Final Reflection for Math

Here I sit looking back at all of my math blogs this quarter and thinking about the lesson that I taught today to my third graders.  I had to teach them about equivalency in fractions, and how to make equivalency chains, something I had trouble making relevant for them other than the learning it will lead to.  I wish I had read my blogs last night before my lesson - I may have tried to figure out how to do it in groups.  I was trying to allow each student to have their own "Aha" moment, and somehow group work didn't seem to fit it.  Now looking back, and thinking about how I learn, those moments can happen anywhere, and probably faster when in kid speak for them.  Oh well, a missed opportunity.

Back to my learning this quarter - the thing that stands out for me to carry to my teaching of math (and other) lessons next week is reflection.  Taking this moment now to think about what I taught from the standpoint of what the students actually learned is illuminating.  It makes clear for me where I want to go next. There are a few cultural things I want to work in over the next little while: group work with roles that make everyone active and responsible in the group; asking questions - no "I can't" or "I don't know."  Having students explore their curiosity and savor their learning explicitly - this is the culture that I want to create.

My tool belt of online resources has grown exponentially from this course as well from the likes of discovering Kahn Academy, Geometer's Sketchpad, and Fathom to playing with online maniupulatives.  And the data sites are extraordinary playgrounds for interdisciplinary lessons - especially Gapminder and Tableau.  It was instructive and fun to see Robin's excitement about and use of apps to make class management easier, from attendance checking to RSS feeds of our blogs.

I also appreciate the readings, which I will keep: Creative Writing and Math; Creating Meaningful Work, Group Worthy Work, Orchestrating Discussions and Don't Say what a Kid can Say.  Each one easy to read with many doable and worthy ideas.  Thank you for those.

Lasting Math

Today we reviewed the 4 key parts of a lesson plan:
1.  What do the students already know?
2.  What do I want them to know?
3.  How do I want to get them there?
4.  Did they get there?  How do I know?
If we cover these bases well and keep coming back to them at the end of each day as assessment of our instruction, our students will surely benefit.

The wolframalpha website is terrifying and wonderful in the same moment.  If students have access to this "computational knowledge engine" in class or elsewhere, they may never actually have to learn the how of math.  This inspires me to further my explorations of relevance.  If I use this ready access to computational information as an impetus to make the students want to learn how to do it, to help them find how and why this math is used everyday, perhaps even talk about how and why it was dreamed of in the first place, I might get interdisciplinary in a very engaging way.

This relates somewhat to the reading for today as well (Exploring our Math by Leatham and Hill).  Helping students to "broaden their views of the nature of math" helps them see its value in real life activities and jobs.  This alone could draw their wonder toward deepening their own understanding.  I also appreciated how the authors talked about students expanding their own beliefs when they hear "other students express beliefs about math that differ from theirs."  I love those moments in particular where we actively take in information from someone else, evaluate its significance for us, and decide to change what we think.  Very Powerful.

Mathematical Meanderings

Wow, I learned a few things today in math.  I've thought about using math journals both as an interdisciplinary tool and as a way to check for understanding, but must confess that looking through all of them each week, sounds daunting, not to mention potentially out-of-date with where they are now.  Today we talked about using online journaling thru RSS feeds.  That makes them seem more relevant to me.  I can find out the same day they write about their confusion and address is readily.  I appreciated learning that they should never be graded - I hadn't thought about that yet.  I mainly wanted them to help inform my instruction.

We also learned a few more tools to add to the toolbox:
* Fathom - a very dynamic graphing software that can even use data sets from the web!
* Data and Story Lab - on the web for finding interesting data sets.  I liked the idea of inspiring our students to be "data detectives."
* Geometer's Sketchpad - we hope to get a demo of it next week.

We talked more about the "Using Creative Writing and Literature in Mathematics Classes" article today. The idea of using multiple disciplines to get students to show their understanding excites me.  I'd love to give groups a video camera and have them tell their story or even explain how to do the math, so that the writing isn't even a block for them.  It could be illuminating and entertaining!

Reflect on Your Teaching Everyday

I like that.  At the end of each lesson, or the end of each day, taking a moment to reflect on how students are progressing and what I can do to further their learning; to make a real study of my effectiveness as a teacher and of my students as learners.  At first this feels burdensome, a heavy brick added to an already back-breaking load (I went for drama because I liked the alliteration!).  The sooner we tend to this however, the sooner we can stop wasting time and resources on an unproductive path and find something that works better for our students.  The best way to get the information we need is to have very regular assessments of all kinds that don't feel like assessments to the kids.  We need to pay attention, formally and informally, finding many ways to check for understanding everyday.  We should also pay attention internally; maybe have some sort of engage-o-meter.  We can feel when the students are engaged, and keep notes about what really works.  I wonder if this comes naturally after a time?

I appreciated Robin's categories on her lesson plan: Share and Summarize; Application and Extension; and Assessment that is followed by Reflection.  Working these right into my lesson plans will help me make a habit of it.

Be an Agent of Change

"Be an agent of change by teaching critical thinking" in your classrooms; a direct quote from our math teacher last week.  That is a powerful statement.  How do we teach critical thinking?  By checking for what students might already know that might help them in this problem; for application of the previous knowledge; for what predictions can they make; challenging them to engage, to connect; to become problem solvers, detectives? 

How do we wake up their minds? It has to be safe. It has to be relevant, interesting, or funny.  Once we get them to connect with the work, we have to help them develop analytical thinking habits - some basic questions they can ask themselves (and each other) to check what they already know and see how what they learned fits or shifts the prior knowledge.

I think maybe I don't like the term "critical" thinking because of negative associations I have with the word critical.  For me it connotes judgement and more of a closed mindset.  I want to cultivate open, distinguishing thinking in my students.  Distinguished thinking.  I like the sound of it!

Gapminder.com

We had another visit with Gapminder World.  Our in-class, small-group project of finding something of interest and creating our own way to display the information was thoroughly enjoyable, albeit a bit overwhelming - too many choices and such different questions in our small group.  Nonetheless we found something that we could all invest in and then had to find a way to display the information.  Interestingly, our questions led to more questions that led to more research outside of the gapminder website.  We had to answer why (education spending flatlined in 2001 with the inception of NCLB) and that led down some controversial paths that had what appeared to be very conflicting information.  Given more time I think students would begin to ask more questions about what is actually being asked and answered in the research, broadening their understanding of how difficult it is to be clear, concise and as "objective" as possible.  This looks to me to be a potentially very inter-disciplinary study of how we get information, how we look at it, and what it really means.  I think this could be very valuable across all content areas.  The implications are very broad and far-reaching in this "Information Age."

Questions

Math class was fast-paced and fun today.  Robin underscored the gift of using group-work projects and problems as easier and more efficient ways to address standards in the curriculum.  This is a familiar refrain in our classes, but the problems she gave us literally had us asking for more.  At the end of class we looked at the standards that we covered - fabulous.  The math curriculum in my district is highly prescribed down to the worksheets due on each day to the unit tests that get sent to the district.  I will eke out time to do some of these group problems.  I still have questions about how to implement groups wherein each student is engaged and responsible . . .

Speaking of questions - I thoroughly enjoyed the article: "Never Say Anything a Kid Can Say!"  The essence for me spiraled around questions, and how to ask thought-provoking, process-oriented questions that lead the students to their own answers and the differences between their answers.  I especially enjoyed thinking of a class where the questions matter as much as the answers, where more students are engaged thinkers.  The little nugget that stood out for today was requiring students to ask questions instead of saying "I don't get it."  Brilliant.