Simplifying radicals? Who needs it?

There was a time I thought radicals should be simplified. A factor of a radicand should never be a perfect square. To do otherwise was just sloppy math—so I thought. Now, I think differently. You should consider it too.

image square roots
pic fromthemathlab.com

Making the square root of 40 look like 2 on the square root of 10 serves no real purpose in the mathematics of real life. You can readily estimate the square root of 45, but trying to do that with three square root 5 is a much more complicated task, and for what? If I am going to the fabric store and I am asked how much ribbon I want, I better not say, “4 root 2” and expect to get the correct amount. At the hardware store, I am far better reasoning that the square root of 32 feet would be a bit less than 6 feet, and a bit more than 5 and one-half feet and just say 2 yards. The lumber department does not want to hear this nonsense about radicals and square roots.  They want to cut my lumber and send me to the register to check out so they can help the next person also get a reasonable amount of lumber.

real square roots
Photograph by question_ev3rything on reddit

Now, I know, one needs to simplify radicals to combine radicals via addition, such as the square root of 27 plus the square root of 12, but seriously. This is not reality. This is a contrived problem that I have never seen come up in real life. Ever. And I sew and measure and do real life things with math—at home. It does not come up.  It’s clever, like a party trick, but not terribly useful.

I do make certain my Math 2 students can “simplify radials,” but just for the “man.” Not for real life. I used to “ding” my students (take off 1 point just to be mildly irritating to get them to conform to convention) for not simplifying radicals. I am totally rethinking that.

Reality says leave radicals as they are so they are easy to estimate to be useful and to check for reasonableness. Done.

Skirt and shirt made out of fabric that has root vegetables that are in the shapes of rectangular prisms.
Last spring’s project…square roots…get it?

 

year two–take two

Happy Saturday all! I’m supposed to be getting ready for a couple PD sessions that I am presenting over the next two weekends, but I can’t get a comment from @SAMSDrSapsara at @mrsstipemath’s Thursday night 7th grade zoom (time stamp 00:27:14) collaboration out of my mind. Dr. Jessica Sapsara said, “I feel like when I’m making my anchor charts for the things, it’s really coming…way…after the unit has passed and I’m like, alright, let’s get something up so when we’re referencing it later as units come through…let’s look at that one again…so we have better working language…visuals…” And I thought to myself, “self, that’s where you were last year, if you made them at all!” That got me thinking about even more exciting differences between years 1 and 2 of implementing Open Up Resources 6-8 Math Curriculum. I know I reflected on this earlier,  but there’s more. Here’s my summary so far:

  • Anchor charts—Like I said, year 1 I was lucky to make them at all. In fact, I did not understand their usefulness until it was too late. Year two, I am deliberate in their creation as well as in pointing to them during lessons and even as students present, intentionally connecting student ideas to the charts.
  • Lesson preparation—I was so tired last year that I would fall asleep as I was reading the lessons. I’d get up in the morning and get about half-way through the teacher guide and then my room was filled with kids that needed support for the other course I teach, so there went my preparation time for Math 8. Year two, I am seeing so much exciting mathematics and even more brilliance in the authoring of this curriculum. I am excited about reading it and doing it and energized by it, so much so, that I read it before I even go home the day or even two days before the lesson. I am copying and cutting my cool downs and black line masters for an entire unit at one time rather than daily. I am importing my slides for an entire unit into one Google slides presentation. I just edit daily to remove what was covered that day in preparation for the next. (Note to self…hide the slides rather than deleting them, thereby making the file useful for next year! Yep, here I am, learning through reflection!)
  • Student copies/student workbooks—Year 1 saw me rushing around daily or all day Sunday editing and copying student pages for the week ahead. Year 2, my district purchased student workbooks. That in and of itself has given me back part of my life. I am so fortunate that my district cared enough about its teachers and time and copying costs to purchase student workbooks.IMG_3565
  • Attention on student learning—this was a luxury rarely afforded in year 1 because I was so intent on my own learning. In year 2, student learning is what fuels me. Seeing the lesson by lesson progress and retention is reassuring that I am actually helping students become mathematicians.
  • Student engagement—what an improvement!. In year one, I had three students per class I felt were really with the program. In year two, I have all but three students demonstrating understanding and actively owning their learning. I need to remember that when I am beating myself up about those three students, but still, that’s 3 students too many.
  • Student results—What a difference! They are truly remarkable. When I review cool-downs I can see student thinking and reasoning and catch misconceptions so they can be addressed timely. Year one, I was lucky to get a cool-down in the same day as the lesson. Now when I pass out the cool-downs, I hear students say, “we’re done already?” Students self-assess daily as they turn their cool-down into the basket based on their level of understanding, thanks to @mrsstipemath.understanding
  • Supplemental activities—Year 1 had virtually zero supplemental activities for students. Year 2, they are actually part of the game plan. They include Desmos activities to further student learning and assess student understanding; Quizziz games so students can self-assess and develop fluency with concepts; Desmos graphing calculator sessions to quickly and easily make math visible; practice problems from the curriculum; review sessions using practice problems for unit assessment preparation. I am still trying to get to Khan Academy  exercises, but haven’t managed to get them worked in—yet.
  • Pacing—This is a non-issue in year 2. I attribute this to not over-teaching as well as to keeping moving even without 100% buy-in from students. I know the material and concepts are coming around again and both the students and I will get another crack at nailing down the standards. I also understand the learning goals more clearly and know that keeping them bite-sized is essential to student success. That my students were successful at all last year was truly a miracle.sample matrix for blog
  • Community support—In year 1, I felt like my blog was my only companion as I learned this new curriculum and relearned how to teach—or perhaps, finally learned how to teach. This year, there is so much community support. There are the organized supports such as the face book groups and Monday night twitter chats (#OpenUpMath) as well as monthly zoom sessions by the Gurus of Open Up Resources 6-8 Math. My district is also providing monthly professional development specifically for users of the Open Up Resources 6-8 Math curriculum. I also have a network of users across the country as my personal Professional Learning Community. I find it hard to believe I made it through last year without these committed educators.Chat.png
  • School-life balance—This did not exist in year one. I worked very hard, but not very smart and it took a physical toll on me. This year, I am more rested even though I am doing more each day. I manage to eat healthier, sleep more, exercise regularly, read for pleasure, find time to support my learning community and even spend time with my husband. These activities have all improved my mood and attitude and help me recover from slumps and meltdowns more quickly.Selfcareisnotselfish

