The Reflective Educator

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Month: October 2012 (page 1 of 2)

Math activities for a measurement unit

Our 3rd grade students will be doing a unit on measurement soon. These are the specific standards for the measurement unit that we hope to address. I’ve been asked to brainstorm some activities for students in this unit which can be extended or modified to meet the needs of a wide range of learners.
 
BC Precribed learning outcomes in 3rd grade related to measurement
  • relate the passage of time to common activities using non-standard and standard units (minutes, hours, days, weeks, months, years)
  • relate the number of seconds to a minute, the number of minutes to an hour, and the number of days to a month in a problem-solving context
  • demonstrate an understanding of measuring length (cm, m) by- selecting and justifying referents for the units cm and m- modelling and describing the relationship between the units cm and m- estimating length using referents- measuring and recording length, width, and height
  • demonstrate an understanding of measuring mass (g, kg) by- selecting and justifying referents for the units g and kg- modelling and describing the relationship between the units g and kg- estimating mass using referents- measuring and recording mass

Here’s what I have so far:

  1. How long is a minute?

    Have students work in pairs. One student has a timer, the other student has nothing. The person with the timer says "go" and starts the timer. The other student waits (without counting or saying anything) and tries to say stop when they think a minute has gone by. Then students switch roles. Play this game once at the beginning of class, and once near the end of class (ideally just before a break), and have some of the students gather the data from the entire class and compare the numbers from the beginning of class to the times just before the break.
     

  2. What day of the week will your birthday be next year?

    Have students work together to try and figure out what day of the week their birthday will be on next year. Challenge activity: What day of the week will your irthday be on in 20 years? In 80 years? Students will choose to adopt different strategies, but you should not let them look it up on a calendar (but they are free to make their own calendar to make it easier to calculate).
     

  3. How many times will my heart beat in an hour?

    Have students measure how many times their heart beats in either 10, 15, 20, 30, or 60 seconds (or all of the above) with a partner, and then try and calculate how many times it will beat in an hour. Some students will realize that this is a multiplication problem, others will start creating lists of numbers to add together. Extension: How many times will your heart beat in a year.
     

  4. How long is a foot?

    Have students measure different things in the room with their feet as the unit of measure (to the nearest half a foot if possible – support tip: ask students, is it nearer to 2 feet or 3 feet?). Have them compare their answers to the same things they’ve measured. Talk about the need for a standard unit of measurement, which is exactly the purpose of centimetres, metres, etc…
     

  5. How heavy are things?

    Activity: Using a balance scale (which we have in the science lab in the senior school) have students measure a bunch of different things around the classroom (like pens, etc…) and compare the weights of the different things together. Now, ask the question: how many pens weight are these things? Now you can have students try and determine, using the weight of a pen as a reference, how heavy various objects are in the room.

Resources for mathematics enrichment

I’m currently putting together a list of resources for our elementary school teachers to use to enrich their mathematics classrooms. Our basic philosophy is to provide opportunities for all students to engage in rich mathematical tasks, and to add breadth & depth to their program of mathematical study, rather than accelerating through the British Columbia curriculum.

I’m looking for more resources for each of the areas below, but I don’t want to over-whelm my colleagues with options. Any suggestions? Ideally I’d like resources which are straight-forward to use, and which promote the philosophy described above.

 

Resources for enrichment

Problems with open-ended solutions.

Puzzles

Math contests

Games

  • Choose games which have some basis in logic & reasoning to solve, or which require students to use mathematical skills in context. Eg. Monopoly is a terrible game for logic & reasoning, but a good game to practice addition & counting in a financial context.

Programming

Real life contexts

  • Find ways the mathematics students are learning is present in their current life
  • Provide opportunities for students to learn interesting mathematics (perhaps even outside ‘the curriculum’!) that occurs in nature
  • Sample activity: Have students take photos of things which appear to be mathematical to them

Math apps

I recently realized that I have a tonne of different math mini-applications that I’ve built over the years, and I will need to take the time to catalog them at some stage (note that some of these will just not run in Internet Explorer). For now, here’s a list of the ones that might be useful, in no particular order:

Is this a necessary use of technology?

Steve Wheeler shared this video on his blog after describing constructionist learning theory. I’m not really clear on what, if anything, this robot adds to the activity of playing Snakes & Ladders. What would be different about this activity if students had to move a marker instead of pressing buttons on the robot to get it to move? Is this a necessary use of technology, or an extravagance?

I tend to lean toward the latter for this particular example. I am a supporter of technology use in schools, but we need to be thoughtful about our use of technology and given it’s expense, try and choose technologies which we can see will have an impact on student learning, rather than technologies which can be easily replaced with something far cheaper.

Can you see other ways that this particular technology could be used in a more powerful way, one which will impact student learning, and which requires this technology?

