Blended Learning Thoughts

As we all ponder what August looks like for schools, I find that my thoughts keep landing on the blended learning option. I imagine that half of the students in my high school would be in the building on Monday/Tuesday, the other half on Thursday/Friday. While at home, students would do additional school work online. Wednesdays are a bonus day with many options. 

Disclaimer 1: I do not have recommendations from my state or school district yet. I have no insider information. This is just my brain doing what it wants to do. It could all be for nothing, and that’s fine. Maybe my thoughts will be helpful to someone else considering this option?

Disclaimer 2: My thoughts are mostly isolated to my own high school math class.

Two Days at Home: Virtual learning. 

·     Students would watch a video. I’d like to try using Edpuzzle for tracking, accountability, and asking thoughtful questions. I’m intrigued by the opportunity to get responses from all students. 

·     Students would practice a new skill. I like Delta math for this. I’m thinking I could condense my list of skills to 36 (by eliminating a few and combining some) so that the focus is 1 skill/week.

·     Students would record themselves working out one problem, describing what they are doing, so I can actually see the math that they are doing. I’m considering flipgrid as a platform for this. 

Two Days in School: We do all the things that we missed during distance learning.

·     Short (15 min?) assessments weekly. Assess a combination of new & retention skills.

·     Focus on applying new and old skills to non-standard problems. I want to focus on the skill students practiced at home but ask questions differently than delta math. 

·     This is the time for open middles, desmos activities, 3 act tasks, and more.

·     Spiral through some skills for retention.

·      I would like to do some additional skill practice so that I can watch what students are doing and look for common errors, but I suspect I’m out of class time by now. I’m hoping skill practice can be done mainly at home or doing intervention times.

Bonus Day: All weeks with five days should have an extra day.

·     This day is an opportunity to be creative.

·     Ideally, it would include some extra teacher planning time. All of this reinventing the wheel is going to require it.

·     What if we could “invite” specific students to attend in person, even for half of this day? Bring me the handful of students who haven’t mastered this weeks’ skill or are having trouble keeping up with the online portion at home. 

·     If face to face isn’t possible, individual and small group tutoring could happen via zoom.

My Brain's Off Switch is Broken

I saw this picture on social media recently, and I feel this so much! 

I told myself that I would not spend my summer worrying about what the fall looks like.

For the most part, I haven't worried. I am confident in my state, school district, administrators, and colleagues' ability to figure it out. I even feel ready to embrace whatever changes are necessary to keep everyone safe.

But that doesn't mean I don't think about it. Every. Day.

At supper tonight, my daughter said "Mom, you keep saying that you don't want to talk about school in the fall and then you keep talking about school in the fall!" She's right. I can't turn it off.

It occurred to me that I have this long-neglected blog, and that this would be a good place for me to tap out my thoughts and clear my head. 

What's New

While I've been busy not blogging the last couple of years, there have been quite a few changes in my classroom . . . 

Integrated Math: Two years ago we stopped teaching the traditional progression of Algebra 1, Geometry, Algebra 2 and replaced it with Math 1, Math 2, and Math 3. I think this was one of the BEST decisions our math department has ever made. We saw a huge jump in our students' state assessment scores as well as their ability to retain concepts year to year (also due to some other things we're doing). Now I teach Math 2 & Math 3 (and continue to have one Calculus and one Physics class). I now teach some geometry for the first time in my career and I'm not mad about it.

1:1 Chromebooks: This year our school put a chromebook in the hands of every student. I have loved students having consistent access to google classroom where I share all of our class materials and information for absent students. I've loved that I don't have to track down a cart of devices every time I want to do a Desmos activity. I was less excited when my Principal said "think about how you can use these to eliminate the use of paper".


Less Paper: We started the school year trying to use a chromebook the same way we would use a worksheet. We converted our sheets of notes and practice problems to PDFs and taught students to use Kami to write on them. I won't detail all the issues, but it didn't go well. Students were frustrated. Parents called. We knew we needed a plan B.


Changing Up Daily Practice: After lots of conversations with my colleagues and trying a bunch of different things, I've mostly settled in to having students do the bulk of their daily practice on individual white boards. I either project the problems for all to see, or I will print a single page per 4-person group. Along the way (and also inspired by the book Make It Stick), I started learning that students don't need to do as many reps of a particular problem as I once thought. If they get a concept after five practice problems, then they don't need to do twenty. What they do need is to revisit that concept in the future to help them remember. Each day we spend part of the class period practicing something new, and the rest of the time on spiral review.


Spiral, Spiral, Spiral: Possibly the biggest change of the past two years has been my commitment to spiraling. Almost daily, my students practice something new as well something they learned yesterday, last week, last month, and/or last semester. Every assessment has 3(ish) "retention" problems where any topic from the year is fair game (I do make sure they've seen these as part of their spiral practice within the week of the assessment).


