Thursday, March 9, 2017

Equity versus Equality, exercise of different approaches to the same Mean, What is this thing called Resiliency?, a couple of videos, and brainstorming on Science and Space

Earlier in this week, Saya proposed that we should have some tests where the format is not open book.  I agreed that we should try this out, since there will be encounters where a teacher may not want you to reference your notes.  For me, "Open Book" tests are about assessing the student's ability to apply the knowledge gained from homework and study to a testing situation.

In the future, I am sure there will be situations where books are not allowed and you will have to rely on your memory to demonstrate your knowledge and expertise.  For me, this causes me anxiety.  In job interview situations I may get anxious and would've benefited from the opportunity to reference a note to help jog my memory or ground my thinking.

There is a graphic which has been circulating on the Internet that is very interesting and made me think about my open book policy.

With all books being open, I have been equal in my practice.  Though, in the class, not all students are operating at the same level.  Some students may have learning challenges and require extra support so they are more on par with their peers; this is equity.  Sometimes this hard for students to get, since they may think that certain students are getting favours.  We are not all starting on the same footing, is how I would respond to this.

This image comes from and looks at this image from a more critical standpoint and takes into consideration the social and political dimensions of Equity, Equality, and Justice.  I won't get into it with the class, but you may want to take a look.

Same mean, different mode & median

This graph, which has been explained to the class, looks at how it is possible that a student may have the same average (mean) for a set of 5 tests, but the results may be different.

 In class, I demonstrated how we can swap marks around and still arrive at the same mean, but our mode and median may shift:

Here we have a case, similar to the graph pictured, where all the test marks are the same and we have all three measures of mean, median, and mode being the same.  5 tests, with a score of 7 = 35 total marks.

In this case, I have moved some of the marks around, but the same total of 35 marks for all 5 tests remain.  Our median is 8, our mode is 8, but our mean remains at 7.
Take two:  same topic

A few students stayed after school to ask about this Math.  I pulled out the cubes to demonstrate how this morning's Math works:

Each column represents the test results.  In this case, all of the results are the same:  Each test produced a score of 8.  So our mean, median, and mode are all 8.

In total, we have 40 cubes (5x8).  This model represents the leveling aspect of the mean/average.

We still have a total of 40 cubes, but now they have been re-distributed among the 5 tests.  From left to right, our scores are 10, 2, 8, 10,10.  Our mean still remains at 8, but our median and mode are now 10.

Sketches on a desk:

The actual marks, for a Mean of 8, could look different than the ones on the desk or the cubes I set up.  The BIG IDEA is that the total of all of the marks equals 40.  So, it could be possible to have the grades for the 5 test be 0. 10, 10, 10, 10, 10 and still have a Mean of 8!

Thanks for asking!  You can always ask for help.


These posters, which are looking a little old, have been on my boards for almost six years now.  I have made some references to them in class, but I have never fully explored just how important they are.

The three of them, with the inspiring quote in the middle, come from the ideas of being resilient or being able to recover, learn, and push forward, when faced with difficult situations.  It is a very popular topic.  Not to plug amazon, but check out this extensive list. and this is only the first of 20 pages on the topic!

I was part of a pilot group of teachers who worked with a program known as Strength Based Resilience (SBR).  It was developed by  Drs. Tayyab Rashid, Afroze Anjum, and Jane Gillham.  I will not get too theoretical and keep the understanding and applicability of the program straightforward for the students.  More information on the program can be found here:

One of the initial exercises around understanding the scope of the project is learning what Resiliency is all about.  Our first exercise will involve using this video.

One of my goals for this term is to weave some of the ideas from the SBR program in with our classroom programming across a number of subject areas.

The story you will be using for jot notes is here:

Short video from Orff/Music:


Great Big Crunch:  


Science Brainstorming:  Space, our current frontier

The new unit in Science will aim to give the class different entry points to explore topics they find interestring around Space and make connections with the expectations of the Science curriculum.  To give the students a sense of what they could explore, I loosely broke down parts of the expectations in this chart:

Along with Ms. Ling, our Teacher Librarian who has committed to partner with our class, we did some brainstorming in the Library this morning.  Here are some of our ideas that we will fuerther develop after the March Break:


- jot notes on Resiliency story in Language book
- Media planning chart (assigned earlier in the week...did your group complete it?)
-Film Festival waiver form
- Math online learning (educational games) for mean, median, and mode
- 2 bar graphs, in Math book, for demonstrating different mode and median, but the same mean (see above example)

No comments: