The Goza Way

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Category: Instruction (Page 1 of 2)

Goals for My Classes in 2016 (Algebra 2 & PreCalc Edition)

One of the reasons I haven’t kept up with blogging is because I always want to wait until I have the final, perfect draft before I post to my blog. But the thing is, I never have final perfect drafts of anything. So I have to get over that. What I do have is a lot of decent ideas and thoughts in the Notes App in my iPhone. Yesterday, as I pushed my five-month-old around the neighborhood, I wrote out 4 goals for this school year in my Note as she slept.  Now mind you, this is a draft. But the beauty of sharing it before it’s finalized is that I can get feedback from all the (zero) folks reading my blog.

So what I have here are my goals and shorter “titles” for the goals.  Neither is an expanded version of the goal, but if I wait until I write the expanded versions this post will never get published.  So there may be a later blog where I expand on the goals and there may not.  I guess it depends on whether I get any feedback and/or how long my daughter naps this afternoon.



Create a culture that encourages positive and meaningful relationships between all members of the classroom community and helps everyone achieve success based on their own ideas/measures of what success looks like in a high school math class.


Increase students’ abilities to think, learn, reason, sense-make, and develop logically sound conclusions both independently and collaboratively.


Expose students to my vision of mathematics:  Math is not about problems and answer getting but rather about questioning, exploring, discovering and adventuring.


Prepare students for future endeavors in mathematics, and education in general, most importantly the ones they will experience in the next 1-3 years of high school. (Most notably PreCalc and Calculus and/or Statistics).

I think those are some pretty solid goals.  I’m not sure if they are well organized.  I don’t want ten goals.  I also don’t want one.  I want my students to know this class is as much about them as it is about Mathematics.  Any feedback would be awesome.

How I’m Structuring Homework in 2016-17

In order to better understand the way I’m collecting and checking Homework it’s important to know how I’m structuring groups. Check out this post and come back (you don’t have to click the link, you can just scroll down – it’s the previous post).  I was inspired by this blog post from Julie Reulbach to come up with a better plan for collecting, checking, and returning homework.  This is what I decided on for this year:

I will have a set of 10 folders for each class numbered 1 – 10 to match each group number. Every class will have a different color so they don’t get mixed up.  At the beginning of class there will be one folder at the corresponding group of desks.

The first HW of each Cycle is due on on Day 2 (there wont be HW on the day between Cycles as we transition to new groups).

When students come to class on Day 2 they will have 2 minutes (1? 90 sec?) to put their HW in the group folder and put the folder in a box on the center table (mine) or it’s late (-2 points /5). Students who come to class late with no pass take the -2.  (Don’t be late.)

HW will be graded and returned to the folders which are returned to group tables before the next class.

When students come to class the next day they take out returned and checked HW, then put their new HW in the folder. They look over their returned assignments for lingering questions.

I will take questions after opening activity (in front of the whole class) or whenever students want (on the side). If there are problems that most of the class had trouble with I will address those as well.

As mentioned earlier there will be no HW assigned on the last day of a Cycle. On that day students have taken a summative group assessment. I don’t have a problem giving them the night off after that, and it avoids me the problem of having group folders with student work that won’t match up with the groups of students the next time we meet.

Positives of this plan include:

  • Takes no class time. Except for questions after papers are returned. In the past I have tried circulating and checking HW at the beginning of class. This would take time and wouldn’t allow me to be present in helping get the class started off right.   With this plan all I have to do is grab the HW box after 2 minutes and address groups or individuals who didn’t get the work in on time. Once they see I’m serious I don’t think this will be an issue either.
  • Makes it super easy to collect and return work as papers never leave the folders. I won’t have to pass out any individual papers.
  • Allows me more time to closely examine homework and give feedback. Occasionally I would do that last year and I liked it. It was a very low stakes way to assess and provide commentary and help. I could give a kid a 5/5 and still point out mistakes and give appropriate hints or help so they could fix them. Obviously this can’t be done if your checking HW during class time.
  • Encourages students to get to class on time and get their stuff out quickly which helps get them focused and ready right away.
  • Adds another element of structure and routine to the class. Students know what they are supposed to do first and from there they can transition to what’s next.
  • Doesn’t give students time to copy HW at the beginning of class. In the past if I circulated and checked HW during class students who saw I wasn’t coming to them right away would try to pull this off. What a terrible way for their valuable class time to start!
  • Holds me accountable for grading the HW in a timely manner. Those papers are not leaving the folders and the folders aren’t leaving my classroom. If I don’t get around to grading them the folders will still go back on the desks and everyone in the class gets a 5/5. Obviously I don’t want to give undeserved credit so I’ll be motivated to stay on top of it, but it safeguards me from ever having stacks of ungraded and unorganized HW. This happened two years ago when I tried having every student, regardless of class, turn their homework in outside my door before school started at 8:00. That works for one of my colleagues but it didn’t work for me.

What about the negatives?

  • The most glaring, and really, only significant negative I can think of is that we don’t go over the homework or address questions on the day of, when the issues are most pressing for the students.  However:
    1. There isn’t a hard and fast rule against asking questions on the most current HW. Students who have a pressing question will be encouraged to write it down or take a picture before class and ask it anyway.
    2. A lot of folks love lagging homework. I agree that it’s a cool idea, but it doesn’t work particularly well with my style of curriculum/instruction. Passing back and going over the HW a day behind does add a bit of the lagging element. There’s a good chance that some of the questions that might have been asked about the HW will be addressed in the lesson in between. (In fact, the way our curriculum is set up I assume that will often be the case.) When students get HW back the next day it’s likely that they can self assess and self correct. So yeah, lagging HW review. I like it!
  • The other negative that comes to mind is the fact that I won’t be giving HW every other Monday, basically just to make my life easier. This doesn’t bother me one bit. Also, I have Quizzes to grade that day/night. Who knows, maybe I’ll do no HW every Monday!

That’s it.  That’s the plan. I’d love to hear feedback especially if you can think of more positives or more negatives for my list.

How I’m Structuring Groups in 2016-17

First off, it’s important that I share my school’s bell schedule so this all makes sense.  We are blocked. Monday we meet every class for 1 hour. The rest of the week we alternate periods 1, 3, 5 and 2, 4, 6 and classes last 2 hours each. So on a given week I see Period 4, for example, 1 hour on Monday, and 2 hours on Tuesday and Thursday.

This year I’m planning on a “2 Week Cycle” for my groups. This means groups will change every two weeks.

I have tables of 4, but I plan to make groups of 3 students. The other table will be used for HW folders (see my upcoming HW post), materials, etc. I’m crossing my fingers and hoping for enough desks and < 30 students per class to make this work.

I have 9 (hope to make it 10) Vertical Non-Permanent Surfaces (VNPSs) in my room so I will have 9-10 groups (depending on how many students I have). I use a deck of UNO cards to create Visibly Random Groups by handing out the cards at the door at the beginning of each cycle.

Cycles will start on the first 2 hour day of the week (Tuesday or Wednesday depending on the Period) and then follow a fairly specific routine.

Note: More instructional routines is my #1TMCthing this year. I saw this graphic


from David Wees at #TMC16 and it made a lot of sense to me. I realize that my class needs more structure this year. The two week cycle is in part a result of this need.  I also want to note that last year we did one week cycles with some of the same structures in place so this is not a 100% change for me but closer to the 10% that Dylan Kane and others have talked about.

Anyway here’s generally how the Cycle will go:

Each Cycle will have 6 days (3 per week in accordance with the block schedule) barring holidays, testing, etc. Each cycle will end on a Monday (1 hr) and on that day we will have some type of summative assessment – for simplicity I’ll call this assessment a “Group Quiz.”

Day 1 (Tues/Wed – 2 hrs):

New Groups. We will start with something to help students introduce themselves. Most likely this will come in the form of a Notice & Wonder, WOBD, or some sort of short enjoyable problem related to the current topic. Then we will continue with the general curriculum program. I will make sure that there is some element that requires the students to get up and work on their VNPSs with their new group mates on Day 1. This should help them get to know each other and start working together.