No More Homework: A completely unintended result of all these above things is realizing that, if my students could get a good 48 minutes of working on math each day, they really didn't need to practice something 20 more times at home. I've assigned almost no homework all year in Math 2 or Math 3. My Calculus and Physics classes still have homework, although it has decreased there too.


Less Talking:  The only way to make more time for in-class practice is to spend less time telling students what to do and more time just letting them do it. I introduce a new topic with just enough information to get students started. When questions or obstacles come up, we figure them out as we go. It is really a pretty big philosophical change that doesn't happen overnight. I've had this "less talking" goal for years, but it has taken time and pressure from these other factors to get there. It turns out my students do just fine (better even) with fewer of my words!

Exponent Puzzles

The other day I spent the teeny-tiniest time on twitter. Fortunately, I was there long enough to read about #MTBoSblog18 and thought it seemed like a very doable challenge. I happen to have a few little files to share, so here goes January!

A while ago I wrote about this strategy for teaching students to solve exponential equations (without logs). It has been a pretty effective lead in for exponential equations and also evaluating logs, as students get to practice using all different kinds of exponents and combining them with different bases.

This year, our school has been going paperless making great efforts to reduce our paper usage, so I had my teacher's aide help me convert this activity to a reusable form for my dry erase sleeves.

For level 1, students choose the correct exponent to complete the equation. Fraction and negative exponents are used.

For level 2, students choose a base and an exponent to complete each equation.

For level 3, students must use the same base to complete two different equations.

 
When they're done, I go straight into solving exponential equations with the use of like bases. It's a super easy transition. Logarithms are next, and this activity really sets the stage for answering the question "What exponent goes with base ____ to equal ____?". 

Here are the files:

Level One
Level Two
Level Three

Happy 2018!

Inside Out Quadratic Formula

I noticed that my students, while using the quadratic formula, typically had trouble in one of two places. They either find the wrong value for b^2 - 4ac, or they have trouble simplifying the radical.

I decided to try having my first-timers evaluate the formula from the inside-out. Maybe if we put our focus on the most-likely-to-mess-up parts of the formula minus the noise of the whole thing, then we would be more successful and consistently correct.

Here's what I mean:

The solution looks like this: First, we find b^2 - 4ac.

Next, we simplify the radical. My students are awesome at this when it is an isolated operation, but often struggle when its part of a larger problem.

Then we put it all together.

At this point you may be done, or maybe you need to reduce.

Time will tell how much of a difference this approach makes (if any), but I have noticed a few other benefits:

We don't have a learning target for the discriminant in our curriculum, but if we did this would be an easy lead in. That number we found first? It has a name, and it can tell you what kind of solution you are going to have before you do anything else.

Also, I kind of like how the solution seems more efficient . . . it feels less noisy and crowded compared to writing out all the parts again and again as you simplify the answer.

How to Drive to Sonic

Recently I noticed my students having a few misconceptions about the different strategies for solving quadratic equations:

A student assumed that a non-factorable quadratic had no solution.

Several were surprised when quadratic formula and completing the square yielded the same solution.

I came up with this little analogy to help clear things up, and it ended up working pretty well.

I started out by talking about how students might drive to Sonic, a favorite fast food place that is 10 miles away from our tiny town. Students named several paths and we talked about their pros and cons. The interstate is fast, but it does not provide a direct path to Sonic. Most students would choose to take Old 40 highway, but it is well known for road construction and can be blocked for days/weeks/months at a time. Someone even pointed out that there is a dirt path through a corn field that many of us have used to bypass the road construction. Perfect.

Solving a quadratic equation is very much the same.

On the left you have your quadratic equation. You want to get over to the solution, on the right. Factoring, complete the square, and quadratic formula give you three potential paths to get there.

Sometimes, when you take the factoring route, you find that your equation can't be factored. When this happens, its like a road closed sign on the path to your solution. The solution is still there, but you'll have to take a different route to get to it.

Other times, when you're completing the square, you run into a bunch of fractions. We aren't afraid of fractions here, but they can turn an otherwise straight path to the solution into a long and winding road. If we're looking for the most efficient way to get there, we want to avoid this situation.

Then there's the quadratic formula. It may not always be the most efficient, but it always works. It is particularly useful for avoiding the road block and the winding road. 

To follow up this discussion, I asked students to be in charge of road signs for these three paths. Your job is to put up some signs instructing people on which road to take. What do the signs say? Here is what one group created:

 My favorite quadratic formula sign said "when you don't want to think about which road to take". They're not wrong.

For a follow up activity, this card sort would be perfect.

Visionary

I always think its silly when people start a blog post by talking about how long its been since they've blogged, but . . . It's been over a year and that's probably worth mentioning. If any dear readers are still here, thanks for not giving up on me.

