Modern Learning with Flexible Structures

“Modern learning” is a phrase I am encountering in more and more places, but still I just can’t seem to find a definition of what exactly it is. The general idea seems to be that a changing 21^st century world demands collaborative creative critical thinkers, and that modern learning involves whatever tools and approaches are needed to help students develop those traits. Discussion about modern learning typically emphasizes the role of the student in learning, flexibility in approaches to the curriculum content, and use of technology to enhance the learning experience and facilitate collaboration.

To experiment with one modern learning idea, I used a flexible structure this semester for the Linear Systems unit with my Grade 10 Applied Mathematics class. I divided the unit’s learning goals into two learning cycles of about five days each. At the end of each day students completed a Google Form to self-assess their progress towards each of the cycle’s learning goals, identify homework, and choose what and how they would like to learn the next day. Content choices aligned with learning goals, and method choices included watching a video, trying an investigation, reading from the textbook, researching online, or participating in a mini-lesson with me. Several times in each cycle they were also asked to choose between writing a quiz and creating a video with Lensoo Create as a method for formative assessment. Each student had a Nexus 7 tablet to use in class to access learning and assessment resources.

OAME Top Three

Year after year the OAME conference gets me thinking about mathematical things in a new or renewed way.  Here are three ideas that have stuck with me from today's speakers at OAME 2015

1.Spiraling through curriculum
The structure of most mathematics courses (or even I suspect most courses) mirrors its curriculum document.  The curriculum divides the course into three or four strands, each with three or four overall expectations that are elaborated on with a half dozen or so specific expectations.  Similarly, long range plans usually divide the course into a half dozen units derived from the overall expectations which are subdivided into lessons to sequentially address each of the skills required.  A linear document (the curriculum) is translated to a linear teaching plan, and most of the time the system works to deliver prepared students to the next grade so long as they don’t fall off the linear skills assembly line (... or if they do so long as we can pick them up and put them back on quickly enough...)

In their tiny five minute long IGNITE talks both Mary Bourassa and Alex Overwijk referred to an alternative approach.  When “spiraling” through the curriculum the linear planning model is gone.  Instead, students wind their way through activities and lessons that span the curriculum.  All of the overall expectations might be addressed within the first six weeks of a course, and then revisited in more depth as the course circles back again and again. 

“Available for group members only” - Now Available!

The Moodle feature “Available for group members only” was just activated last week on our Moodle server, and it could save us all lots of time maintaining Moodle courses.  With this addition any resource or activity can be visible only to a group of students enrolled in a Moodle course rather than all students. 

 

Often I find myself teaching two sections of a course, and often there are small changes in the lessons for each section because of the composition of classes or external factors like assemblies and fire drills.  In the past I’ve maintained two parallel and virtually identical Moodle courses to be able to make those minor modifications when needed.  With “Available for group members only” I can now use a single Moodle course for the students in both sections and show specific resources (or activities) to only one section of students when needed.

Here’s how it works... 

Five ideas from OAME

Recently I attended the OAME 2014 conference at Humber College.  Here are five speakers who got me thinking.

1. Jo Boaler: With a Growth Mindset, anyone can learn mathematics
Performance praise like “You’re smart” actually encourages a fixed mindset, a belief that ability is inherent rather than developed.  In contrast, growth mindsets are cultivated by practices of: persistence, learning from mistakes, determination to keep going, and being encouraged by other’s success (Carol Dweck).  Those with fixed mindsets underachieve when compared with those with growth mindsets, regardless of high or low present ability.  She believes that with a growth mindset, all people can learn mathematics, except perhaps those few limited by cognitive disabilities.   I think I agree with her point of view, with the great challenge being that some students have established habits of behaviour and belief that reinforce fixed mindset behaviour.

Describing Graph Transformations with Input / Output diagrams

I regularly stress to my grade 10 and 11 students that when transforming a function it is imperative to dilate before translating in any direction. In other words, if a function is both stretched and translated horizontally the stretch must happen first. Ron Watkins’ demonstration of Input / Output diagrams at OAME2014 has helped to see how rearranging the equation that describes a function can translate to rearranging the kind and order of transformations

An Input / Output diagram shows the sequence of operations applied on a function’s argument, x, to arrive at its value g(x). Naturally this sequence follows order of operations. What is interesting is that transformations are made clear through the diagram. Look first at the parent function indicated by the red arrow, which in this case is f(x) = x². Moving towards the right are the vertical transformations: stretch by factor 3 then translate 5 up. Following the arrows towards the left are the horizontal transformations: compress by factor one half, translate 4 right.

 Often students don’t see why horizontal transformations on the parent function are related to the inverses of operations seen in the function’s equation.  The diagram shows that to go from the input of the parent function (red arrow) to the horizontal coordinate x requires inverse operations, while going from the output of the parent function to g(x) does not.

Why I’m excited about Google Apps for Education

After several years of consideration and deliberation, Google Apps for Education has been launched throughout the YRDSB. Google Apps is a collection of services including the Google Docs collaborative suite of office applications, 30 GB of Google Drive cloud storage, email, calendaring, website creation, and more. Every student and staff member now has a Google Apps for Education account with the username and password synchronized to their school computer login.
With Google Apps comes many new possibilities:

• Students can collaborate on documents, spreadsheets, drawings, and presentations from any location at any time.
• Teachers can see students’ work as it develops, and give feedback by adding comments.
• Teachers can see which students contribute to a collaborative document by viewing the document’s revision history.
• Documents cannot be forgotten at home or lost on a corrupted USB drive.
• Departments can share a folder of common resources to access them anywhere, and even offline using Google Drive Sync
• All students now have a Google Account, so can use that to easily access services like Khan Academy.
• All students now have an email address under the gapps.yrdsb.ca domain, so they can now enrol services like Prezi’s Enjoy Edu which are free for educational users only.
• Shared calendars which can be added to mobile devices or embedded in Moodle courses can help with communication with departments, classes, clubs, and teams.

What you should do right now

This year, resolve to change your Passwords

My family's online presence started in 1987 when we signed up for the pre-Internet communication provider CompuServe. After dialing in with our modem, we logged in to the service with a nine digit username and a password supplied by CompuServe. Twenty five years later that password is still in use....
I must have hundreds of accounts with passwords on different web sites, and I expect you are the same. Our passwords protect information that ranges in value from inconsequential to critical banking and email details. Wired magazine senior writer Mat Honan discovered first hand this summer how vulnerable our password protected services are when hackers compromised his email accounts and remotely deleted everything on his iPhone, iPad, and MacBook. Lacking proper backups, he lost significant personal data including every picture he had ever taken of his 18 month old daughter. Most photos were later retrieved (at considerable expense) by a forensic disk recovery lab, but Honan was left shaken. Reflecting on the incident in December's edition of Wired magazine, he concludes that passwords alone are a flawed way to authenticate identity in a networked world filled with inexpensive and powerful computers. Though it might be a little frightening, I highly recommend reading the full article, or listening to last Friday's interview on Q.
Even if Honan is right that "the age of the password has come to an end," the reality is that we keep using passwords dozens of times a day. We need incorporate practices that give as much protection as possible until more robust authentication methods gain wide-spread use. Here are five things to consider as you decide how to manage your passwords: