Year: 2012 (page 4 of 14)

Update: This doesn’t work anymore. Instead, make a copy of this spreadsheet and then look at the associated script to see how it needs to be updated.

Our junior school is using Google forms as a sign-up system for our parents for co-curricular activities. This way we can automate the sign-up process, and use the data to generate our lists of students who are going to be in each club. Apparently quite a number of parents were not sure they had actually submitted their requests, and so our administrative staff asked if there was any way to send parents an email confirmation with the co-curricular choices they had made. Using this tutorial, I created an email confirmation script.

First step, make the form, something like below.

Next, navigate to the spreadsheet form, and under the tools menu choose the Script Manager, as shown below.

A dialog box will appear, and you will want to click on the New button at the bottom of the dialog bow, which will then lead to the following screen.

From here you will want to select "Blank project" although you can see that you have a number of other options to explore later, should you decide to write other Google Apps scripts.

I wrote this script, which you are welcome to use as the basis for your own email confirmation script.

/* START COPYING HERE */
function emailConfirmation(e) {
  var userEmail = e.values[2];
  var pickUp = e.values[5];
  var otherNotes = e.values[4];
  var class = e.values[6];
  var firstChoice = e.values[7];
  var secondChoiceOptions = e.values[8];
  var secondChoice = e.values[9];
  
  /**
   * Un-comment this to use it for debugging
   */
  //for (var i in e.values) {
  //  Logger.log("" + i + ":" + e.values[i]);
  //}
  
  
  MailApp.sendEmail(userEmail, 
                    "Clubs sign-up confirmation", 
                    "Thanks for signing up your child for a club. You have indicated the following:\n\n" +
                    "Pick up:\n" + pickUp + 
                    "\n\nOther notes:\n" + otherNotes + 
                    "\n\nClass:\n" + class +
                    "\n\nFirst choice:\n" + firstChoice + 
                    "\n\nSecond choice:\n" + secondChoice + 
                    "\n\nSecond choice option:\n" + secondChoiceOptions,
                    {name:"Stratford Hall clubs"});
}
/* STOP COPYING HERE */

So now what this script does is takes specific values entered into the form by the parent, and turns these into an email confirmation. Each value in the form is an item in the e.values array. The biggest stumbling block I had was figuring out which form values corresponded to which items in the original form, because as I quickly discovered, the position of the form item in the e.values array does not necessarily correspond to it’s position in the form. In the code above, I discovered that I could use the log to determine what each form value actually corresponded to. If you need to do this trouble-shooting, uncomment (remove the // from the code above) the section of the code as per the instructions in the code above.

You can then look at the logs (see above) after you have submitted a sample and use the output of the logs to determine which value of e.values corresponds to which form item.

The second part of the code that starts with MailApp.sendEmail actually sends the email to the parent. Hopefully you can see what I wrote above and adjust it to meet your school’s needs (helpful hint: \n corresponds to a new line in the email).

If you need more information on Google Scripting, I highly recommend the tutorials that Google publishes, but these are much more useful to you if you know the coding language they are based on, JavaScript. I learned JavaScript from a lot of experimentation, the W3Schools tutorials, and a very helpful and extremely dense book.

I’ve been participating in Keith Devlin’s "Mathematical Thinking MOOC" hosted by Coursera. The purpose of my participation has been to evaluate the MOOC as a learning environment for my students. I want to see if we can find ways to bridge the gap between the type of thinking required for my students to be successful in their current k-12 environment to what it will take for them to be successful at the university environment, particularly in mathematics. We’ve already spent some time thinking about what they need for their success outside of school. I really want my students to think mathematically, so any resource I can share which will improve that will be valuable.

Unfortunately, I will not be suggesting the current version of Keith’s course for my students, but I will continue to follow the project to see if becomes something that will be more valuable for most of my students. Below is a critique which outlines some of my reasoning behind not recommending this experience for my students (yet).