Year two just keeps getting better too. I actually feel valued and appreciated by my colleagues across the country. I feel confident in my classroom and I am excited about the future. My community members experiencing year one now who are taking advantage of the support of the Open Up Resources 6-8 Math community are doing so many wonderful things for their students. I am grateful for them and want to support them as we move forward together, as a community of learners.

A Tale of Two Years

“It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness…” Thanks to Charles Dickens for igniting my thought process.

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This is year two for me teaching 8thgrade math using Illustrative Mathematics’ curriculum published and distributed by Open Up Resources 6-8 Math. Year two is everything I had hoped it would be. I marked my Unit 3 assessments Wednesday and was pretty pleased with the understandings my learners demonstrated. I tallied the individual scores just to get a macro feeling of how the classes were doing this year on the Unit 3 formal assessment. I felt pretty good about student work, but mildly disappointed in myself. As I was marking, I wish I had some student copies from last year’s assessment to compare similarly situated learners’ progressions. (Year one people—make and save a couple student copies to look at next year for each assessment. I thought I was going to remember, but I didn’t.) I did find my teacher copy with the tally marks of last years’ results. Drum roll please…the scores are better. And more students are able to put their understandings on display on the assessment. And, dig this, I am a month ahead of last years’ pace. And the results are significant. [Timeline correction…Last year, I started Unit 4 on February 2nd. February 2nd!!!! This year, I started Unit 4 December 7th. That’s almost 2 months ahead and we have already had 7 or 8 days out of school due to weather issues. And my learners understand more and perform better.] This is all because it is year two. My class sizes are a bit larger than last year, but the mix of historical performance measures (skills, abilities, levels—all horrible words to describe children’s current placement) is about the same. This year-two teaching experience with this curriculum is a wonderful feeling. I attribute improvements to the following changes, in no particular order.

  • Focusing on not over-teaching is a giant change affecting pace issues of the past. This revelation came during summer PD sessions with the good people of Illustrative Mathematics fame.
  • I am also better at formative assessment on the spot so I am not waiting until I can look at a stack of cool-downs to know if students got the intended learning or not. I have better interventions, earlier.
  • This year I made a commitment to move along regardless of stragglers. If I have learned one thing comparing last year to this year it is that you are going to have stragglers no matter how slow and thoroughly you go. Slowing down only harms the learners who are ready to move. It’s like walking in a line with a class of students. No matter how slowly you walk, the end of the line gets further and further from the front. Continually stopping so they can catch up is necessary, but holds everyone back. I need to work at incentivizing the back of the line, aka the stragglers, so they want to keep up and be part of the learning group.
  • This year I am using the practice problems whenever I can. This may be as filler at the end of class or as a pre-class activity to review the prior day’s concepts. I also assign targeted practice problems as Unit reviews before a Unit test. I’ve also put in a Quizizz activity once in a while. I’m going to give the Kahn Academy practice problems a shot next. That retrieval/practice routine must be played out regularly.
  • The launch for each activity is better year 2 because I know where I am going. I know what the focus of the activity truly is and I know where the stumbling blocks are. I am not removing the productive struggle, but I am better with my instructions and communication to learners of the expected outcomes.
  • Both activity and lesson syntheses are better than last year in that they exist, usually. They are focused and tight. They tie to the lesson summary or they come with a note or a highlight on the activity page in the workbook to seal the deal. I am still working to improve all of this and it’s not nearly as good and tight as it reads here.
  • The professional development, I am receiving on the unit materials and elements, is better this year since I can actually attend the sessions. Last year they were not held at a time when I could make it without missing one class of each of my two courses during the day, plus I was sooooo far behind I was afraid to be gone.
  • This year I have the support of my nationwide PLC. I am also supporting other users of the curriculum so I get better and think more carefully as I respond to inquiries and participate in twitter chats. I also feel a sense of accountability to my nationwide PLC and this makes me prepare and research at a much higher level than I otherwise would.
  • I spend more quality time reflecting as I prepare Guru Zoom chats and draft the weekly #OpenUpMath Twitter chat questions. Nothing sharpens skills like leadership.
  • Taking some of the preparation off of me and putting it on students, by having student workbooks, is a positive change for which I am grateful. I am not certain learners took the copied version of the activities last year as serious as they do the official workbooks this year. I am also able to invest in better preparation because I am not making copies of the materials. Workbooks also save valuable class time not having to pass out papers.

unit 3 question

Just look at the understanding that is demonstrated here. This learner is testing algebraically as well as graphically to determine if the ordered pairs are indeed solutions to the given equation. And look! Going beyond what was given, she tests a point not provided (4, 3) that works in the equation to see that it is on the line. I cried–in the best possible way.

