theories about teaching? Do teachers need to be nudged into theory?

    6. Would it be pleasant for teachers to talk theory? Would theory-talk lead to uncomfortable disagreements?

    Thanks for the thought-provoking post!

  5. Patrick Honner:

    What does a high-quality, coherent, pre-packaged curriculum look like through this lens? (Whatever those adjectives mean).

    CMP has a particular theoretical framework – launch, explore, and summarize – that runs throughout their material. As a framework it isn’t so complicated you have to take days to think about it (much less apply it) but it’s opinionated enough that one can easily identify examples and counterexamples.

    Michael Pershan:

    here’s the hypothesis: if teachers believe that task-design is complex, they’ll be more reluctant to ask the world for resources.

    That isn’t my hypothesis, really. The analogous hypothesis is that if students try to understand math more they won’t try to get answers as much. And I don’t believe that either. Answers should inform understanding and vice versa. Similarly, some of my favorite conversations about theory emerge from talking about good and (especially) bad lessons.

    More theory-talk will result in more resource-talk because it’s hard to talk about theory without referring to resources. (It’s easy to talk about resources without referring to theory, though.)

    You’re saying that certain twitter conversations are unproductive.

    I don’t have much to say about Twitter in this post. This happens to me all the time via email, for instance.

    What can teachers do to develop their theories about teaching? Do teachers need to be nudged into theory?

    Maybe: “Take three lessons you think are good and three lessons you think need improvement. Could be yours or someone else’s. What do they have in common?”

  6. The analogous hypothesis is that if students try to understand math more they won’t try to get answers as much.

    I’d argue that the analogous hypothesis is that if students try to understand math more they won’t call out “what’s the answer?” in class as much.

  7. Let me clarify that comment about #MTBoS. We are all trying to ramp up our classrooms, to get our students learning and sharing, but usually, we are in the minority. We are salmon fighting the current! I was showing the whole math department Desmos, teacher.Desmos and Function Carnival. I had some of the teachers gasping with delight! The math dept head cut it short and then apologized later, saying that even the best programs won’t be used by “some” teachers! I just needed 5 more minutes!!

  8. Very interesting. Dan, have you read “Building a Better Teacher” by Elizabeth Green yet? If not, I recommend it. I think you are treading on some of the same ground that is discussed in the book.

    tl;dr:

    An unsolved problem in education is communicating effective teaching practices and have that language be used universally.

    This is the point of Deborah Ball’s Teaching Works project, Magdalene Lampert’s focus on Instructional Activity Structures project at Boston Teacher Residency, and Doug Lemov’s Teach Like a Champion.

    Some similar structures that have emerged around this same issue are things like “I do, We do, You do” or “Think, Pair, Share”. The problem is that this language is insufficient to really describe what makes these kinds of structures potentially effective. We have extremely articulate language to describe high school mathematics to the point that almost all mathematics teachers can have substantially similar understandings of the core concepts of the mathematics (at their grade level at least), but we do not have the same level and verbosity of language to describe teaching.

    Other examples of language in the same genre:

    “DOK”, “High cognitive demand”, “Formative Assessment”

  9. The search for effective “answers” can be used as a tool to build effective understanding. So, first, I notice that I get a lot of wrong answers. Then, in place of genuine understanding I find ways to at least get right answers. Then, I get tired of having to look so much, so I try to create my own right answers that match the answers I’ve been finding, and in so doing develop a sense of understanding about what makes those answers “right”.

    Same process is certainly true for me, the math teacher. I got tired of giving weak lessons and activities. So, I go looking so that I can steal effective lessons and try them in my class. Then, I start to notice the patterns, and get tired of spending so much time looking, so I try to make my own effective lessons. As I try and notice the shortfalls, I make updates, which is a manifestation of a growing understanding of the essential elements of an effective lesson.

