**What I Like**

Growth mindset is useful as a descriptor of students — I can better understand the challenges or successes of students by considering their mindset towards learning mathematics, or perhaps mindset toward learning a certain area of mathematics.

Students should be praised for effort and progress rather than intelligence.

Comments contribute more to learning than grades, or grades combined with comments, because they show students a clear path forward without judging their ability.

A growth mindset reinforces the idea that mathematics is more about process than product.

**Some Challenges**

Talking about a growth mindset can send the message to students that if they are unsuccessful, they must just not be trying hard enough.

I used some of Jo Boaler’s resources to do a growth mindset intervention last year, and it was pretty unsuccessful — it seemed to affirm students who had growth mindset beliefs, but did not change the beliefs of more fixed mindset students.

There are many accompanying tasks that are low-floor and high-ceiling, and students seem to enjoy and persevere on, but I’m skeptical these transfer to build content specific skills, and these same students still turn off when confronted with more challenging mathematical content that I am required to teach.

I’m unsure how growth mindsets in different areas interact. Do students have a general “learning mindset”? What about a mindset for math learning in general? Do students reform their mindsets each year, with each teacher and classroom? Are their mindsets specific to different content areas within math?

**An Approach**

Principles to Actions names productive struggle as one of the eight essential teaching practices:

Support productive struggle in learning mathematics.Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.

I’m skeptical that talking about a growth mindset or putting a poster on the wall makes much of a difference for fixed mindset students. I think actions are much more powerful than words. Students need productive struggle — if they are either continually successful without struggling, or are struggling without experiencing success, students are unlikely to build a growth mindset in my classroom. I need to choose questions and tasks that make this possible for all students, and in particular make sure that it is not the same students experiencing success each time.

When students experience productive struggle, in particular students who have a fixed mindset, that is the moment for growth mindset language. There’s no big realization or overnight change here. Just a little bit of progress every day, a powerful idea to reinforce the growth that students experience and a name for the type of perseverance we want to instill in students.

I keep coming back to the words of Dylan Wiliam, which I think capture this idea perfectly:

If a student struggles and is successful it’s probably a good thing; if a student struggles and is unsuccessful it’s probably a bad thing.

Michael Paul GoldenbergLet’s focus a bit on what comprises success for students who generally have not been successful in mathematics classrooms. I suspect that part of the problem they face is what usually counts in typical K-5 classrooms: quick, accurate calculation. If you’ve been trained for 6+ years that being good at math being a facile computer and you don’t happen to be one of those, how can incremental success at mathematics as problem solving be satisfying and work as an impetus to further efforts at solving a given problem or future, more challenging and demanding ones?

In general, it cannot, at least not until students have been convinced that their efforts, no matter how small and incremental, comprise meaningful success that should bring about self-satisfaction and redoubled efforts to go further. Teachers trying to promote that kind of mind-set are trying to counter a deeply-rooted culture of mathematics that is, quite frankly, idiotic. But it’s the idiotic culture we’ve had here for as long as I’ve been around (some 65 years) and as far back as I’ve been able to trace through conversations with older friends and relatives, including my 95 year-old-aunt (a firecracker of a person who came through NYC Public Schools convinced that she “couldn’t do math,” despite having a dad who quit school at six and was renowned as a fine mental calculator with great skills at pinochle and gin rummy because of his steel-trap card memory. My mother, seven years her junior, fared no better with school mathematics, and both remain utterly astounded that I have gone into mathematics education professionally (particularly since I did so after nearly earning a doctorate in literature and studiously avoiding math from my sophomore year in high school until my early thirties). It’s very difficult to unlearn certain sorts of lessons that our schools and culture inculcate. I wish I’d been available to reeducate them.

I concur with your notion that slogans and posters and the like aren’t going to suffice, at least not for kids who’ve been beaten down by the traditional math teaching culture to the extent that they’re just about completely insulated and defended against any possibility that math isn’t what they think it is and that they might be perfectly capable of doing it. I began my high school teaching career in math with two years at an at-risk alternative high school. Most of my students had earned no credits in math (this at a time where 2 credits ( = 4 semesters) of math was all that was required for a high school degree in Michigan; twice that is now required), and I was really clueless as to how to reach them. My naive attempts to promote a problem-solving curriculum pretty well went splat! Adopting one of the integrated high school textbook series that emerged in the 1990s from NSF-sponsored projects didn’t succeed a lot better. But I will say that there were moments of success, flashes of breakthroughs for some kids, that gave me the sense that if someone more adept than I was at reaching these students in more than just academic ways were to take on the job, it would be possible to get more of them to take the bit in their teeth.

