A Matter of Trust

Let me start by saying it's been a GREAT week!

It's been a challenging school year to this point, and the weeks before Thanksgiving Break were a struggle. I've ended more days than I can count feeling ineffective. I admit I expected this week, as students returned from Thanksgiving and looked ahead to Christmas, to be just as challenging.

My students have put forth great effort this week, and it's been one of those weeks where things have seemed a little smoother and easier.

I'm thankful for the positive week. And making a "note to self" to remember this week when the next rough patch hits.

What I really want to talk about, though, is trust. Trust in my students.

I was talking with a colleague this week, and I theorized that every teacher is somewhat of a control freak. It's MY classroom and MY students, and I want things to go (and be done) MY way.

Flipping my Algebra 1 classes two years ago was the beginning of me giving up some control. Of me trusting my students.

Moving direct instruction into the control of my students led to changes in my classroom (wow, that's an understatement!).

Students were given choices of activities. Students were allowed to work together more than ever before.

Then I began to notice I was allowing students more control in how they approached problems. To use strategies that made sense to them.

(Incidentally, just this week I was looking at a student's work and I heard myself saying, "Well...that's OK, but what I really want you to see is _______ and do it this way." No, no, no, Mrs. Gibbs! *smacks own hand*)

I confess to being slower to trust my (inclusion) Pre-Algebra students. When we first moved to Common Core-based standards, my thought was, "There's no way! These kids have so many difficulties and challenges, and you want me to teach them to do WHAT?!?!"

So I baby-stepped them through things, confident there was no way they would understand as deeply as they were supposed to understand. I would tell them what I wanted them know and hope a few of them got it.

Then this year I began an in-earnest in-class flip. I began to notice that my Pre-Algebra classes were still much, much quieter than my Algebra 1 classes (read: boring!). They were still working largely individually.

I decided they needed the opportunity to work together just as much as my Algebra 1 students. They needed to talk and learn from each other.

Could I trust them to stay on task? Could I trust them to choose who to work with?

The short answer: Yes.

I used to hate "group work." It was often a waste of time and such a management nightmare. I didn't trust my students, so I never gave them sufficient opportunity to show me that they could do what I needed them to do.

Now, working together - in Pre-Algebra and Algebra 1 - is just how my class runs.  I am often amazed (and always do a little internal happy-dance) as I circulate around my room and hear mostly mathematical discourse. Yes, they are teenagers and need redirection from time-to-time, but most of the time there is a nice "hum" of engaged activity.

The other area I am trusting my students more is content. I admit to many times not going deep enough out of fear. Out of lack of trust.

This is too hard.

They won't get this.

I will have to give them every answer.

This will be a headache.

This year - with both groups - I've been giving my students tasks and seeing what they can do with them. Sure, Pre-Algebra needs more scaffolding than Algebra 1, but I am learning they are perfectly capable of going deep.

There are still questions. I spend class periods moving from group to group having conversations. I ask lots of questions. I smile and encourage and walk away (boy, that's hard!).

But students try. They think. They make connections. They learn.

I have spent years complaining about students being "lazy thinkers." Nothing is more frustrating than giving students a task and them seeming paralyzed.

How do you Number 1? Number 2? I don't get it!

Yes, students still have to be taught and encouraged to find joy in the struggle, but I was thinking recently that I am hearing much less of these statements this year.

Is it this year's group of students?

Or is it me? Was I the reason my students were lazy thinkers?

Was it simply a matter of trust?

"It's so HAAAARRRRRDDD!!!" and What I'm Learning

(Please read the first part of the blog post title in your best whiny voice.)

Sometimes I feel like this baby. I feel like I become one big whine. Like my friends should ask if I want some cheese with that.

It's that time of year again. The time of year that produced this post last year and this post two years ago.

I'm beginning to notice a pattern. I don't understand the pattern, but it obviously exists.

Yes, things are hard. I have a challenging group of students. Students who are pushing and stretching me and wondering if I mean what I say when I say I care about them and am committed to their learning. I am still creating and changing lessons and doing things differently than I have done them before. I am still at school way too late each day. I am still out of my box and in an uncomfortable space where I wonder if I'm doing things correctly. I end many days feeling like a failure. I am still challenging kids to go deeper and think harder; they don't always like or appreciate that.

Teaching is hard. And lately it's felt dang hard.

For THIS post, though, I don't want to explore all those challenges in depth (again).

I want to list some things I've learned. Or continue to learn. What is happening as a result of the challenges.

1) Challenging kids...challenging groups...need something.
     a) They need to be challenged. They need depth, context, something to hold on to that lets them know what they are doing matters.
     b) They need choice. A voice. Ownership. They need to know we're in this together.
     c) They need to know I have their back. I'm on their side. Their behavior may need correcting, and they may need to be reminded what is and is not acceptable or appropriate, but they need to know that I will never give up on them.
     d) They need ME. The best me I can give. They need a me that is unswayed by frustration or fatigue.

2) There are lots of good, thoughtful, kind kids. Kids who look out for their fellow students. Kids who step up and do the right thing. Kids who smile and tell me, "Good morning, Mrs. Gibbs," and "Have a good afternoon, Mrs. Gibbs," and make each day a little brighter.

3) I have good friends. Friends who listen, offer encouragement, pray for me, assure me I'm not alone. Friends who laugh with me and cry with me.

4) A lot of the time, even in the midst of difficult times, I still have way too much fun doing what I do.

5) My kids are growing. They are budding mathematicians, and I beam with pride when I read a coherent, mathematical explanation or hear one of them explain a concept to a peer.

6) The darkest week of the year - the week before the time change when I'm driving to school in the almost-dark - has beautiful sunrises.

So far, it's been a challenging year. I really don't see that it's going to let up. But I'm trying to embrace the process and let the struggle produce the growth - in me AND my students - I know is possible.

What are Students Saying? - First Grading Period Reflections

As I've often said, I like giving students regular opportunities to reflect. I've had a goal for some time to gather student reflections at the end of each unit. That has not become a reality, yet, but there are few points of the school year in which I make sure I ask some reflection questions: the end of the first grading period, the end of the first semester, and the end of the year.

Believe it or not, it's the end of the first grading period.

