Building Enduring Mathematical Understanding, one lesson at a time.

Archive for the category “Reflections”

Reflections: Lurking to Learning

Today is my one month “blogversary!” I don’t have much to add to the conversation on Advisory for msSunFun, but I do have an item on my To Do page that I would like to tackle: My journey to becoming a blogger.

I first “lurked” onto the “mathedublogger” scene just over SEVEN years ago! At the time I was teaching at an Alternative High School, and we had just been “chosen” to participate in a 1-1 program beginning during the 2005-6 school year. We (the teachers) had some training at the end of the school year and then took our laptops home over the summer. Wow! The Internet in your lap! During the hours/days/weeks spent searching for online tools and resources I ran across some “bloggers” talking about what they do in the classroom – especially in regards to technology. It was still a fairly new idea from my perspective. Every once in awhile I would wander back and take a look at what was happening. Often one site would link me to another, and so on, and so on. . .

Meanwhile, I moved to one of the middle schools in the district and was no longer involved in the 1-1 program. However, our Computer Lab teacher shared GoogleReader with us, and my lurking seriously went up a notch or two. My tiny iPod touch became my window into the “mathedubloggosphere.” I don’t have the data to back it up, but I really do believe that the MathEd blog scene has grown exponentially – meaning that the growth was actually quite gradual to begin with, but then started to take off! I remember running across dy/dan (what a cool blog name, I thought) before he WAS dy/dan! I “lurked” as some of my favorites, Continuous Everywhere but Differentiable Nowhere, f(t), and MathMamaWrites built their followings. ThinkThankThunk next slammed onto the scene along with his SBG cohort Point of Inflection. Even though most of the bloggers were teaching at the high school level (or higher) and I was now working with sixth graders, I could relate to a lot of what they were saying – especially in regards to SBG. I thought, hmmmmm, maybe I should do this. However, I am the LAST one in a large group of people that I don’t really know to actually speak up. . .And I wonder why my own kids are so shy. . .

The next “jump” in my lurking occurred when I got my iPad and found Flipboard, that I shared in this post. It makes scrolling through blogposts pure pleasure! I would look at the blog rolls of the bloggers I was reading, check out new writers, subscribe to their posts, and so on, and so on. . .

After returning from our vacation this summer, I read some posts about Twitter Math Camp. Seriously? These people just planned their own “retreat/workshop/conference!?” Wow! More new bloggers were added to my feed. . .and then one afternoon I was weeding out in the yard, listening to my iPod when I heard the lyrics, “This is your life, are you who you want to be. . .” and something just clicked. Yeah, I can do this! You know, it makes so much sense to do it NOW, when I am just going back to teaching full time after being part time for 16 years. Sure, I have PLENTY of time n my hands! Oh well, I downloaded the WordPress app (recommended by Sam) and signed up for Twitter to boot! After all, I had already picked out a name and everything. The rest, as they say, is history. . .but not really what I expected.

It has been a roller coaster ride over the past month. I started out with ideas about what I wanted to “say,” but I find myself “saying” a lot of other things too. msSunFun came onto the scene shortly after I first started. “Ok, I’ll try that.” Then I noticed the Made4Math Monday. “Suuuure, that too.” Sam posted his New Blogger Initiative. “Hey, that’s me! I’ll sign up.” All of a sudden I have more ideas to share than there are hours in the day. How to keep up? Oh yeah, and school is starting up soon, too! My Start, Stop, Continue post includes blogging goals that I hope I can keep. I even made a To Do’s page to keep myself honest.

Posting comments on other blogs was one of my first “baby steps” after I started my blog. I really appreciated it when the blogger would then reply back. Especially now that I added all of the NBI bloggers to my feed, I find myself overwhelmed with how much there is to read. I want to make “meaningful comments,” as opposed to “I really love that idea.” Maybe that’s more of a “Twitter” response to a post.