I can separate my critique into three areas; user interface, course content, and course structure. I’m hopeful that this critique can be used to improve this experience for future students (or at least to have points I’ve brought up rebutted). Keith has mentioned many times that this is an experiment, and of course with all experiments, we try things out and see what works, and see how we can improve the experiment for next time.

User interface

This is likely to be out of Keith Devlin and his team’s control, but is worth mentioning because of how important it is for student learning especially in an online setting. It seems to me that something which is so crucial to how students develop understanding is so often outside of the control of the people responsible for their student’s learning. We spend an awful lot of time trying to improve learning environments for students in offline settings; we should spend at least as much time trying to improve learning experiences in online settings.

The course is basically divided into course videos, course problem sets, and discussion forums. The biggest problem I’ve noticed with this way of dividing the course is that there is no way for a user to know what videos they have missed, what problem sets they have not yet done, and who has replied to their discussion posts or comments without visiting all of these areas of the website each time. The system, of course, does keep track of this information, as it will let you know when you visit a particular lecture if you’ve watched it before, so why not aggregate this data for students?

The structure of the course is designed around containing the information in such a way which is easy for an instructor to follow but which should be re-arranged in such a way that the most relevant information necessary for a student is delivered to them. See Edmodo for an example of a fantastic user-interface which does exactly this. Courses, and the relevant user interface design for a course, should be designed around the experience of the user, not around the way the information is categorized by the facilitator of the course.

This user interface makes a difference. For example, one of the course suggestions is to join a study group for the course. As many of the participants of the course may be participating in isolation, making those connections and setting up a study group for one’s self is incredibly difficult. There are no spaces within the course where an effective study group could meet and discuss ideas. Given the emphasis placed on this by the course designers, this space should be woven into the structure of the course in a meaningful way. Improving the user interface so that it has more of a social feel, much like what Edmodo has done, would do a lot to improve retention of students through-out a course.
 

The course server itself crashed, just as Keith was set for students to complete the final exam for the course. This critique has nothing at all to do with the server crash, as this is outside of the control of Keith and his team. This is a problem that could have come up for anyone trying something so ambitious as to deliver a course for more than 50,000 people.

Content

When I heard that Keith Devlin was running a course on mathematical thinking, I had in my mind a much different experience than what has been offered. My students are exposed to formal mathematical reasoning of the sort offered in this course; in fact I have a student who is continuing learning about formal logic in university due to the interest in this area that arose as a result of my classroom. However, one thing which is often missing for my students is a result of what I like to call the black box approach in math education.

Here’s a story to explain what I mean. I had a professor in university who had a habit of giving lectures on how to solve specific problems related to concepts he introduced in class. Almost every single time, he made some error while presenting the solution to us, and ended up with some sort of impossible situation or contradiction. He would give up on his solution and say, "Okay, but you get the idea." He was always incredibly embarrassed, and he would promise to come with the correction in his solution for next class; which he always did. Unfortunately he created a black box around mathematical problem solving for us. I always wanted to know, given that I’ve found an error in my solution, what process can I go through in order to find my error and fix my work? This aspect of problem solving is usually not shared with students, and certainly wasn’t by my professor, often because of the complaint; we just do not have time.

So when I heard about a course about mathematical thinking, I thought that it would include more than just the formal symbolic portion of mathematical thinking and give students opportunities to learn what is in the black box.

I also recently watched a lecture by George Polya in which he describes the beginning of mathematical thinking as starting with a guess. What Polya attempts to do is to lead a group of students through an activity in which he tries to make his thinking, and his process of turning a guess into a certainty, completely clear. I know that this approach is something that many students never get to experience, and understand, and I was disappointed that there very few opportunities for students to see this type of approach discussed, or even modelled.

My hope was that students would be given some examples of mathematically challenging ideas and problems from throughout history, and given some of the tools to try and work out the solutions for the problems themselves, and more importantly, to have some of the creative thinking required for these solutions laid bare.

