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!