I'm starting the third week of a brand new school year. There have been some growing pains, but I will talk about those another day. I want to talk about one of our back-to-school inservice meetings. Our principals shared about the book Soup by Jon Gordon. At one point, they would describe a characteristic of a good teacher, and ask our groups of four to name one of our colleagues who most represents that quality.

One characteristic that was mentioned was "visionary". We were asked to name a colleague who is always evolving and learning new things, striving to get better. I was touched that many of my colleagues named me. This is the kind of teacher that I want to be and that I try to be, but I haven't felt particularly visionary in the past year(s). Even this year is off to a rough and chaotic start.

In all fairness, I've had a lot of life happen outside of the classroom. Our now two-year-old son has had multiple surgeries to repair his cleft lip and palate. Then last spring our family grew by one more through what can only be described as a surprise adoption. The rare and special nature of how our family has grown is not lost on us, and we are thankful.

Being parents of three (particularly the two littles) is exhausting. Some days are all about survival. I'm going to cut myself some slack for my absence from blogging, but still . . .

I've been thinking about how this is the place where my vision began . . . The blogosphere is where I began to be more adventurous as a teacher . . . trying new things . . . writing about them . . . learning from others. I thought if I came back here it might trigger what I've been missing.

So here I am . . . inspired by my colleagues' perspective of me, inspired by a gentle nudge from @druinok a few months ago, and inspired by watching TMC17 from afar. I could spend a few more hours re-reading and editing this post, but instead I'll #pushsend.

Best TMC Ever!

I think twitter math camps are like children or students . . . you're not supposed to have a favorite. But if I HAD to pick a favorite, it would be TMC16. The reason is largely because there was so much usefulness in the sessions I attended. I came home excited for the upcoming new year and ready to implement what I've learned. 

Here are a few things I hope you will hear more about this year . . . 

1. Debate and Discussion in math class! My HOPE for this year . . . my #1TMCthing . . . is to put structure to the discussions that happen in my math class. I've had my students seated in groups of four for years. Years! And yet I've never felt like the conversations they are having have reached the productive level that I desire. Chris and Mattie did a great job of showing us how to structure discussion so that it focuses on answers AND reasons. There is always a "because". If you would like more detail, I recommend you read this post by Sam (specifically "Talk in the Math Classroom" near the end). He did a beautiful job summarizing our morning sessions.

2. Make it Stick! Unlike every other session, this one stressed me out. It exposed some weaknesses in the way that I teach that I really want to address. The problem is that the correction involves more of a fundamental shift than just a little tweak here or there. And I'm really ready for a year when "change everything" is not on my to-do list. So I decided to commit to making two baby steps: First of all, I'm reading the book and participating in the chat on twitter. This one is already underway. Yay me! Secondly, I'm going to begin spiraling practice of content through warm-ups. It's a start. 

That's it. That's my 10%. Well, that and a few other takeaways . . . 

*Getting Triggy: Kristen shared a great collection of trig activities. I heart trig, and I'm excited to add her goodies to my toolbox . . . and to make some of my old favorites BETTER.

*Box Method: My math department has just decided to begin using the box for all things polynomial, so I was excited to see how Anna presents these to her students. I love how the box pulls together multiplication, factoring, and division in a way that will hopefully lead to better conceptual understanding.

*New Desmos Stuff: Sadly, I did not get to attend the Desmos pre-conference. But card sorts and marble slides oh my! I'm as excited as everyone else to bring the latest in Des-awesome to my classroom.

*Warm-ups: I've decided to go the spiraled-practice route for my warm-ups this year, but thank you to Jessica and Lisa for a really nice list of resources for great problems that can really be used for more than the beginning of class. When it's time for trig, I want to try a counting circle and clothesline for counting/ordering in radians!

*The Fun Math Game with The Lame Name

*Regrets: This is almost verbatim from last year's TMC post . . . I was lucky enough to travel to TMC with my entire math department (all four of us) for the third year in a row. I love sharing this experience with them, and coming home with some shared vision for our school. I get how rare it is to have that kind of collaboration at home. But once again I really missed out on connecting with the other attendees. 

*Lunch: Following the Make it Stick session, I asked a few others if they would like to have lunch and continue our conversation. It was a GREAT time talking with some people who I really admire, and I learned so much it was like a whole other session. It took some stepping out of my comfort zone to make this happen, but I'm so glad I did. If I'm lucky enough to attend TMC again next year, more of this is on my list of goals FOR SURE. I don't want to come home from another TMC regretting that I didn't seize the opportunity to speak in person with those I admire and learn from throughout the year.

The Post Before THE POST

I just got back from TMC16. It was amazing, but I couldn't bring myself to write a recap without writing this post first. This year has been hard, and my personal story was so intense that it changed the lens through which I see all other things…

Disclaimer: This post is long and it's not about math. I'd love for you to read but it's okay if you don't. I wrote it for me. 

Last fall I posted about the birth of our son and his unexpected diagnosis of cleft lip and palate, but the challenges didn't stop there. 

