End of Term Reflections

Phew…exams given…check…exams graded…check…comments written…check…kids on bus…check.  Now I can relax.  Oh wait, don’t I leave tomorrow to drive to my sister’s for Thanksgiving?

Such is the life of a teacher, no?  Just when you think you are on “vacation” there’s always something else to do.  I had an exam on Saturday then worked the rest of Saturday and Sunday finishing up that grading and writing my comments that were due this morning at 9 am.  But wait, I told some people I would write a blogpost about what my classroom is like, so I really wanted to do that too.  That’s OK though, I think it’s important for me to reflect back on this fall term – what worked and what didn’t for my classes.

I have three sections of geometry this year that I teach with PBL and a calculus class that I would say is something of a hybrid because we do have a textbook (as an AP class I needed to do what the other teachers were doing), but I do many problems throughout the lessons.

In my geometry classes, the student have iPads on which they have GeoGebra, Desmos and Notability where they have a pdf of their text (the problems we use) and where they do all of their homework digitally.  My class period for that course alternate between small group discussions in the Innovation Classroom in the library on Mondays and Thursdays and whole class discussions with student presentations of partial solutions (a la Jo Boaler or Harkness) on Tuesdays and Fridays. (We meet four times a week 3 45-minute periods and 1 70-minute period.)  Because my curriculum is a whole-curriculum PBL model, we spend most of the time discussing the attempts that the students made at the problems from the night before.  However, in class the discussion centers around seeing what the prior knowledge was that the presenter brought to the problem and making sure they understood what the question was asking.

classroom-shot1

Whole Class Discussion in regular classroom

 

geom-class-2

Small Group Discussions in Innovation Lab

If this didn’t happen we end up hearing from others that can add to the discussion by asking clarifying questions or connecting the question to another problem we have done (see Student Analysis of Contribution sheet).

One of the things that I had noticed this fall in the whole class discussion was that the students were focusing more on if the student doing the presentation was right immediately as opposed to the quality or attributes of the solution method.  There was little curiosity about how they arrived at their solution, the process of problem solving or the process of using their prior knowledge.  Unfortunately, it took me a while to figure this pattern out and I felt that it had also weeded itself into the small group discussion as well.

One day in the small group discussions, it became clear to me that the students were just looking for the one student who had the “right” answer and they thought they were “done” with the question.  This spurred a huge conversation about what they were supposed to be doing in the conversation as a whole.  I felt totally irresponsible in my teaching and that I had not done a good enough job in describing to them the types of conversations they were supposed to be having.

This raised so many questions for me:

  1. How did I fail to communicate what the objectives of discussing the problems was to the students?
  2. Why is this class so different from classes in the past (even my current period 7 class)?
  3. How can I change this now at this point in the year?
  4. How can I stress the importance of valuing the multiple perspectives again when they didn’t hear it the first time?

In my experience, sometimes when students are moving forward with the fixed mindset of getting to the right answer and moving on, it is very difficult to change that to a more inquiry-valued mindset that allows them to see how understanding a problem or method from a different view (graphical vs algebraic for example) will actually be helpful for them.

My plan right now is to start the winter term with an interesting problem next Tuesday.

“A circular table is pushed into the corner of the room so that it touches both walls. A mark is made on the table that is exactly 18 inches from one wall and 25 inches from the other.  What is the radius of the table?”

table-picture-problem

I have done this problem for many years with students and I have found the it works best when they are in groups.  I usually give them the whole period to discuss it and I also give them this Problem Solving Framework that I adapted from Robert Kaplinsky’s wonderful one from his website.  I am hoping to have a discussion before they do this problem about listening to each other’s ideas in order to maximize their productivity time in class together.  We’ll see how it goes.