It is probably true that this may mostly be a matter of differing definitions and I may be being especially pedantic here. Obviously formal mathematical logic is a critical part of mathematics; I’m not trying to argue that. It is also true that many students are never exposed to formal mathematical reasoning in the current k-12 system. All I’m trying to argue is that there is more to mathematical thinking than formal logic, and that I would probably not have this complaint if Keith had labelled his course something like "Introduction to Formal Mathematical Reasoning."

Structure

The course has a series of videos which have to be watched, and which include in-video quizzes, which have to be completed in order to gain course credit. There are also a series of problem sets which also have to be completed. In order to gain the certificate of achievement for the course, and a related course grade, students need to complete the quizzes and problem sets (submitted in the form of a solutions to a multiple choice exam). There are also problem sets which do not count toward course completion and have a much more open-ended set of solutions.

Despite the fact Keith has repeatedly said that people should not focus on the lectures and the quizzes, people continued to do so in the forum discussions, even taking the time to point out minor mistakes and omissions made. Why would they do this, if the teacher of the course is telling them not to worry too much about them? Quite simply put; when you place a series of tasks in front of people in the context of a course, they will naturally choose whichever of those tasks is most necessary for them to complete for credit. So even though the forum discussions and study groups could be a far more effective way for students to figure out how to solve the open-ended problems, they will focus on the lecture quizzes and problem set quizzes because these are what are necessary for completion of the course. For an example of platforms which put emphasis on the discussions, questions, and comments of their users (such as Keith wanted people to do as per his emails out to the participants of the course) explore Stack Overflow or Quora.

The course had time limits set for completing the in-lecture quizzes, and the problem set quizzes. It seems to me that this is completely arbitrary. Why set time limits when the quizzes are all machine graded anyway? We set time limits as teachers mostly for administrative reasons (it is really hard to grade a bunch of assignments that come in at different times) or as some would argue (can you tell I disagree with this argument?): "to teach people how to meet deadlines." Since neither of these is a concern for Keith and his team, I do not understand the use of the time limits at all, except that it replicates one aspect of what happens in an offline university course as well. My recommendation: set the time limits for the very end of the course, or perhaps a day or two earlier. This allows students to catch up without penality, which again would lead to a greater number of students completing the course.

The positive

I really liked the problem sets I looked at. Some of the problems given were so good, I shared them with colleagues from outside of the course. One of my colleagues incorporated some of the problems into her own classroom, and at one point three of us discussed one of the problems, and a possible solution to it, at length. The problems themselves were an excellent source of discussion, and I noticed a lot of strong positive discussions around the problem sets on the discussion boards.

Having an ability for people to have essentially unmoderated conversations around formal mathematical logic is excellent. The discussion forums were filled with people discussing the intricacies of formal mathematical language, and trying to explain these concepts to each other. It cannot be a bad thing to have thousands of people discussing mathematical ideas.

The distinction Keith made between how language systems work and how formal mathematical language works was an important point, which is often missed by people studying mathematics. We use formal systems for a reason; they prevent (or at least minimize?) ambiguity. Ambiguity in language is a problem that mathematicians struggle to avoid, and which the non-mathematician sometimes has no patience for resolving.

The peer review system for grading assignments is a very interesting idea, and one which I wish I had more opportunity to observe. I think that the idea of peer reviewing work in an online setting is a powerful one, as it allows us to move away from quantitative (and sometimes misleading) descriptions of student engagement and learning in an online setting, and move toward a more qualitative description of student learning. The numbers rarely give the entire picture when students are learning, and so anything that produces a different picture of that learning is valuable.

Summary

I think that creating an experience through which students learn mathematical reasoning is a terrific idea, and I’m impressed with the work Keith Devlin and his team did to work on such an experience. Many people I’ve spoken to think that the course content for Keith’s Mathematical Thinking course is excellent; I do not disagree, I was just hoping for a different emphasis.

I believe that online learning has the potential to be more centred around the needs of students, and connecting people in new ways, who learning similar information, but I think that the Coursera course structure has a long way to go before this will be easy to do in their environment. We don’t need to emulate the pure classroom experience any longer, we can create new experiences and allow students to learn material in wholly new ways.