When Silas was five days old, a routine eye exam showed that there was a structural problem on the inside of his eyes called a coloboma. Doctors told us it was too soon to know how severely it would affect his vision, but they made sure we understood that there was no surgery to correct it. My husband and I were heartbroken as we thought about what his future would be like without sight. 

There were other challenges, too. Silas cried. A lot. He struggled with eating and was eventually hospitalized with severe reflux. He needed a feeding tube to help him eat without pain. He had two surgeries to repair his cleft lip, get ear tubes, and repair a hernia. He had countless doctor appointments and tests, four ER visits, and another hospitalization. I spent every day terrified of what the future held for him. 

When he was two months old I went back to my classroom, but I went through so many days on autopilot. I was numb. And weary. And I wasn't sure that I should even be there at all. 

It has been the hardest year of my life. And it has changed me.

This year I learned to wake up every day knowing that, even when the unknown is way more than I can handle, I always have what I need to get through this day. 

I learned that fears and worries are only good for one thing … robbing us of the beautiful thing that is happening at the same time. 

I learned to rejoice, not because of our circumstances, but in spite of them. There is always something to be thankful for. 

One day this song came on the radio: Tell your heart to beat again . . . every word applies to me, but I'll just share the chorus here:

Tell your heart to beat again

Close your eyes and breathe it in

Let the shadows fall away

Step into the light of grace

Yesterday's a closing door

You don't live there anymore

Say goodbye to where you've been

And tell your heart to beat again

Your heart to beat again

Beat again

And so I made an effort to jump start the pieces of my heart that had stopped beating. I reconnected with friends . . . I put on my running shoes and trained up for a half marathon . . . I even wrote a blog post about something that was happening in my classroom. It felt foreign, but good.

Along the way I also made peace with Silas's differences. I realized that I spent so much time worrying if he was going to be okay, when there was never any question that he was going to be okay. Silas is okay because his life is a gift from God and because he will always, ALWAYS, be deeply loved. No diagnosis will ever change that.

Meanwhile, my husband landed his dream job as a building principal in our home town. His new schedule would allow him to be home with our kids during twitter math camp. Could I go this year? SHOULD I go this year? He said that I should. I think he knew that reconnecting with my teacher self would be another small step towards my healing.

I'm so glad I did. 

This week my teacher heart started to beat again. 

P.S. I can't close without letting you know that there is so much good news for this happy boy! He is almost 11 months old and he amazes us every day! We conquered reflux and he now eats entirely on his own. He healed beautifully from lip repair surgery. We have learned that he does have low vision in his left eye, but with both eyes together his visual acuity is in the typical range for his age. His ophthalmologist says he will definitely be a visual learner! We are so thankful for the good news and for how far he has come.

It's Not About the Points

While many math teachers have stopped giving points for practice/homework, I confess that I'm over here still giving points. This semester, I decided to at least challenge my own attachment to points . . . particularly the thought that students will not do an assignment if there are not points attached to it.

So I set a lofty goal: 100% of students completing 100% of assignments. Whenever I had time to walk around the classroom, I carried a clip board and asked students to show me their completed assignment(s). Not done? No problem. What questions do you have? What can I do to help you finish up?** I did some repeated asking and follow-up and asking again. Over time, it got easier as students realized that not completing the assignment was not an option.

I also discovered that, more frequently than I expected, lack of completion was really due to lack of understanding. Many times it came disguised as laziness, disinterest, and the like . . . but really the student just didn't know how to do the math.

When an assignment was complete (and correct!), I recorded the points on my clip board. I used circles to indicate assignments that were late and highlights for assignments that took more than two weeks to collect. I ended up with a sheet for each class that looked like this:

Notice fewer circles/highlights during the second half of the quarter?!

Since everyone ended up with all of the points for all of the assignments, it really brings one big question to mind . . . What's the point of the points?!

I'm finally believing that students don't complete assignments because of points. Students complete assignments because of accountability. I would argue that there are forms of accountability that are more affective than points. I never had 100% completion when I was only assigning points.

Another unexpected outcome (which shouldn't have been surprising), is that assessment scores were higher as a result of "Operation 100%". In the past, I spent a lot of time orchestrating/scheduling remediation and re-assessments. Since students ended up understanding the content better on the front side of assessments, I spent significantly less time on that type of thing this semester.

**My school has some structures in place that helped tremendously with follow-up here. I assigned many students to our school's tutoring room. It is held during the school day and staffed by a few teachers and lots of National Honor Society students. For students who understand the content but were just dragging their feet on completion, I had the option to assign them to academic lunch.

A Way to Make Their Day

One of my nephews is in my Algebra 2 class this year. Today is his birthday, and I gave him an assessment. Happy Birthday, Kale.

I wanted to make the day special for him, so I wrote some notes and drew some pictures on the inside of his assessment. Then I did a little magic as I was passing them out to make sure the "special" assessment landed on his desk.