Northwest Mathematics Conference resources

I’m presenting twice at the Northwest Mathematics conference, once on computers in math, and the other on programming in math. Here are my resources from the day, which you are welcome to adapt and share (for non-commercial purposes) provided you give me attribution. Despite the titles, both of these presentations are focused on the use of computers in mathematics education, rather than the more general topic of computers in mathematics itself.

 

Computers in Mathematics

Programming in Math

Resources shared by participants

Lightbot 2.0 – A game which introduced programming concepts

Star Logo TNG – A 3d programming environment which uses the block system made popular in Scratch & Turtle Art.

Number line activity

Father and son playing catch
(Image credit: bterrycompton)

I co-coached my son’s blastball team last year. We spent a lot of time playing blastball, but we also spent some time practicing some of the skills needed to be able to play (while emphasizing how these skills fit into playing the game). One of the skills we practiced was throwing and catching a blastball.

How this worked is that each kid stood one or two steps away from their parent and threw the ball to their parent. If the parent caught it, the parent took a step back, and threw the ball back to their child. If their child caught it, the parent took another step back, and so on. This meant that very quickly parents and children tended to be separated by a distance where they catch the ball about half of the time. This is by itself a good activity that relates to the number line, if you think of each step apart being 1 space apart on the number line.

My son and I went through a particular fun exchange where his objective was to make sure I didn’t catch the ball, requiring me to continue closer to him. As I moved closer to him, I kept indicating where I was like so: "Okay, now I am three steps. Now I am at two steps." Eventually, I ended up zero steps away from him. To continue the joke, he managed to find a way for me not to catch the ball even though we were directly on top of each other. I continued stepping toward him, which meant that we were now facing back to back, with one step in between us. "Okay," I said, "now I am at negative one step." He had lots of questions about negative one step, and continued the game a few more times as I moved into smaller and smaller negative numbers.

While the introduction of the concept of negative numbers is obviously secondary to this activity, it is a way to tie together some fun physical activity with some conceptual understanding of the relationships between different numbers.

 

 

Disrupting education

Children are the living messages we send to a time we will not see. Neil Postman
(Image credit: Steve Slater)

I’ve read a lot of articles over the past few years about education is being disrupted. Most of these disruptions are focused on schools as systems (think financial disruption, not pedagogical disruption), not schools as ecosystems. The distinction is important.

I’d like education to be disrupted as well, but I think in some ways that are much different than what many education reformers are pushing.

  • I’d like every student to have a teacher, a school, and to feel comfortable to be in that space. For my school’s partner school in Kenya, we’ve put up a wall to add a level of security to their school, but it would be nice if all of the students had access to latrines, clean water, and food. When we can fix this problem everywhere in the world, I’ll consider education disrupted. Note: I’m also in favour of ensuring that the education we provide everywhere is suited to the needs of the local communities the schools support.
     
  • I’d like every student to feel safe to speak their mind in front of their teacher, and to feel safe in their presence. In too many places around the world, corporal punishment is still acceptable, and students are taught obedience over independence. It is possible to know when to follow the rules, and not have to sacrifice the ability to reason independently.
     
  • I’d like Neil Postman and Charles Weingartner’s chapter 12 of this book (at least) to be required reading for every teacher. Teachers (and parents) need to at least be discussing their role in quelling the questions of students.
     
  • We need to recognize that Daniel Pink’s idea of "Autonomy, Mastery, and Purpose" as drivers of human motivation, especially for highly demanding cognitive tasks, does not just apply to adults, it applies to students as well. Unfortunately most schools do not give students opportunities for any of these three guiding principles of human motivation. How often does your school let students completely master a skill before moving onto the next skill? How often do students have choice in when, how, and what they learn? How often is the purpose of school given so base that it does not actually invite students to participate?

Email confirmations from Google Forms

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.

Google form example

 

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

Script manager

 

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.

New script dialog box

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.

 

Log

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.

Programming for kids

I was recently asked about some programming environments I’ve used with students, and I thought I might as well compile a list of them, as well as some environments I’ve considered using.

Younger students:

  • Blockly

    Blockly sample
    (Image credit: Blockly

    Blockly is an open-source online programming environment developed by Google. It is currently very much a work in progress, although the language itself seems pretty stable, getting it to a state of usability for a group of students is not for the faint of heart. I mocked up a version of Blockly that resembles some aspects of the Logo programming language that I used with kindergarten students.

     

  • Turtle Art

    Turtle Art
    (Image credit: Sugar Labs)

    Turtle Art is a derivative programming environment of Logo, having been heavily influenced by the Logo programming language, and developed into a visual block version of it. It is multi-platform, and free to download (well sort of free – you need to email the developers of the program and request a download link for the program). I’ve used it with third and fourth grade students with some success. Turtle Art actually comes installed on the OLPC laptops.