Day 2 ( Thurs/Fri – 2 hrs):

I will pass back the Group Quizzes (from Monday) with scores but usually without comments. Now that groups have been switched I will ask students to compare answers within their new group and work together to complete “Corrections” for Group Quiz. I haven’t decided exactly how I want the corrections to be done but I’ll get there. The rest of the class period will be used to continue with the curriculum.

Day 3 (Monday – 1 hr):

Students will break apart their groups for an Individual Assessment. This will be short and summative.

Day 4 & 5 (2 hrs each):

During the second week the groups should be comfortable and we will continue with the curriculum. Should be good stuff going on in Week 2. Two things will definitely happen:

  1. Students will get back their Individual Quizzes and do corrections with their group mates. Lingering questions can obviously be addressed with me.
  2. The groups will do a Presentation. In my class “Presentation” has a broad definition but basically it’s an answer to a prompt that requires a lot of explanation and students have to present their explanation in some organized format (usually on their VNPSs).

Day 6 – Last Day (Monday – 1 hr):

As mentioned before students will complete a Group Quiz and bid their group mates farewell. So ends the Cycle.

There will be some nuances and exceptions. Now and then I like to let students choose their own groups for specific tasks, and I will probably continue to do that. Holidays will throw the cycles off at times and we might skip a Quiz as a result, but in general I think this should last throughout the year.

I’m determined to stick to it and see how it goes at least through the first semester.  Please, please, please give me feedback or suggestions now if you have any. I’m putting this in place in 2 weeks and after that there’s no turning back!

Still Going Strong: Success on the Homestretch

Today in my Algebra 2 class we solved equations.  I started with a simple worksheet – solving linear and quadratic equations with one variable.  Easy stuff.  But as I looked around the room I was very happy with what I saw.  My students were all working diligently.  More importantly they were working together.  Many had left their seats to ask for help. Others were moving between groups confirming their answers.  At this point in the year, I was proud to see my students motivated and working hard.  I remember in my early years, as the year wound down, my students would become less and less willing to work and more and more likely to try to distract me from teaching.  I suppose I’ve come a long way.  Some thoughts…

My students like easy work.  This is somewhat bothersome.  I don’t blame them for liking what they are already able to do, but I would like to think they they would prefer a challenge, something that would lead to real thinking, new understanding and growth.  I often get the feeling that they would rather just practice math that they already know.  Like they just want to stay inside their comfort zone, all the way in the middle of their own personal ZPD.  Today’s class was engaging, not because it was a great mathematical exploration but because it was review.  This is frustrating for me.

Opportunities to build confidence are important.  This is a counter to my last point.  I think it’s important to embed math that my students are already good at into my lessons.  For one, it’s always good to review.  Secondly, it gives students opportunities to share things they know with new people.  Third, and most importantly, it helps them remind themselves that there is some math they are good at.  As my students worked through the problem set, I heard them saying things like, “I feel smart!” and “I get this!”  That’s got to be worth something.  And I think it turned their brains on for the rest of the class period.  Like they got a little confidence/adrenaline boost from completing the problems.  It also gave the students who typically struggle an opportunity to be on level footing with the ones who typically thrive.  Definitely worthwhile.

My students have learned to work well together.  This is huge.  As the students worked through the problems I saw groups of students sharing answers, freshmen helping seniors, and pairs arguing about solutions and debating pathways.  I see the collective effort of my class in a way that I haven’t seen in previous years.  I feel great about this.  It can’t be understated.  It got me back to this blog!

Cancelling out is a thing for my students.  Ugh.  Everyone solves by cancelling out.  I asked students to share how they answered the first problem:  2x + 7 = 17.  Almost everyone shared that they had subtracted 7 from both sides.  Okay, good.  (I refrained from asking why both sides.  We’ve been over this many times.)  Then cancelled the 7.