I love Google Forms for student reflections. I can ask multiple choice questions and short answer questions and easily see responses and trends. I also save lots of paper. :)

I used a survey I used at the end of the first grading period last year that I called "The Goldilocks Survey." There were five multiple choice questions addressing such areas as how the class has been going, course difficulty, class structure, student-teacher interaction, and (self-perceived) student effort in which the answers were some variation of "too much," "too little," or "just right."

The three short answer questions asked students to describe something they enjoyed about the class, something about the class they would change, and anything else they would like me to know.

I questioned Algebra 1 kids and Pre-Algebra kids separately, so I could see responses of kids in the same course together and notice any trends for a particular course.

Most of the responses to the multiple choice questions fell overwhelmingly in the "just right" category. I was thrilled to see a large percentage (almost 40%) of my Pre-Algebra kids say that the class was going "better than expected."

I haven't done a specific survey about flipped lessons this year - I might do a short one when we return from Fall Break - but videos were mentioned frequently as a favorite part of the class for both Algebra 1 (videos for homework) and Pre-Algebra (in-class videos).

Students appreciate light homework loads.

The aspect of the class brought up the most and that has me doing the most thinking is group work.

What do you like about the class? Group/partner work
What would you change about the class? Group/partner work

I have become a huge believer in partner work. I found several years ago that students are much more focused and accomplish so much more with a partner as opposed to groups of 4. With a partner, there is less hiding and letting two or three other people do your work for you.

I was reminded this past week that groups of three or four are not as successful as partners.

On the survey, my Pre-Algebra kids asked for more partner work. I agree. I had an "a-ha" several weeks ago that my Pre-Algebra kids were not getting enough opportunities to work and talk together. I've made it a point to give them more of those opportunities.

Several students in the survey mentioned how helpful it was to discuss their thinking with someone else. One student likes that they have a partner to ask for help if I am busy.

A few students talked about how groups are selected. I've been giving students more choice in who they work with. But occasionally I pick the groups. Sometimes I allow students to work alone, if that's their preference.

All of these aspects were alluded to in the responses to the survey questions.

Some students want me to pick groups/partners less often. I am a (developing) believer in student choice (I have made great strides), but I believe it's important that students learn to work with a variety of personalities and not just their peer group (I am reminded, though, of teachers' reactions when we are made to "mix it up" and sit with someone different in a meeting).

Some students never want to work with someone else. My heart hurts for my introverted students who would rather crawl under their desk than work with somebody. I do feel it's important they learn to work with others; it is unlikely anyone will go through life and not have to work with another person.

Some students feel alone in class; this makes me sad. I've seen those kids who are excluded when students are allowed to choose who they work with. I appreciate the kids who make an effort to include them.

I think a balance of all the options - sometimes I pick their partner, sometimes they pick their partner, sometimes they are allowed to work alone - is necessary to keep most everyone happy most of the time.

I find that's true with most things in the classroom. Keep things mixed up, and don't ever do something the same way every time.

I might give my "Partner Preference" survey when we start the second grading period (have I mentioned how much I like Google Forms). That way I can lend a little bit of structure plus choice to our work with partners.

Overall, I believe students have had a positive experience in my classroom to start the school year. I think we've laid a good foundation, and I can't wait to see the growth - in them and me - as we continue to work through the 8th Grade.

A Mathematical Gallery Walk

"Writing in math class" has long been a topic of discussion. Like many, many other topics of discussion it is an aspect of my teaching practice that is undergoing transformation.

It started with "write your answer in a complete sentence."

Mary bought 2 dozen apples.

THAT was writing in math class?!? Yep, pretty much.

My transformation probably began with Laying the Foundation training. I was introduced to what was expected of students' writing on Advanced Placement tests. And I began to expect more of my students' explanations. (For the record, they hated it.)

Then we began administering the ACT Aspire as our spring test; there's an entire "Justification/Explanation" section of the scoring. And our students are not scoring as well in that area as we would like.

I determined this year to focus on students' mathematical writing. In the past I would be thrilled if students could tell me ANYthing when asked to explain their work. Now I want to focus on those explanations being thorough and precise and using correct mathematical language.

I knew I wanted students to read and evaluate each others' writing as part of our work on justification/explanation, but I was unsure how to do it. Our instructional coach mentioned a gallery walk in one of our department meetings, and I realized that was the approach I wanted to take. I found this post to help me organize the gallery walk for my classroom.

Completed Gallery Walk

I split my Algebra 1 students into groups and gave each group a multi-step equation to solve. On chart paper, they had to show their solution and explain how they solved the equation. Then the groups rotated through each problem, making notes (via post-it) of what they liked about the explanation and any suggestions or questions they had about the explanation. When groups returned to their own problem, they revised their explanation.

Solving a problem and writing the explanation

Making post-it note suggestions

For my first attempt at a gallery walk, I think it was very successful. Students have to be taught how to critique each other's work, but that is also a Mathematical Practice standard, and all-in-all they did pretty well. Each class - unprompted - was able to pick an explanation that they thought was well-done. One class picked up on a explanation that was a bit wordy and made suggestions for making it more concise.

My goal is to incorporate more gallery walks throughout the year.

One issue I face when working on student explanations is TIME. It is hard for me to take time to work on writing and justification when there is so much math to cover. But I'm learning to work it in where I can. I am trying to put at least one thing on every test that requires students to explain in words. On the equations test, it was an error analysis problem. After the tests were graded, I made a warm-up for each class that included snapshots of actual student answers to the error analysis problem from that class. We discussed what was good about each response and elements of each response that should be included in the "ideal" response. Then I had students rewrite the "describe the error Carlos made and explain what he should have done correctly" part of the problem. I got some impressive rewrites!

As with everything else in my classroom, writing/justifying/explaining is a work in progress. Seeing student progress in that area is exciting and motivating.

Adventures in Speed-Math-ing

I discovered task cards a few years ago. I was amazed at their effectiveness. Students who will shut down (understandably) at a worksheet of 20 problems will happily get a comparable amount of practice working one problem at a time, particularly if they can work with a partner and check their answers as they go (hurray for QR codes!).

I've used task cards in a few ways, including scoots (not my favorite) and through the app Classkick, but I've wanted to try Speed-Dating Math-ing for at least a year. I was just never sure how to make it work for ME.