I felt like there were a lot of positive aspects of the MOOC Keith created (as per above) and I look forward to keeping track of this project as it evolves over time. I’m also going to post a summary of an idea I’ve had around creating a space for learning mathematical ideas in an online setting. After all, if I am to critique someone else’s work, I should put my own work out to be critiqued as well.

I was recently asked to share some talks which might inspire parents who have come from a traditional schooling system to think differently about how schools should be operated. Here is my list (please feel free to add your own in the comments below as I am sure I have missed some gems out there).

The following was shared to me and I felt it deserved a wider audience, so with permission of the author, I am sharing it here. The author has asked me to point out that this writing is copyrighted by her, and that permission is required from her if you wish to copy it or publish it in another format. You can contact me through the contact link above if you want to get in touch with the author.

Ah, yes, homework.

To mark it? To leverage the pressure by counting the marks in the final average? Perchance not to assign it at all?  Why can’t we seem to settle this, or at least find a way to get students to do their homework without all this agony?  I believe we have met the enemy, and he looks familiar.

It is partly the system and partly ourselves creating this culture that teaches students in a perverse and relentless way to view the whole school experience as oppositional and adversarial, from mildly so to unbearable.  However, when most of the work of learning is handed over to students, when performance happens only as they feel ready and at low risk, when acts of learning are full of interesting, varied experiences and fun, when learning happens within a really functional community of interacting,supportive peers, when every stage is completed so that students are fully competent to move on to the next, and when many or most things to learn are self-chosen, students become almost driven to work hard, and for their own reasons.  Result:  they learn like clappers.  We all know it when we see it.  It’s what teachers live for.  

There are several sticking points on the way to achieving this, and then homework becomes almost a non-issue.  One is the absolute refusal of the system to give up some control, especially over timing.  The system overall has never paid anything but mealy-mouthed lip service to the part of our official Mission Statement that says people learn in different ways and at different rates.  We seem to say "Sure…yeah…but you still have to complete FOM10 in one semester, or X number of classes, or you FAIL, get no credit for learning anything, and have to start all over again."  "You have to move on to grade 6 now, and never mind all that grade 5 work you didn’t complete.  Good luck to you."

This leads to "squeaker passes" and the awful pattern of moving on to the next thing when not ready for it, and probably another fail.  It tells students in a loud voice that they don’t have to be really competent to "get out" of a year-grade or a course of study, and avoidance or disengagement has rewards (relief from stress, getting out of work they don’t want to do, elimination of risk, "sticking it to the man," declaring a pseudo-independence, status among peers, and more).  Remove these pernicious rewards, and their origins, and avoidance vanishes (perhaps after a short period of trying frantically to make it work again!).  Create an environment in which intrinsic rewards abound from genuine engagement, and they will come to the table.  If they engage learning it feels fabulous; if not….well…nothing.  And definitely not fabulous.  And no way out but another chance tomorrow to get ‘er done.  This is key:  we have to learn patience, and WAIT.

We have never just accepted that learning mathematics, for instance, is a  continuous process of acquiring knowledge and skills.  As a student, it just doesn’t matter to you what age-appropriate or development-appropriate peer group of fellow learners you are with this year, or where any of those kids are on the continuum, as long as you are somewhere on the continuum, moving steadily forward, and riding on a solid history of competence in all of the previous work.  We have to learn to trust kids to get there in their good time – with our help, of course. We have to let go of our insistence that every learner in a group must be nearly at the same place academically at any given time, and they all have to be doing the same thing at the same time, all day long.  

Step back a bit, and it looks as crazy as it really is.  Kids aren’t widgets and education is not mass manufacturing.  "Scientific management" was NEVER appropriate for schools, and never will be.  I am staggered by the human cost of this over the last two centuries, by the effects on millions of lives that we will never be able to guage fully, nor redeem.  Despite widespread, largely unfounded belief, it’s not even efficient.  In 2012, we know better, and yet we permit this one, tragically misguided set of notions about learning to dominate education worldwide to this day.

As competent, trained, experienced, caring adults, teachers do have the upper hand, but in many cases, we don’t use it as deftly as we could.  Observing where the real intrinsic rewards and natural consequences fall can be disturbing, but very helpful.  Interrupting the patterns of urging and resistance, of coercion and punishment, of risk and reward, means becoming very astute observers of what the school landscape feels like for students.  How can we change their view of school from jail-like institution to a resource-rich playground where the goodies are?

Piaget so rightly did advise us that play is, above all things, "the Great Work of children".  Play is hard work and results in rich, deep learning.  Children do not have to be forced to do it.  They are inwardly driven to play, and very inventive withal. Play is efficient, because it is child-selected, directed and timed; the energy and effort are focussed where they need to be, and exactly when. Maria Montessori proved how powerful this can be when we provide children with a truly rich environment, model civilized behaviour and true mentorship, and collaborate with children on their learning.  How can we transform ourselves from authoritarian keepers, lecturers and judges, to become preparers and guardians of rich learning environments, protectors, mentors, record-keepers, directors of traffic, facilitators and fellow-learners?  But that would mean reinventing our own identities somehow, and even adjusting our point of view, before we can transform learning in schools!

Another issue is our very difficult and uncomfortable relationship with the concept of evaluation.  Although we have all kinds of ways to determine whether a person can perform a skill or demonstrate knowledge at any number of levels of mastery (recognition, recall, application, synthesis, etc.), we are still collecting marks from early performance, or even formative stages, and averaging them with information from summative performance, sticking in some "credit" for what amounts to compliance or engagement attitudes, and claiming that this represents some kind of accurate picture of competence in a scope of challenges.  I have struggled with many iterations of this, none of them even in the ball park of real validity.  And none address the likelihood that skills may improve with time after instruction.

Many teachers do have a good grasp of the use of rubrics, checklists, and testing theory, and use them every day.  More and more are finding ways for students to demonstrate levels of mastery for summative evaluations that really do represent what students can do reliably and independently after learning and practice.  Too many of us are still wallowing in a miasma of mixed messages, imprecise language, unsupported beliefs, crossed wires, lack of guidance, administrative confusion and just plain muddleheadedness about what we’re really trying to do here.  And you can’t write comprehensive anecdotals on 150 kids every couple of months.  Get real.

The first thing is to admit that this is a much bigger, wholly systematic problem, and cannot be fixed with a few hints about marking or not marking homework.  We have work to do.  (Don’t we always?)  Psychologists speak of the "dances" of dysfunctionality, and admonish us that if we don’t like the dance we’re in, there’s only one way to move toward something better.  Each of us can only act individually; we can’t change others.  But if we change our own steps, we change the dance, and that can make all the difference.

When we do it together, we can change the world.

Oh, and in the short term, make a Big Deal of homework.  VALUE it.  Assign adjustable amounts of work (according to self-assessed need for gaining competence).  Assign tasks that are very high quality and meaningful.  Be sensitive to students’ need to have a life outside of school.  Teach students explicitly how to know when they can perform a task confidently and independently.  Set and insist on very high standards of work and presentation.  Talk about it, go over some of it in class.  Require completed, fully-documented corrections before checking off.  If it isn’t done right, it isn’t done.  Keep records.  Don’t count them, but show them to parents.  And there’s always after school.  On Friday. 😉

KT Pirquet

KT Pirquet is a professional writer/editor and retired high school mathematics and science teacher. Katie lives near Victoria, B.C., where she is currently a writing instructor at the Western Academy of Photography.

 "If I am to have faults, I would rather they be my own." Vi Hart

Vi Hart is somewhat critical of math teachers in this video, and of systems which prevent exploration into mathematics in their desire to ensure that all students have equal exposure to mathematical ideas. Of course, as she points out, students rarely have exposure to mathematical ideas. Instead, what they usually experience are mathematical procedures to solve problems that aren’t their own.