One moment that remains bright in my memory is a student who despised me, to put it mildly, almost as much as she hated math. But during a unit on discrete math, something clicked. In particular, it was the chapter on graph coloring that engaged her sufficiently that she wound up succeeding in class: she ultimately wrote an A exam, possibly the only A she ever earned in high school math. I suspect that there is a lot in discrete math, particularly in graph theory, with which students who’ve not done well in other areas of math and for whom algebra is a death-filled swamp can be successful. Since a lot of what’s required with Euler paths and circuits and graph coloring, at least at the beginning levels, can be attacked with counting and some trial and error, and because it entails drawing and, yes, coloring, there are elements there that appeal to previously-untapped areas of kids’ mathematical thinking.

While I can’t swear to it, my guess is that had I been able to couple the above insights with the patience needed to reeducate my students about math as problem-solving and recognizing incremental successes (and taking genuine pleasure in small victories, which includes finding the good in legitimate efforts that fail*), these students might have done far more than I was able to help them attain. They were difficult for me to work with and my lack of experience with students who were so resistant to school, learning, and mathematics probably made me the wrong teacher for them. But I still think the potential was there.

*One thing I saw not only with those kids but in many other classrooms in the ensuing 17 years was that students’ willingness to do very little and then quit or to quit without making any apparent effort at all to grapple with a problem deeply undermined the sort of things mathematics requires for any kind of success. A willingness to write things down, to try to be organized about one’s efforts, and in general to bring a scientific approach to mathematical problem-solving was for the most part absent among these students. Basic habits of mind and work habits that promote successful problem-solving were missing. I suspect they’d never learned them and were now deeply resistant to being taught such things. Their idea of working hard on a problem was taking one or more wild guesses at a numerical answer (this habit is rooted, I’m nearly certain, in that computational definition of mathematics that gets drilled into kids in elementary school) and if that didn’t suffice, well, screw it! And my refusal to allow one second of blind guessing to suffice just reinforced their beliefs that math was stupid, that they were stupid, that I was stupid (or cruel), and that sullen withdrawal back into their shells was the best possible move.

A couple of other things about your blog-piece: I’m not sure that I completely swallow Dylan Wiliam’s comment, at least not without more context and discussion. Student perception of success and failure matter a lot. And of course the mathematical culture of the classroom in which they’re working helps determine that perception (or at least it can).

As for tasks that ensure that it’s not just the same subset of kids succeeding: there are likely going to be students who succeed at just about any task you give in math class (if anyone in the class at all will succeed at it), so I assume what you mean is that you want to try to ensure that it’s not JUST those kids who are succeeding, rather than trying to make them NOT succeed. That might sound ridiculous, but I’ve seen conversations where it seems like some traditionalists (and parents) worry that progressive math teachers are trying to rig things so that students who do well in typical math classes will fail, while those who usually fail are successful. This is discussed in terms that remind me a lot of broader conversations about robbing the rich to pay the poor. And I’m not sure that at heart that the thinking on the part of some people is all that different. While I hardly think that’s my goal or the goal of a lot of teachers (if any), it’s an undercurrent I see frequently enough in the Math Wars era to be concerned about.

dkane47Post authorThanks for sharing your experience, Michael. I think you make a good point about the importance of thinking about how we communicate what it means to be good at math. This is a point that Jo Boaler makes very well, and is, I think, one of the most important aspects of her work.

I think your skepticism about engaging all students in productive struggle is well founded, but I do believe there exist plenty of tasks that can both engage and challenge all students. Barbie Bungee is a good example of a task that is accessible at multiple levels, and has valuable extensions that will challenge the vast majority of students and push them to do new mathematical thinking.