I read this blog post that made the most sense to me, and I finally took the plunge (disclaimer: Randi explains the process much better than I do, so please read her post!).

I tried speed-math-ing with my Pre-Algebra kids first. My two collaborative, inclusion Pre-Algebra classes are small, so I set up two sets of 8 desks in the room. One reason I decided on two sets was to allow for a bit of differentiation; students in these classes work at vastly different speeds, and splitting them up would allow students to work at a pace comfortable for them.

A couple of days after Pre-Algebra, Algebra 1 did the same activity with the same cards.

I started with a brief, probably inaccurate, description of speed-dating and added that we were were calling it speed-MATH-ing. I also noted we were not emphasizing speed.

I gave each student a card and told them they were to become the expert on that card. Each student checked their answer with me (these cards didn't have QR codes). I told them to make sure they could explain how to work that problem (we were simplifying expressions) to another student.

After each student assured me they understood their card, they traded with the person sitting across from them. They were given a bit of time to work their partner's card.

They checked their answers with their partner.

If they missed the problem, their partner was to explain how to get the correct answer to them. At first, students wanted to depend on me to check their answers or explain how to work the problems correctly, but they quickly figured out how to depend on a card's "expert."

We had an odd number of students, so my partner teacher became a student partner.

 When everyone could work their partner's problem, they got their card back, and one side of partners moved seats.

After everyone had partnered with everyone in their set of 4, a row from each set traded places.

The activity was a success. Students said they enjoyed it. They liked changing partners frequently. I think being the "expert" on one card and knowing their partner was an "expert" on the card they were working on boosted confidence. The activity was no-risk.

There were a couple of small issues I would still like to work out. Timing was still an issue with my Pre-Algebra classes, even though I tried to accommodate for it. Splitting the classes into two sets meant some students never partnered with each other.

I'd like to be able to arrange the room into one large row of desks, but I'm not sure I have room for that. I might make a U with the desks next time?

I'm thrilled I finally got to try speed-math-ing. I will definitely use it again with a couple of modifications.

The In-Class Flip and the Magic

Since flipping my Algebra 1 classes two years ago, I have tried to figure out how to successfully flip my Pre-Algebra classes.

My Pre-Algebra kids are different from my "pre-AP" Algebra 1 kids. Less confident, less motivated, many of them trying to be successful despite learning disabilities and obstacles at home.

I decided early on that watching videos at home would not work for my Pre-Algebra kids. I tend to not give these kids homework, anyway. And if a large percentage of them enter class having not watched a video (usually only 1 or 2, if any, of my Algebra 1 kids don't watch a video), it would make each day's class difficult and stressful...for them AND me.

So I've been contemplating an in-class flip with them for over a year, but I wasn't sure how to organize it. Some in-class flippers use stations, but I wasn't sure how that would look for me.

I did a few in-class videos with last year's Pre-Algebra group, but I started late in the first semester. After the pretty successful "flipped review," I no longer made any videos for Pre-Algebra second semester. I'm not exactly sure why I didn't; it just didn't seem to click with that group, or I had too many other things going on, or all of the above.

I changed my order of topics this year (again, LOL), and we started with equations, which is the content for which I made videos last year. So...let's use those videos this year! Kids were exposed to flipped lessons starting around the third week of school. We discussed how to watch/interact/engage with an educational video.

The kids took to the flipped process right away. Many talked about how they liked the videos over a "normal" lesson. One young man said, "I like the videos; they sort of force you to pay attention."

I'm not ready for a completely asynchronous classroom - I like group and class activities too much - but flipped days have become self-paced days. I give the students what they need to accomplish for the day, which normally includes a video and some practice. Students like that they can watch the lesson at their own pace. They are getting better at asking questions at any point in the video where they are confused. After finishing the video, they have something to immediately begin working on. My partner teacher and I get to work with lots of students one-on-one as they practice.

We flip a couple of days a week, and then the rest of the time we get to do the collaborative activities. We've done speed-math-ing (blog post coming), bingo, scavenger hunts. Students have worked together while doing otherwise-boring skill practice, helping each other, talking math, finding success.

And the magic is happening.

I would say this group has a better understanding of solving equations than almost any of my previous Pre-Algebra groups. Sure, they're making they typical sign errors, but they KNOW the process.

They're talking math. To me. To each other.

Their confidence is high. I have put a couple of equations in front of them, telling them to wait and let us work them together, and I am met with a chorus of, "That looks easy! We can solve that! Let us try it first!" They are often finding and correcting their own errors.

I think a few parents and students are using the videos at home.

Make-up work has become MUCH easier.

I am seeing GROWTH in students. Students who could not solve a two-step equation two weeks ago are finding success with many multi-step equations. Their work looks beautiful (gushing math teacher here). I am seeing beautiful smiles as I praise effort and progress.

I can't claim that the in-class flip has made all the difference. These students have been working with common-core based standards, deeper thinking, and collaborative work for several years, and each year I can tell a positive difference in the mathematical abilities of my students.

But I think the in-class flip is another piece of the puzzle I have been searching for to help grow my developing mathematicians.

I Notice...I Wonder...The Pythagorean Theorem in 3D

I am pretty tired and close to brain-dead, but I wanted to post while today's activities were fresh in my mind.

I had a brainstorm Saturday morning. Algebra 1 was finishing up the Pythagorean Theorem this week, and I wanted to take a look at the Pythagorean Theorem in 3D. I tried it last year with not a lot of luck. A few saw it, many did not.

My "A-Ha" came at the strangest time, but I went with it and began planning. What if I approach it with an "I Notice...I Wonder..." angle? What if I can get kids to see where we're headed without telling them?

I decided to show kids a diagram of a rectangular prism with the interior diagonal in blue and ask what they noticed and wondered. Then I showed them the same diagram with the dimensions of the prism and the question, "What is the length of the blue line segment?"

I split kids into groups of three, gave them a copy of the diagram they could write on, and I gave each group a box (various sizes) with string as the interior diagonal so they could have something to touch and see.

And then I turned them loose.

I was scared. What if they all stared at their papers and said, "We don't know what to do!"? What if I had to walk everybody through step by step by step? What if it was a total flop of a lesson?