He volunteers as a junior firefighter and carries a pager to alert him when help is needed. He's not supposed to leave school for fires, but oh how he would love to!

Kitty inspired by this post from Jonathan.

17!

I loved the grin on his face as he worked his way through the assessment. That's when I realized that I have lots of other students who celebrate birthdays on assessment day, or who just need a little extra encouragement . . . This is going to have to be my new thing.

Expecting Turned Unexpected

I wrote my last post here on August 19, shortly after the first day of school. I was excited about learning all my students' names and looking forward to a great year. I had no idea that, just seven days later, life would change in so many unexpected ways.

On August 26, a routine doctor's appointment showed some significant concerns with my pregnancy. Instead of sleeping in my own bed that night, I was admitted to the hospital to deliver our baby four weeks early. Even though I had planned ahead and we had a great substitute teacher lined up, I had hoped to be a little more organized before beginning my maternity leave. The timing was unexpected.

Baby didn't tolerate labor very well, so at 8pm the following evening he came into the world via emergency c-section. After hearing our little boy cry, I heard someone say the words "cleft lip and palate". We had no idea. He always had a little hand covering his face during sonograms. 

Little Silas was having some trouble breathing, so the decision was made to transport him to a children's hospital in the big city three hours away. I got to see him for a few minutes before they took him away. There was no holding my newborn until the next day when, fueled by pain medicine and a lot of motivation, my husband and I made the journey to see him.

Baby's breathing stabilized quickly, but we were in the NICU for three and a half weeks as he learned to master the art of eating. We met lots of doctors and specialists, including the plastic surgeon who will later repair his lip and palate. Silas will have three surgeries during his first year of life . . . more when he gets older and as he grows. It is not a journey we would have chosen for our son, but he's a tough little guy. He's going to be okay.

What we did expect is how much we would love him. 

P.S. I don't suppose I will be blogging much this year, but I hope you will be patient with me. I plan to pop up in your reader again some day.

Day One: ALL the Names (and High Fives!)

Learning the names of students has never been a strength of mine. I've been known to take a week (or two) to get them all right. This year I decided to make it a priority, so I challenged myself to learn all the names on day one.

Day one, 35 minute class periods:

1. Students get a high five and a copy of "Mrs. Gruen's Life in Numbers" as they walk in the room. I borrowed this idea from Heather Kohn, as recommended at Global Math Department.

2. A seating chart is projected via the document camera and students find their seats. The seating chart is key. I could not have done this without it.

3. I introduce myself, then call out names from the roster while students are working at matching numbers from the answer bank to ten facts about me. I make note of preferred nicknames and pronunciations and such.

4. I show a brief slide show to reveal the answers to the quiz. I share an adorable pic of me with my family last Halloween . . .

And one of my dog Sophie, in big trouble after snitching a few almost-ripe tomatoes from my daughter's tomato plant.

5. I ask them to write 3-5 number facts about themselves. Share with your group members. Ask each other questions like "Which four countries have you lived in?" or "What's it like to have six toes on one foot?". I collect the papers when they're done.

6. Noah's ark problem from Fawn. Also recommended by Heather via Global Math.

7. As I watch students work and listen to their conversations, I have a good ten minutes to silently study the seating chart while looking at their faces. I practice covering the chart and saying their names in my head. We didn't finish the Noah's ark problem today, but that's okay.

8. As students leave the room, I say goodbye to each one individually. Bye Tate, bye Robert, bye Kyanna, bye . . . I overhear someone say "Holy cow, she knows our names already!"

Day two, before students arrive:

9. I go through the stack of number facts. I try to picture each face as I read what they've shared.

And then the final test:

10. As students enter the room on day 2, they get a high five and a "Hello Tate, Hi Robert, Good morning Kyanna . . . ". I only got two names wrong on day 2, and I think that is pretty good.

I also realized that learning names quickly has added another dimension to my daily high-fives. Every student gets to hear me say their name, along with their high five, every day. I definitely feel more connected to my students than I normally would be this early in the year. And the look on their faces when I welcomed them by name on day two? Priceless.

This is going to be a great year!

TMC15

My long overdue TMC15 reflection. . .

First of all, I am determined to not re-invent my teaching/curriculum/procedures this year. I went to TMC looking for smaller nuggets of inspiration that would improve my classroom, sans any dramatically huge changes.

Here are a few things that spoke to me:

Desmos activities. I consider myself to be a pretty proficient Desmos user, but I learned that there is so much I do not know yet. Among the features I learned about is the Desmos activity builder. I have already written a bunch of worksheets with Desmos instructions for students to follow. On these days, I spend the class period running around looking at screens when students reach particular checkpoints. No more. Now I can put the same exact set of instructions into the activity builder, have students enter the activity via a code, and watch all the action from my computer screen. Nice. I feel inspired to convert my current activities, and to build more.