    And the understanding of a decent lesson doesn’t necessarily remove the need to resource-find. On the contrary, it likely would make the process more fruitful. So perhaps a teacher who goes out looking for resources isn’t evidence of a teacher lacking understanding, but could be a sign of a teacher whose understanding is growing.

  10. Hey Dan,
    I love the parallels between math students and math teachers – I try to do that when thinking about my learning and my students’ learning (and my students this year range from math students to preservice teachers to practicing teachers, depending on the class).

    I’m math ed grad student, interested in supporting teachers in their math classroom tech use. I’m TA’ing for a math class (algebra for future elementary teachers) right now, and trying to create investigations that use technology to fill gaps in the textbook. This is so hard – I feel like I have to develop my “feel” for what good use of technology means. And that depends on so many factors. I know it’s a growing process, and that I’m productively struggling, but it’s hard to strike out into this tech territory that is both familiar and unfamiliar.

  11. Dan, I have been following since maybe 2010 and I could take one of your 3act lessons or ideas from your high school Algebra class and it would just be a side trip into something interesting before going back to the boring book. Once I began to use more coherent materials that made me think about math in a deeper way and had experience with methods that failed many of my kids, I find that looking at the mathematics under the lesson and making sure that that is solid allows me creativity and the courage to go outside the text to use others’ ideas with more confidence. The reason why your graphing exercise is so potent is because even though the context is very fun, the deeper need for a dual measurement system and the fine tuning of the graph tool itself as the lesson progresses is an outcome of understanding the mathematics underneath the graphing.
    It is easy enough to memorize the elements of graphing and teach the mechanics and different forms of linear equations and have no idea of the value and meaning of those tools.

  12. What makes a math lesson good? I’ve spent the last 15 years studying Cathy Fosnot’s tasks because she is a master at creating what she calls Truly Problematic Situations. Hers are for elementary math, so lately I’ve taken what I learned and have begun creating algebra Truly Problematic Situations and professional development to go with them. What I think is unique about our work is that we both are not only interested in what makes a task good, but what makes a sequence of tasks good. In other words, not only a task but an entire sequence of tasks should be multiple-entry, multiple exit – where struggling students can have access to at least begin to mess with the situation but it is also complex enough to keep advanced students intrigued and working. Some call these “low threshold, high ceiling”. Another imperative is that the sequence of tasks “tells” when the knowledge is social but constructs relationships and connections when the knowledge is logical-mathematical (Piaget). In other words, build on students’ understanding whenever possible and keep the rote memorization to a bare minimum.
    Just like traditional teaching has been about telling students (as if mathematical understanding is transmittable through telling), traditional professional development has been telling teachers how to teacher better (as if teaching well is transmittable through telling). Many university teacher prep programs feed into the “give me a good task” teacher mentality because they “tell” teachers how to teach or supply them with tasks. Better pd and teacher prep has had teachers engage in good tasks to give them the experience of constructing relationships and using the connections to solve problems. Too often it ends there, leaving teachers with lots of resources but a lack of discretion to choose well and certainly not to design well, especially not a sequence of tasks.
    After studying Fosnot’s pd, I am developing pd and teaching my method’s courses to teach teaching like I believe teachers should teach – helping students construct mathematical relationships and helping teachers construct the art of teaching.
    If your interested in an example of a type of lesson format I believe is essential in a sequence of tasks, see http://www.pamelawharris.com/algebra/algebra-problem-strings_introduction/. This blog is my first attempt to get my work out there – Dan, you are to blame. Thanks for encouraging me.

  13. Interesting discussion. I’m having a bit of a hard time because it seems like we’re conflating resource with lesson. I may ask others for tasks that are rich and lend themselves to discussion and multiple entry and exit points and I feel like there is a fair bit of discussion on the twitters about specific tasks and problems and why the teacher thought they were good. What I think we don’t discuss much is how we actually teach because I think that’s much harder to articulate and is quite personal. To me, how the lesson is structured and how the problems/tasks/resources are used is much more fundamental to what students will learn. As I’ve been teaching longer, that’s what I think about and plan much more than the specific questions or problems. I wish there was more discussion of that, but it’s easy to upload and share a worksheet and hard to capture one’s teaching.