I’m not sure I understand very well the way that a specific classroom culture interacts with students’ mindset beyond the actual mathematics being done, and it’s something I want to explore more.

trigotometryYou’ve got some great points that highlight the pitfalls and possibilities of growth mindsets. Students walk into our classrooms with mindsets that have a certain amount of inertia. As much as we like to think that any student with a fixed mindset can be influenced by teachers and eventually embrace a growth mindset, we have to consider that years of school and learning experiences have built a student’s construct towards learning. When this prior experience is laid bare, posters and words can be empty for students. A teacher’s positivity and words about learning can be influential, but these actions can easily be heard and ignored by students. Real change is incremental and requires time filled with authentic experiences. By authentic, I mean great tasks that result in genuine learning of the content of a course (be it math or some other subject). While generic inspirational activities can be helpful, some students (especially those most critical of growth mindset) will see the randomness and disconnectedness of the tasks. A student may ask,”Why are we doing this? Are we going to learn real math today?” An approach that uses experience with productive struggle provides a solution to these pitfalls of growth mindset. Varied and frequent learning experiences that place a student in the genuine role of learner (uncertainty, struggle, experimentation, collaboration, analysis, and the elation of resolution) produce results that can force a student to reconsider his/her thoughts about learning. Regardless of the subject, the goal of a teacher should be continually placing students in the role of a genuine learner. This task is much harder than it sounds, which probably explains why teachers (or anyone involved in education) would rather use posters, feel good phrases, and inspirational activities that can seem random to the average student.

dkane47Post authorI totally agree, Tom. One idea I think is really interesting is the opportunity to change a students’ mindset at the beginning of a new school year — a new teacher, a new classroom — and balancing that with the challenges of long-term, incremental change. I do believe that for most students there is a chance to change their mindset early in the year, and I don’t think it’s through inspirational activities — I think it’s through giving that student effective on-ramps into the content that the class is learning . That said, I do think that tempering that optimism with the reality that it takes time to change negative mindsets is important. I’m not sure where that balance lies.

MaryAnn Moore (@1mooreorless)I am so grateful to see another person speaking about the possible pitfalls of growth mindset ‘instruction’. I thank this post by Elizabeth (http://cheesemonkeysf.blogspot.com/2015/04/if-it-is-in-way-it-is-way-only-true.html) got me started thinking about it. There are good reasons why students have adopted fixed mindset. If we are going to tell them that they can improve with more effort, we need to make sure we hold up our end of that promise and create a learning environment where they will see the results of that effort. We need to teach them that not all effort is equally effective. Some types of work/struggle will produce more learning than others. Students need guidance and instruction in learning how to engage in productive struggle. I love that you shared the quote by Dylan Wiliam. That is one of about five things he said that just keeps replaying in my mind.

dkane47Post authorThanks MaryAnn! I also think that what you’re doing spiraling your curriculum has a huge potential to create impactful learning experiences for students’ mindset. I’m excited to hear more about how that goes!

Michael Paul Goldenberg@MaryAnn Moore: thank you for the link to Elizabeth’s post. Very close to my own heart, beliefs, and classroom (and personal) experiences. She does slip once or twice into a little absolutism herself (when describing the Rogerian approach, she says that this is THE ONLY way that works, when it makes more sense to say that it is A way that has been shown to work). But in general, her post is well-informed by therapeutic and meditative practices that can be effective in helping people change their mindsets.

I agree that what she attributes to Boaler and Dweck is unlikely to work for a lot of students and, in fact, to drive them further away from self-reflection and engagement. I’m reminded of the students I had at that alternative school I mentioned previously here when I put the well-known poster of Einstein on my wall. He says, “Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.” I took that to be motivating, saying that even brilliant physicists and mathematicians hit walls and have to struggle to understand the problems they’re working on (interestingly, when I just searched for the exact quotation, I found pages where people come up with many interpretations that differ dramatically from mine and have Einstein saying many things that, from what I’ve read about him, I can’t picture him ever saying.) But my students took it as a put-down: from Einstein, from me, saying, in a nutshell, that they were stupid. I was really shocked by that viewpoint, as I was certain that Einstein wouldn’t ever intend anything of the sort. And I was certain that I didn’t. But thinking about that take in the context of what Elizabeth has written, it’s a perfectly CONSISTENT misinterpretation, and of course what matters is what they perceived, not what I (or Albert) intended.

I wonder a couple of things: has anyone tried to communicate Elizabeth’s criticism to Boaler or Dweck. If so, what was the reaction? And in keeping with this notion I’ve had for the last decade or so about math teaching – everything we figure out about student difficulties with mathematical learning and our teaching thereof has a dual in the difficulties teachers have teaching mathematics and efforts on the part of teacher educators and professional developers to reach teachers about that area of struggle – so what is the dual here for those of us who want to help teachers be more adept at helping their students with fixed v. growth mindsets?

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