Okay, how?


How did you “cancel” the 7?

Huh?  That’s just what you do.

But why does it cancel?

*Blank stares.  Nobody knows.*

I think they know that 7 – 7 = 0, but I don’t think that’s part of the solving process for them.  I talked about additive and multiplicative identities for a bit.  I made a fuss.  We moved on.


Solving without crossing anything out.

My students use procedures before thinking.  After students shared the “cancelling method” I asked if anyone had done it another way.  Everyone was quiet for a while so I asked Ruben.  I knew he had a different method.  “I just looked at it, and I knew it had to be 5,” he said.  I looked at the rest of the class.  “Yes?”  Many of them smiled.  “Well yes,” their eyes told me,  “but that’s not how you do it!”  I disagree.  That’s how I do it!  2x + 7 = 17 ? Two times what is 10?  5.  Done.  They must have been taught that they shouldn’t do the problem that way.  It was as if they knew they weren’t allowed.  But why not!?  I’m a fan of doing easy mathematics the easiest way possible.  It’s efficient.  If a problem doesn’t require an elaborate strategy then you should only use one if you like that sort of thing, not because you’re a robot who recognizes problem types and executes procedures.  Eventually problems will get more messy and students may need a more sophisticated strategy, but until then they shouldn’t be deprived of an approach that results in the correct answer.

My students want to know why.  Another huge win this year.  They expect this from me.  They know that I am going to talk about the whys.  They knew there would be more explanation for 2x + 7 = 17, even when they already knew how to do the problem.  I hope they take this with them to their next math class.  I hope they demand this from themselves and their teachers.  Math is not the same without the whys.

Random grouping matters.  This will be another blog post.  I used UNO cards this year.  New seats every week.  My Algebra 2 classes have students from every grade:  advanced freshmen, seniors who haven’t been mathematically inclined, and everything in between.  I mentioned earlier that freshmen were helping seniors.  In previous years, I’d keep them separate for fear they’d make each other uncomfortable.  But random grouping didn’t allow for that.  The result is a classroom where more groups and pairs of students are comfortable working together.  As the year has gone on I’ve become more lenient about students leaving their seat or even group to seek help and the results have been great.  Again, I will post about this later.  Thanks to Alex Overwijk and others at TMC15 for convincing me to do this.

I’d like to share what I did next, but that is for another post.  Now, like my students, I need to stay motivated!


My Igniting Experience at CMC – South (With Video)

Okay so Igniting is a doozy.  Seriously.  I was sitting at a table with my fellow Igniters, in the front of that huge room buzzing with math educators from across the country, and we were all nervous.  Robert Kaplinski and Laila Nur had done this before – didn’t matter – nervous.  Blue Taylor had flown across the country to be here, done two talks earlier in the day and was completely fried – still nervous.  Even NCTM President-Elect Matt Larson (who was about to completely crush his talk) was nervous.  We all talked about what a challenge preparing an Ignite had been and how many hours we had put in trying to get it right.  And then we were off.

And I gotta say – We rocked it.  Everyone was awesome.  It was fun, it was funny, it was informative, and it was inspiring.  I’m so proud to have been a part of it.  Kudos to everyone and thanks to the Suzanne, Annie and Math Forum for making this happen!  You can catch all the Ignite Talks from CMC-South here.  Watch them all!

As for myself I felt surprisingly fired up when I stepped on stage.  It was cool to have Brian Shay up there to roast me a little to calm the nerves (I knew he would) .  Once I got rolling, despite the fact that I was about 60% blacked-out, I felt like I was going to get through it, like it was going to work out.

And then the dry-mouth set in.  I saw it coming actually.  I kept looking at my empty water bottle as the people ahead of me were speaking, wishing it would magically fill up on its own.  I even went to try to get some water in the back.  But there were hundreds of folks in the room and one little jug so that didn’t work out for me.  I wished I had followed Robert’s lead and brought a Heineken up there with me.  Anything would have helped.  As soon as I started talking my mouth started significantly drying up.  About halfway through I realized I had to say something before it was too late, before I just stopped talking altogether and no one could figure out why.

