Wednesday, February 15, 2017

MHF Cycle 2 Reflection

I have previously posted a reflection of our first cycle here.

Here is the plan that we used for our first cycle.
(Most of the activity credits go to Jamie Mitchell and Steph Girvan in the Halton Disctrict School Board - Thank you for sharing your resources - including your blood, sweat and tears guys!)



One of the things we have found as a department is that students often struggle with the algebra portions of this course. Because of this I offered my students an "algebra crash course". I attempted to remind them the core of algebra and solving equations through manipulatives and a clear reminder of what inverse means (i.e. that log is a function, so has an inverse). These should be ingrained ideas that these students have and I find myself often wondering how to best help students at the high school level with these skills. If anyone reading this has any ideas please share!

As you can see in our plan we had two traditional tests in this cycle. We split the algebra portion up into two sections, polynomial & rational functions and logarithmic & trigonometric functions. The last part of the cycle has students explore combinations of functions through investigation of graphs and getting students to do their best to generalize rules for different types of combinations. As a final evaluation in this unit we had student-teacher conferences.

Students had a conference like this one during cycle one as practice (for all of them I was using Google Forms to track and DocAppender to give student immediate access to feedback). For this conference students were given two functions in small groups. They were asked to identify the characteristics of those two functions and then to as a group predict the superposition characteristics of those two functions. On the day of their conferences students rolled a die to get a random second combination. Students were given 5 minutes to prepare and then had 5 minutes to share as much as they could about that combined function. The key was that they were to explain why they believed those were the resulting characteristics, not just to list them.

I found this evaluation very insightful into student reasoning and understanding of characteristics as a whole. It also provided insight into the emphasis that I should consider putting onto the graphical representation of functions in earlier courses. I have started to think that we take for granted what students take away from graphs.

I really enjoyed the experience with conference with these classes and definitely plan to continue working on using them in other courses. Getting students to explain things verbally has an ability to show student learning that reading a written response just cannot do. The power of triangulation of evidence.

Wednesday, February 1, 2017

MHF Cycle 1 Reflection

As mentioned in a post early first semester we made an attempt to spiral the MHF4U0 curriculum at our school. I will try to create some more posts to share more details, so for now this post will just focus on the first cycle we used.

If you missed the planning post, you can find it here.

I personally started off with a couple of classes where we did some collaborative problems solving. I wanted to introduce my intention to use visible random grouping (VRG) and vertical non-permanent surfaces (VNPS) in the class. I used this with a couple of fun tasks (such as the Tax Man problem) and then continued with them working on the boards while having them do some review problems together (factoring, radicals). It was a rough beginning. My madness was very new to the students, particularly since I was completely new to the school.

Here is the plan that we used for our first cycle.
(Most of the activity credits go to Alex Overwijk and his team in the Ottawa-Carlton District School Board and to Jamie Mitchell and Steph Girvan in the Halton Disctrict School Board - Thank you for sharing your resources - including your blood, sweat and tears guys!)


The textbook references made above are for the Nelson Advanced Functions book. I very rarely assigned work from the book but students were given the sections as a reference for if they needed it or wanted to do extra practice.

Part way through the cycle (probably about 2/3rds of the way through) I asked the students for some feedback. They were struggling with my use of Desmos Activities and lack of "traditional lectures". We added some more structure to the daily work we were doing. At the start of class we went back to the previous day's lesson (took any questions, which we were already doing) and then co-constructed success criteria based on what they had done. This criteria was added to the lesson plan that the students had access to. I also made a pointed effort to make them read that day's learning goal and asked if anything needed to be clarified. This seemed to help students realize that they were learning.

In retrospect, the vast changes they were going through were a lot. I would create brief google forms for each Desmos Activity the next time to help students consolidate their learning (which would have helped them build their functions portfolio we had asked them to do), essentially they would be exit tickets of some sort. I could collect data for myself while giving students a chance to reflect. And the form could be attached to student documents via DocAppender so that they could have a copy of their own responses.

Our formal evaluation for this cycle was a large group stations task. Students were in groups of 3-4 such that there were 8 groups in one class. There were 8 stations in total (we did 4 per day) that were designed to last approximately 15 minutes each. Of course there turned out to be some they spent more time on than others. Students were to use the time in their groups to work through the problem (i.e. match a graph, table of values, and equation and justify the match) and then record their answer in their own words on their answer sheet.

Students found this to be a very valuable learning tool and, for the most part, the results seemed to align with what we, as teachers, thought that student had shown they knew and could do. They were not big on the fact that it was the only formal evaluation we had done in the first 6 weeks of the course, but appreciated that it was less stressful than a unit test.

In retrospect, the task was too huge for the teachers to deal with all at once. We each had 2 sections x 2 days worth of tasks to go through. It took a lot longer than we anticipated. I would love to do something similar to this again, but would definitely consider splitting it up somehow so that it is not all happening at once. Suggestions are welcome if you have any!

Reflections on cycle 2 to come!

Wednesday, October 12, 2016

Planning a Spiraled Course

This year I am embarking on a new journey - I am working at a different school and have more math in my schedule than I have had since my first year of teaching. As a part of that journey our MHF 4U (Advanced Functions) course team is taking a crack at "spiralling" the course.

Over the summer I spent some time laying out the course to begin to plan. I started with the skeleton Overarching Learning Goals (OLGs) that were created last year for math to come up with OLGs for the course (I wrote about these skeleton OLGs here) so that I would have already wrapped my head around the overall themes of the course.

Then I created a new document to start the actual planning. I pulled the overall expectations (OEs) for the course and the front matter of the math curriculum (math processes (MP)) into the chart by strand and then created a new column where I put in only key words (content & skills) from those OEs and MP. From those words I looked for common themes in the skills/content that I noticed and colour coded them.

