Category Archives: Teaching

Year-End Reflection and Changes

This is another first year in a new school for me, so there was a lot to learn this year. I am very excited to be teaching the same two classes (Algebra 1 yearlong and Precalculus) and building on these two classes. Here are some of the ideas I have for next year, in no particular order.

  • I need to rethink my textbook organization for Precalculus. At the end of the year 2 textbooks went missing. I keep textbooks on a shelf in the room because we use them every day in class and students are allowed to take their textbooks home. Two are unaccounted for, so I need to rethink what classwork looks like in Precalculus, which goes hand-in-hand with the next one.
  • We need to do even more spiraling. I assigned weekly HW assignments which were all review, but too many students didn’t do their homework and too many copied their friends (a few even admitted as much!). I need to have them do review problems in class where I can monitor and give feedback. This will require me to make/copy problems into “sets” which have current material and review material. I want to read “Make It Stick” to get a feel for the optimal re-learning time.
  • Students need to be more independent when doing the “work together” time. It’s almost always on the whiteboards, but I could do something where students use part of the board for their groupwork effort and then part of the board for individual effort. This can be recorded using the next point.
  • FreshGrade. It looks like an app/website/system where I can take pictures and record, both with photos and with videos, student work. The students have a stream and, if I can setup SBG, then we could use the stream to grade students on their success on a given topic as we’ll have lots of evidence. This will also help with spiraling, even in Algebra 1 where I’m loath to do it (but that means I need to do it all the more!)
  • I also want to include some peer evaluation components to the groupwork.
  • I need to model more of all of this. I need to model:
    • Good groupwork
    • Good self-grading (even when they get an answer key!)
    • How to watch the videos
    • How to do test corrections
    • How to talk about each other’s math ideas in a non threatening way.
  • I want to leverage my teacher website as a resource. It can have all the problem numbers from the textbook, but of course, I now want to include problem sets, so ideally I’ll add those to the website.
  • I want to improve my visibility in the community and for the students. Attend more sports and academic competitions. Attend more events, performances, and just things in general.
  • I want to make students grading themselves as a point on the standards based grading scale for their quizzes (does this fit into the SBG mindset?). Too often I find that students aren’t so much correcting themselves as just marking “right” or “wrong”. Sometimes I’ll hang out by the turn-in tray just to ask students “Can you correct this paper better, please?”
  • I want to continue to improve the videos, certainly re-recording some of them, but also focus on the questioning in the videos: always moving from low level (recall) up through high level questioning (analysis). Perhaps I should make a “question chart” to have next to my desk so that I always follow Bloom’s Taxonomy or DoK or something like that.

What will be the biggest change? Probably the FreshGrade, if it works. If it does, then I’m going to use a different grading scheme and get permission from my principal. I’ll need to have it all laid out clearly. That’ll come in a later blog post. Oh, and we’re supposed to have access to Schoology at some point, but we don’t know very much, as in “will we be allowed to plug in grades there?” And “Can I do SBG there?”. If not, I may just have a separate program to keep track of SBG grades and then update them weekly into the school system grade book. Yes, it’ll take longer but that time will be spent reflecting on where my students are and where they need to be.


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[SBG] Grading Idea: Points for Ss Correcting Themselves

This year I’ve used a 3-2-1 scale for grading all quizzes: 3 = mastery, 2 = proficiency, and 1 = Not Yet. Students can receive a 0, but it’s if they show absolutely no understanding (in other words, it’s very, very simple to get at least a 1).

I also provide answer keys in the back of the room and students grade themselves (with my blue felt markers) immediately after every quiz. I want students to go beyond grading and actually correct themselves, but many ignore that and/or forget to do it over time.

So I thought “What if I graded out of 4 and one of the points was for correcting all the missed work?” That means if they got everything right, they automatically got the extra point. I could also penalize students for not checking themselves carefully (another thing that bothers me! Students counting their scores as correct when they’re actually not!) Of course I still grade after all the students, but it shows a lack of effort and attention to detail that I want.

Right now I still have to translate all these grades into numbers, so 3 –> 100, 2 –> 85, 1 –> 50 and 0 –> 0.

