*Warning* *Long Post*
I also unleashed the power of twitter yesterday, where I spend time lurking. Sending myself even more resources from the conference, filling up my inbox quickly:
Well now that I am completely overwhelmed and don't know where to start, I decided to shop. I had this idea while listening to a session of overhauling how I do Open Middle Tasks. Typically, I let students write out the problems using dry erase markers on their desks. But during the NCTM conference I thought - why not make number tiles and have students manipulate the problem using the tiles, while keeping track of their trials on their desks with their dry erase markers? So I went to Amazon and I bought the following:
What I plan to do when they come tomorrow is paint the letter side of the tiles black, number them 0-9, and place stickers on the back noting the set they would belong to in case one gets dropped on the floor. I will also place the same sticker notation on a ziplock baggy so the students and I know which set goes in which bag. Then I will spray the lacquer on them seal them up. I envision something like this, but 32 sets of 0-9, without the operators. Now that those are ordered, I have decided to clear my inbox. This. Could. Take. All. Day.
One of the sessions I missed and am kicking myself dearly for it, is Mathematical Mindsets; Creating a New Future for Math Teachers and Learners by Jo Boaler . Fortunately, someone on my feed, shared a link to this article where a similar talk given to the National Council of Supervisors of Mathematics a few days earlier. Just as I sat down to watch it, my computer decided it was an awesome time to update, so I switched devices.
Reading the article and watching the video only further solidified other thoughts that had been rambling in my head since attending the conference. Math class is no longer about speed and procedures with homework consisting of page 456 #1-31 odds. It's about connecting with the math in meaningful ways and know that each student has their own way. Sigh. I know I can do better. I know I need to do better. But where do I start?
THIS:
One thing at a time. But what is that one thing? Then diving deeper into my inbox, I came across this We are Powerless Ignite talk from Megan and #7 hits me like a rock. "We humbly admit that no matter how hard we work in this profession, we will always have shortcomings" BAM. I finish reading the rest, and I am so glad I have this linked. And even happier that she provided a pdf of the 12 steps.
On to the next item in my inbox. This was a simple link to follow up on - more resources for Which One Doesn't Belong. My students love these, and I have come to the realization that we sometimes only scratch the surface. There are days though, that I do feel I deserve a well meaning pat on the back for diving deep. This I what I need to keep in mind, and realize that it is time worth being spent.
Something non-NCTM related that caught my eye was this tweet by Laura Wagenman. While I'm not sure the Graph of the Week is something I'm going to full embed into my classroom, it is an idea worth pursuing. I particularly like the resources linked like the graph of the day from StatChat.
One thing that has to wait because I want to see the video is the NCTM Ignite session. I am stalking this page, waiting for the video link to be added. I chose to go to the MathCounts Reception instead of Ignite so I could network with seasoned coaches from across the country, having just completed my first year as our school's MathCount coach. My colleagues spoke so highly of Ignite, and while I was able to view Megan's slides from We are Powerless, many slides looked like you needed to be there to understand them. - So I am tabling this resource.
It's now 12:53, since this is a DitLife post. I've been consumed with combining through resources and pouring my thoughts out. I guess I should go get some lunch.
1:25 - and I'm full and ready for a nap! And as tempting as it may be, I really want to go through, organize and find out what instructional impacts I am going to make in my classroom when school resumes next week as a result of attending the NCTM annual conference.
The next item in my inbox is this Tweet from Annie Fetter about Notice and Wonder. It provided a link to this handout. Last year I did a book study on Powerful Problem Solving where Notice and Wonder was one of the instructional strategies. I have been hooked ever since. Unfortunately, multiple times during the NCTM conference several sessions were hard to choose from as many overlapped other ones that I wanted to go see. Annie's was one of them. Reviewing the handout, infused more ideas and got my thinking cap back on regarding the Notice and Wonder strategy, and I hope that the video of her session is posted soon too!
I went through a few other items I had sent to myself but I'll spare you the details of those duds. They looked more promising on my phone through a tweet.
Something that caught my eye was this tweet by Alice Keeler who talks about feedback and having the students choose 3 to submit (it's the third bold faced item). I found the strategy interesting to ask the students to pick three problems they want feedback on. Alice describes a way to do it through technology (her speciality) but I really like the idea of giving the students the power to chose which problems they would like me to give them feedback on.