Taming the firehose of resources. I enjoyed Bree's session on planning units using the MTBoS. I realized that my problem is not so much the planning stage . . . it is saving the resources I've found so that I can access them later at the time that I actually would use them. When I read something interesting, I generally bookmark it in feedly. And then I never see or hear from it again. I decided that it is okay for me to be more discerning in what I choose to save. When something is worthy of saving, I need to put a little more effort into saving it so it can be found later. "It is okay to appreciate something you've read and not save it", Bree said. I've been thinking about this a lot, as I am guessing 3/4 (or more) of my bookmarks are blog posts that I simply enjoyed reading but don't directly apply to my classroom. I am going to focus on those things that I intend to implement later on, and do a better job saving them with searchable tags and such (Evernote, perhaps?).

High fives at the door. Glenn's "my favorite" has been popular for good reason. It is simple, but we have already discovered it is powerful. My colleagues and I decided to make it a department thing, and also roped in the two non-math teachers in our hallway. So the 200 hallway is officially the "high-five hallway" at our school. I am surprised by how something so small has already helped me feel more connected to my students, and how the classroom atmosphere gets an immediate boost. You just can't be too grumpy after a high-five.

Music transitions. Playing music snippets to speed up transitions is something I've wanted to do for a while, but I was not sure how to execute. Or maybe I just didn't take the time. I don't know. Anyway, I am pumped to scan Vaudrey's resources and implement some tunes for all those routines that suck more class time than they should.

Do what you love. My colleagues and I just want to have fun teaching math. We are thinking of finding activities that share a common theme to implement on the same day/week. Barbie day, for example, could involve Barbie bungee in one classroom, Barbie zip line in another, and Barbie _____ elsewhere . . . We don't have the details worked out, but we do know there will be costumes.

Regrets. I was lucky enough to travel to TMC with my entire math department (all four of us) for the second year in a row. I love what this experience does for us. We have fun together, and we get excited about the same things. We come home and we implement our plans as a group. I get how blessed I am to have a work environment like that. But I really missed out on connecting with the other attendees. There are so many people who I follow and admire and learn from on a regular basis . . . I feel sad that I didn't sit down and have a chat with many of them.

Coming Soon: The Year I Won't Change Everything

I wrapped up the 2014-2015 school year a few weeks ago. Since then I've been simply enjoying the time at home. This week I hope to work in my classroom a day or two, so I thought it was time to reflect and collect my thoughts a bit.

I am proud of the two major projects my colleagues and I accomplished this year:

1.  We implemented SBG. We still have some work to do . . . but the best part is that we know, better than ever, what our students do and do not know.

2. We used our standards as the starting point for deciding what to teach. We focused on making sure we had all the standards covered and worked on a cohesive skills list to follow students from 9th grade through trigonometry. It is not a finished product, but we made a ton of progress!

We set a few goals to accomplish as a group for next year:

*Continue refining skills lists for 9th-11th. Add 12th to the list.
*Adjust how SBG scores are converted to grades . . . we are concerned that a few students ended up with passing grades even though they had multiple skills still un-mastered.
*Stop giving points for things that don't directly reflect students' knowledge. (Looking at you, binder organization grade). Figure out how to encourage & support organization skills without this grade.
*Work on strategies to help students RETAIN what they've learned beyond the assessments.

In other news . . . an exciting family update as depicted by our five-year-old:

We're blaming our daughter, as she has ended almost every day for years by praying for a brother or a sister. Baby brother arrives in late September . . . and so I am hoping for a productive summer and crossing my fingers for a very capable substitute teacher to take care of things while I'm away in the fall.

So here's my (paired down) summer list:

1. Leave calculus and physics (mostly) alone.
2. All changes for my Algebra 2 classes should be smaller adjustments. No re-inventing of the wheel. Not this year.
3. Plan all my classes through the first semester. Is this realistic? Repeat #1 and #2 out loud.
4. Look for ways to incorporate review, but more in a spiral-y way vs. the "review this because its going to be on the test tomorrow" type.
5. Stay calm. Take some guilt-free naps. Enjoy my summer.

Solving Exponential Equations (No Logs)

This is my second year teaching a "not advanced" Algebra 2 class. One of my goals has been to avoid simplifying or watering down the curriculum, even though my students are lacking in pre-requisite skills.

Instead, I've been taking more time for almost everything.

I've learned that the extra time is often better spent on the front side of a new concept, rather than after the fact like "Oh no, they didn't understand that so let's just repeat it for a couple more days".

I try to start with what they know, then gently stair-step them into the new thing.

Case and point, our recent venture into solving exponential equations (without logs) like these:

On the first day, I equipped students with white boards and said we were going to work on some puzzles. (Don't you just love the word "puzzle"?). Try to write an expression that equals 8, using a base of 2 with an exponent.