Twitter has been hard to “jump into.” I once tweeted that I felt like the “new kid at school,” just listening in on other conversations – except they may have happened hours ago! It is very strange sometimes. I will “reply” and then realize that the person may have already moved waaaay beyond that part of the conversation. I don’t know how people can even BEGIN to follow as many people as they do!

When I was lurking it was so much more of a passive experience. Now that I am “in it,” I have been learning sooooo much more from others. I am reading posts and tweets from Middle School Math teachers who are out there in force, (@jruelbach, @4mulafun, @fawnpnguyen, @mr_stadel, @Borschtwithanna, @mathbratt, the list goes on, and on, and on) and I didn’t really know about them before. I LOVE the posts and twitter conversations with/between those involved in Math Education (@delta_dc, @mathhombre, @ChrisHunter36, @trianglemancsd) that make me think more deeply about learning mathematics! I feel a kinship with other “newbies” like me (@danbowdoin – although he is on the fast track to blogger stardom, @G8rAli – who should really start a blog, @aekland – who has such thoughtful posts, @ray_emily – who has an abundance of enthusiasm, and Pai Intersect – who I haven’t seen on Twitter, but has great insights on his blog.)

I vacillate between thinking that “nothing I have to say has any value when compared to all of the ideas that others have shared” and “oh, I really want to chime in,” or “I think I should share that. . .”

I am surprised at how much I have learned about myself and my teaching from writing posts for the blog. @ray_emily tweeted earlier today: “I’m finding I have a new clarity / fresh eyes on a topic after blogging about it.” I entirely agree! I am especially looking forward to learning even more as I blog about my experiences in the classroom 🙂


msSunFun: Start, Stop, Continue


For this week’s msSunFun, I will have to opt for the goal-setting post, as my room is still somewhat in chaos. (I “inherited” a room from a retiring teacher and he left me lots of “gifts.” It took hours to sort through and decide what I wanted to keep, so now I am finally making some headway. We don’t actually start with students until September 5, but we do have an Open House a week from Tuesday – yikes!) After using 12 different rooms over the past 17 years, sharing with another teacher in all but one, am I hopeful that I have found a “home” for awhile!

Soooooo, on to the “real post.” Not much discussion – just a list. (I rambled on far too long yesterday for the New Blogger Initiative post.)


-Blogging about one lesson (success or “failure”) each week to share/get feedback.

-Incorporating the use of “monster” whiteboards in group problem solving.

-Implementing ideas I read about on blogs/twitter by figuring out how they will work best in my classroom.

-Introducing other teachers in my school/district to some of the ideas I read about.


-Staying up too late and/or falling asleep while reading with my daughter and then not being able to fall asleep later.

-Thinking critically about teachers who teach in an “ultra-traditional” manner and try to look for ways to help them see things differently. (Ok, that’s a stop/start.)

-Putting off following through on incomplete/missing student work. Help students understand how much I value homework even if it isn’t part of their grade. (Another stop/start.) 😉

-Allowing “little things” to disrupt the learning environment without addressing them in a simple non-threatening way.

-Applying too much pressure on myself to be the “perfect teacher.”


-Trying to focus on EMU (Enduring Mathematical Understanding,) especially when first developing concepts in the classroom.

-Using SBG to help students (as well as myself) see where they are really at in terms of their learning.

-Thinking “outside the book” when it comes to planning lessons and activities in the classroom.

-Writing posts for the New Blogger Initiative and msSunFun on a fairly regular basis (depending on the topic) and throw in a little Made4Math Monday and My Favorite Friday for good measure.

-Reading all the wonderful ideas that others are willing to share while attempting to find time to comment on them as well!

I think that’s all for now. I’ll check back in about a month and see. . .

Reflections: Why “findingEMU?”

There is a blurb on my “about” page that describes the title of my blog:

Enduring Mathematical Understanding is found within, built upon your own foundation, framed by your current perceptions, and constructed from your experiences. By sharing my thoughts, ideas, and ramblings with others, I hope to encourage the growth of positive dialogue towards this lifelong goal for myself and others.