My fears were unfounded.

Students noticed and wondered some good things. They were advised to give serious, math-related observations before they began. :)

As I distributed diagrams and boxes, everyone got to work. Almost everyone tried SOMEthing. Maybe two groups all day said, "We don't even know where to start."

I tried to not give too much away as I helped groups. "You're on the right track." "Tell me why you approached it that way." "Does what you found have anything to do with the length of the string?" I'd ask a question or two, smile, and walk away.

I would say by the end of the activity, most students saw the two triangles they needed to see to find the length of the string/blue line segment.

It was interesting to see their incorrect approaches and misconceptions. Many wanted to start with area of the rectangular faces or the volume of the box. Some would find the diagonals of the rectangular faces and add them. A few had visualization difficulties (interestingly, some of my strongest math-y students had the most trouble with the visualization of the string in the box).

A few went right for what is the formula/shortcut for finding the length of a box's diagonal, extending what they knew about the Pythagorean Theorem, but since they couldn't explain to me why it worked, they had to find another way (the "8th grade way") to get the correct answer. Those groups got mad at me. :)

The cardboard boxes were a MUST. I didn't start the day with enough boxes for every group, but after some searching by a dear friend, I ended up with enough, and I'm so glad I did. Being able to hold, touch, and outline what they were finding on a real box helped make the lesson a success. One kid even said, "I'm glad we had this box; I can't tell anything on the picture!"

I'm wondering if I needed some triangles of the proper sizes cut out so that students could SEE the triangles they were trying to see. I would need the same size boxes for everybody to make that process easier. It's something I'll think about before I do this activity with my Pre-Algebra kids.

I wish I had added one thing to the notice/wonder start to the lesson. After their initial observations and questions, I wish I had said, "If I told you we were dealing with the Pythagorean Theorem in 3 dimensions, does that add anything to what you notice or wonder?" I wanted to tell the students as little as possible, but it took a few of them a little bit to realize this activity was tied to what we've been doing in class for the last week.

The next part of this lesson I need to tweak is the wrap up. All the groups in my 3rd Period class finished, saw both triangles they were supposed to see, and found the length of the string/segment. But I'm pretty sure a couple in my 5th Period and a few more in my 7th Period never got there, even with prompting and hints. I hate feeling like some students leave a lesson thinking, "That was nice. What on earth were we doing?!?"

So...how to get them all "there" and tie up the lesson with a nice little bow without just giving it all away?

I'll keep thinking on it...sleeping on it...and waiting for the next Saturday morning "A-Ha!".

#flipclass FlashBlog On Parents, Support, and Homework

I try to keep the parents of my students informed about what is going on in my classroom. I could always do a better job.

I have one main "parent goal" for this coming year. I would like to get more feedback from parents about what is/isn't working for their child in my class. I collected email addresses at the beginning of the year and plan to form groups so I can send reflection forms to parents similar to what I have students complete throughout the year.

The biggest problem is finding the time to get all of that set up. Since I'm still in the process of finding my groove, email groups have been low on the priority list. But I don't want to forget about them.

Support from parents and administration for my flipped classroom has been amazing. My admin has been behind me from the beginning, and as positive comments started coming in from parents and students, support strengthened.

The only question I've been asked by a parent was during the Open House at the beginning of my first flipped year: "Are YOU making these videos?" OK...there were two questions. The follow-up question was "How are you going to have time to do this?"

Parent feedback is always positive. I hear from parents from time to time; I hear from their children what they are saying at home. I've even heard positive parent comments from tutors who work with my students.

I assign my videos as homework. There. I said it.

My videos are short (10-15 minutes), and I keep them to about 3 videos a week (sometimes more, sometimes less).

Parents and students appreciate the manageable, light homework load. Parents appreciate that they no longer have to try to figure out how to help their students with their math homework. They appreciate that they get to know me in a way as they listen to videos their child is watching.

Moving direct instruction outside the classroom allows me to do things in the classroom I would otherwise not have time for.

I am grateful for supportive parents and a supportive administration. I like the format of my flipped classroom and what it does for my students. I look forward to continuing to improve all its facets.

Trying to Find my Groove

I just finished Week 2 with students, and I have to say it's been a rough two weeks. My students are fine. I have one challenging class, but we are approaching the place where we understand each other. :)

I have just felt perpetually behind the past two weeks. I feel like I'm barely staying one step ahead of where I need to be. I don't have my sea legs, yet.

There are probably good reasons. We moved my son to his freshman dorm last weekend. I had to miss a day this week for a committee I'm on. There have been after-school appointments, which completely cramp my stay-at-school-until-I'm-done style.

I have been reminded of when I returned to teaching after 5 years at home, with two small kids. It was Christmas before I felt I was in a routine.

I really hope I'm not going to feel this way until Christmas.

The point of this blog, however, is not to whine about how hard everything feels right now (at least, not too much).

I want to reflect on what has happened in the classroom in two weeks.

I've pretty much followed what I did last year in Pre-Algebra and Algebra 1, but - as usual - I tweaked a few things.

I ditched last year's growth mindset lesson. I believe growth mindset is important and work on it all year, but I was bored to tears with the lesson I did last year. And if I'm bored, I know my students are.

This year I did this activity by Sara VanDerWerf to introduce cooperative learning and looking for patterns. I loved it! Students did, too! And it seems to have been beneficial; when we work together, students show many of the characteristics we talked about with this activity.

I did part of the lesson I blogged about here. It was a fine lesson; we had some good discussions. It highlighted some misconceptions. But it still didn't accomplish quite what I was looking for in my review of subtraction. I'll try another iteration - which I've already outlined - next year.

The tech start to the year has gone very smoothly. I've used Google Forms - including on a sub day! - and Flubaroo to quickly and efficiently assess students and adjust the next day's instruction. The newest updates to Google Classroom have me a very happy teacher.

The new annotation feature in Google Classroom is awesome!

I started my flipped lessons with Algebra 1 a little differently this year.

Typically, we watch an intro lesson to square roots together, then the remainder of the week's videos are completed at home.