Step 1: We did a whole bunch of those, starting with positive integer exponents and working up to the use of negative integers and even a few fraction exponents. Students needed some reminders here and there, but we kept practicing until they were answering them all with accuracy. Then . . .

Step 2: We continued with more, but now students needed to choose what base number to use. There were some great moments here to capitalize on, like when students tried to use a base of 9 to get 243 but realized it wouldn't work and had to use a 3 instead. Or, when two students each used a different base and both answers were correct. I made a huge deal about these when they happened. Next . . .

Step 3: I gave students TWO goal numbers. They must write an expression for each, using the same base number for both.

And now, without realizing it, they've really learned how to do the hardest part of solving the equations for tomorrow's lesson.

Step 4: (Same as step 3, really) To finish the class period, I grabbed a copy of the practice set I wanted them to do the next day and pulled sets of goal numbers directly off of it.

On day 2, students easily transitioned into solving these.

On day 3, extra practice with Add Em Up.

BONUS! From here I introduced logarithms, and found that students were completely prepared to answer the question "What exponent goes with this base number to make this value?" The extra day spent on the front side of solving exponential equations ended up having a double payoff.

Giving Immediate Feedback Without Breaking a Sweat

Our entire math department is transitioning towards SBG. Recently, we were having a conversation about scoring of assessments and giving feedback and such, and I thought about THIS. I remembered conversation about Frank's orange pen strategy a few years ago, and I can't imagine why I only just decided to give it a try.

For the setup, I wrote out a key for the assessment. Since students would be looking at this, I tried to include more detail than I would for my own personal key. I made copies and set up these little stations around the room. My pens were red, pink, orange, purple . . . any color I could find that wasn't green. Green is my signature color.

Students did their assessment-taking in the usual fashion and then, before turning it in, they made a stop at one of these stations to mark what was wrong and make corrections.

And Voila! That's it.

The good:

Any given day, when I take the time to write feedback on a student's paper, I have no idea if the student is actually reading that feedback and taking it to heart. I don't know if they understand what I wrote, either. When a student writes their own feedback, I can clearly see their level of understanding of their mistakes.

I used this in my lower-level Algebra 2 class first. These students who are not usually super interested in their assessment results had more buy-in than usual. A few of them immediately stopped by my desk to explain their mistakes to me . . . just because they wanted to share!

Another student left a perfect note to herself after making a classic mistake while squaring a binomial. She was able to find exactly what she had done wrong and identify what she needed to do differently next time! I am sure this note IN HER OWN HANDWRITING is way more meaningful than anything I could have written on her paper.

And, at the risk of sounding lazy, I am also going to mention how much faster I am able to finish grading a set of assessments! Of course I still look at each paper carefully, but in most cases the student feedback is adequate. I just determine the level of understanding and BAM! Done. No additional comments needed.

The not-so-good:

Not every student left stellar feedback to themselves. A few just put a slash through the problem number if their answer was wrong without identifying their mistakes. I sent a few of them back to write more. One of them gave me a heavy sigh. I can live with this, but I will continue to coach students regarding my expectations here. I also updated my instruction sheet. Much better.

I really love #3. I have found that, if a student can convince me they understand their mistakes, it can actually influence the level of mastery I select for that skill. The writing of feedback almost becomes part of the assessment itself. An unexpected result that I am happy with.

Other thoughts:

If I want students to assess and do feedback in a single class period, I have to make sure that my assessments are not too long.

One colleague is concerned about students early in the day sharing information with those who take the same assessment later in the day. I have four different preps, so I am never giving the same assessment more than twice in a day. And even if an answer were shared . . . a student can't demonstrate understanding by simply writing the correct answer. I just haven't felt that this is a problem in my classes.

The first time through I underestimated the number of stations I would need. To avoid students waiting very long for a station, I found I need about 1 station for every three students.

On Review and Remembering

Recently, our high school math department met up with the middle school math department to discuss all kinds of things. Part way through the discussion, someone mentioned the need for a magic pill to help students remember what they've learned.

We all agreed. We have all experienced the frustration of believing that our students have mastered a concept, only to discover they can't remember what they've "learned" just days, weeks, and certainly months later. By the next year, we're hearing that they have "never" seen whatever thing we are expecting them to remember.

In the middle of this conversation, it occurred to me that maybe we are teaching students to forget. A traditional math classroom (including mine until I started SBG) looks like this:

1.  Teach a unit
2.  Review the unit
3.  Test over the unit
4.  Move on to next unit
5.  Start forgetting previous unit

The end of each of my units always had a review day, where I would have students practice a bunch of problems that were really similar to the ones they'd see on the test the next day. Only the numbers were changed. The next day, my students would (generally) do pretty well on the test. I would pat myself on the back for my good teaching ability, and away we'd go to the next unit.

Now I'm thinking . . . Do those big-review-days-that-look-just-like-the-test-right-before-the-test-day just train students to stuff in the information, hold it in for 24 hours, and regurgitate it the next day? If our students do very well on such a test immediately following such a review day, does it give us a false representation of what they've actually learned? What if the "forgetting" we see is really just "never learning"?

