Monday, July 20, 2015

Week 27 - Using Investigations to Teach Quadratic Functions

Part of using a flipped class model means identifying lessons that will not be best taught by mass instruction (i.e. video) but will be better served by something like an investigation. A big part of my current philosophy of math education is that most (if not basically all) students memorize algorithms and never really have a strong grasp of the material, so I seek to change this trend and try to push students to make connections between ideas and really understand why it works. "If you understand the basics, you can use them to figure out the hard stuff" is what I am often heard saying. I think I came to this realization when I was in my B.Ed year and/or my first year of teaching when my friends (a year ahead of me in school, so already teaching) were commenting that they couldn't believe how much they realized they did not understand in high school. In fact they did not understand it in university and were only getting it now because they had to teach it!

As part of these ideas I wanted to find a more effective way to teach quadratic functions that would (hopefully) lead to less memorizing. I set out to find/modify/create some investigative tasks for students to work on. This usually involved them doing the intro portion for homework the night before and then working through the rest of it in class in their groups. The first two investigations explored and linked step property (the pattern created by the changing slope - the idea being that students start to make a connection between linear and quadratic relations), first differences, and congruence (as well as symmetry). In the third investigation they were given some challenging problems that they would hopefully be able to solve using the ideas they had discovered.

These classes were then supported afterward with short video lessons to hopefully help students consolidate and to make sure everyone took away the key ideas I was hoping for. One of my biggest challenges has been creating that authentic, risk-taking environment where students are not afraid to be wrong while working through tasks like this. Many of them have never really worked through such challenging tasks or ideas and they seem to fear the unknown, to fear trying new things. I sometimes feel like a broken record, but I really do wonder if this might have been different if these tasks had come later in the semester.

What I am hoping to do in the future is to work toward creating this elusive learning environment is to focus more on talk strategies in class to help students enhance the communication among themselves (so they do not always have to have a conversation with me to feel like they have gotten anywhere). I think that this, in combination with a higher confidence with linear relations before embarking on this unit, will lead to better results (i.e. less memorization!).

I would love to hear from others who are trying anything similar. What worked in your class? What didn't? Why?

Monday, July 6, 2015

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 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.

Saturday, July 4, 2015

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 :)

Friday, July 3, 2015

Week 20 - Setting up MPM 2D

Here I sit trying to set myself up to teacher MPM 2D this semester (OK, really it was 5 months ago...but I fell of the blog bandwagon and am playing catch up) with way too many ideas of what I think is needed going through my head. How am I going to set up my LMS? What gamification ideas am I going to try? Where am I going to source my videos from for my flipped lessons? What will my classroom routines be? (See - so many decisions to make! The next time someone accuses teachers of being lazy I think I will read them this opening paragraph). Here is what I am hoping to accomplish:

1. Use Edmodo to set up an online area where students can access resources, connect to each other, and have one account to do multiple things. I use EduCanon (which allows me to embed questions into YouTube videos for my flipped lessons and students automatically have an account for when using Edmodo) and am hoping to make some use of the cK-12 resources for online practice and quizzes.

2. Badges on Edmodo for a bit of gamification. I struggled with this last semester. My efforts often peter out and students cannot see what badges they have not earned yet so there is no added drive for them really. I will make use of the badges to connect to the University of Waterloo Problem of the Week - I am going to post this problem every week and for each month there will be a badge for 2 things

  • attempting at least one problem that month and submitting a solution
  • completing a min of 3 problems that month with a consistent effort and mostly correct results
3. Make use of a known YouTube channel (alrichards314) for some of my flipped lesson videos and search YouTube for at least one other with a lesson style that I like. Here is the one I ended up using because the lessons are usually set up so that an explanation is given for the tool/skill/concept before examples are used to show how to use it.

4. Every class will start with a 10 minute warm up that is developed to help students work on core numeracy skills to improve confidence (i.e. multiplication, division, fractions, etc). I hope to attempt to make sure what we do here is somehow related to that days work but feel it is important regardless. I am planing to focus on one skill per week where the difficulty builds up and Fridays will have some kind of game component.

5. Tracking student achievement using an excel tracking sheet for learning goals throughout the course (recording what learning level the student is at based on what I hear/see/mark - the long term goal being the observations/conversations piece of triangulation of data, for now I just want to get used to using this so that it can be a tracking method in the future). I also hope to have the individual student have access to this in the future so they can see what areas they should keep working on. I have also started using a OneNote file to track student work and am hoping to keep doing this (I soon realized that while this was doable first semester with a small class it was not feasible to do myself with 28 students - I made an attempt to get students to do this for themselves as an eportfolio but did not follow up well - now a goal for the future!).


Week 19 - Taking Risks

Well if it is not obvious this is a very delayed post as the school year is technically done, but image for a second instead that first semester is just ending and second is around the corner. I had been thinking a lot about taking risks at the time - both from the perspective of taking chances as a teacher, and the perspective of getting students to take risks in the classroom.

My own psyche fascinates me as I seem to be able to take risks in my teaching (both in class and online) despite having trouble with this in my everyday life. Perhaps it is something to do with my comfort in my profession and my confidence in the support I get from my PLN, colleagues, and admin. If it is not that, then I really do puzzle myself. This is not to say in any way that the risks I am taking do not feel that way - many of them do.

In my classroom I am always trying to do something a little different. Trying to come up with things to engage students in my flipped classroom (which could mean a new lab, different investigation, new attempt to use manipulations to teach a concept, or using a new strategy altogether) means that I am taking a risk with what students are going to learn (or if they will learn) which always feels like a personal risk. I think that most of that personal risk is related to pride. I feel thankful that this first semester had some good students so there was more room for me to take personal risks or my ego (I find it a lot harder to do that when I am having a rough semester already).

These risks lead to a feeling of vulnerability. Every time a teacher posts a blog, admits to defeat, publicly asks a question on Twitter she is risking feeling vulnerable or judged by others. Now it is not very common to be challenged by another educator, as there is a mutual respect and desire for personal growth and learning, but in doing so our thoughts and ideas are published for everyone else to see (students - current and former, - parents, and community members sometimes monitor what we do as well) and I have experienced first hand how these things can be misunderstood or twisted out of context to make them seem something they are not.

This has become a bit more of a ramble than I had intended, so if you are still reading I thank you.

The other side of the idea of risk taking is trying to get students to take risks in the classroom. I will be the first to admit that I have had a lot of trouble getting this to become more common in my classroom. Teenagers often carry with them an innate desire to fit in (and for many to blend in) and risk taking in front of their peers may be the last thing they wish to do. But it is with these risks that learning comes from. We learn by making mistakes, by making new connections. I have challenged myself to come up with a time that I made a mistake that I did not learn from...and could not come up with one.

For now one of my goals is to try to use conversation in the classroom more as a means to get students to start to talk about their thinking, to admit when they are unsure, to work through problems together. I have tried giving students an online place to do this as well to give them 24 hours access to things, but have not had much luck. One thing I do know is that if these things do not get initiated by students that usually are not authentic enough to get them to use it. I have tried even giving them anonymous ways to post online to ask questions and still have had no luck.

If you have any ideas to share for in class or online risk taking for learning please leave a comment below!