To Hillary, With Gratitude

This morning as I woke up and found out about the results of last night’s election I was at first filled with despair and finally got myself somewhat out of that funk.  Then I thought about what Hillary Clinton must be feeling – she must be exhausted of course.  What did it take to put all of that energy into this campaign?  And those years of service to this country? And to put up with her husband? And the criticism?  This is not to say she didn’t make mistakes in the public eye of course.  I’m not saying I didn’t disagree with some of her stances, but I just want to look at it from the female perspective.  What I want to say to Hillary right now is thank you.  Thank you for being the first woman to have to go through the ordeal of running for president and dealing with all of the mess that goes with that.  I can’t imagine what that was like.

I have to say that in my career I know what it’s like to be one of two women in a meeting room and have to work extra hard to get a group to listen to your point.  Or perhaps to couch what you want to say in terms that the men will want to hear until they come over to your side in order to get them to vote your way on a certain agenda item or thinking twice about what I wore so as not to get judged.  The diplomatic skills that are acquired in just being a woman in an administrative position are invaluable because of the ways in which you know you need to listen and be heard. Being a woman in mathematics, the message is usually clear at national meetings when the majority of conference-goers are female classroom educators and the presenters are more often male speakers who are not currently classroom teachers.  In my graduate school education in mathematics I had one female professor and I was the only female in the Masters program.  You learn to “blend in” by speaking like them, working like them and going about your business like them.

I wonder if there isn’t a little part of Hillary that this morning just said “Phew, no more of that faking it.”  She was tired of being the male-culture-created part of herself that she had to be in order to run for president.  A few female heads of school that I have spoken with have said that in order to lead, many women are expected to downplay their feminine qualities – to not cry or be emotional, to be sure they are surrounded by male advisors so no one can say you made mistakes because you “are a woman.”  Spending so much time worrying about balancing speaking your mind with being nice to everyone so you are not labeled “bitchy” gets really tiresome.

What this election taught me overall is that misogyny is alive and well in the U.S. (not that Hillary needed to learn that) even more than racism.  My guess at this point is that we will elect a gay man in the future before we elect a woman but either way, I am grateful for Hillary and all she has done to pave the way for each other woman who comes next.  I read that Kamala Harris (CA) was the second black woman to be elected to the Senate, Ilhan Omar (MN) was the first Somali-American woman elected to Congress and Catherine Cortez Masto (NV) was the first Latina Senator to be elected.

I’d like to think that Hillary is waking up today really looking forward to spending some time as a grandmother, writing a book and working on the next great way to help kids, health care reform and education.  Sure that’s just me being idealistic, but as a woman, I would like to think that’s what I would do – well, after crying after losing for a little while.

Modeling with Soap Bubbles

I am so very lucky to have a guest teacher with me this year at my school.  Maria Hernandez (from the North Carolina School of Science and Math) is probably one of the most energetic and knowledgeable teachers, speakers and mathematicians you could ever find – and we got her for the whole year!  We are so excited.  I am working with her and she is so much fun to work with.  I have been teaching calculus with PBL for almost 20 years now and thought I had all the fun I could but no!  Maria is bringing modeling into my curriculum and I’m enjoying every minute of it.

As we started teaching optimization this week, Maria had this wonderful idea that she had done before where we want to find the shortest path that connects four houses.

picture-of-houses

I let the kids play with this for about 10 minutes and then did this wonderful demonstration with some liquid soap bubbles and glycerin.  We had two pieces of plastic and four screws that represented the houses.  As the kids watched, I dipped the plastic frame into the liquid and voila-file_000

Right away the students saw what they were looking for in the shortest path.  Now they had to come up with the function and do some calculus. As they talked and worked in groups, It was clear that using a variable or one that would help them create the right function was not as easy as they thought.  However,  I was requiring them to write up what they were doing and find a solution so they were working hard.

file_000-1

We have been doing a lot of writing in Calculus this fall so far and they are getting used to being deliberate about their words and articulating their ideas in mathematical ways.

Here is the outline of the work they did in class: Shortest Path Lab

and here is the rubric that I will be using to grade it.

rubric-for-lab-3-2

The engagement of students and the buzz of the classroom was enough to let me know that this type of problem was interesting enough to them – more than the traditional “fold up the sides of the box.”  The experience they had in conjecturing, viewing, writing the algebra and solving with calculus was a true modeling experience.

