Deep Understanding

I currently have the pleasure of taking a course with Tina Grotzer, a cognitive scientist and educator at the Harvard Graduate School of Education.  One of the assigned readings was a piece that she wrote on deep understanding back in the nineties.  Although much time has passed since then, it is still a concept that is met with much resistance in some respects.

For example, in 2010, Alberta introduced a new math curriculum.  Seven years later, parent groups and a political party still take issue with many aspects of the curriculum and put out a steady call to go ‘back to the basics’. (As a side note, this is a concept that always intrigues me in the education realm.  We would be quite distraught if our medical professionals ‘did things the way they always did’ rather than have them advance their practices as knowledge and technology advances.  Why do some people hold opposite expectations for education and not want practices in this field to advance as our knowledge about teaching and learning advances?)  One of the components that was a source of frustration in the 2010 curriculum was that it reduced the number of concepts that were required to be taught, and the assumption was that this would lead to less learning.  In her article, “Understanding Counts!: Teaching for Depth in Math and Science”, Tina explains why this is not true.  She builds a strong argument for deep learning and explains why teaching fewer concepts with greater depth is more beneficial than teaching many concepts superficially.   I believe that this is the intent of Alberta’s 201 0 math curriculum.  Yes, there were problems (particularly that the roll-out of the curriculum was poorly done and that teachers, who themselves lacked deep understanding because they had been taught superficially, were therefore ill-equipped to foster deep understanding in their students), but the curriculum’s intent at deepening students’ understanding of math is not one of those problems.

Tina has graciously allowed me to post the pdf of her booklet.  Take ten minutes to read it through and see why deep understanding matters!

Grotzer: Understanding Counts!: Teaching for Depth in Math and Science (shared with permission from Tina Grotzer)


Research-based vs. Preference-driven Teaching

I recently had a Twitter conversation with a researcher from the Netherlands who was reiterating the importance of using research to guide practice.  He pointed me to this journal article from the mid-90s, which raises concern over educators who have a tendency to use preference to guide their practice, even if their preferences defy research.  The paper identifies this as both (understandably) problematic and (surprisingly?) common.

This brings to mind a relatively recent article from the Edmonton Journal.  Ever since this debacle a few years ago, Edmonton media does a great job of portraying this part of the country as a hotspot of poor assessment practices.  I hope that there is a disconnect between the reports of the media and the actual practice being employed in classrooms there, but their local media sure seem to have a love affair with promoting practice that is based primarily on preference and that laughs in the face of research.  It tends to paint such practice as bold, brave, and desirable.  Equally as concerning are the public comments which further support such preference-driven practice while bashing research.  I find this “if it feels good it must be good” approach to be troubling.  Why does statistical data not have a more prominent role in determining what happens in our schools?  Why is so much left to preference?  (As an aside, I do realize that statistical data can be taken to the extreme and used in places where it doesn’t apply.  Particularly when dealing with people, not everyone fits into typical statistics and I’m aware of that.  I’m looking forward to reading this book for more on that topic).

It’s tough to stay on top of the research.  There is so much to know and limited time to learn.  Educators have a never-ending stream of tasks to be done in any given day, and sifting through journals to find information pertinent to our individual areas of desired growth is a nice wish but not a reality for any educators I’ve ever met.  Not to mention that for many (most?) people, sifting through journal articles doesn’t make it into the “ways I enjoy spending my time” category.  Even if it was something a particular teacher enjoyed, Hardiman et al. point out that “teachers do not typically possess the background knowledge that is necessary to parse research articles and apply findings in appropriate contexts”(p.136). And yet, despite the difficulties that are inherent in being wise consumers of research who use research to inform and drive our practice, I firmly believe that we can do more; we can do better.  There simply must be a way.

