Portfolio: Shared Responsibility: Developing Autonomous Learners

I am taking the Teacher Leadership Part 1 AQ. Our culminating task involves creating a leadership portfolio by choosing items from each module of the course to share and reflecting on its contribution to my growth as a leader. I have chosen to share my portfolio as part of my blog.

This entry is from the module entitled Shared Responsibility where we looked at parent communication reasons & strategies, inquiry-based learners, mental health & resiliency, and student success stakeholders and planning. The item I have chosen is the inquiry-based activity (lesson) that I developed as part of the Developing Autonomous Learners section of the module.

In this section I was forced to come back to an always-repeating thought "what does inquiry-based learning really mean in a math classroom?" So I did some research to find out what others thought this means and discovered that for a math teacher this really should be thought of in the lens of discovery learning or problem-based learning. The goal, in the end, is to get students learning/asking questions in the context of the learning so that it has more meaning and leads to better retention. For instance, the teacher can introduce students to a basic idea (i.e. factoring trinomials) and then use problems for students to work through so that they can start to identify patterns or methods that work. In this model the teacher (who I now prefer to call the coach) can answer questions, connect groups of students, do mini-lessons, or stop the whole class to discuss something.

Our assignment had asked us to submit an inquiry-activity. Going through the above process helped me to realize that I am doing more inquiry-learning than I had realized and then forced me to think through an activity more thoroughly. I now feel like I am better equipped to answer the question "but what does this mean in math?" and to be an instructional-leader in this area.

The assignment was to outline an activity, describe the assessment process(es) involved, and to describe how we would share the resulting data with others.

Here is the activity that I submitted for this assignment:

Inquiry-Based Activity

The idea behind inquiry-based learning is that students use an activity as a learning opportunity (to discover or uncover new learning). In many classes this might involve a topic that is introduced (or an open-ended question) where students come up with a question to investigate. In mathematics there is not necessarily a chance to come up with big issues to get students interested in the learning but we can use problems to get them to investigate a main idea and learn the details of that idea from the problems.

Activity

Prior Knowledge: Students have already learned what a function is and they have reviewed characteristics of 5 main functions (such as asymptotes, vertexes, etc).

1.      Review characteristics of 5 functions, address any concerns or questions.

2.      Get students onto student.desmos.com to complete Domain and Range activity. Most slides in the activity have students submit work and then they will see the responses of 3 peers (so they can self-assess immediately) and teacher can see all responses to monitor class progress (so the whole class can be paused if needed or teacher can go to discuss with specific students). The activity progresses as follows:

                           i.          Graph is given and domain and range are described in words. Student is asked to describe what they think domain and range mean.

                          ii.          A graph is given with description in words. Students identify whether they agree or not.

                         iii.          Graph is given. Students are asked to describe domain and then range in words.

                         iv.          Graph is given and “select all” list using algebraic description of domain and range.

                          v.          Graph is given with algebraic description for domain. Students have to correct the domain.

                         vi.          Graph is given. Students submit algebraic description of domain and then range.

                       vii.          Algebraic domain and range is given. Students create a graph that fits description. ( x 3 )

                      viii.          Graph is given with MC question asking for which algebraic statement is false.

3.      Teacher leads a discussion to consolidate learning of domain and range and add full notation and review function vs relation.

4.      Students add domain and range to characteristics in chart from previous class.

5.      Students pair up to check each others domain & range and to give feedback.

Plan for Sharing Successes, Challenges and Next Steps

This particular inquiry will help to determine the preparedness of the grade 11s to discuss functions (based on introduction of domain and range briefly in grade 10) and on student preparedness to complete investigations (which is an important thinking skill in mathematics and ties directly into the math processes of reflection and connection and this particular task ties into representing). In addition it will help inform the grade 11 team for readiness to move onto the next lesson (immediate next lesson is an activity to practice using the domain/range vocab and we will do some algebraic lessons before coming back to characteristics of functions).

I will share the above with the current grade 10 team so they can make informed decisions about introducing domain/range and with the rest of the grade 11 team to get a conversation started about next steps for investigative thinking. If admin want to know how we are looking at skills continuum in mathematics I will also share this information with them. 

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.

We Need to Stop Testing and Start Thinking

I heard something that was music-to-my-ears today. Apparently there was a presentation to senior leadership in my board a few weeks ago that included a prof from UTM and one from UGuelph (both from math departments) that passed on this message (I am paraphrasing of course) that I hope makes its way around the board sooner rather than later:

"We need secondary teachers to stop using tests as a crutch claiming they need to "prepare students for University". Your students are coming to us as great test takers, but without critical thinking and problem solving skills. These skills are vital, and students who have these skills will be able to succeed no matter the assessment environment they are put in."