Not everything is rosy, however. Horizontal and vertical lines as well at the shifting of proportional lines (y=kx from 7thgrade) was horrible last year and no better this year for the most part. Why??? I know I did a better, more explicit job connecting points and coordinates and lines. I did better, but the students weren’t doing enough. I need to beef that up and I am going to go back through those lessons again and see what it is I am NOT doing. The lessons are good in the moment, but they are not sticking with learners. I have got to make them stick. There needs to be struggling retrieval and spaced practice. All those sticky things must happen more and better than I have been doing. I will also check with my Tweople and see what their experiences and remedies are This is one area that did not improve from last year, yet.

I am going to continue to tweak and ponder, reflect and revise. I pledge that to my self and to my PLC.

Look Who’s Learning

It’s no secret I am an Open Up Resources 6-8 Math junkie. I love what the curriculum does for learners. Today, I want to expand my definition of learners. I am a teacher, but I am also a learner. I have learned more about teaching, learning and math in the past twelve months than I learned in the prior 14 years. I have Open Up Resources 6-8 Math, Illustrative Mathematics and my international PLC to thank for that.

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It’s not just that I have quality material with insights spelled out for me. It’s not that my students are challenged and required to think differently than they ever have. All those things are good. And true. The fact of the matter is that this curriculum makes me a better teacher. I teach better than I ever have. I am more prepared and I have greater insights. I am a better listener. I want to hear how my students are interpreting the math. I want students to share their interpretations. As prepared as I feel each day, I seem to always see and hear and feel something new about the math my students are doing. I am learning. I am the learner and I LOVE IT. Open Up Resources 6-8 Math curriculum makes me a better teacher and learner. Every. Day.

I was starved for quality professional development ever since Common Core was rolled out. The minimal training received on Common Core was ill-conceived and not informative. I remember building fences with posts that were the supporting standards and rails that were supplemental or connecting standards. But I didn’t learn how what I was to teach was better for my students. Everything was theoretical. There was no comparison of how students were expected to learn differently or how I was expected to teach differently. I didn’t practice teaching anything. I was also not given resources with which to teach other than an outline. I learned much more about Common Core as I was teaching seeing my students make connections I had not previously considered. Because North Carolina gutted education funding on the heels of Common Core’s implementation, teachers were left to find and develop their own resources in order to teach and learn the standards. That took a while and I learned much through the school of hard-knocks. Eventually, I was seeing the connections and the wisdom of the sequencing. I was excited. Unsupported, but excited.

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Then Common Core got killed in the court of public opinion. Had Common Core had extensive, quality public relations communications, I like to think the educated public would have bought into the sequencing dictated by the standards. But they didn’t. The only public communication was parents posting homework problems without a context and calling the whole thing folly. There were even teachers that ignored the adoption of the standards and taught what and as they always had. Perfect strangers would come up to me in the grocery store line and see my teacher ID and say something like, “What do you think about Common Core?” expecting me to bash it. I wouldn’t bat an eye. I just said, “ I love it. The connections that students make all throughout the standards are solid. The insights that both students and teachers are gaining are profound. I hope the state has to courage to do the right thing for our schools and ignore the ignorant neigh-saying public. Why do you ask?” I typically didn’t get a response.

I want a do-over on the release of the Common Core Standards. I would start by rolling it out to the elementary schools for three years. Move to the middle schools for a year or two and then finally get to the high schools. Changing horses in the middle of the stream and then providing little to no professional development for teachers and no quality public relations education killed Common Core. Teachers were asked to implement without understanding. Teachers don’t do that. Teachers demand and deserve to understand why. That is a sad fact that was disregarded. We are now getting a do-over, of sorts, via Open Up Resources 6-8 Math, but better. It’s the third word…RESOURCES.

I am fortunate that my district is investing in teacher professional development with the implementation of Open Up Resources 6-8 Math. It seems the phrase Common Core is now somehow forbidden by the state. What we teach are the Common Core standards, but they are simply rebranded. Clever. But the standards are better than solid and it’s working so let’s just keep that little secret to ourselves. Open Up Resources 6-8 Math and the professional development I am receiving through Illustrative Mathematics are helping me connect my teaching to the standards with better understanding and execution than ever before.

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Now for the real purpose of this post. I am concerned there are teachers reluctant to change their ways regarding what they teach and how they teach it and some of these teachers are merely going through the motions as they roll out the Open Up Resources 6-8 Math curriculum. Teachers are learners too. Remember, you can’t get more out of something than you put into it. Just because something is good and nationally acclaimed doesn’t mean it will work without effort. Teaching is work. Teaching with Open Up Resources 6-8 Math is a lot of work. It is this work that is making me a better teacher and it’s hard. But my students are worth it. I am worth it. I am grateful that my district sees that we are all worth it.