This year, I went with an explore-flip-apply approach. I wanted student to build the conceptual foundation for square roots. So I started with this lesson from Illuminations. The extra time it took to do the discoveries and lay the foundation was worth it. I was so thrilled yesterday to hear a student - several days after the lesson and well into the next topic - define "square root" as the "side length that gives you the area of a square." SCORE!

We watched all the week's videos in class. Square roots, cube roots, sets of real numbers, classifying real numbers. My thought was students and I might benefit from me being with them as they watched their first videos. I could give tips for how to take notes. I could check their notes as soon as they finished a video. And all of that happened, but I think students were more distracted watching the videos in class. It also messed up my class time. My timing was completely off for class activities (mostly too short and having too much leftover time at the end of class). Another iteration will come next year.

One change I made in a particular video was very positive and much needed. I made my real number video two years ago, changed it a bit last year, and changed it again this year. It started entirely too long (about 15 minutes), and last year I got it down to 11. But I was still not happy. It was a lot of listening/writing.

So I decided to split it into 2 videos. The first video defined the sets of real numbers and gave examples, the second video looked at the Venn diagram organization of the system and how to classify numbers.

I'm happy, now. :)

Yes, it's two days instead of one, and if these videos are watched at home next year - which I think they will be - I'll have to find a few more meaningful activities to fill class time, but I'm happy with the two videos in place of one.

I continue to focus on shorter videos.

I didn't take a lot of pictures this week, but I did catch what is still one of my favorite activities: a search & order where students have to properly classify numbers and order them least to greatest. I heard lots of great discussions and answered lots of good questions. It was made even better with the new Classroom annotate feature.

So...I'm confident I'll find my groove. Before Christmas. I already feel better after completing the "big" activities currently on my calendar and staying at school way late yesterday to get a handle on things.

Do you know how quickly a school building gets dark and quiet on a Friday afternoon?

Goal for the Year: Keep Taking Risks

I didn't intend to blog today, but I had a "moment" yesterday, and I need to share it, mostly for my own benefit.

As a teacher, I do not tend to avoid risks. I flipped my classroom. I implemented a broad retake and redo policy. In the last few years I have used methods and strategies and lessons completely outside my comfort zone. I play around with new technologies.

Does everything always work smoothly? No. But the rewards of all those things have been greater than the hiccups.

So...it's a new school year (students start tomorrow) with new opportunities for growth. I have pushed myself and my students HARD the last couple of years, but there are still improvements to be made.

One area of focus is developing students conceptual understanding of math. WHY does math work the way it does? An understanding of the math is infinitely preferable to blindly using a rule and not having a clue why it works.

One topic where I find students' conceptual understanding to be particularly lacking is subtracting integers. Students really have no idea what subtraction means. They've been given rules to follow (this is improving!), but most students will miss subtraction most of the time.

Integer operations are not an 8th grade "thing." We use integers, but the foundation for integer operations happens in the 7th grade.

But I start the year in Pre-Algebra with a review of integer operations. It is familiar to students, it boosts their confidence as we begin the year, and it is very important to the work we do the rest of the year.

In years past, this has meant a review of "the rules." Singing songs, writing rules in foldables, practice problems.

This year's 8th graders didn't learn "rules" in the 7th grade. They learned how integers worked. So there will be no singing this year. We're going to work with number lines (I started this some last year).

I was looking around over the summer for a good, conceptual integer lesson, and I found one using temperature as a context that focuses primarily on subtraction. Perfect! I thought it would be great to have a nice collaborative lesson at the beginning of the year to show students that THIS is how this class is going to work.

Last night I printed the lesson out to look through it and get a better feel for it.

And I began to panic.

"This is confusing."

"This is too hard."

"This is too deep."

"This will take too long."

"They'll never get this."

"This will be a disaster."

"We're going to have to scrap this lesson. Now."

"We'll just teach the rules and do some practice."

And then I stopped myself.

Do I want my students to develop better conceptual understanding?

Do I want my students to "make sense of problems and persevere in solving them"? (Mathematical Practice Standard #1)

Do I want my students to improve their modeling and justifying skills?

Yes, yes, and yes.

So there will be no scrapping of this lesson. It may need some scaffolding and students will need lots of support and cheerleading. But my students can do this. I can do this.

If I want to continue to move my students where they need to be, I must continue to push myself. Teach the risky lessons. Don't revert to what's comfortable just because it's easier and less of a headache.

After I had this little conversation with myself, the inspirational people I follow on Twitter unknowingly confirmed my resolve.

"What's worse than failure is not trying in the first place." - @teachergoals

"Doubt kills more dreams than failure ever will" - Karim Sedikki, posted by @teachergoals

"Don't be afraid to scrape the paint off and do it again. This is the way you learn, trial and error, over and over, repetition. It pays you great dividends, great, great dividends." - Bob Ross, posted by @NFLaFave

The goal for the year (well, one of many areas of focus)? Keep taking risks. My students deserve it.

Summer School Reflections

Summer School wrapped up 3 hours ago, and I've debated whether to wait a day or two before blogging, but I decided I wanted to clear my head of anything school-related for a few days, so here goes....

I've taught summer school for 5 years. It's something I feel called to. It's always challenging.

This year was TOUGH. Maybe one of the toughest months of my professional life. I can identify several reasons for the difficulties, but I decided that was not the point of this post.

I approached summer school differently this year (more problem-solving and less skill-based) and had a few things I experimented with, and those are the things I want to talk about.

Number Talks - I read the book Number Talks Matter in the week between the end of the school year and the beginning of summer school and started each day for the first two and a half weeks with a number talk. We did dot cards, then addition, and one day of subtraction. The kids seemed to enjoy the number talks. They picked up on new strategies quickly. It was good to see their number sense develop. I loved hearing, "I want to justify!" coming from multiple students. A few were stuck on algorithms, but I think almost all of them were seeing ways to find answers without resorting to "carry the 1" as their strategy. Subtraction is where the rubber hit the road (and, unfortunately, I did not spend a lot of time on subtraction). I've known this from working with students for years, but they do not understand subtraction.
Number talks are definitely going to be a part of my classroom routine this coming year.

Multiplication Facts - I always want to work on multiplication facts during summer school and usually approach it through timed tests and sometimes some sort of fact practice.  I decided to ditch the timed tests, and - since we had done the dot card number talks - made a set of subitizing multiplication cards for students to use as flash cards. I liked the cards, but I wasn't able to get the kids to be as productive with them as I would have liked.