So I did.  And thank goodness for Suzanne.  She had a cup with some ice in it.  Which was funny, because my initial reaction was, “This is ice.”  I said it right into the mic.  I think it was hard to process anything besides what I was supposed to be saying in talk.  Like, “Hey, there wasn’t any ice in my slides.  What am I supposed to do with this?”  And I remember thinking, “Should I take a whole piece?  Won’t that make it hard to talk?”  But the thing about ice is – it melts.  So there was a little bit of water at the bottom.  Like the tiniest amount.  It was all I needed.  Problem solved.

So I got right back to it and only missed about a half a slide worth of words.  I didn’t get to show Christopher Danielson as much love as I had planned.  I mean “Find what you love about the Mathematics you teach.  Do more of that with your students.” was pretty much my whole message and I pretty much got it from him.  So yeah.  I was going to tell everyone to look up his keynote from TMC.  It was awesome.  Go look now.

Anyway, the second half was a bit of a race against my slides, and I lost by a narrow margin.  Fortunately my last slide, which was my call to action, was still there and I got to tell people to share their mathematical experiences and adventures.  Cause adventures are super fun, and I want to see what other people are doing!  #AME

Igniting was a lot of work, but it was crazy awesome.  I’d do it again.  Maybe someday I’ll get that chance.  Until then I look forward to seeing what other Igniters come up with.  My words of advice – Have fun and bring a drink!

* In a couple days I’ll post my script and my slides if anyone’s interested.  I’ll try to remember that #nobodycares.

CMC 2015 Session 473 Arithmetic Sequences and Series

Here are the materials from our session:

Session 473 Arithmetic Sequences and Series Powerpoint

Session 473 Handouts

Nate Goza and Liem Tran’s Year 1 Unit 3 – Arithmetic Sequences and Series

Thanks for coming.                         -Nate and Liem

CMC 2015 Session 278 Scenario Based Tasks

Here are the materials from our session:

Session 278 Scenario Based Tasks Powerpoint

Session 278 Participant Handouts

Nate Goza and Liem Tran’s Year 1 Unit 1 – Relations and Functions

Thank you for coming. -Nate and Liem

TMC 2015: How I was Wrong About the MTBoS

I think I went to Twitter Math Camp this year to prove myself wrong.

My biggest fear going into TMC 2015 was feeling like an outsider. I had never known the MTBoS to be an exclusive club, but I had always feared that the “Power Elite” and “Shadowconers” might have joined forces to form some sort of super-crew that I wasn’t going to feel comfortable joining.  Apparently other folks call them the “Rock Stars” but I often thought of them as the “Cool Kids” of Math Ed.

Let me make it clear that I never thought of the Cool Kids as being bad.  I consider Fawn Nguyen, for example, to be one of the coolest of the Cool Kids, and I’ve always thought Fawn seemed as cool as you could possibly be.  I have as much professional respect for her as anyone I can think of.  (Even more so after her incredible keynote!)  In my opinion the Cool Kids weren’t doing anything wrong.  It was more like – In the school lunchroom of the Math Ed world, I wasn’t sure if I could sit at their table.

So as a typically confident person I had some unusual feelings going into TMC that I hadn’t had prior to CMC or NCTM or even PCMI.  I was scared that if I spoke up at TMC people might think, “If this guy had anything good to say, I’d have heard of him already.”  And I had thoughts like, “How much better are these folks than I am?”  After all, if you start applying proportional reasoning and you have 45 twitter followers …

I make voice memos all the time when I’m driving. This is literally what I said in the “Pre-TMC” memo:

TMC is gonna give me the opportunity to see about the cool kids hypothesis that I’ve always been afraid of.  And to sort of see, not whether or not I’m a Cool Kid, but if the Cool Kids act like ‘the cool kids.’  Or if they’re just chill people who are happy to interact with everybody and want to teach and learn all the time and just be cool.