Home Communication Logs (HCL)

What can I do instead of homework to make a difference with consistently, under-performing students? I need something that will provide learners with the opportunity to intentionally think about and talk about math outside the classroom. I also want to make sure family members, as stakeholders in children’s educations, are kept up to date with what students are learning.

Screenshot 2018-09-17 18.32.14

 

To help address all of these issues, I developed the HCL—Home Communication Log. Students are required to discuss math outside of school for five to twenty minutes each day with an adult. Students then turn in completed logs each Friday.

So far, results are mixed. I still have reluctant students not turning in the logs. I even had a couple students copy somebody else’s log the first week. But, most of the submissions are good. Parents and children are talking about math daily, and without doing homework! I suggest that students review the lesson summary, from the student workbook (Open Up Resources 6-8 Math) if they are stumped about something to talk about with their selected adult.

After the first week I asked students, “when do you talk to your parents or special adult?” A few told me that they have dinner at the table every night as a family. My heart melted. I didn’t think families did that any more. A couple kids told me that mom or dad is not around in the evening so they had trouble with the log. I told them it was fine to talk on the phone with their parent. I also offered up staff members as special adults for students who have trouble connecting at home. I also told them to come see me before school or at lunch if they wanted.

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I know this is not perfect, but it is more than I have done in the past as far as homework. True confession: What prompted this year’s HCL is a devastating failure on my part last year. I had a student performing below grade-level and, here’s the bad part, because that is what I saw in her file, I didn’t contact the parent. I saw it as normal for that student. I made a terrible assumption that I am embarrassed and sad about. The parent came in and we talked about the situation and I apologized. I then tutored the student each morning she came in. I provided additional information for afterschool tutors as well as private tutors for this student. She still performed below grade level and didn’t grow a bit according to state test results. And it was my fault. I didn’t push her enough. I didn’t let her parents know that she was sandbagging all year. I failed her–my student.

So, fast-forward one school year. I now have 38 kids in one class. 75% of them were determined by the state to be below grade level last year. These learners are like the kid I let down last year. I know a simple Home Communication Log is not going to fix that, but neither is homework. That’s why I thought I’d try this log. Students at my school keep Reading Logs so I thought this would fit in with what they were accustomed to doing. Perhaps it is again, naive on my part, but if parents see their kids making progress, they can encourage them. If parents see their kid struggling to articulate what went on in class that day, that should alert parents to an issue and again prompt encouragement and/or action. But once again, the students that don’t turn in the logs are the same students who would not have done homework had it been issued. I don’t think it’s a coincidence that these are the same students having trouble making their paper and pencil make contact during class. I do my best to check with all 38 students throughout each activity. Much of my time is spent getting reluctant learners started. They want to hide in a class of 38, but I try not to let that happen. Truth is, if a reluctant learner is also a wallflower, I may miss him or her. It pains me to admit it, but it’s true. That happened, as I said.

So, back to the 75%. On a good day I feel like half of them make progress. Am I supposed to feel good about that? Is that enough? No. Clearly the answer is no. I am doing the best I know how to do, but my boat is taking on water and I feel like I’m bailing out with a sieve. I love my kids and that helps for sure, but love is not enough. I need more. My learners deserve more. Maybe they wasted time in earlier grades. So what! All that matters now is how we fix it.

So now back to HCLs. I’m toying with the idea of adding just 1 practice problem from the workbook to the HCL per day for next quarter. At that point it could be a spiraled question. I don’t know though. If you read this, please know, this is my processing process. This is how I think things through. Don’t take advice from me like I’m some expert. I’m just figuring out this teaching thing one day at a time like every other honest educator in the world.

I am going to continue to refine and adjust the HCL as I work with it this year. If you have suggestions, please let me know in the comments.

 

Gearing Up for Open Up Resources 6-8 Math Year 2

A couple weeks ago I quickly responded to Leeanne Branham’s question about what makes good teacher PD.

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Had I given more thought to Leeanne’s question I would have added PD must have a common thread running through it, an over-arching theme, aka a number 1 takeaway you almost don’t realize is there until near the end of the session.

As I was reflecting on Year2, Day2 of Open Up Resources 6-8 Math PD with Kevin Liner of Open Up Resources 6-8 Math and Illustrative Mathematics Curriculum fame, it occurred to me that Monday and Tuesday’s PD hit every mark. (Aug 13-14) The number one takeaway, over-arching theme, common thread was simply this: in order to be effective and efficient, don’t over teach the lesson. Do not go beyond the Learning Goals set out in the lesson. Over-teaching, getting off on tangents and celebrating spoilers rather than quietly acknowledging and telling smarty pants students (I mean that in the best possible way) to keep it to themselves for now are the main reasons we get behind during lessons. Teachers are the problem. I am the problem. I need discipline and self-control and first of all self-awareness. Now, to get down to the nitty-gritty of how this unfolded throughout training—not exactly in order.