If you decide to do this problem or have done something like it before, please share – I’d love to do more like this.  I am very lucky to have a live-in PD person with me this year and am grateful every day for Maria!

 

Need Some Help Looking Forward

So I’m trying to figure out how to reach more people and thinking about the future of my professional development plans with PBL for all levels of teachers.  I’ve gotten some great feedback from people about the PBL Math Summit so far (from the two years we’ve had it) and I have some ideas about how to create some better online resources too.  If you have the time, and are interested in helping me out, would you please fill out this short survey about PD Needs for PBL Math Professional Development.  Also, tell others who could give me insights too.  Thanks so much for reading my blog and for also being inspired to be interested in PBL math teaching!

 

A Math Girl’s Story or the Introduction to My Dissertation

I am not really a negative blogger but I do have to say how tired I am of research reports that over and over again talk about the way we are not doing enough to support girls in math education (or other underrepresented populations of students).  There is enough evidence now from many research reports (NCTM, 2016, Why so few? AAUW, 2010, Riegle-Crumb, et al, 2012 I could go on…) that show that there is little difference in math ability by gender and that the reasons that girls and women choose to leave STEM fields are culturally related.  And yet, we still need a white male to make statements like:

“I believe that this issue of women’s confidence is cultural, not biological. It fits in with all we know about stereotype threat. When the message is that women are not expected to do as well as men in mathematics, negative signals loom very large. Calculus—as taught in most of our colleges and universities—is filled with negative signals.”

  • David Bressoud, MAA Blogpost, Launchings, October 1, 2016

Now, I don’t know Mr. Bressoud and perhaps this most recent research study really pushed him over the edge to being a believer, so no offense meant.  But I’ve just had enough of it.  My life experience had been based on all of this and it’s enough for me.

We need to do more to change the way math is taught in the U.S. so that more girls (and other underrepresented students) feel connected and desire learning, feel like they belong and their ideas and voices are valued within the context of mathematics and the community of mathematics learning – at the secondary level and the college level. Period.

Here is the introduction to my dissertation, “Dismantling the Birdcage:  Adolescent Girls’ Attitudes towards Learning Mathematics with a Relational Pedagogy in a Problem-Based Environment” (2013) (don’t feel the need to read the whole thing).

“If you look very closely at just one wire in the cage, you cannot see the other wires…You could look one wire up and down the length of it, and be unable to see why a bird would not just fly around the wire any time it wanted go somewhere…There is no physical property of any one wire…that will reveal how a bird could be inhibited or harmed by it except in the most accidental way.  It is only when you step back, stop looking at the wires one by one and take a macroscopic view of the whole cage, that you can see why the bird does not go anywhere; and then you will see it in a moment.  It is perfectly obvious that the bird is surrounded by a network of systematically related barriers, no one of which would be the least hindrance to its flight but which by their relations to each other, are as confining as the solid walls of a dungeon”. (p.5)

-Marilyn Frye, Oppression, in The Politics of Reality (1983)

I will begin with a story.  It is the story of a young girl excited and interested in learning and doing in all aspects of her elementary education.  Luckily, her parents were always encouraging and supportive of her learning goals and her initial schooling included “enrichment” class for which she was chosen to receive out-of-class group instruction in advanced topics – including mathematics and science.  The girl was confident, motivated and eager to move forward in her exploration of new topics and share these ideas with her friends and family.  As middle school approached, it became clearer to the girl that categorizing students by ability became more important and she realized that her work and grades in her classes, as opposed to her interest in mathematics, would begin to determine her path through her education.  The pressure of this realization, and possibly other determinants, affected her performance and she was placed in a pre-algebra course in the eighth grade, which she knew, even then, would set her on a trajectory that somehow indicated less success.