EngageNY - We began working through an EngageNY 6th grade module on ratios. We talked about the definition of a ratio and how to find equivalent ratios through tape diagrams and a common multiplier. The EngageNY lessons ask good questions. And I liked the conceptual foundation that is laid. But I find them boring (OK...there. I said it). They are very teacher-driven and teacher-centered. With a group of struggling, less-than-motivated students, it's like pulling teeth. I tried to bookcase lessons with kid-centered activities, but I still found the lessons hard to get through. I need to figure out to take what I like about the lessons and make them more my style.

Mathalicious - I signed up for a free trial month of Mathalicious. They have created suggestions for units that have an introductory, middle, and end lesson, with "conceptual understanding and procedural fluency" in between. That was sort of the approach I took. I did three Mathalicious lessons with the students: "Jen Ratio," "Downside Up," and "Leonardo Numbers." "Jen Ratio" and "Leonardo Numbers" were both ratio-related; "Downside Up" dealt with integers but was a short, accessible lesson to build conceptual understanding.

Looking through newspapers to determine the number of positive and negative headlines.

I like the Mathalicious lessons. They give students context. They connect to students' interests (they were so excited to see a clip from "Family Guy" in one of the activities!). They do a great job of providing practice with mathematical skills but making it just part of the process and not a "Here's 20 problems; do them" sort of experience.

To finish up summer school, I took "Leonardo Numbers" and combined it with some other resources, and we looked at the Fibonacci Sequence and the Golden Ratio.

Measuring the faces of celebrities to see who is the most mathematically beautiful.

Measuring each others' hands and faces to see who is the most "golden."

I liked the Mathalicious lessons. The kids seemed interested (most of the time), if a little harder to manage (mostly because of the mixture and number of kids). A year-long subscription is pretty pricey, so I plan to write a grant in the fall to have access to all the lessons (they have a few lessons available for free).

It was a tough month. But I did see evidences here and there that learning was taking place. Vocabulary was being used correctly. New strategies were being applied. Hopefully foundations were being laid and connections were being made.

I want to take several of the things I tried in summer school and use them next school year.

For now, it's time to sign off and give this tired ol' teacher brain a break. I wrote before summer school that the teacher side of my brain rarely shuts down. This month has succeeded in allowing that to happen. Not only is the switch off, I think the power has been disconnected.

I'm going to take a couple of weeks off, and I'm sure by then I'll be ready to begin planning and gearing up for the start of a new school year. But I really don't want to think about how close that is right now.

Innovation in My Classroom

Andrew (@thomasson_engl) will fuss at me for saying this, but I'm not very creative. I can follow someone else's lead with the occasional A-Ha of my own, but I have very few ideas original to me.

I've said it before, but I stand on the shoulders of giants. And I am oh-so-thankful for those giants.

So...how does innovation show up in the classroom of this not-so-creative teacher?

A few years ago I began Interactive Notebooks with my Pre-Algebra kids. That was decently innovative (although not original).

Two years ago I flipped my Algebra 1 classes. That was hugely innovative (still not original).

Last year I played around with an in-class flip for my Pre-Algebra students.

The structure of my classes continues to change. More student choice. More student-centered. Moving towards more open-ended, collaborative lessons that give students context.

All of this is innovative for ME. Way outside my comfort zone and definitely outside my box. It's pretty innovative for my students, too. And their parents.

Math class has been conducted largely the same way for a looooooong time. Current changes in the MO are new for everyone.

And I am, by no means, the only teacher trying these things. I learn from others, decide to take risks in my own classroom, and tailor the "innovations" to my personal style.

Innovation by my students?

Unfortunately, I am not as far along with allowing them to be innovative.

I have made huge strides in allowing them to approach and solve problems in ways that make sense to them (believe me, that's a HUGE shift).

I assigned a project to my Algebra 1 students last year that allowed them to make some choices and be creative. They did an awesome job, and I need to do that more often.

It's not that I don't want my students to be innovative. I just don't know all the how-to's...yet. I continue to work on it.

My classroom and I are ALWAYS a work in progress.

That's a Wrap (...but Always Planning)

The 2015-2016 school year is finished.

It was a good one. Oh, there were tough times and struggles and frustrations, but that's part of the process.

I feel good about growth I made as a teacher and where I'm headed with my practice.

I feel good about the foundation I laid for my students and hope what they learned with me will benefit them in high school.

Here's my evaluation of what I see as the major aspects of my classroom.

Flipped Classroom
Flipped learning is in my bones. It's who I am. I recognize the teacher I was before, but I am a completely different teacher now.
I did not experience the "love fest" from this year's students that Year 1's students provided, but they were very clear in their end-of-year reflections that they liked our flipped classroom.
My flipped classroom began to change this year, and I see it continuing to transform. I see shorter videos and more discovery/exploration before content videos.
I experimented with an in-class flip for my Pre-Algebra students this year, and I would like to develop that further.

Interactive Notebooks
I use these primarily with my Pre-Algebra students. Students like having a resource to use, and I believe INBs are beneficial for my students. But I'm a bit discontent with them. I can't quite put my finger on what's wrong or how I want it to change, but as I look at how I want my classroom to be next year I have a feeling the INBs are going to change, too.

Retakes and Redos
I found this process very tiring this year. Even more so than last year, when I was developing all the variations of tests. By the end of the year I found myself wondering if this was something I wanted to continue.
But all the reasons I chose to begin retakes and redos still exist. The benefits are all still there, too.
I believe retakes are best for my students, so I will continue to offer them with the same policy until I find something I like better.

As I wrap up this school year, my brain is already working on next year. I can't decide if it's a good thing or not, but it seems my brain never quits. I seem to ALWAYS be planning. The few times a year I actually turn the teacher part of my brain off for a few days always surprise me.

Here's what my brain is chewing on right now.