  14. Julie Cornelson

    September 6, 2014 - 12:01 pm -

    I would have to agree with Andrew Shauver. As a student, I find greater understanding while searching for answers. This post reminded me a lot of my high school geometry class. In this class, we were taught several rules and the teacher demonstrated why the rules were true. Then we were set loose to figure out some problems. We had to use our understanding of algebra to figure out how to find the answer using the rules that we had just learned to be true. I am not yet a teacher, but it seems to me that what makes a good resource good (or a good lesson good) is that it works. When the resource is used, do the students have a greater understanding of the concepts presented? Unfortunately this can not be judged only by whether they found the correct answer. Judging understanding requires class discussion and asking questions. Why did you use that formula? How did you find that answer? How do you know the answer is correct? Etc.

  15. As soon as I saw this post I bookmarked it to respond to because it is something that resonates strongly, but then the Davids went ahead and said much of what I was going to say. So, instead, I’ll throw out two hypotheses for why this happens:

    (1) it’s easier/quicker to grab a resource and plug-and-play than it is to think critically about why it’s effective (and provides an easy scapegoat if a class period doesn’t go well), and teachers are often tired/pressed for time– this may be unique to the context I work in, because I imagine overwhelmed novices may succumb to this type of pressure more often than veterans

    (2) sometimes, teaching is presented as a set of best practices– you do this checklist of things and you are therefore a good teacher– rather than as an infinitely complex set of choices that are constantly being made. when good teaching is about doing xyz, then the reason that xyz works (or works in some cases but not others) doesn’t matter as much as how to do more of xyz or how to do xyz better. if good teaching were about constantly making choices, however, then it becomes more important to understand the principles or consequences or factors you’d want to consider to make good choices.

  16. My opinions on this have changed from when I first started to teach. Early in my teaching I kept a very narrow focus: what does today look like, tomorrow? Oh man I have no idea how to introduce this topic, I’ll go talk to a colleague. Rarely did I talk to them about more than a lesson’s worth of detail at a time, and sometimes it was far shorter: “I need a worksheet on ____, you got any?”

    My biggest change in opinion is about scope: you can string a ton of great lessons into a horrible tapestry, especially if those lessons were constructed independently. What comes right before this, what comes next, what came three months ago, what came last year, what comes three months from now, what comes a year from now? If the focus is on higher-order mathematical thinking, these questions have huge impact on a lesson’s effectiveness.

    These questions also make it almost impossible to judge an effective-looking lesson in a vacuum, or to recommend a specific lesson on a topic above another. It’s hard for me to recommend a specific lesson from Illustrative, or a three-act, because the whole is rarely being taken into account. For example, one could probably take lessons from Illustrative, and build a curriculum using those precise lessons. In my opinion, this curriculum would be great on the microscopic level and horrible as a cohesive whole. Every single one of those lessons could be effective, but they’re not telling a consistent story.

    I also see this with the ways schools use textbooks, and this is really the textbooks’ fault. “We’re going to start with Chapter 9, then do Chapters 3 and 4, then 12, then back to 5-8.” What the hell is that, nobody would read a novel that way, but we do it all the time when designing math courses. This is possible only if a textbook is agnostic to the order of its units, and the consequences are disjoint pieces that cannot build on one another by design. The textbook won’t expect students to remember what they did a month earlier, because it’s impossible to know! The teacher must then add this cohesiveness to the curriculum on their own, and that is truly difficult to accomplish.

    In my opinion, teachers do far too much editing or adapting of materials. It takes a huge amount of time to do so effectively, and that is time that could be spent in many other positive ways. Unfortunately this seems to happen by necessity at times, due to nonexistent or poor materials. I don’t feel teachers should be required or expected to write their own curriculum.