What should review look like? When do you review? What do you review? WHY do you review?

Fighting Assessment Freak-Out

Our school was asked to present a "high school" perspective on preparing for state assessments. I don't know that we are doing anything all that unusual, but here are some of the things we shared.

1. Teach the standards. I don't want to over-simplify this, but at a time when so much is unknown, it makes sense to focus on what we do know. In the CCSS, we have a document that states what our students need to know. Make sure you're teaching that stuff.

2. Focus on the essentials. While it is our goal to teach every standard, we know that might not be possible. We printed out the standards for each of our classes, one to a page. One at a time, we took the standards for each class and sorted them into "most", "somewhat", and "less" important. Then we took the "most important" stack and narrowed it down to the 8-10 most essential standards for each class. If we don't do anything else, we'll make sure our students don't leave our classes without mastering those standards.

3.  Assess what they've learned. All of our departments are working on regular formative assessment. Data is brought back to weekly PLC meetings where we discuss the teacher side (how can the teacher approach this topic more effectively) and the student side (what interventions can we provide for students who didn't learn).

I am piloting standards-based grading, soon to be joined by the rest of our math department and more. Each skill is based on 1-2 standards from the CCSS.  The difference is the data. Instead of identifying that a student scored a "74% on chapter 3", I can identify exactly which skills each student has mastered, and which ones need more work. If the class doesn't learn a particular skill, I can devote more class time and/or spiral back to that skill as we move forward in the curriculum. If individual students don't do well on a skill, I can provide opportunities for them to continue to work on that skill.

4.  Provide interventions. We have all kinds of interventions.

If a student is deficient in a lot of skills: We provide an extra hour of instruction in addition to their regular math class, called "math lab" or "opportunity room". Here they spend a portion of the time working on skills like math facts and solving equations. The remaining time is spent reinforcing what they are doing in their core math class. Right now this option is only available for math. English will be next.

If a student needs help on a particular concept: They may work with the teacher before or after school, or be assigned to our tutoring center "irish hub" to work with a national honor society student. We could not do this without our NHS students. They are amazing, and they often explain something in a different way that clicks with a student. This intervention is available to all students for all classes.

If a student just refuses to do something: They go through the "non-compliant" side of our intervention plan, which involves a lot of follow-up and administrative assistance to help the student be successful. This is also a school-wide intervention. Here's the flow chart:

I was surprised that standards-based grading was the portion of our talk that received the most questions/responses when we were done. There are so many in the world of blogging and twitter who use SBG that I forget it is actually not that common (in our area, at least, SBG is fairly rare). The room was full of mostly administrators who were very supportive of the idea, but they were meeting resistance. The idea (specifically the unlimited re-assessment) is apparently a tough philosophy for many to embrace. 

Changing Everything, Using Blueprints

My Algebra 2 classes have been textbook-free since 2007. It started when my school purchased a textbook that I eventually came to hate. I started changing the order that things were taught, customizing lessons, re-doing units, adding activities, and so on. Over time I developed an "Amy Gruen" version of Algebra 2.

All was well and good until Common Core. I read the standards and I tweaked things regularly and added a few new units here and there, but I couldn't shake that "re-arranging chairs on a sinking ship" kind of feeling.

The problem is that I was planning for Common Core in the way that I think a lot of teachers are planning.  I started with the hodgepodge that was Amy Gruen's Algebra 2 curriculum on the left, and over there on the right was the pile of CCSSM. I tried to file those in where they fit, but I had some left over. And there were things in my curriculum on the left with no matches in the CCSSM.

So here I am. I am ready to pitch everything in my Algebra 2 classes and start fresh. After much thought and reading about lots of approaches, I keep coming back to a great session I attended at TMC14 . . . Blueprints*.

Blueprints are a joint project by Kate Nowak, Mathalicious, Illustrative Mathematics, and others. The Blueprints include a sequence of CCSSM that makes sense, justification for decisions, and links to activities that coincide with each standard. What draws me here above other approaches is that they have STARTED with the common core standards. None of this taking a thing that's already done and stamping it up with the words "common core".

Now I can reverse the planning process . . . starting with the CCSSM on the left and a pile of resources on the right and filing those in where they fit.

I've decided to go all in. Start from scratch. Possibly planning just a few days ahead. I am the kind of person who usually shows up August 11 with the year (somewhat) planned out, so this is a bit of a stretch for me. But it feels good and right to start each lesson plan with a standard rather than matching the standard to an already-existing lesson.

I am excited for this new adventure.

Update since I started writing this post: So far I've used the Blueprints to plan a few weeks and I am already seeing a lot of positives. I will write about those soon I hope.

*I got a sneak peak at the "almost final" version at TMC14, and I'm using that to get started. The final version is to be published this fall.