Through this process I noticed a major theme in recognizing characteristics of functions and making connections between representations of functions (numerical, graphical, and algebraic). This seemed to be the backbone of a large portion of the course so it made sense to make this into a group of expectations - and cycle 1 was born.

Here are images of that document (they are a work in progress, evolving as we work our way through the course):




Creating the other cycles became largely about noticing the layers involved in the course. I wanted to build the remainder of the course by adding on layers of difficulty, which would allow us to revisit the same concepts. You may have noticed that the second cycle adds on algebraic techniques but is still focused on the same things introduced in cycle 1. This is the purpose of spiralling - students are able to see the same things over multiple exposures to better build their understanding of the material.

Studies are showing that the use of spiralling techniques will help with long-term retention for learners. It is not necessarily about improved results within a particular course, but will help with the foundations moving forward for longer-term success. My hope is that this type of pedagogy can also help with engagement and mindset for learning in the mathematics classroom.

The planning process was somewhat time consuming but was worthwhile for moving forward into the course as I knew what the purpose of the first cycle was and could see the long-term goals. The difficulty was not being able to co-plan with my course team (complicated by it being summer, going into a new school, etc). Now that we are a few weeks into the semester the team is more on the same page and is starting to be able to see the long term plan more easily.

One of the ideas we added to this plan was to have students start and maintain a portfolio where they would put information as it is learned organized by type of function. We are also going to do part of our final 30% as a conference with students - so students have been told that maintaining their portfolio is to aid them with this conference at the end of the semester. The possibilities are exciting.

Wednesday, August 17, 2016

Finished with the Status Quo

I am currently making my way through Starr Sackstein's Hacking Assessment: 10 Ways to Go Gradeless in a Traditional Grades School. I will likely do a blog when I am finished and will include my takeaways in more detail but one of her lines has inspired me to bring up some provocative conversation.

As are many of you, I am tired of the argument "We have always done it this way." It may be true that there are some thing in our lives that can stay the same year after year and still be the most efficient way to do things but life changes, and often things need to change with it. Most of the stages of my life have come with pretty significant changes and I have also watched the world evolve - computers, internet, cell phones - and would be significantly behind in current knowledge if I had ignored those changes.

Of course, I have also watched the world fail to evolve (lack of change in carbon footprint despite the research and negative effects we are experiencing; decades long wars (in so many cases started by some misunderstanding and a failure to learn from history) that are sometimes ignored by the rest of the world; etc.

I can no longer watch education become something that does not change.

On page 28 Sackstein had me out loud proclaiming "Yes! This is the articulation I have been looking for!" when she said:
In the industrial era, schools were intended to train good workers, so students went to schools that prepared them to enter the work force. This model of education valued obedience, conformity, and rote learning.
We are no longer in the industrial evolution.

Of course, I will not pretend to believe that we do not need workers who can conform and follow specific steps to complete a task, but the majority of work that we need to prepare students for requires people who can be creative, who can think for themselves, and who can solve problems. This is the world I want to prepare my students for - I want them to find success in whatever passion or skill they find for themselves through the use of transferable, valuable skills (not rote learning they can look up on YouTube).

Hopefully my journey can help to bring along more teachers, students, parents, admin, and community members who want to see a change.

Thursday, July 21, 2016

SE2R Comments in Grade 9 Science

I have been distracted from blogging but am trying to catch up and am back to trying to deprivatize my practice more. And so, I am resolved to blog about my assessment practices (including failures and questions) and hope that I can spark conversation, collect some feedback, and crowd source some ideas. So I have one request - if you are reading these entries, please share them with someone else and/or comment at the bottom and join the conversation. :) The first entry from this series can be found here.

Our wonderful Instructional Coordinator, Assessment, Kristen Clarke, organized some assessment-related book chats on Twitter in the latter half of the school year. I was able to participate in two of them and helped moderate a third. One of the books we discussed was Mark Barnes' Assesssment 3.0: Throw Out Your Grade Book and Inspire Learning. Mark is the pioneer of the Teachers Throwing Out Grades movement in education (check out #TTOG on Twitter).

[We also discussed Rethinking Letter Grades (which inspired mot of my Overarching Learning Goal and Learning Map blog entries) and Myron Dueck's Grading Smarter Not Harder (which inspired this entry related to reformatting tests and using learning goals).]

Barnes' book is largely about his feedback process that allowed him to go gradeless in his classroom. By giving students an appropriate avenue to find out what they had done and could improve on the traditional need for grades virtually disappeared. Reading his book has inspired me to make further efforts to reach for the same goal - a classroom of students who want to learn and grow (not students who want to do what they think I want and get marks). I want to build a community of students with a growth mind set that, therefore, believe in themselves as a learner and can reflect appropriately on their own work and the work of others.

Barnes' feedback method is referred to as SE2R. This means that every time he gives feedback he follows this pattern (and thus, teaches his students to do the same):

  • Summarize (what has the student done to meet the requirements of the specific assignment)
  • Explain (what mastery of skill/learning is shown)
  • Redirect (indicate what lessons should be reviewed to master concepts/skills not yet mastered)
  • Resubmit (encourage student to review and rework and give directions for resubmission)

I tried to put these ideas into practice a couple of times in the following weeks to test them out. Here is what I tried and how I did it:

  1. I put a paragraph writing question onto Edmodo as an assignment for students to answer that I told them would be on the unit test. Students were told what the learning goals were and were told that this was a chance to answer the question and get feedback before the test.
  2. I was able to practice writing comments that followed the SE2R model. Here is an example of what I wrote
    • :
  3. I created a "comment bank" using the SE2R model and based on the learning map I had created for the course. I sometimes had to modify comments to make them better fit an individual student work, but in the end I saved myself time AND was able to be more consistent and focus on the important areas only.