However, the following year, the girl’s work in algebra was so successful that her teacher that year recommended that this adolescent girl now double-up in her mathematics courses and take geometry and a second year algebra course concurrently. Reinvigorated and more confident in her abilities, she regained her momentum and faith in herself as a mathematics student, although the fun with her peers and connections with the teacher from her “enrichment” classes were now a thing of the past.  Mathematics seemed made up of a set of disjointed courses that needed to be passed sequentially in order to fulfill the requirements for graduation.

Finally, the ultimate course in mathematics came during her senior year of high school where she would be able to truly show that she had made it to the top – Advanced Placement Calculus.  However, difficulties arose when little interaction occurred between the teacher and the students surrounding mathematics in the classroom.  Utilizing a textbook that was published almost 25 years earlier, the now young woman felt isolated and alone in a class where asking questions seemed to signify weakness and demanding an explanation also showed that a student was incompetent. Students who could easily and quickly replicate the mathematical exercises performed by the teacher were praised and favored whereas those with difficulties were dismissed and even asked not to take the Advanced Placement exam at the end of the year.  Sadly, our young lady was among those disinvited to be part of the elite exam takers.  This was a turning point in her desire to continue with mathematics as an intellectual endeavor.  She vowed to never take a math class again and moved on to college to pursue music as a major field of study.

On arriving at her chosen college in the fall, the young woman was required to take a mathematics placement exam in order to fulfill her natural science portfolio requirement.  Begrudgingly, she took the short test and a few days later she was told she could register for Calculus III.  How was this possible?  She did not even take the AP exam in May and barely passed the course in high school.  Would this roller coaster ride of messages of encouragement and discouragement ever end?  Who did they think were, telling her to move into Calculus III?  She would show them and just retake Calculus I and be done with it – get that natural science requirement out of the way and move onto much more interesting and meaningful courses so that she could leave mathematics in the dust.

However, something surprising happened in that basic Calculus I course that fall.  The young woman had an interested professor that saw her potential and talents.  The professor engaged her in conversation about mathematical justification and questioning. Citing the young woman’s exceptional ability in Calculus, the professor questioned why she was even in the class.  At the end of the term, the professor had convinced the young woman to continue on and even elect to take a computer programming course to see if she liked it. “Why not?” the professor said, “and it’s required just in case you decide to be a math major someday.”  The young woman laughed out loud.

One by one mathematics courses came and went.  The smaller seminar style of the upper level mathematics electives worked extremely well for her learning style.  Although she was often one of two, or the only female in the course, the girl believed that she was supported and encouraged by the professors she met.  There was a community of mathematicians who allowed her to grow and develop her skills, as opposed to suppress and discourage them.  Abstract courses like Linear Algebra, Number Theory and Topology connected much of the mathematics that for too long seemed discrete and disconnected. After serving as a teaching assistant for much of the department and receiving honors on her senior thesis, the girl was encouraged to apply to graduate programs.

In graduate school, once again the girl found isolation among a male-dominated community of academics and senior mathematics professors seemed to look differently at her, wondering why she was not in the Master of Arts in Teaching program with the women.  After two years of struggling with the environment, but quite enjoying and thriving in the teaching classroom, the young woman realized her gift and decided to find a way to make her journey complete.  Combining her love of mathematics and her talents for teaching was the way to make a life worth living while also bringing the consistent support and encouragement to students that she so greatly needed all those years.  Although it took her 20 years to realize this direction, ultimately it became a passion and lifelong commitment.

At this point in stories like these it is generally tradition to state “The End.”  However, at this point, I would change the phrase and say “The Beginning.”  Yes, it was just this story that has led me to this place and passion in my research for gender equity in mathematics education.  Now, 22 years into my teaching career I can look back and see how it began with this personal experience, but when I started my teaching and my doctoral program, I am not sure I was as aware of the implications my own story had for my research and teaching interests.  As my career brought me in and out of single-sex schools, my research interests led me towards a relational pedagogy.  As individual students that I crossed paths with shared their own hopes and fears about their relationship with mathematics, it began to be clear to me that it was more than a coincidence that my dissertation research, and perhaps my life’s work, would be centered around finding ways to improve the education of marginalized students in mathematics education, if possible.

And so it was the beginning – the beginning of a long journey with this question about how it might happen – how to improve the learning of students who feel marginalized in the world of mathematics as I once did.  But I would begin with one group of marginalized students in the mathematics classroom to whom I could relate most readily; adolescent girls.

What is “Low Ability” Anyway? Comparing a Point to “Room”

One of my big “beefs” at my school is the fact that we have three levels of tracking – count ’em, three.  There’s the honors track, that of course at a college prep school, most kids think they belong in.  There’s the regular track, that which is still pretty quick and difficult, and there’s the track that the kids who are sometimes, I would say, just not very motivated to learn math, or have less interest in math, or maybe come from a school with a less rigorous math program, are placed in.  These are the kids who probably all their lives have been told they are not “math people” and have been pigeon-holed as an “artist” or “writer” so they won’t actually need math when they get older.  This really, really irks me.  But I do it – I go along with a system that has been in place way before I got here.  I’m only one person – even though I cite Jo Boaler’s list of research showing why “tracking” in general is just a bad idea and hurtful – I know I can’t win.

Anyway, I really shouldn’t complain because the department has let me do my thing with the geometry curriculum and I have written a PBL curriculum for the three levels.  In my 201 book, I have created scaffolded problems that I think work really well with these “low-abiity” kids and often challenge them enough to make them realize how much ability they actually have.  We just started talking about dimension and we watch these clips from Flatland: The Movie, where Arthur T. Square meets the King of Pointland and then meets the King of Lineland.

We had a great conversation about why the King of Pointland keeps saying “Hello Me, Hello Me” and can’t really understand why there’s anyone else there.  We talked about why the King of Lineland doesn’t understand where the Square is because he only understands the directions of left and right.  One of the kids goes, “Is this kind of like what happened in the movie Interstellar? I think he went through a black hole and just appeared in the future or something.” Now, I hadn’t seen that movie but then another kid said, “Well, I’m not sure it was like that.” But then one of the other students says, “No, the King of Pointland is kind of like the kid in the movie Room.  Did you see that movie?”  I nodded in understanding and so did many of the others in class. The student went on, “In Room, the little boy grew up thinking that “Room” was his whole universe so that was all he understood, and that’s why the King of Pointland seems so nuts. That point with no dimensions is all he can understand – there’s no one else in the world.”  I was so blown away by that analogy.  She really had an understanding of the idea of the limitations of being alone in the universe of a point. I had never had a kid in a “regular” or “honors” class make a connection like that – but then again, Room just came out!

Repost: Always Striving for the Perfect Pose

Back in 2010, I wrote an blogpost comparing teaching with PBL to doing yoga. Since I have been doing Bikram Yoga for almost a year now and still can’t do “standing head to knee pose” *at all* – I thought I would repost this one just to give myself some perspective, and possibly many of you out there who might need a little encouragement at this beginning of the year time. I know that every year when students begin a year in a PBL math class the obstacles return. Parents are questioning “why isn’t the teacher teaching?” Students are questioning “why is my homework taking so long?” Teachers new to the practice are questioning “When is this going to get easier?” and “why aren’t they seeing why this is good for them like I do?” The best thing to remember is that it is a process and to understand how truly different and hard it is for students who are used to a very traditional way of learning mathematics. Give them time, have patience for them and yourself and most of all reiterate all of what you value in their work – making mistakes, taking risks, their ideas (good and bad) and be true to the pedagogy.

Here’s the original blogpost I wrote:

I don’t think my professor, Carol Rodgers, would mind me borrowing her yoga metaphor and adapting it to PBL. I use it often when talking to teachers who are nervous about falling short of their ideal classroom situation or teaching behaviors. I think this can happen often, especially when learning best practices for a new technique like facilitating PBL. There are so many things to remember to try to practice at your best. Be cognizant of how much time you are talking, try to scaffold instead of tell, encourage student to student interaction, turn the questions back onto the students, etc. It really can be a bit overwhelming to expect yourself to live up to the ideal PBL facilitator.

However, it is at these times that I turn to Carol’s yoga metaphor. She says that in the practice of yoga there are all of these ideal poses that you are supposed to be able to attain. You strive to get your arms, legs and back in just the right position, just the right breathing rhythm, just the right posture. But in reality, that’s what you’re really doing – just trying. The ideal is this goal that you’re aiming for. Just like our ideal classroom. I go in everyday with the picture in my head of what I would want to happen – have the students construct the knowledge as a social community without hierarchy in the authority where everyone’s voice is heard. Does that happen for me every day? Heck no. I move the conversation in that direction, I do everything in my power for that to happen, but sometimes those poses just don’t come. Maybe I just wasn’t flexible enough that day, or maybe the students weren’t flexible enough, maybe we didn’t warm up enough, or the breathing wasn’t right. It just wasn’t meant to be. I have exercises to help me attain the goal and I get closer with experience. That’s all I can hope for.

So I tell my colleagues who are just starting out – give yourself a break, be happy for the days you do a nearly perfect downward facing dog, but be kind to yourself on the days when you just fall on your butt from tree pose. We are all just trying to reach that ideal, and we keep it in mind all the time.

Being Imaginative in Problem Solving

Sometimes my ignorance with respect to Twitter just floors me. Today alone I made two huge faux pas (is that plural?) with two people that I really respect and just made a fool out of myself – typos, misinterpretations, and misunderstandings abound in my tweets. But I have to say I press on – because I have found so much that informs my teaching and learning that I can handle the fool-making and embarrassment.

So here’s one thing that I did a few weeks ago – someone tweeted about this great article that I, of course, then went and read, took a picture of the great diagram in the article – but forgot to “like” or “favorite” or whatever it’s called now. So now I can’t give credit to whomever brought me to this wonderful enlightenment about which I will now write. So if you are reading, sir/madam, who tweeted this article, please forgive me.

I read this short blogpost entitled “Brennan’s Hierarchy of Imagination” and immediately made the connection to PBL.


The author, John Maeda, wrote about a conversation he had with Patti Brennan about Maslow’s famous Hierarchy of Needs of students in their learning. These two were talking about the fact that teaching creativity is really hard and Patti Brennan was thinking that it was a bit easier to teach someone to use their imagination. She was talking about this in the context of the health care field – trying to help people empower themselves to help themselves.

Of course, the first thing I thought of when I saw this pyramid was problem solving. I thought this was brilliant! The foundational, lower level of reflex or instinct is analogous to doing problems that you have seen before. Students love this instinct – the idea that if you can do a problem that someone has shown you how to do, that you are problem solving, – it gives them a reaction of completing something, some kind of satisfaction.

The next level which is appropriately called problem-solving is when you are actually solving a problem that has occurred but is constrained and you are executing skills. I love this. It still takes some talent and analysis, but you are still just reacting to a given situation. Perhaps putting together two different methods that someone showed you and seeing what happens?

The third level that she calls creativity is the first step to unique ideas and methods. The first attempt at doing something in a different way – saying what if we tried this? Has anyone every done this before? Why not? It’s still bound by the reality that we experience, but seeks to move past the knowledge that we have.

And finally imagination is what I think happens when my 4-year-old niece explains how the clouds got up in the sky because the stars moved so fast pieces came off and clumped together, or when a student can’t figure out if there are more real numbers between 0 and 1 as there are integers and they try to describe the size of those sets to me with things they imagine.

If I’m lucky, I’d say some of the kids in my classes get to creativity – in fact I think that’s been my goal as of late. To get them at least to experience it with some projects, assignments and good problems. To get them to realize that mathematics is more than just a reflex or even just reiterating a process.

Hopefully, this coming year the number of kids who will get to that third level will increase, but who knows? I do love this framework because at least I know I don’t want them stuck on that bottom level for level for long.

Journals: Paper vs Digital: The Pros and Cons

I was totally honored the other day when I saw some tweets from TMC16 from @0mod3 and @Borschtwithanna

 

And yes it’s true, I’ve been writing and practicing the use of metacognitive journaling for very long time – probably since 1996 ever since I read Joan Countryman’s book about mathematical journaling and heard about it in many workshops that summer.  I wrote a rubric (make sure you scroll to the 3rd page) while I was at the Klingenstein Summer Institute for New Teachers (that’s how long ago it was) and since then I’ve been refining that rubric based on feedback from students and teachers. A few years ago, I finally refined a document called How to Keep a Journal for Math Class to a degree that I really like it now.  However, please know that lots of math teachers do journaling differently and without the metacognitive twist. I do believe that metacognitive writing is essential to the PBL classroom (read more here)

So this morning, I was asked this question on twitter

 

Which is something that many people often ask so I thought I’d respond with a more in-depth answer.

Here are the pros, I’ve found over the years of having students journal digitally:

Speed/complexity: Students are used to typing, using spell-check, inserting pictures, graphics and naturally including documents, links and thinking in the complex way that digital media allows them to.  It allows their journal to be more rich in content and sometimes connect problems to each other if their journal is say on a google doc that can connect to other html docs.  If they create, for example, iBooks or Explain Everything videos, there is even a lot more richness that can be embedded in the file as well – their creativity is endless.

Grading/Feedback: I found grading in Notability or on Google docs or some other digital platform really nice that allowed you to add comments with a click or audio extremely easy and quick.  I did not receive feedback from the students very often about how the feedback helped them though.  If you use an LMS like Canvas that integrates a rubric or integrates connection to Google it’s even nicer because you can have those grades go right from your assignment book to your gradebook.

I love having kids use digital platforms for writing/creating in mathematics when it is for a project or big problem that I want them to include many pieces of evidence, graphs, geogebra files and put it together nicely in a presentation or portfolio.  Not necessarily for their biweekly journals. Some guys who make use of digital journals in interesting ways are @GibsonEdu and @FrasiermathPBL at the Khabele School in Austin TX.

Here are the cons, in my mind of using digital journals: (which might be the “pros” of paper journals) – which is the side I have come down on.

the “real” writing factor: there is some research about the actual physical process of writing and the time it takes for kids to process their thoughts.  I do believe that when i want kids to be metacognitive about their learning and also want them to be thoughtful and take the time think about their initial error, think about what happened in class discussion to clear up their misunderstanding and also then what new understanding they came to.  That’s a lot of thinking. So I want them to take the time to write all that down.  Sometimes typing (like what I’m doing right now!) is a fast process and I’m not sure I do my best writing this way.

practice in hand-writing problem solving: this is re-enacting doing homework and sitting for assessments (in my class at least) and I want them to do this more regularly.  If in your class kids take assessments digitally or do homework nightly digitally then maybe they should do their journal digitally as well. This also give me practice in reading their handwriting, getting to hear their voice through their handwriting and seeing what it looks like on a regular basis.  In a time crunch on an assessment it honestly helps me know what they are thinking.

Conversational Feedback: I feel that when I hand write my feedback to them I can draw a smilely face or arrows or circle something that I want to emphasize more easily than when it is on something digitally (this is also true in a digital ink program – so that is something to consider, like Notability for example). I give feedback (see some journal examples on my blog) that is very specific about their writing and want the to improve not only in the math aspect of their writing but in how they are looking at their learning.  I want them to respond and I want to respond in the hope that we are starting a mathematical conversation about the problem.  I have received more questions about the feedback in the paper journals (like “what did you mean by this?”) than on the electronic feedback – not sure why.

Portability: I find that small composition graph paper notebook is extremely portable and easy for me to carry home to grade.  The students bring them to their assessments and there is nothing else in the notebook (no homework at all and no access to the internet) so I am not worried about academic honestly.

There are probably more but this is it in a nutshell – please add your comments below or tweet me to let me know your thoughts!