    It’s hard to say how or if this problem can be solved, but one thought is to look for chapters and units as resources rather than looking for lessons. The same cohesion problems can occur, but at least the entire unit will be internally consistent.

  17. Math students : Answer-getting : The ending :: Math teachers : Resource-finding : The beginning.

    Answer-getting might be a goal for students, a good and humble goal if they are invited to struggle and allowed to explore in the spirit of seeking understanding.

    Resource-finding may just be the beginning for teachers. No resource, no matter how good, teaches itself. That very good resource may lead a teacher to create an entire new lesson with little resemblance to the original, but the resource was there, nonetheless, to inspire her.

    Answer-getting means nothing without deep understanding. Resource-getting means nothing without thoughtful implementation. Ah, but high test scores, shiny technology, and well packaged resources are hard to resist.

  18. The trap I fall into is finding a ‘fun’ resource and forcing to work into a lesson. This rarely goes well and I often wish I had spent that much more time starting from scratch.

    Really, we need to literally go back to questions such as ‘Why am I teaching this?’ ‘Where does this fit into the students learning journey?’ and ‘How am I going to structure the learning so that the student wants to learn this?’ before we even think about where resources fit into our lesson. This takes a lot of time to think about and process. Time and space many teachers just don’t have.

  19. While I agree with many teachers on here that my first years were more about finding something – anything that I could use to teach, there is something else that I have noticed.

    Early on I would edit resources and end up reducing cognitive demand in the interest of making things clearer for students. Now I edit resources to remove material and increase cognitive demand. Or even more often, I’m taking bits and pieces because I have a learning goal, learning process goal and study skills goal that I have to meet with one lesson.

    There is also the problem that I would rather edit materials and build lessons than grade and see how I never get every single student to learn everything I hoped for.

  20. I had a lovely discussion about this very issue with you, Dan, et al at the NCTM conference in Louisville last year. So glad to continue it here.

    As discussed at length here, part of the issue is that we often take up lessons without reflecting on the purpose/intent of the tool. Worse, we enact lessons without a deep understanding of the mathematics at play, which cripples our ability to provide feedback in class that centers on the core ideas. We may ask a great first questions, but the second and third, arising from student thinking, fall short. Looking for resources on a unit or larger scale may help make sense of the progression, but I’m not sure it helps us uncover the deeper structures at play.

    The underlying and unsaid trait of humanity here is that we take any resource and bend them to our own practice. I’ve seen a 3 ACT over scaffolded, a card sort turned worksheet, a “sometimes, always, never” busted up with the hammer of over-simplification. I’ve also seen many a well intending teacher get into a great lesson, only to find they lack the classroom strategies (usually around feedback questions and discussion) that empower them to reveal and give space to the student thinking.

    So –
    Learning takes place in layers. A lesson lives within a classroom experience. To be effective depends on my mindset, my methods, and the tools I have in the moment.

    Great lessons in the context of learning around mindset and methods are the instruments we use to “do” our work. But the reflection and coaching conversations where we “learn” about our work are critical as well. Without them, we use scalpels like hammers.

    But this work is much harder, much more personal, much more in the moment of the classroom. Can we harness the power of tech to share this work as well as we have to share the tools?

  21. @Kelly & Chris, really helpful commentary. I pushed excerpts up to the main post.

    This from Kelly is rattling around pretty hard:

    But this work is much harder, much more personal, much more in the moment of the classroom. Can we harness the power of tech to share this work as well as we have to share the tools?

  22. RE: harnessing tech to share learning work

    The good news is YES. We definitely can.

    Video clips of lessons, capturing teacher reflections where they discuss the decisions not the actions, virtual coaching, virtual professional learning communities. We have great access now. The work I think is on our conversations. Critical conversations where we name and articulate core ideas that drive our strategies and resources. Peer reviews where we challenge each other’s practice and provide feedback that goes beyond the superficial “this is what I do.” Comparing the enactments of common lessons?

    I’m excited by the potential of where tech can take us, but the work will be around us learning how to learn through the new medium.