We talked about what it really means to reflect on our teaching and, in particular, a lesson we have taught. The take-away here was that we as educators must reflect on our planning processes and not just what went well or poorly during a particular lesson. In this refection of our planning process we must not only look at the short term planning of the lesson, but also the long-term planning, both forward and back. Reflect forward. Whoa! Failing to do this risks understanding the learning progressions that are so carefully written into the curriculum. In edu-speak, this is coherence. It matters what comes before as much as what comes after. Sequence matters. The big reveal is not going to be in the first lesson of a unit. Ever. Teaching for conceptual understanding necessitates learners progressing through the concepts and building understanding that each individual personally owns. Seeing far into the future in the planning stage will help us as educators honor the conceptual learning progression. We are learning to teach differently so our students can learn differently. We keep hearing, “trust the curriculum” and this deep dive and reflection into long term planning reveals why the curriculum can be trusted. It’s all there.

We were reminded once again of the Five Practices, and looked at them from the perspective of planning.

  •  Anticipating students’ solutions to a mathematics task
  • Monitoring students’ in-class, “real-time” work on the task
  • Selecting approaches and students to share them
  • Sequencing students’ presentations purposefully
  • Connecting students’ approaches and the underlying mathematics

NCTM , 5 Practices for Orchestrating Productive Mathematics Discussions

Kevin said these practices are the ingredients that create magical conversations among learners. For our training session, we focused on anticipatingand sequencing. When planning anticipating and sequencing it is always better to do that with our peers rather than in isolation on a Sunday afternoon. To that end, establishing group norms for PLCs at our schools is necessary. Day 2, we spent quality time broken into our school groups discussing, developing and revising PLC norms. This is where we got something tangible to take back to our schools to put into motion. Having a group protocol is the difference between a productive PLC and a non-productive PLC. Highlights of the group norms for planning developed by the wonderful teachers at Northwest Guilford Middle School in Greensboro NC follow. Please know, this is NOT a final, polished, static list, but rather a summary of the norms we discussed as a group. They will change as we change as educators.

  • Doing Math Together (like actually work problems)
    • Respect think time
    • Do not interrupt others
    • Be “all in”
    • Drop your pencil and listen
    • This is not a race
    • Pick a topic with a longer term focus so the PLC can go deeper with exploration and problem solving
  • Sharing Our Understandings
    • Focus on teaching goals as they relate to learning goals, meaning goals for my actions as a teacher, for the future
    • Use a timer to move things along
    • Listen more than you speak (a rather BIG deal)
    • Be fully present
  • Discussing Students and Their Understandings
    • Strive for more than antidotal evidence
    • Speak of learner understandings and common errors
    • Focus on the product, i.e., what students are producing as evidence of their understandings
    • Confidentiality is critical
  • Connecting and Reflecting on Our Own Practice
    • Just as assessment informs instruction, so must past experiences inform planning and teacher-moves
    • Help is on the other side of vulnerability. Open up and be vulnerable in your PLC as you plan and reflect and get feedback
    • Leave with a plan of action for the future
    • As peers, we must hold one another accountable

With norms also comes the issue of what to do with breakers of the norms. Some suggestions were a yellow card or a light bell ring. A taskmaster, timer, rule enforcer, norm police position needs to be assigned on a rotating basis. Not it! Please don’t pick me!

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So what is missing from here from the past? Notably, negativity, comments about what students can’t or won’t do and war stories. As teachers, we must have an outlet for frustrations, but such actions can run the productive PLC train off the rails. Take these frustrations to the gym or to the track or the bar. Work them out and get over them, but please don’t derail your PLC.

We spent a good deal of time learning about how to use Cool-downs more effectively. I thought I did Cool-downs great last year. I did them everyday. I reviewed them at the beginning of the next class. I thought I nailed it. I was wrong. Other teachers at the training stated they periodically used the Cool-downs as homework or just used them when and if they had time. Cool-downs were rushed through and never truly sorted and analyzed by teachers. We went through a lot of motions last year, but none of those motions were great. Kevin helped us see a productive, more intentional way to use Cool-downs.

The biggest shocker was that we do not have to use Cool-downs each and every lesson. As we plan, we decide if we are going to use the Cool-down and budget the time for it. Maybe even do two in one day. When we do Cool-downs, we will look at them with a focus on student understandings, not merely, did the kid get it or not. A student can get a correct answer and still not truly know what they are doing just as a student can get an incorrect answer and make a computational error while the conceptual understanding is solid. What is understood is quite different from what we see in a mere answer. You want kids to show their work? You better really LOOK at their work. The information gleaned from the Cool-downs will then be used to actually plan subsequent teacher-moves.

So here is this great concept of teacher-moves. Not teacher reactions. Not teacher assumptions. Not teacher experience. Not teacher instincts. Actual planned out teacher moves designed specifically to intentionally address student understandings. These get noted on the daily clipboard roster so they are addressed and not forgotten by the frazzled teacher.

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Another shocker—not every lesson/activity is a five-practices activity. Wait. What? I still don’t quite have my arms around this one. Note to self: pay more attention during PD. More on this when I figure out why I’m confused here. Truth.

How to differentiate daily and live through it has never truly been taught to teachers in a way that is actually possible to successfully pull off. Asking administration for help and advice on differentiation will keep them out of your room because they don’t know how to do it either. (This is obviously, just one snarky gal’s opinion.) What we can do in our teaching, however, is make small tweaks that get the actual support to the learners in need. Planning multiple lessons at multiple levels to be monitored and evaluated and assessed all at the same time day in and day out by one teacher in a class of 35 students is pure folly. Small tweaks. We can do that.