And then Twitter Math Camp happened.  It was 3+ days of awesome and definitely the best thing I had been a part of professionally since PCMI in Summer 2013.  I feel like I learned so much about teachers and teaching and learners and learning that it will take months for me to digest it all.

TMC tweet

But my most important takeaway from TMC 2015 is this…

I’m happy to report that the Cool Kids don’t act like cool kids at all.  They just are cool.  In fact, I don’t even think MTBoS has cool kids.  Everyone at Twitter Math Camp just wanted to share and learn from each other.  There was excitement and wonder and gratitude and humility all around.  Everything was inclusive, everyone was awesome.

And as far as the lunch table goes, there’s open seats for anyone who wants to learn and grow.  I got the feeling that people wanted me to be involved because they knew I was cool too.  Not because I had 45 twitter followers, but because I wanted to maximize my ability to help young minds develop.  And to drive that fact home this happened yesterday:

Sam helps

Thank you Sam.  And thanks to everyone who made me feel welcome at TMC 2015.  You folks are amazing.  I’m so excited to have met you and look forward to being a part of your/our online community moving forward.

If there’s anyone else out there who’s afraid of the “Rock Stars” or “Celebrities” or “Cool Kids” in the MTBoS, I promise, you have nothing to fear.  TMC 2015 showed me that there’s room for everyone in this fantastic community.  I’m taking my lunch to the MTBoS table from now on.  I encourage you to come too.

Unit on Functions: A Work in Progress

TMC15 has me much more active on Twitter.  Today there has been some talk about building the concept of functions.  Last year Liem and I made functions the main focus of our course.  We feel like a solid understanding of functions, their notation, and their graphs is critical for growth in the direction of Calculus.  The file below contains a series of Scenario-Based Tasks we used last year and some new ones I wrote this summer.  It is very much a work in progress and I would love some feedback if anyone ever takes the time to look through it!

Relations and Functions – N. Goza & L. Tran

The Unit starts by discussing sets of numbers and then moves into relations, functions, and all the related vocabulary and notation we could think of.  I would personally highlight “1.4” and the bike riding part of the “Unit 1 Exam” as the most refined and ready-to-use tasks.

2014-15 Drafts 2: End of the Year Vibes (& Stuff)

I’ve spent the last couple of nights at awards banquets. I’ve watched a lot of graduating seniors get a lot of cool awards and finally get some much deserved recognition as students, leaders, and athletes.  I’ve spent the last couple of days signing yearbooks and explaining to seniors that I’m not going to Grad Night because I don’t really want to and I’m not going to the senior picnic because I have to give finals to my other students who don’t get to close out the year with fun activities.  They remember the feeling.

Around this time of year I start thinking a lot about next year.  I’m worn out, my students are worn out and my class isn’t humming along like we were in November.  I start to forget the good and start trying to think of ways to remedy the bad that has reared its ugly head down the homestretch.  I think this is good for me.  This year I have pages and pages of ideas for next year, and I’ll be more prepared than ever when next year starts.

But tonight I’m reminded that it’s important to focus on the now a little bit too.  My seniors are done with AP Exams and Finals.  The stress of content and grades is gone and finally we can interact without worrying about what we need to get finished or what we can be doing better.  And I’m reminded that my students really like me.  They want me around, they want me at events, they want me to write something profound in their yearbooks and they want me to congratulate them for everything they’ve made it through.

Tonight I can’t help but think of how absent many of these positive vibes and feelings can be in the middle of the grind as we try to meet all my curriculum goals and their desires to pass my class and score well on AP Exams.  And I know why it happens.  It’s pressure, stress, and fear that we will fail each other somewhere along the way.

I doubt it can be avoided, but I can’t help but think there are ways to remedy it a bit.  I’d like to think that throughout the year there have to be ways for my students and I to take a step back, remind ourselves that we like each other, and remind ourselves that this journey we are on together isn’t all about work and results.  It’s also about getting to know each other, learning from each other, enjoying ourselves, and growing as people.  And maybe even acknowledging that we’re having a pretty good time doing it.


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