Summer School
Summer School is one reason I can't turn the teacher-brain off. I stay in teacher-mode through June.
While I feel the effects of fatigue in summer school and sometimes struggle with how to reach that particular group of students, I really enjoy it. I lay foundations in summer school. I build relationships that pay off hugely during the school year.
I normally make summer school very skill-based, reteaching algorithms that students find difficult. As one would expect, not a whole lot of remediation is accomplished in 4 weeks.
I'm approaching Summer School differently this year. I'm using a 6th grade module about ratios from the EngageNY curriculum as my base. We're going to work on conceptual foundations. We're going to justify answers, practice mathematical discourse, critique the reasoning of others, and create our own problems. I plan to include activities I know my students enjoy as well as interesting, non-routine problems from resources such as Yummy Math and Mathalicious.
I'm also going to do daily number talks. I believe number sense is one of the keys to a student finding success in math.
I'm hoping both the content and the methods will help my students in the fall.

Next School Year
I want to give my students context. I want to ensure conceptual understanding. My goal this summer is to peruse my go-to sites - Mathematics Assessment Project, Yummy Math, Mathalicious (after a free trial this summer, I'm thinking about writing a grant in the fall for a subscription), Laying the Foundation - and find interesting problems and explorations to deepen my students' understanding of content. I want to start each unit with a problem, give and practice the necessary skills along the way, and end each unit with a problem.
This is really a continuation of changes I made last year, but I want to take those baby steps deeper and farther.

I've come to end of this and concluded I should not try to blog on a Saturday morning before I've had my coffee. I've rambled, and I apologize. All these thoughts about last year, summer school, and next year have been bouncing around in my head, and I wanted to get them out.

And if you've read along through the second year of my flipped classroom journey (which has become so much more), thank you. Sometimes I feel a little silly putting my little thoughts out there in cyberspace. But blogging is good for me; being able to go back and read and learn from things I've gone through previously in my classroom is extremely helpful. And maybe somebody, somewhere can get something out of my experiences.

I'll be around some through the summer. I'll have to report on how summer school went and how the plans for next year are progressing. :)

End-of-Year Student Reflections and Evaluation

We've almost made it! The end of another school year is here.

I love student reflections. I like to check in with kids periodically to see how things are going. I want to know what's working, what's not, and their perceptions of things. Students often have very good ideas, and I want to know how they think I could improve my class.

I realize that I'm not always going to get the most serious of answers from 8th graders, but overall they do very well with reflections.

I gave this year's end-of-year reflection in a Google Form. I really like the recent updates to Google Forms.

The Google Form had 30 questions where students evaluated various characteristics of me on a scale from "Strongly Disagree" to "Strongly Agree." Students rated everything from my patience to organization to enthusiasm.

Nothing really surprised me about the responses to these questions. There were very few "Disagree" or "Strongly Disagree" responses, so I looked at the "Unsure" sections for areas that might need improvement. The questions with the highest percentage of "Unsure" - like giving clear directions - where areas I agree I could improve.

The final five questions were open-ended.

When asked about enjoyable aspects of the class, flipped lessons and videos were mentioned the most. I expected retakes to be mentioned more than they were. Students enjoyed working with partners and several different activities and games.

Next I asked about things about the class that can be improved. Students want to work with partners even more. The most popular answer was "less Punchlines." I did feel toward the end of the year - particularly the factoring unit - that I "Punchlined them to death." I had my reasons, but I agree that I needed to mix it up more.

Students also mentioned wanting more competition activities. There is a relay activity I do during equations that students love, and it's the only time of the year I do it. Next year I will find more activities like that one.

Another suggestion that I want to focus on is to find a better way to start a class after students have watched a video. Some sort of summary to make sure students understood what they watched. It's an aspect of my flipped classroom I have struggled with and wanted to improve since I started. I've tried a couple of different ways to move students from the video to classroom activities, but I haven't found "the way" I'm happy with. I'll work on it this summer.

Most students believed they demonstrated their best work and behavior. They would admit to occasionally slacking off. :)

When asked what one thing they learned they thought they would remember or use, Pythagorean Theorem was the clear winner. Factoring was mentioned more often than I expected. A few students wrote of life lessons like "always be positive and try your hardest."

"Retake more tests" was one of the most popular answers to "What would you do differently if you could do this course over again?"

Students were very nice in their responses to "Is there anything else you would like Mrs. Gibbs to know?" Reading "it was a fun math year" and "this year I love [math] and look forward to it everyday" did my heart good.

I'm pretty reflective, and for the most part I know where I'm weak as a teacher and need to improve. But I also know students have a perspective all their own, and they will often notice things I don't. They are the reason I teach, and I want to make every effort to meet their needs. Reflections and evaluations help me improve my teaching practice.

Improving the "Unit with Room for Improvement"

Last year I wrote a blog post about "The Unit with Room for Improvement."

So, how'd it go this year?

Much better!

I divided the not-so-successful unit into two units, as I decided last year it needed to be. We did polynomial operations, tested, then moved into factoring.

My students rocked polynomial operations! It was one of the most successful tests of the school year.

(As a side note, I taught multiplication without FOIL, hoping to help students understand it better, and I think it worked. I sort of needed the "OI" part when it came to checking their factoring work, but they seemed to even check their work better this year having NOT been taught to FOIL.)

As we got ready to transition into factoring, I was once again staring at the calendar. So few days left, lots of interruptions coming, but factoring AND quadratics left to go. The panic tried to set in.

But I determined to ignore it. I was going to take my time and make sure students understood material as we covered it, even if it killed me.

So I started factoring in class, sort of in an explore-flip-apply style. And I only covered one thing: the simplest case, all positive numbers.

And I started with an activity that revolutionized my students' understanding of factoring.

I took from a couple of different sources, and created these sum-and-product-X's in each of the different factoring possibilities.

The first day I had the first one on the board, handed the students a sheet as they came in, told them there was a pattern, and instructed them to find the pattern and fill in the rest of the X's.

A few students saw it quickly, and a few struggled. I let them think about it individually for a few minutes, and then let them discuss with an elbow partner. Everybody was excited when they finally "saw it," and they filled in the rest of the page.

By the end of the lesson, they were factoring the simplest case like champs.

Their video that night was the next simplest case.

So I took what was normally a one day lesson (and covered completely in one video last year) and made it two days.

And it paid off in spades.

Students quickly got into the mindset of finding pairs of numbers that gave a certain sum and product. Many students used the X's throughout the factoring unit.