Twitter has become such a tool for me, (read more about how I use Twitter for my professional development here), but it has its limitations too.  Twitter can become a venue for groupthink or a means of propagating  preference-based practice if opinions are left unchecked.  With the right connections and knowledge of where to look it can, thankfully, also be a sharing space for research.  Unfortunately the latter is more difficult to find.  There are opinions aplenty but sharing of research among educators seems to be a much less common occurrence.

I’m not sure exactly what this means for educators in general, but I do have some ideas of what I’d like it to mean for me.  I’d like research to take a more dominant role in my practice.  Not the “I think I read it in a book somewhere so I’ll defend my practice by prefacing my conversation with generic ‘research says'”kind of research (oh, I’m guilty of using that tactic!), but the more authentic “these researchers in this study in this year found these findings and this is the conclusion that I’m drawing from that” kind of research.

Don’t get me wrong.  I don’t think that’s the answer for everyone.  I think that most of us, certainly, could benefit from having an increased general awareness of education-related research data and we could be more intentional in sharing that data and in using that data to drive our practice, but I think there’s room for variation in specifically how that looks from one person to the next.  Could we each agree, however, to be a little more intentional in reading, finding, and sharing data that can inform our practice?  I’m willing to venture a guess that the results of this would be noteworthy.  After all, ‘research says’.


Photo source


Two Common Misuses of Rubrics

Rubrics are not a new concept in education.  Their benefits have been touted for by many and a quick Internet search reveals large amounts of literature on the topic for anyone interested in learning more.  Likewise, one does not have to look far to find examples of rubrics or websites that will create rubrics.  Given this familiarity, it seems a bit surprising that they are still used incorrectly.  While the benefits of rubrics are significant (see information under “Why use instructional rubrics” here), these benefits are not harnessed when they are used incorrectly.

There are two major misuses of rubrics that I see in action on a regular basis and I would like to take a moment to address them:

  1. Rubrics are not assessment checklists.

Itemized lists with point values, like this, are not rubrics:

non rubric


One of the dominant benefits of rubrics is that it forces the teacher to have a very clear understanding of exactly what the student did well and what they would need to do to improve and this information is communicated to the student.  If a rubric is used well, the student will have a very clear understanding of what they need to do to improve in each category and will not have any need to ask the infamous, “why did I get this mark” question for any item on the rubric.

Rubrics, then, should have a descriptor for each level of achievement.  On the above example, if neatness is a category on a five point scale (assessing neatness to determine if students know a social studies concept is a whole other topic for discussion), students should have a clear explanation of what category five neatness looks like, what category four neatness looks like, and so on.

In her article, “Using Rubrics to Promote Thinking and Learning”, Heidi Goodrich Andrade provides the following example of a rubric:rubric example

In contrast to the non-example rubric, Andrade’s rubric has clear explanations for each level of achievement.  There is still some degree of subjectivity within the descriptors (as will typically be the case), but it is far more clear how each level of achievement is attained.  Thus, the student knows what must be done to arrive at the next level of achievement for each category and can use this to inform his/her work from this point on.  This is how rubrics become tools for learning.

     2.  Rubric grades and descriptors need to match

Rubrics are often written into a scale of four or five levels of achievement.  Mathematically speaking, five levels of achievement would mean that each category on the rubric is calculated out of five.  If percentage grades are given (another assessment issue that is yet another topic that needs to be addressed), that would mean that the categories compute to the following percentages:

  • 100% (5/5)
  • 80% (4/5)
  • 60% (3/5)
  • 40% (2/5)
  • 20% (1/5)

The problem with this is that the descriptors for the rubric can often be generalized into something like this:

  • 5/5 – great work.  No improvement needed.
  • 4/5 – really good work.  Just a slight tweak needed somewhere.
  • 3/5 – pretty good work.  A bit of a misunderstanding or oversight is present.
  • 2/5 – beginner stages.  On the right track, but at the very beginning of the road.
  • 1/5 – not there yet.  Shows significant lack of understanding, or no evidence of understanding, or this component of the assignment was not included in the project.