Another non-related NCTM tweet that caught my eye from Tony Vincent was this one about printing on sticky notes. I use sticky notes all of the time in my classroom, and this could just kick their use up a notch.
WOAH. This Desmos Tweet. They have introduced a Geometry Tool in Beta that you can read about in their blog. I spent some time trying this out, and can understand why it's in Beta version. I am hoping that it's not too long before a measurement tool is added so angles and line segments can be explored too.
Going deeper into by inbox, I looked at this tweet from Donna Boucher which actually led me to this Youtube video from 2015 Ignite on Hidden Decision-Making in the Math Classroom, another Ignite by Annie Fetter. I am glad I stumbled upon this one, and while not from this year's NCTM annual, the message is is very applicable to any classroom. It's summarized in the pictures below, however, you should watch the 5 minute video to really get the whole picture.
Next I moved on to this internet gold mine, from a tweet by John Stevens about the #MTBoS Google Search Engine. This internet resource searches all of the blogs of the #MTBoS members on topics that you put in the custom search bar. Amazing!
It's now almost 3 pm. I've seen a lot about 15/2 avocado's on twitter and found this tweet from Christopher Danielson that links to this post. Hmmm. I've read this twice. A third time may be warranted. What sticks out to me the most is the question he posed "What prevents attending to number structure?" His example illustrates the point perfectly.
I am now down to my last email link from NCTM. This is actually a blog post from MathyCathy about her highlights at NCTM. I enjoyed her session and reading this blog. She and I attended many of the same sessions and it's interesting to me to read her take on the same presentations. It's like hearing the same thing but revoiced. She also attended a few sessions I did not, so that added to my list of items to follow up on. One thing I want to dig deeper into is the PBL CCSS maps from Emergent Math. I briefly clicked on the 7th grade map, and found the resources they have linked to - I see that this is could be a go to resource. Another resource linked was this one from Henwood Math. I've linked to the resource page where topic folders are arranged. This is something else I will need more time to dig into.
Whew. My inbox is finally cleared.
But I have yet to dive into the resources I brought home. I think I'll take a short break and vacuum the house.
Now 5:02 pm and my break was enough to give me time to vacuum, fold a few loads of laundry and dust the pollen off of my furniture (one of the many benefits of living with your windows open in the spring is dusting often). My husband sent a text saying he is going grocery shopping, so I am going to postpone trying to make a magically delicious dinner out of the few remaining items in the pantry and refrigerator since grocery shopping hasn't been done since before I left for San Antonio. This means I can dive back into what I brought back from the #NCTMannual and further think through instructional implications of my attendance.
First, I take a look at my session notes with the goal to pull together cohesive thoughts and complete any to-do items I listed as a follow up in my notes.
- Making Connections Between Proportional Reasoning and Algebraic Thinking
This session used the Ti-Nspire to show the progression of proportional reasoning through evaluating patterns made either through cuisneaire rods or pattern blocks. We were given a laminated card with three designs on it and asked to draw the next two. Then we were asked to identify the number of rods or blocks used to create each design. Once completed, we broke out the Ti-Nspire and created a spreadsheet that created a graph and eventually moved through to making a line and equation. Since I don't have access to a Ti-Nspire, I thought about ways to modify this task with Google Sheets and Desmos. I also began to look into funding sources for the Ti-Nspire.
- Monitoring Your Classroom Canvas with Formative Five - You Can Do This!
Broken down into these five categories: Observations, Interviews, Show Me, Hinge Questions, and Exit Tickets; the speakers (who included past NCTM president Skip Fennell) detailed each of these. They provided this link to resources. This is something that I need to dig out and spend more time going through. One thing that stuck with me is the idea of hinge questions - are the students ready to move on? I know I have always asked these types of questions, but have I framed them in a way to give me the correct information? Have I used them often enough?
- Boost Conceptual Understanding and Procedural Fluency with Rich Number Sense Tasks
Trying not to be #MTBoS star struck, I arrived at this session in order to get a good seat, not because of Andrew Stadel, but because the session write up. Although, coming back to class to tell my students who routinely do a Estimation 180 task that I was in a session given by Mr. Stadel would help elevate my coolness factor. There were several things that struck me through this session. The first was that students have a "lack of access to opportunity to banter with numbers" and we need to "not blame the students and their previous teachers". Just pick up with what we've got and go from there. We do this by using visuals. When we don't use visuals, we rob students of a sense making opportunity. Andrew showed several visuals to include a clothesline. He combined the Estimation 180 task with a clothesline, to include a too high and too low, and measures of center. An ah-ha moment was when I realized this one task could be done over multiple days. Another ah-ha moment came when he showed the video answer up until just before the answer - and asked us to revise our answer. Math is a rough draft. We can revise. Moving on to talking about Place and Space - making sure that students know there is a place and a space for all of math before talking about how to design the tasks using 2-3 colors only, being walk in ready, and labeling each number line using units.
- Promoting Classroom Discourse Through Open Middle Problems
This session talked about Open Middle tasks to promote student discourse to deepen student learning. We discussed and tried our hand at several Open Middle tasks. These tasks are something I use in my classroom and I was hoping to kick them up a notch or perhaps learn a way to create a few on my own.
- Proportional Reasoning - The Building Blocks of Linear Thinking
This session discussed ways we discuss proportional reasoning with students and how we can uncover misconceptions. A few things that I took away from this session - the handouts, so I can reflect back on them - what makes a proportional task worthy? The idea to make several number lines - one side blank with no intervals, one side with lines that are roughly a thumb width apart from each other to create 25 un-numbered intervals and the idea of a process column. A process column is a column between the input and output columns on a table that show the process of the function. This helps to show the students the relationships.
- The Winning Equation: How to Get More Students to Love Math
Given by John Urschel who talked about how his teachers never talked to him about becoming a mathematician. And to become a mathematician, especially with his ethnicity isn't at all expected. He wants to get his message out that without mathematicians many things are not possible, and as teachers we need to inspire students to look towards this as a legitimate outcome of education.
- Illustrative Mathematics - Open Educational Resources: Designing a Middle School Curriculum
Here's another session where I tried not to be #MTBoS star struck with Kate Nowak providing background information on Open Education Resources. This resource is made with the most broad copyright license so even a textbook publisher can take it, tweak it, and sell it. They want it that way so that it ensures there is quality materials making it out there. We were able to log on and take a look at it as it is in a pilot stage readying for a release this summer. The one thing Kate said that resonated with me was "Set up dominoes in 6th grade that you don't want to knock down until 8th grade" - that's why you need coherence. Apparently I wasn't the only one who was struck by that statement, because I saw it show up on twitter several times.
- An International Perspective on Modeling: Implications for What We Teach
An interesting session where the presenters talked about their ICME Conference experience. One thing that I walked away from this session was how perspectives frame modeling. For instance - how much water do you need to make pizza? It depends - are you camping, and need to consider water for hand washing? Washing vegetables? Are you a farmer in charge of growing your ingredients and therefore need to look at water for animals and crops? Or are you making pizza for a family in your kitchen? If so, how big is your family? So many things to consider when you pose one problem without any specific constraints.
- Middle School Number Talks - Shifting the Classroom Culture
Given by Sherry Parrish she talks about how understanding needs to come before procedures and number talks are 5 to 15 minutes of classroom conversations around purposefully crafted computation problems that are solved mentally. I have done number talks in my classroom before, but I feel that I haven't done them with the proper coherence they need. Listening to Sherry, I realized that I can restart these talks and still get the benefit. I need to start small, with dot cards, moving on to basic facts, then whole number computation and then on to fractions. I also need to be aware of my moves to support risk taking and record student answers without names and posts. By using number strings, I can move into more complex problems and carry this number talk into several days. But I must always provide a safe environment, allow wrong answers (and encouraging proving/disproving with another example), strategies & modeling (attached to one another) and misconceptions. Then comes where do I start?
- Rich Real World Problems
Here's another #MTBoS member where I tried not to be star struck. Given by Robert Kaplinsky, it was nice to work through one of his problems with him as a leader. We switched back from our teacher hats to our student hats as we worked through a task. I've used several of his tasks in my classroom and was able to pick up some ah-ha items to take back. One thing is to give students alone time to fill in the "What do you know/What do you need to know" on the graphic organizer he handed out and then give the students time to collaborate. When we give time for students to work alone we make sure the alpha student doesn't just take over. One slide that really stuck out to me was the Level of Convincing. When we have students who need to turn and talk to each other, this is what we need to strive for.