We spent time looking at multiple representations of mathematical concepts and limitations of each. The point is, buildings of conceptual understandings have varying entry points that may expire when the situations get more complicated. This necessitates higher-level thinking and abstraction. We start with accessibility by honoring coherence in concepts layered throughout progressive courses. Colloquially, the punch line may be the algorithm, but you must lead up to it—lay foundation on which to build. For the record, my English teacher, bestest buddy, has told me on many occasions that my analogies, while useful at times, take a bit to get used to. My apologies, but I must be me.

Now, how to plan a lesson as a PLC:

  •             Do cool-downs together for upcoming lessons
  •             Read learning goals and learning targets
  •             As you go through the steps above: Do, Share, Discuss, Connect
  •             Read the synthesizes–ALL of them
  •             Read each activity and complete and then Do, Share, Discuss, Connect

The focus must be on WHAT’S THE MOST IMPORTANT THING!!! for each lesson.

Every piece of feedback to a member of the PLC has an action associated with it:

  •             I like the way you did…I’m going to do that too!
  •             Oh, I didn’t see that part. Can you re-explain that form to me?

Teachers are to a PLC as students are to a classroom. Self-discipline and focus as individuals are essential. Just as we want our students focused on the learnings of the day, so too must be focused on the learnings of the PLC. Teacher-management is like classroom management for PLCs. It is essential for successful group planning.

I have been working on this post for two weeks off and on—mostly off. I apologize if it seems disjointed, but I wanted to share and may not have polished like I should. I’m sorry.

So fearing that TLDR has set in for most readers, (I would have bailed long ago) if you made it this far, you have earned a merit badge. Enjoy.

smiley merit badge

 

 

 

Reflecting on My First Year Experience with Open Up Resources

Please let me disclose up front that I am a user/fan/evangelist of Open Up Resources (OUR) and have absolutely no affiliation with them whatsoever. I do, however, have enormous respect and gratitude. Statements here are opinions and reflections on my experiences. Your mileage may vary.

2017/2018 was the best school year in a long time. I learned a lot; I was organized; I felt prepared; I tried several new things; and most importantly, I left school June 14thexcited to return eight weeks later to build on the year’s successes and improve any mediocrity and shortcomings.

My school dove into OUR headfirst and didn’t come up for air until at least Christmas. My district provided training all along, but given my course load, I was not able to attend the large majority of training as desired. I wrote about my initial experiences here. I finally got into a groove and became much more efficient in preparing for my Open Up classes. Rather than preparing daily as I had done September through January, in February I started batching my lesson preps. By April, I built my PowerPoint for an entire week in one file. At the close of each day, I deleted the slides covered and saved the rest of the file for the next day. Because I used Variable Random Grouping each day, I needed a new seating chart slide anyway. I finally began importing the pre-made slides provided by Open Up. I imported the slides I wanted and just edited my student sheets using textboxes for more efficient printing rather than duplicating them into my homemade ppt. Send me a message and I am happy to grant you access to my files. Samples may also Files may be accessed through the PowerPoint I am preparing prepared and edited for TMC18.

Here is a simple graphic of the way I think OUR looks. Move clockwise, beginning with the Warm-up.

OURgraphic

The job of synthesis is to connect every aspect of the portion within the lesson as well as to connect new learning to prior learning. If there is ever any ambiguity about connections throughout the lesson, they are hammered home during the final synthesis. If the final synthesis is skipped, there is an obvious hole in the lesson. Each portion of the lesson is also synthesized as one lesson phase transitions to the next. The relative sizes of the circles in my graphic are indicative of the amount of time allocated to each portion of the lesson. Lessons follow this consistent pattern throughout the course.

I like how the Cool-down bleeds into the Warm-up in the graphic. Fairly early on through the year, I began reviewing the Cool-down at the beginning of the next class. This allowed learners to review my feedback on the Cool-downs as well as to access newly acquired knowledge for the prior day’s learning experiences. That is a example of how I made OUR my own.

Another example of making OUR our own at my school is a sixth grade math teacher came up with the idea to have learners place completed Cool-downs in green, yellow or red folders depending on their individual confidence levels. The information gleaned from the placements was telling in a couple ways. It was easy to spot false confidence. It was also helpful to see at a glance how students were evaluating their own learning. We still sorted and wrote meaningful feedback on the Cool-downs each day.

Here are errors that I made this year that I want to spare anyone else from making.

  • Notice the graphic. Without the synthesis, the lesson has a big hole in it. Don’t shortcut that, rush it or heaven forbid, skip it. Be explicit as you make connections. What we as teachers think is obvious, may not be to learners and frequently, they just need that small nudge forward to make the desired connections.
  • Give at least 5 minutes for the Cool-down. Some kids can demonstrate understanding with more time. If they don’t nail it, you need to figure out what you missed along the way. This is valuable information and not a step that you can afford to skip.
  • Keep the pace up from the very beginning. Trust the curriculum. Concepts will come around multiple times from multiple angles. It works well. The authors are geniuses. Respect and trust it.
  • Focus on student work and having students share their perspectives on your cue. Sequencing student responses is an art that I am far from mastering, but it is valuable to student learning.
  • Allow enough time for assessments. Learners are actually excited about showing what they have mastered.
  • Score assessments with an open mind and an open heart. Learning is a process and you are looking for progress toward mastery. This material is challenging in a whole new way. Don’t defeat learners before they get a fair chance. Fairly recognize progress.
  • Stay organized. The curriculum makes that easy. Follow the OUR sequence even if your district thinks they know better. They don’t.