Wow! I really came up with that on my “first day” blogging, what seems like ages but was just over three weeks ago! (I did say “ramblings,” and that’s sure the truth.)

I have thought about writing a blog for quite awhile now. (Still to come – my “From Lurking to Learning” post.) Over time I toyed with different choices:

“MathMom” because I was a part time teacher / part time stay at home mom. My kids were (ARE) both math fanatics, and I would like to share some stories about watching them grow as mathematicians. (While I don’t exactly have their permission, I have put a few memories down on “paper” over the past few weeks.) However, “Math Mama Writes,” a blog that I have read, appreciated, and enjoyed for many years now, already had a claim on that type of title, so I decided to move on. (In addition, my kids have grown and I don’t find nearly as any opportunities to “be” a Math Mom anymore 😦 .)

My next thought was “Making Math Meaningful” (shortened to M^3….ooh!) While it has a nice ring to it, and it IS a part of what I try to do in my classroom, what does “meaningful” mean? Definition: full of meaning (duh!) significance, purpose, or value; purposeful (you mean, like “full of purpose”?); significant. I DO want to help students find meaning in math, see its value, know that it has purpose. However, my lessons are not “chock full of 3-Acts,” so it didn’t seem to quite capture the “spirit” of my classroom.

Recently, the phrase “Enduring Understandings” seems to have taken its place alongside “Standards,” or “Essential Learnings,” but I really like the use of the term “Enduring.” Teachers complain all the time about lack of retention – students can learn something for a week or a month, but it is no where to be found after that. What is it that makes the learning endure?

Now, “Understanding,” that’s a whole ‘nother can of worms. It seems like last spring, but it was only in June that I read Richard Skemp’s paper on Relational Understanding and Instrumental Understanding. I ran across it by linking from a Math Mama Writes post to The Republic of Math blog. (I can’t imagine why I didn’t read it when it first came out – oh yes, I was still in Elementary School!) It is a powerful piece, written 36 years ago, that, for me, emphasizes the difference between when a student says, “I understand!” and when they truly do. “Conceptual Understanding” vs “Procedural or Algorithmic Understanding” are more commonly used today, but I feel that, in reality only “Conceptual” actually reflects true “Understanding.”

So, that’s what it all boils down to for me. How DO I help my students FIND Enduring Mathematical Understanding? I can’t find it FOR them – sometimes I have a hard enough time finding it for ME. I don’t want the “I can do it!” math, I want the deep comprehension down in their core that builds and branches off from what they DO really know and understand. What I do in the classroom: the questions I ask, the answers I “don’t give,” but the way in which I respond to questions, the student dialogue I promote, the activities I provide that lead without “dragging them along,” and the culture of the classroom that I help establish, are all ways that I can help them on their journey.

I love the crafty stuff, notebook organization, games and activities, and “monster” whiteboarding plans (tooooooo Monday links to post!) that I have been bombarded with over the past few weeks, (I think I have at LEAST tripled my Google Reader) and the discussions about SBG, (or sbar?) how to deal with the homework hassles, and uses for technology on Twitter. However, what I really cherish from the past three weeks are the conversations about teaching fraction division with/for understanding (“I hate “magic math”,”) introducing integer operations with meaning (“I abhor – is that too strong a word? – the “follow the rules” approach”, and re-defining slope (NOT just “rise over run” – KA), running across David Coffey’s ideas about flipping homework that gives “practice problems” an entirely different level of meaning from back in February, and finding Michael Pershan’s fabulous new (in addition to his insightful “regular” one) blog, Math Mistakes where readers are faced with the tasks of identifying not only “what don’t they know,” but what DO they understand and thoughts on remediation – how can I meet them where they’re at?

Deep breath. One sentence?! I’m not editing. (Except to add MORE words, I suppose.)

findingEMU – oh, like “Finding Nemo!” Well, yeah, I went for the “catchy” goofy title that resembles a wonderful little Pixar movie, but with an odd looking flightless bird instead of an adorable clownfish.

Only I guess I really didn’t, because I really AM trying to find ways to reach EMU.

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