The problem here is the disconnect between the descriptor and the grade.  If a 2/5 reveals that a student is in the beginning stages, can we confidently assign a failing grade of 40%?  It seems more logical to assign a grade that is at the lower end of the spectrum of a passing grade.

Just because something can be computed mathematically, does not mean that it should.

The lesson here is that, when designing a rubric, the numeric grades sometimes need to be skewed.  Again, if reporting is done in percentages, the teacher needs to look at the descriptors of the rubric and determine an appropriate percentage equivalent that matches the descriptor, rather than assigning a percentage based on a mathematical computation.  For example, a 90% might be more appropriate for a 4/5 on a rubric, rather than the computational score of 80%.  Just because something can be computed mathematically, does not mean that it should.  When using a rubric, it is often necessary to give each level of achievement a grade that is not mathematically derived.

As a side note, there really is no need to put an actual numeric score on a rubric.  In fact, many would argue that that actually reduces the instructional component of a rubric.  When a numeric grade is written on a rubric, students tend to look at the numeric grade and derive their sense of achievement from that, rather than having to read the descriptors to learn how they did and what they could do to improve.  Putting a word descriptor for each level of achievement (rather than a 5-4-3-2-1) will be more informative for students and parents and will allow the teacher to assign a value for each level of achievement that better matches the descriptors than a grade out of five.


Rubrics can be incredibly effective tools to use to assess students, to teach them, and to show them where they are at and where they are heading, but it is necessary to ensure that our rubrics clearly communicate each level of achievement and are calculated in a manner that is fair and accurate.



What Can Neuroscience Teach Teachers about ‘Aha!’ Moments?

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I love it when I can read about research and immediately see some direct implications of that research in my teaching practice.

For the results to be legit, researchers must surrender control of the outcome.  Due to this, sometimes scientists devote a chunk of their life to a project that didn’t reveal what they thought it would, or didn’t reveal what seemed useful.  What a terribly frustrating thing, yet inherently necessary due to the very nature of research.

Gabrieli referred to such unusable research as “file drawer research”. Interestingly, he stated that there are issues with this.  No one wants to publicize research that they’ve done that didn’t work, or that didn’t cultivate useful data, yet if they did, it would contribute to the greater field of knowledge.  At the very least, it would enable others to ensure that they didn’t repeat the same research, but it also would contribute to the pool of studies.  If data reveals that ‘all studies showed X results’, but in reality there were studies that didn’t show those results but they weren’t published, then the full story is not being revealed.

But, I digress.  My point is that sometimes research doesn’t seem to work.  Other times, it generates data but it’s not immediately apparent how that data is useful.  Again, this makes sense given the nature of research.  In light of this, it feels like a treat when there is research done and shared that contains workable, useable data.  I enjoyed such a treat when I read this article about the ‘Aha!’ moments of insight, summarizing some of the work of cognitive neuroscientist John Kounios.  Here is some of the useable knowledge I pulled out of it:

  • Finding: prior to that moment of enlightenment, or sudden ‘knowing’, our brains have been processing the information but at a subconscious level. Thus, it feels like a sudden state of enlightenment but our brain has actually been thinking about it for a while.
    Application: that dreaded “blank stare” that students give when they have no idea what we’re talking about, does not necessarily mean that they are not taking in any of the explanation that is being given.  They might be processing on a subconscious level.  Persevere through those blank stares – they might just be the precursor to sudden insight.
  • Finding: a surge of brain activity happens immediately before sudden insight. One of the changes in the brain during this time is a sudden burst of alpha waves visible on EEGs.  This is interesting because alpha waves inhibit the visual system – the higher the amount of alpha waves, the more the visual system is inhibited.  It seems, from what Kounios shares, that the brain essentially dials down its use of visual stimulus to allow for greater use of other brain activity for that short moment of time.
    Application: teachers often struggle with the concept of ‘wait time’.  It can feel uncomfortable and unproductive to have moments of silence during conversation with a student.  Watching a student’s eye movements could help encourage effective use of wait time.  If a child is looking away, it’s probably a good idea to help with their brain’s attempt at reducing stimulus.  Stay quiet, let them think, and see if a moment of insight arises as a result.
  • Finding: Those who are prone to have moments of insight show different brain function (even when not having ‘Aha!’ moments) than those who have fewer such moments.  Kounios is working on developing “different type of thought exercises” that can be administered to further develop the areas of the brain that are activated for sudden insight, but even with his existing research, there are some implications for teaching.
    Application: Kounios himself gives some application here:
    – He speaks of the importance of having a positive mood. For more learning on developing this in the classroom, a great place to start is to read Carol Dweck’s work on growth mindset (#growthmindset on Twitter) or follow the culture of learning chat (#COLchat) on Monday evenings on Twitter.
    – He also speaks of the benefits of large rooms with high ceilings (most classrooms) or, more ideally – the outdoors.
  • Finding: ‘Aha!’ moments cause an emotional rush. It doesn’t matter if the outcome of the problem that was solved has a positive or negative connotation to it, simply solving a problem through sudden insight creates this rush.
    Application: This indicates the importance of working within a child’s zone of proximal development (if you’re not familiar with this concept, I highly recommend reading more on this important work by Vygotsky).  If we give students work that is consistently too difficult or too easy for them, they will not have opportunities for such sudden insights and that emotional rush of learning will not be something that is accessible to them.

Throughout the article, Kounios references his book eureka factorThe Eureka Factor” and explains that it contains much more information about his work (written in lay terms) and many more ideas for the practical applications of it.  The positive feedback loop of reward from sudden insight is something that I greatly value in my teaching – it’s a large piece of what makes the job both meaningful and rewarding.  If there is some way that I can further cultivate such moments in my classroom, I’m all for it.  I’m looking forward to ordering his book and learning more about this.

The Early Years: What I wish I had known.

I remember well my first few years of teaching – they were intense.  Over the years, I have concluded that there are a few lessons that I wish I had learned earlier in my teaching career:

Lesson 1:
I wish I would have known that I would feel like I had sold my soul to my new profession
To eat, breathe, and sleep ‘work’, yet still always feeling like you can hardly keep your head above water – this was my first year of teaching.  Social events were a distant memory, a balanced life a foreign concept, and stress an ever-present companion.  To add insult to injury, public perception of the job includes many who believe that teaching is a cushy job: a few hours of work each day and copious amounts of time off – and random people would cross my path and remind me of this.  Have they no idea?

And that I wasn’t alone in feeling overwhelmed
I worried that the extent to which I was overwhelmed and ridiculously busy with work meant that I was doing something grossly wrong, but what I was experiencing is often the norm for beginning teachers.

And that ‘overwhelmed’ would not forever be an inherent aspect of this career.
I had been told that the stress and time commitment would be greatly reduced as the years went on, but I doubted.  I wish I would have known with certainty that that was true.  It would get better – so much better.

Lesson 2:
I wish I would have known to tap into others as resources.
My third year of teaching saw me land a job at a huge school.  This school was the queen of collegiality and there I learned how to utilize my colleagues for the powerful resource that they were.  Beautiful, wonderful, time-saving, quality-enhancing things happened there.  They gifted me with binders of all of the materials that they possessed or had developed in years past.  Someone would do something new that worked well and would give their materials to the rest of us to add to our collections.  Someone else would try something new that ended up being terrible and would let the rest of us know so that we could avoid doing the same thing.  We would revamp tests and we would tweak each other’s work while giving feedback and encouragement.  We would share frustrations and joke together on the tough days to make them more bearable.  We journeyed the school year together, and it was wonderful and it was beautiful and somehow, suddenly, this whole teaching thing felt like it was becoming so much more manageable and so much more enjoyable.

Lesson 3:
I wish that I would have had access to the amazing network of teachers on Twitter.
My first year of teaching was in a tiny school.  We are talking three-teachers-kind-of-tiny.  The kind of collegiality described above just wasn’t a possibility.  I had so many questions, and wished I would have had more resources for finding the answers.  Twitter didn’t exist yet (even the Internet itself was still a novel concept) but it would have been the perfect tool for me if it did.  We are not all going to work in a huge school that loves to share resources and work as a team, but we can all access that same type of resource.  It’s all there – it’s online.  Twitter is an amazing meeting ground for teachers to empathize with each other, encourage one another, teach and mentor others, and to journey the road of teaching together.  It’s invaluable.  I hope new teachers know how to use it (more on that in a forthcoming blog post), and know that it’s wonderful, and know that it will remind them that they are not alone.

Lesson 4:
I wish I would have known more about balance.
I had no idea how to live a more balanced life those first few years of teaching.  I wish I would have known that things didn’t have to be perfect – that the students can still learn from less-than-perfect lessons.  I wish I would have lowered my expectations for myself a bit that first year – to have given myself a little more breathing space – and just focused on making it through.

Lesson 5:
I wish I would have known about teacher attrition rates.
Teacher attrition rates are quite high.  That means that many teachers leave the profession – particularly during their first few years.  I wish I would have known that.  I wish I would have known that simply making it through the first year alive was a huge accomplishment.  That might have helped me with lesson 4 – lowering my expectations for myself.

As much as I would have loved to have known these things when I began teaching, there was one lesson that I learned pretty much immediately.  It was this one lesson that enabled me to put one foot in front of another and make it through those first years, and it’s the same lesson that keeps me going today.

The Ultimate Lesson:
Teaching is worth the sacrifices, the stress, and the everything else.  It’s worth it.
It’s worth it – this teaching thing.  It really is.  It’s not a job for the faint of heart, it’s not a job for the lazy, and it’s not a job for people who just don’t feel it (this is one job that you have to love if you’re going to stick with it).  But if you love it and if you stick with it, you’ll reap the benefits, because it’s worth it.
It’s worth it to see the eyes of a child light up with the wonder of new knowledge,
To see a child who always thought “I can’t” learn “I can”,
And to hear a child pose a deeply reflective question about a topic that’s being discussed.
It’s worth it to see a child from a tough home situation come to school – his safe sanctuary.
It’s worth it to see a child with a learning disability learn how to compensate and discover that his perceived limits are less limiting than he realized.
It’s worth it to hear laughter bubble out of a room full of children,
To see the look of pride for a job well-done,
And to experience the development of a micro community that happens each year.
It’s worth it to watch a child with Autism be cheered on and supported by his peers,
To see the students stand up for what’s right and confront what’s wrong,
And to witness leaders emerge from the group.
It’s worth it to hear the students debate after class about a controversial topic that was discussed during class,
To push a child to work harder and do more and have him come back and thank you when he does,
And to see a child five years later and have him still express gratitude for ‘those lessons I learned about life’ while he was in your class.
It’s worth it.

I could go on.  The list is long and it certainly doesn’t end here, but I don’t want to spoil it for you.  Part of the joy of teaching is composing your own list of ‘worth it’ items.  It’s a list that will keep growing.  It’s a list that you’ll need to remember.  There will be hard days, and there will be harder days, and then there will be days when you feel like you can’t even go on.  Reflect on your ‘worth it’ items.  They’ll keep you going.

The first few years of teaching might not be inherently wonderful, but they will be filled with wonder.  Dwell there and know that it will become easier.  It will become less time consuming and overwhelming.  Know that you are not alone.  Any veteran teacher was once a beginning teacher.  We’ve all been there, and we’re here to help.  You’ll make it through.  The second year will be so much more manageable than the first, and the third much more than the second.  You’ve got this.  We’re cheering you on.  Your ‘worth it’ list is ready to be written.