I am most excited about the improvements I plan to make this coming school year.

  • My district is getting student workbooks, so I will not have nearly as much copying to do. I will still copy the Cool-downs, but I have those all set.
  • I am going to take my own advice and focus on sequencing student responses more deliberately and improve my process here.
  • I am also going to improve my syntheses. I really didn’t help my students make the connections and recap the concepts the way I should have last year.
  • I am going to keep my pace up in the beginning so I do not have to condense and shortchange my learners at the end.
  • I am going to use VNPS (Vertical Non-permanent Surfaces) every chance I get. Learners did far too much sitting last year.
  • I want to adapt some student tasks to Desmos so students have the opportunity to dialogue with other learners and critique their work. Desmos is well suited for this.
  • I have to work calculator use into the lessons. No calculators for learners at first for sure, but after my students have conceptual understanding, I need to teach them to use the tools at their disposal. I totally dropped the ball on that one and need to figure it out.

I could write for days about how jazzed I was each day as we learned math in an entirely different way this year. I could tell you how I learned something new each and everyday, not only about student learning, but also about math. You need to experience that for yourself though. Please be smart enough to do that the week or at least day before your students do. It will make you so much more efficient and effective than I was. I eventually got ahead of them, but not far. I am excited for next year for sure!

OUR made me love, adore, and treasure teaching Math 8 for the first time ever. It was fun. It was meaningful. It was amazing. I cannot thank OUR enough for bringing joy into my classes through quality curriculum. I would have never thought that possible, but I lived it.

After finishing the year, I am incredibly in love with OUR. I hate myself a bit, but that is true every year. No matter what I do, I feel like I could have, should have done more. However, OUR helped me give my learners more conceptual understanding than they have ever had. The stage is set for explosive learning in high school. This is both my prediction and prayer.

Best Review Day Ever

Today my intern planned a review for my OpenUp classes. (Gosh, that sounds so much better than my Math 8 classes.) I attended our vertical math PLC yesterday and @BethSize shared a review game they do in 6th grade where the kids play connect 4 with post-it-notes, earning them as they solve sets of problems as a group. When my intern had all these review sheets I thought, “what the heck? Let’s do this.” I checked with my next door 8th grade teacher neighbor to see how big the board was supposed to be. She didn’t recall, so we made up our own rules. Three teams of four. A 6×6 grid on a white board. Different post-it-notes for each team. No building from the bottom. Put your mark anywhere on the board. Teams solve a sheet of OpenUp problems harvested from problem sets and elsewhere in the OpenUp resources (goosing some up by adding solve or show or prove directions.) They are checked by me or my intern. If there is an error or two, we say something like, 3 of those are correct. Learners then return to find their own errors. Once all are correct for each member of the team and we ensure all members are on-board doing the learning, the team earns a sticky note. (High tech can be over rated.) A member of the team places the note on the board. We played three groups of 4 per board. We called it Connect 4, but once teams got four, they challenged themselves to get a whole column or simply the most stickies on the board. I teach middle school. We are very flexible.

The conversations and teaching, one learner to another learner, were out of this world!! Now, true confessions, we had two adults in the room so groups got quick attention and directions. That cannot be under emphasized. More adults is better. Period. Done. Who doesn’t get that? Oh, yes. The state of North Carolina.

The second OpenUp class was even better. We had time to reflect and resequence the problem sets for that delicate balance of success, challenge and learning. Intentional sequencing is so important and yields amazing results. Getting good at it is a work-in-progress.

This activity went so well with my OpenUp classes that I tried a variation on this with my Math 2 classes. They too have a Unit Test soon. I created MC problem sets off of SchoolNet and made a packet of questions for each of the 8 groups. Some packets were 12 questions, some were 4 and everything in between. It all depended on where the nice page breaks occurred in the printed versions rather than planned sequencing. This is designed for online, so the printout isn’t pretty. It’s easy to harvest–by–standard though, so vetting time is minimized. Because they got many more problems per packet than my OpenUp classes, I decided to do two groups per tic-tac-toe board rather than Connect 4. It worked. It wasn’t perfect, but for the seven out of the eight groups that worked, it was great. I told teams which if the questions were incorrect so they could go back since there were many more problems and they were all MC. (Easy to check, but still challenging/standard aligned questions.)

Unit 4 Practice Problems my intern compiled are here, though the ideal sequencing is not in the order the problems are presented here. This is Unit 4 of the Open Up 8 grade curriculum.

Everyone in room 209 has been working like crazy since we got back from winter break. Today we had fun showing off our learning.

Opening Up about My Affair with Open Up Resources

I feel like a first-year teacher drinking from a fire hose. A couple days before school started, we were offered the opportunity to pilot the Open Up curriculum in our county for mathematics in grades 6 through 8. Because I had taught math 8 with zero resources for the past 12 years, other than what I harvested or created myself, I jumped at the opportunity.

There are many things I love about the Open Up Curriculum.

  • I love that I have to be more organized, focused and deliberate.
  • I love that I learn and see math differently each and every day.
  • I love the warm-up and learning routines and structures.
  • I love trying new things.
  • I love that the materials are already prepared.
  • I love that my kids are challenged and then they still have second chances if they don’t get something the first time around.
  • I love that they finally respect my kids and me enough to develop some real resources.