I was a little concerned once we got to the more difficult cases - such as a leading coefficient other than 1 - but even the harder cases were easier after the foundation laid in the simpler cases.

Students did well on the factoring test, and I feel much better about their grasp of the material. Now, will they remember it when they get to Algebra 2 in two years? We'll see....

I still used the Punchline pages more than I would have liked. They gave great, self-checking practice, and I could see while they worked that they were understanding the material, but a few students felt they were experiencing "death by Punchline." I will continue to work on that part of the unit next year.

Balancing time in the classroom is a delicate art. Don't go too fast, don't go too slow, get everything covered. But my flipped classroom has continued to teach me that slower is better than faster. Smaller chunks of material is preferable to large boulders. Student understanding is much more desirable than confusion and tears.

Just Keep Swimming....

Wow...It's been a long time since I've blogged!

I've been trying to channel my inner Dory. ALL of us at school have.

It's that time of the school year.

Very little sun...very little warmth (although this has not been that brutal of a winter)...very little energy...restless students...Christmas Break is a distant memory...Spring Break seems so, so far away.

One reason I haven't blogged is there hasn't been much to say. We keep on keeping on. Algebra 1 students watch videos, we do activities in class. Pre-Algebra students got to shift gears to some more skill-based topics, and it's been fun to see them expand their understanding of the real numbers and the number line. They're currently doing the Pythagorean Theorem unit Algebra 1 did early in the year. I love that unit.

Another reason I haven't blogged is I've felt so "blah." I'm not in the funk I was first semester, but I've been in one of those phases where I just put one foot in front of the other, knowing the spark will return at some point. Hopefully sooner rather than later.

Things began trending up this week. The sun came out late in the week, and the temps are rising a bit. I have seen students make connections, question, investigate, remember, and discover this week, letting me know they HAVE paid attention throughout the year and haven't checked completely out, yet.

I NEED their enthusiasm. And I'm sure they need mine. We need each other. And when we're all in the doldrums, it's difficult.

On the flipped classroom front, I did make some transformations over the past couple of weeks.

Algebra 1 is learning exponent rules. They are in 3 sections in our textbook. I usually cover them pretty quickly - here are these rules: learn them, understand them, use them.

And then I see terrible grades on the exponent rules test.

I decided to approach it slower this year. I spent a day reviewing exponents, paying special attention to negative bases. While some students are still struggling with negative bases, that day has paid off in big ways.

Last year, I spent one day discovering the multiplication and power to a power rule, and the rest of the rules were covered in videos. Each video was close to 15 minutes long.

This year, we discovered the rules and did basic practice with them in class. The videos demonstrated how to use the rules all together. The next day in class we worked with the more complicated problems.

What I've usually tried to cover in a week will have taken almost 2 weeks.

And it's been worth it.

My students' understanding of the rules is much deeper than it's ever been. I'm expecting pretty good grades on Tuesday's test.

The unit has made me make a new goal for my videos. I blogged last year how I discovered 15 minutes was the max video length my students could digest.

But I'm beginning to think 10 is the upper limit.

Oh, they can watch 15 minutes. They can take notes on 15 minutes.

But they can't process that much information. They can't really get to know and understand it.

So my new goal is to get all my videos to 10 minutes or less.

Yes, that will mean more reworking of videos and more recording (my original thought when I started flipping my classroom is "Once I have the videos made, they're there forever!"). But I've gotten so much faster at the process. Making 4 videos over the last couple of weeks was no big deal. I didn't stay at school until 6 PM any day (it happened MANY times last year).

My whole goal is to allow students to understand and learn. And I need to be able to make changes to my teaching that allow that to happen.

Flipping my classroom has taught me/is continuing to teach me how to break material up into digestible chunks. It is much more important to spend time on concepts and attain true understanding than throw material - lots of material at one time - at students and pray some of it sticks.

And once again, I apologize to former students. I can only quote Maya Angelou: "When you know better, you do better."

This is already a long post, but I want to share a find from the past couple of weeks. Every math teacher should bookmark openmiddle.com. Rich, open-ended, DOK 2 and 3 activities for grades K-12.

I did my first activity with my Algebra 1 students yesterday: Rational Exponents.

We did one attempt at the problem together. Students worked together, and I rewarded the largest result, smallest result, and the result closest to 1. While we didn't have enough time (there's that time factor again) to discuss all the implications of this activity as I would have liked (it was the ending activity of the day), it gave students some great calculator skills, and a few students were seeing how the numbers worked together and how to manipulate them to get the result they wanted.

So...we keep pressing on. Spring Break is 3 weeks away, state testing is just over 4 school weeks away. YIKES! Let's not go there today.

Let's just keep swimming.

My Top Ten Posts of 2015

I realize my blog is still relatively little, but I enjoy seeing the number of views grow over time. I'm a sucker for stats (I am a math teacher after all), and I love watching the daily views, number of post views, and where the views are coming from.

I've seen a couple of "Top 10" blog posts floating around, so I thought I would post my own.

1) #flipclass Flash Blog: Late Work (This is, by far, the all-time most popular post on the blog.)

2) Transforming as an Educator (This post was difficult to write.)

3) Spending a Week with Pythagoras (What a fun week!)

4) #flipclass Flash Blog: Building Community Outside of School (I always love promoting Twitter!)

5) #flipclass Flash Blog: Thanksgiving (I have so much to be thankful for.)

6) #flipclass Flash Blog: Grading (How I tackle this necessary evil.)

7) #flipclass Flash Blog: Building a Positive Classroom Culture (I am convinced positive relationships are the most important thing I can develop in my classroom.)

8) The Most Tiring, Most Rewarding Year of my Career (This is my reflection on the 2014-2015 school year.)

9) #flipclass Flash Blog: So Far This Year (I post my reflections on the beginning of the 2015-2016 school year.)

10) A Flipped Review (I'm so happy I changed the way I handled semester reviews!)

It's interesting to me that over half of these posts are of the #flipclass Flash Blog variety. It's obvious that #flipclass is an important part of my blogging practice.

I guess it's obvious, but I like to reflect. I need to reflect. And while I still get a bit nervous when I think about others reading my reflections, I hope at least a few people find them helpful.

Here's to a blog-filled 2016!