A teacher trying his best to make math enjoyable for students.


Tuesday, February 23, 2016

Low Stress Access

From what I understand, years 3-5 can be among the most transformative years in a teacher's career. That lands me right in the middle of that range. And despite my distaste for the New Mexico teacher evaluation system, I am thankful to my current principal, who uses it effectively as a way to reflect upon and discuss my practice. Recently, during my post-observation meeting, I sat down with my principal and we decided the next areas for me to focus are tweaking my questioning techniques and taking a deep look at methods for assessment.

With that said, I have been really focusing on low-barrier versus high-barrier questions when engaging students in a lesson. I found, that in my first two years of teaching (starting to breakaway in year 3), that I was so ready to introduce students to new content that I would introduce new procedures before I even gave students a chance to use their own reasoning and demonstrate what they already knew. I was so caught up in the idea that a diagnostic had to be a written test and I didn't want to waste a class period so why not quickly move ahead?

Now, in my fourth year, I have really made it a focus to open up new ideas by giving students an opportunity to try their own strategies for solving problems I will ultimately give them a new strategy for solving. Recently, the idea I wanted to introduce was using a line of best fit to make predictions about future data. Old me would have simply said today we are going to learn about lines of best fit and then I would move full speed ahead, using the "I do, you do, we do" method of instruction" (I shudder just thinking about my confidence in this strategy as the only logical form of instruction). Now, I present my students will the following problem:

The Google Doc version of this file can be found here.

The goal is for students to come up with their own strategy for predicting these future data points and some of the ideas are incredibly sophisticated and show a deep level of understanding. Some students said they noticed a positive correlation and estimated where the points would be at 750 and 1400 minutes. Others created an elaborate box structure to create a high and low option for each set of minutes and then put their point in the center (if I remember, I'll post a picture of this). and still others, estimated by drawing a line through the top and bottom points to estimate future values, showing they were already thinking about lines of best fit.

Year 3 me would have said, "Cool! Thanks for working through this guys (without having students show off their work). Now let me show you the correct way to do this!" Today, wiser year 4 me takes mental notes of different lines of reasoning that students came up with on their own, which they then share with the class. In this way, I am not the owner of new knowledge. Student ideas are validated and multiple lines of access to the content are opened up. Now that students have had a chance to develop their own reasoning and share it with the class, they are primed for me to demonstrate the alternative method of using a line of best fit (which some students came incredibly close to generating on their own).

In the end, opening with students presenting what they think is a powerful motivator and leads to deeper initial understanding of the underlying concepts in new material. This is similar to my opening activity for linear equations seen in an earlier post about constant difference. I find that even my lowest level learners are capable of accessing mathematics when they aren't required to "crunch numbers" right at the beginning, but can reason through the process. I am going to continue to explore these opening activities and try to generate even more. Maybe this will become a serious hobby and lead to a blog in the style of Visual Patterns produced my Fawn Nguyen.

I just want to give the MTBoS a shoutout for pushing me to be better and move beyond teaching how I was taught.

Tuesday, January 5, 2016

Thoughts on MTBoS

I was intrigued by Brett Gilland's post on scaling the MTBoS community to include more teachers because I can tell he has a vision for what this online community can be. I also think it fits with Dan Meyer's vision of having an open-source, digital math curriculum that challenges conventional methods for teaching mathematics. With these posts in mind, I have a few thoughts:

First, having recently earned my MA in secondary education, it is clear these open-source resources, the reflections of educators, and the quality virtual discussions are more important than ever for teachers looking to improve their practice. The rigor of my MA program was offensive to me and many of my peers, resulting in limited growth for me as a professional. The worst part is that these programs are not free, though they result in modest pay bumps. What are teachers paying for if they are simply going through the motions of taking classes to get a degree because there is no challenge beyond two page reading reflections? This begs the question, what are state/federal governments hoping to accomplish by requiring teachers to earn an MA to become highly qualified? If it is simply to have nice statistics to include in reports to state departments of education, while failing to push teachers to challenge their own practice and grow as professionals, then it is a useless exercise. I know there has been increased discussion on the national stage about the quality of teacher ed programs, but I won't be surprised if that topic disappears from conversation in the next six months. MTBoS offers an alternative, a place where teachers can reflect, gain access to new lines of thought and resources, and ultimately grow into better educators. But what percentage of math teachers in this country are actually participating? Despite these benefits, the reality is that schools/districts do not recognize this informal professional community because it is not part of a formal institution. When I think about scaling this community to meet Brett's vision, maybe it involves formalizing the community in some way so that it is recognized by districts/state departments of education to incentivize trad teachers to join. National Board Certification does not necessarily mean an increase in pay, but it does garner a certain amount of respect and increases a teachers' attractiveness to schools around the country. But the National Board Certification costs a significant amount of money, yet MTBoS is free and if it remains free, many trads may be attracted to partake if they are recognized in some way by their communities for their involement.

Second, I am still a young teacher (4th year) and the MTBoS is intimidating. I do not mean this in a negative way, but it is scary to become an active participant. It has been great using resources developed by quality teachers, but giving back to the community can cause new members to tremble, fearing they will be found out as a fraud. I admire people like Sam Shah and Jonathan Claydon, who are confident writers and have incredible resources to share, but viewing them as the standard can be a deterrent to posting one's own resources (I am definitely speaking for myself in here). I think it is great that the MTBoS blogging initiative was created and pairing new bloggers with experienced bloggers is brilliant, but will this encourage more traditional teachers to join the conversation? I lean towards no as the answer to this question. So this brings us back to Brett's question. Is this community designed to be a safe space for teachers already open to progressive pedagogy to discuss teaching and share resources so that they can do more for their own students, or is the idea to transform the profession and the teaching of mathematics around the country. If the goal is transformation, how do we continue to decrease the fear associated with involvement. The blogging initiative is a great first step, but I think more has to be done.

Third, and last I think, the final point Brett made was there is an absurd amount (maybe approaching infinity) of materials out there for teachers to sort through. As a result, sometimes it feels like luck that I stumble upon something that I can use in my own classes. For those teaching the same class as Sam Shah for example, his virtual filing cabinet is like walking into Narnia. Resources from his entire curriculum can be found and so there is a foundation to build upon and tweak as one likes. But without access to teachers that have put together these filing cabinets for classes I teach, the hunt for resources is daunting and often times I feel that I am settling for tasks that I am not as excited about just for the sake of sanity. I am excited to see Dan's work on curriculum in the future, I know Brett loves CPM, and there are the virtual filing cabinets, but this is a very small amount of order in an otherwise chaotic system. There must be a way to start consolidating resources and organizing them. Maybe a MTBoS virtual filing cabinet that organizes resources from all blogs based on their tags. I'm not saying I know how to accomplish this, but too much random information can be almost as damaging as too little and for those of us early in their careers, trying to work some of the amazing tasks that are available into our curriculum can make things feel disjointed. Is there a way to create a foundation for teachers looking to change their practice, a place where the MTBoS community has organized various contributions/tasks into a skeleton curriculum for all grade levels/content areas? At this point I am simply rambling and spit balling ideas for creating a vision for the future.

In the end, I love MTBoS and it has had the greatest single impact on my teaching practice. I am excited to see what this community grows into and I have great admiration for all of its members. Thanks for reading and I apologize for any grammatical errors.