Struggles:

I cannot get ahead. I barely keep up. Each day I rush to get ready for the next. I prepare a PowerPoint to keep the class and me on topic. I snip screen shots into a PPT and prepare Student Task Sheets using what Open Up provides. Problem is, I frequently have to heavily edit so the information fits nicely onto a printable document. Mastering Textboxes has helped enormously in this area. I am saving all of these edited documents, so hopefully next year will be better. If that holds true, it will be the first year I have ever used what I made the year before. I have always created everything new each year in response to what my kids need.

I know that Open Up is integrated with OneNote and I even spent a couple hours being trained on how to do that. On my own, I cannot for the life of me figure it out though. I have to get ready for the next day. I don’t have time for trial and error where it is mostly error. I want to learn how to do all of that, but I also must be ready for the next day. I cannot sacrifice my kids for my learning curve. I also know there are Google slides for many of the lessons, but I have no idea where those are. I had them in the last unit, but can’t find the link now. There’s just too damn much to keep track of. I have to use what I know I can pull off now. I must survive.

Adjustments:

I am working on pacing myself and my class based on the recommended time estimates for each activity. I have a hard time not getting each and every comment and contribution out of students before I move on, but a timer is helping me. I hate leaving a kid unheard, but we need to move.

Many kids are used to waiting you out. They will copy what you do, but they will not venture out on their own. I am now waiting many of them out, but I can’t wait them all out. There just isn’t time. I love mistakes that kids learn from, but too many won’t even try until the bitter end. Working in extra supports and re-teaching is tough. Where? When? With what?

I struggle with formal assessment as well. I hate grades and love learning. Unfortunately, we are required to take a minimum number of grades a quarter. On what? There are only end of unit formal assessments, but that is not enough. There are no quizzes. I collect daily work and cool downs periodically, but are they really formal assessments or are they just part of the learning process? I started the year doing my own quick quizzes, but have gotten away from that. I need to get back to that. Now.

The formal assessments created by Open Up are really great, but they are a bear to evaluate. If we were doing standards based grading, I could see where this type of assessment would be really helpful. We are not though, so making the grey into black and white is a challenge for sure.

 Misconceptions about conceptual understanding:

For years I was told to dig deeper to get students to better understand. Problem was, nobody showed me what that meant. I was left to my own devices. I thought I was doing that when I insisted students understand why certain math algorithms worked. Turns out, I missed the mark. I am finally starting to understand what conceptual understanding means. If somebody was writing about it, I wasn’t reading it. Open Up Resources is actually showing me what it means to have/get/show/teach conceptual understanding of mathematics topics.

What I worry about now, is what my NC Math 2 kids are missing along the lines of conceptual understanding. These are the kids who have done well so far because they have been able to get away with memorizing stacks of mathematical algorithms. My only evidence that I am actually teaching for understanding in Math 2 is that I have a few kids that have historically gotten all As now struggle to get Bs because they do not truly understand what they are doing. I digress. This is about my experience with Math 8, Open Up Resources. I long to crack this conceptual understanding nut though.

I confess, I tell my Math 2 kids everyday how excited I am about what I just learned in Math 8. The ones that truly listen to what I am saying are very curious and want to know more. How I wish I could teach them this Math 8 goodness as well. I know next year I will work much of this into the Math 2 warm-ups. I do a bit know, but not like I wish I could.

Sharing:

I want to share with others, but I am slow. I know I should put all my stuff on Google Slides and share that way, but I haven’t learned all of that yet either. I need help figuring out how to efficiently share my stuff. I am re-creating all this and I am not sharing. That’s not who I am. I need help figuring out how to do that without spending an additional thirty minutes a day. My biggest problem is that I stink at asking for help. I will do anything for anybody, but I am not good at asking for help for myself. I’m getting better, but I still have a long way to go.

Goals: (These are actually wishes because I do not have actionable steps for them—yet.)

  • Create a Desmos activity of each lesson. I experimented with a cool down, but I want more. I think the tasks could be adapted pretty easily in Desmos.
  • Figure out how to use the parent resources created by Open Up. I am not even sure how to show parents that they are available. What I print stinks, so there must be a better way.
  • Figure out how to get students to utilize the reflection piece created by Open Up. That looks pretty deep and by deep I mean valuable.
  • Design a notebook or filing system for students to organize work papers so resources are available for review.
  • Figure out how to work training into my schedule. I teach Math 2 second and last periods. Math 8 is first and third. Trainings are half days. This takes me out of half of each of my classes. We have a dozen cross-teamed kids so adjusting the schedule is not practical.
  • I want to find or develop a group of learning tasks that show kids that their efforts matter even if they don’t get to the end. Too much of math is about the end and we need to start to praise and celebrate the middle because that is where the learning happens. I think this will help that perseverance piece a great deal.

Closing:

I hope I don’t sound like Debbie Downer. I am really digging this curriculum. I even showed my pharmacist brother-in-law how cool it was over Thanks Giving. He said, “I don’t fully understand, but I can see how it would be exciting for a math teacher.” Now, granted, he is above average intelligence. The point is he appreciated what Open Up is trying to do for kids’ understanding. He also enjoyed how excited I was about it.

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