- Using Digital Tools To Give Every Student a Voice
I ended my #NCTMannual experience with this session, and again was trying to keep my giddiness in check. This session given by MathyCathy of #MTBoS and I thought about introducing myself a couple of times when I saw her over the few days. Maybe next year. She used NearPod to deliver her session, a platform I am very familiar with. Through her session, I realized I don't utilize it nearly the way I should. Throughout her session, she gave us a voice. And I began to wonder, how often do my students feel they have a voice? And she kept us anonymous - that's a nice feature. That creates a safe and open environment. Everyone participates but it's okay to answer incorrectly - it gives us a base to start a conversation. I just cancelled my $120 subscription because it was self funded and under utilized. I may need to rethink that decision. Things that make you go hmmmm...
So now it's 7 pm. And I've poured through the resources but I haven't thought about dinner. My husband came home and unloaded the grocery (and put them away, and acted surprised when he saw the dishes were clean....). He went out for a short run, so I guess I better take some family time, and figure out dinner....
Now that it's 8:30 and I have my son on dishes duty, I realized that I dedicated a good chunk of my time today in cultivating the resources from the NCTM annual conference. And I've barely scratched the surfaced. And I think back to this tweet.
So what is the 1 thing I will do? I don't think I am ready to narrow it down to just one thing. But here's a list:
- Have number tiles available for Open Middle Task so students can manipulate the math.
- Look further into Jo Boaler and YouCubed.org, changing my mindset about teaching mathematics.
- Continue to use Which One Doesn't Belong.
- Look into Graph of the Week and how can they relate to Graphing Stories, something I already do.
- Continue using Notice and Wonder, but look at how I can do this better, with more consistency.
- Have students choose 3 problems for feedback. Perhaps even add a spin - one you are proud of, one you are unsure of, and one you think you have an incorrect solution for.
- Print Sticky Notes - and use creativity. What is the purpose for their use? Can I add a graphic? Something visual that will help the students respond to the problem?
- Stalk the Desmos Geometry Tool. Introduce it to students. Watch its impact on student understand.
- Stop saying "Right" and start saying, "Tell me more" or "How do you know".
- Start explicitly uncovering the structure of problem, when needed.
- Remember the Google Search engine for the #MTBoS.
- Look at Emergent Math and Henwood Math for resources. Could they be added to my go-to list?
- Look for funding sources for a class set of Ti-Nspire. And Cuisaire Rods.
- Start helping students make explicit connections in their proportional thinking by having them look at visuals, then tables, then graphs and finally lines & equations.
- Look over the resources for the Formative Five and use hinge questions to assess student readiness to move on.
- Order rope. Lots of rope. Nice rope, the kind that won't give you splinters when you touch it. And think of ways of organizing my classroom so I can have multiple clotheslines. Buy 2-3 colors of card stock so I can make the cards for activities that I use the clotheslines with. The first activity I am think of is probability from 0-1 (decimal, percent, events, fractions, etc) This has the potential to be several levels!!
- Make sure the proportionality tasks are worth while. Do they present students with the ability to reason with the mathematics while building their understanding?
- Help students know that math is needed, and there really isn't a person type. Anyone can achieve and be a mathematician. Grow their mindset.
- Dig deeper into OpenResources for Illustrative Mathematics. How can their scope and sequence help our county realign our pacing? What are my existing must do activities that I can embed, should I be able to use this curriculum? Where would I put those activities? This is a summer activity.
- Rework Number Talks in my math classroom. Remember it's okay to continue this over multiple days. This is where my flip chart paper can come in handy so other classes cannot see each others conversation.
- Use Robert Kaplinsky's problem solving framework along with time to work silently before working collaboratively. Also think about the levels of convincing.
- Revisit using NearPod to give students a voice. Compare and contrast this with GoFormative. What are the pros and cons of each platform?
If I had to choose just one thing, it would have to be #9, followed almost tied with #16 & #21.
Now that it's 9 pm. I feel that my day is done. It's time to turn on some tv, perhaps catching up on an episode of Dancing with the Stars. For tomorrow, I need to take these items and think about how I am going to put them into my plans for next week.
I am already excited to return to school and I am already looking forward to the NCTM annual conference in Washington D.C. next April.
PS: Here's a screenshot of my open tabs... they are going to stay that way until tomorrow....
PPS: Here's a picture of my coffee table now. I have organized my materials into piles - free resources, student books from MathCounts, papers to grade, NCTM notes/items.
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