I have been saying for years now that we are graduating hordes of students who do not know how to think - even the ones getting 90s. This was confirmed by the numerous peers who have become math teachers and admitted that they now realize that they never actually understood the math they did in high school (until they started teaching it). We need to stop testing and to start giving students the opportunities they need to do some true learning and thinking.

To this I add....we need to bring back the Al Geo course! That had to be the course that I did the most thinking for in high school, without a doubt.

Week 23 - First Time Using Mathalicious

A couple of weeks ago I blogged about my experiences at the 2015 OMCA Conference in Niagara Falls, ON. I wanted to try using it as soon as possible (as they say, if you do not use the new thing right away you probably never will). We were starting off the Grade 10s (after doing a bunch of numeracy review) with Quadratic Relations (not my first choice, but I went with it) so I chose their Wiibates lesson to hope that it would be something engaging as I was planning to use it to introduce the topic (no lessons done in advance at all). My hope was that by starting off with an application it would show the students why they should bother to learn about quadratic relations.

Being the first time trying to do something that was going to be very new to me, and new to my students, I knew that I was going to run into some snags...so here they are:

- I had planned on about 1.5 periods to compete the task and it ended up taking 2+ periods

- All of my students had basically forgotten how to find the equation of a line (seemed to have a weak grasp of slope in terms of its equation although many found it in the context of the question) - this is why I would prefer to start the course with Linear Systems - which is greatly what contributed to the added time needed to complete the task.

- Students were not very engaged by the end of the task, though it started out decently (of course those who actually play video games were the most interested).

These snafus got me to wondering how our Grade 9s are being taught slope? why so easily forgettable? My instinct is that this should be something they remember well because it seems like the Gr 9 curriculum puts a lot of focus on the equation of a line and linear relations in general. I did not find this easy to reflect on as I have only taught MFM 1P once (and it was only 60% of the course as I started at the end of October) and this was 5 years ago. But this is something I would greatly consider when I do finally get to teach MPM 1D.

I definitely plan to try other Mathalicious stories during the semester. The overall concept is still well worth the time and it can only get better with more failure :)

I did ask the class what they thought overall afterward (using thumbs down/sideways/up) and most of them gave it thumbs sideways. At lunch I asked a couple of them for their honest opinions and the consensus was more or less that the lengthy time it took to complete was what made it into a less than ideal experience. They were willing to try something similar later on.

Week 21 - OMCA with Mathalicious

As a mathematics educator I am always looking for ways to show math in an authentic light. It often feels like curriculum limits these opportunities as we feel forced to cover certain topics in a fairly short time-line and we get sucked into it easily. As they say, we often resort to methods and ideas that we were taught with. It takes effort to find new ideas and make changes in education.

So when I heard about the OMCA conference this year and heard that it was featuring the Mathalicious website I wanted to jump on it. Their website has one goal - to use real-life problems to show how math is used as a tool to solve them. Textbooks generally used what is referred to as "canned" math - that is to say that questions are created for the sole purpose of using a specific math tool. What Mathalicious does is take something that is a problem first, and narrate it in a way that allows math to clearly be used as a tool - and generally the end result is something the students will not expect. This can be anything from taking a scene from a play, to looking at pizza to crust ratios, to deciding if a university education is worth the money.

The conference turned out to go as well as we had hoped (I went with a colleague) as the presenter was engaging and sold his product well. We got to try out a bunch of the activities on their site and experience a bunch as an audience. I must say that I don't know that I will ever do the site justice as a presenter myself, but I am still excited to try things out - we got a 6 month subscription with our conference fee. I think what really hit home about the whole experience was that he really forced you to reflect and recall why you had become a math teacher to begin with. We were forced to look at the core of math education and decide what was important - and that is exactly what we did.

By the end of the two days we were ready to head back to work to try something new! The timing of the conference was both terrible (leaving our classes for 2 days in the very first week of he semester was difficult, routines are yet to be established) and perfect - we were able to head back to immediately start using what we had learned. We intend to make use of the website this semester to test out how it might work, where things can be used, gauge student engagement and try to master the art of presenting these well-planned, authentic problems.

First goal is to use one to introduce a topic and to just see how it goes! Basically, to throw ourselves into the deep end - and either sink or swim! (probably a bit of both).

Looking forward I can also see how this has the potential for authentic assessment, great opportunities for collaboration, and the hopes for observation and conversation! It will take me some time to get there (and I can only hope that I will get to teach this course again in the near future - not 5 years down the road again). The excitement of having access to a well-planned, thoughtful resource is invigorating and a great opportunity. I am hopeful that the time they put into these lessons (literally a team putting in at least a week into ONE lesson - time I could never hope to have for one lesson) will only add to my students' experience.

If you have had the chance to try one of the Mathalicious lessons I would appreciate you sharing your story :)