     

  • StarLogo TNG


    StarLogo TNG is the extension of the original Logo programming into a 3d world. From their website, "StarLogo is a specialized version of the Logo programming language. With traditional versions of Logo, you can create drawings and animations by giving commands to graphic "turtles" on the computer screen. StarLogo extends this idea by allowing you to control thousands of graphic turtles in parallel. In addition, StarLogo makes the turtles’ world computationally active: you can write programs for thousands of "patches" that make up the turtles’ environment. Turtles and patches can interact with one another — for example, you can program the turtles to "sniff" around the world, and change their behaviors based on what they sense in the patches below. StarLogo is particularly well-suited for Artificial Life projects."

     

  • Hopskotch

    Hopskotch is an iPad, which is still in development, which allows children to do block programming in a very similar fashion to Scratch, Turtle Art, and other programming environments. I’ve not used Hopskotch myself to verify that it works.

     

  • Scratch

    Scratch
    (Image credit: Chris Betcher)

    Scratch is probably the most well known program for programming with kids. It has the same basic block structure that Turtle Art uses, but it has some additional features (ability to customize icons, object based programming) over and beyond the Turtle Art feature set. It can be quickly used to create simple animations, which is an attractive feature, but I found it harder to create simple geometric shapes than it is with Turtle Art.

     

  • Move the Turtle

    Move the Turtle Screen shot
    (Image credit: Move the Turtle)

    Move the Turtle is an iPhone/iPad app. It has a feature set very similar to Turtle Art (although somewhat reduced programming functionality). One thing that is compelling about it is that it includes a series of tutorials through puzzles which means that students without the support of a teacher can play around with the puzzles and learn how the application works. Obviously there is a certain amount of playing around necessary with any programming environment in order to learn it, but the tutorials Move the Turtle provides are useful when students get completely stuck.

     

  • CoffeeMUD 

    Coffee Mud screenshot
    (Image credit: Coffee MUD screenshot)

    Coffee MUD is easily the most difficult of all of the programming environments listed here to set up, and certainly amongst the most complicated environments to use. Coffee MUD is an online multi-user dungeon environment which means that it is both a somewhat collaborative game that students can play (and build their literacy skills in) and create.

    How Coffee MUD works is that it provides a server to which each student connects using some client software (recommendation: Jaba Mud client). While playing Coffee MUD, students navigate through a text based world, moving from room to room, and interacting with objects and non-player characters (NPCs) within the game. Many MUDs have no combat at all and have users interact with each other (social role-playing) or with the digital world provided via quests that the users solve.

    It also provides a way to interface (through a web browser) to the code that runs Coffee MUD and let trusted users add rooms, objects, and NPCs, as well as add a specialized coding system to allow players to interact and change these objects, rooms, and NPCs during the normal course of play.

    One enormous advantage I see with Coffee MUD is that the system is flexible and stable enough to potentially allow an entire school to interact via text in a virtual Coffee MUD world. While obviously this interaction shouldn’t come at the expense of face to face time, it could replace the traditional book report (create a virtual version of the story of the book instead!) or some creative writing time. For example, it would be an interesting interaction of the 7th graders attempt to create a portion of the game that the 3rd graders then play in.
     

Older students:

  • Alice

    Alice logo
    (Image credit: Alice 3 logo)

    I’ve not used Alice myself (except in a rudimentary way to test it out a bit), but I have heard some good things about it. One strength is that it relies on building object based programming with students, which is much more powerful and flexible than more traditional procedural based programming. From the Alice website:

    "Using an innovative 3D programming environment that makes it easy to create animations or games, the Alice Project seeks to provide tools and materials for a conceptual core of computational thinking, problem solving, and computer programming.

    The Alice Suite of educational tools is designed to support teaching and learning across a spectrum of ages, grade levels, and classes in K-12 and in college or university courses."


  • Python

    Python is both a command line programming language, and a language that can be used to build web applications. Many of the web applications created by Google are powered by Python. It’s not an especially new programming language, but the benefit of this is that there are an awful lot of great resources out there to learn how to program in it. See, for example, this excellent online tutorial.

     

  • Visual Python

    From the website for Visual Python (which I have successfully installed and played with myself): "VPython is the Python programming language plus a 3D graphics module called "visual" originated by David Scherer in 2000. VPython makes it easy to create navigable 3D displays and animations, even for those with limited programming experience. Because it is based on Python, it also has much to offer for experienced programmers and researchers."

     

  • JavaScript

    JavaScript is actually a pretty difficult language to learn because it requires an understanding of HTML and CSS first. It is probably best learned as a companion piece to making HTML websites more interactive. It also happens to be the base language for the scripting language Google uses for their Google Apps scripting environment, which means that students could potentially learn some JavaScript through programming directly in their browser. Students who want to learn JavaScript will also want to learn HTML, a mark-up language that JavaScript is often used to give dynamic capabilities.
     

  • See also:

Evaluating the Mathematical Thinking MOOC

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.
 

Coursera error
 

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.