With the extra point, I could make 4 –> 100, 3 –> 75 (or 80 or 85), 2 –> 50, 1 –> 25, 0 –> 0. It would still be easy for students to get “1” and then bump it up to a “2” with lots of corrections, but of course then they’re writing down all the correct work on their quiz in my blue pen, which is, I guess, a good exercise.

I’m going to file this away for next year (I don’t want to change grading practices too much in the middle of the year!)

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Teaching Reflections + One Good Thing

After school today we had a staff meeting where we talked about reflecting on teaching and I realized I hadn’t reflected here in a while.

One reason I think I “took my foot off the gas” was because at the start of last year, an 8th grader told me “I found your blog and read what you’re teaching us–will we also be doing this activity and that activity?” On the one hand, that was great. On the other hand, this student had the potential to spoil and surprises that I had for others, so it kinda killed my blogging momentum.

Right now I think no students know about this, so I’m going to get back in the habit of reflecting on my teaching regularly.

So for today I just wanted to say one thing that happened in my class that has solidified one practice I do for the rest of my teaching career.

A student walking into my room to ask me a question. Her friend, probably an upperclassmen (Jr. or Sr.), who I do not know, came in with her and commented “that’s cool” pointing to my birthday whiteboard where I write student’s birthdays and half-birthdays.

If a student whose name isn’t on there likes that, think how much more that means when I recognize students’ birthdays and half-birthdays by writing it on the board even if I forget to tell them Happy Birthday on their birthday.

I will forever write student’s birthdays somewhere in my room for as long as I teach.

Yes, a student wrote down a fake name while they were in tutoring and I was out of the room at a faculty meeting.

And yes, it’s my wife’s birthday this week. Don’t worry, I’ve got a really good birthday present for her! I just hope it arrives on time.

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[SundayFunday] First Day of School

Blogging always tremendously helps my reflection and helps me grow as a teacher. However, I struggle to be motivated to do it, which is why I’m so glad that Julie (@jreulbach) is great at starting these initiatives.

MTBoS SunFun Logo

This week’s topic is “First Day/Week of School”

In the Past

In the past I’ve done everything from hand out and read the syllabus (and hope the bell rings by the time I get to the end) to ignoring the syllabus entirely. If every teacher shares the syllabus on the first day, the students just hear “blah blah blah”. But if you do something different, you can always hand out the syllabus later in the first week. Or never[1].

I often have them fill out a “get to know you” form, either online if I know I have access to a Chromebook cart, or on paper. Last year I kept the papers in a binder and used them throughout the year, both studying students’ likes and dislikes, as well as keeping a record of contact home, and I was really glad for that. This year with fewer students at one time (3 block classes each semester instead of 5 non-block classes all year long), I should be able to focus and learn students’ better than in the past.

My father-in-law offered this wise advice: Make sure you do math on the first day to set the tone and the idea that “we do math in this classroom every day.” I think he even recommended starting with math before doing any sort of icebreaker or survey.

This Year

I’m going back to High School, and I’m sure that my Precalculus class will look very different from my year-long Algebra class, both in academic and social maturity.

This is also the first time that I’ll be teaching a block class on the first day.

One thing that Mary Bourassa mentions that she’s done on her first day was to show students a bunch of functions/lines/curves on Desmos without the equations. Students then work out how to graph them on Desmos. I’m going to do this in Precalculus and I’ll throw in some moving parts and some that are very difficult for the “reach” so that everyone is challenged. Here’s her Desmos Activity that she created based on the graph (I kind of like how the original activity was open-ended and students could pick which graph they want to try to create first!)

I’d like to do something like this in Algebra I, but I need to be careful not to throw too much over their heads because I think I lost a lot of students last year that way.

I’ve been reading others “First Day/Week Back” blog posts and here are some that caught my eye (in no particular order).

  • Feedback Name Tents, from Sara Vanderwerf.  I first saw “Name Tents” and thought “oh, Middle School. I taught that last year, I don’t need that”, but I know I DO need to build relationships with the students and her idea of giving individualized feedback every day for the first week is incredible!
  • What is Math and What do Mathematicians Do, from Sara Venderwerf. This post is great. I definitely want to get all my classes to consider what Math is and what a Mathematician is. I’m used to using “I notice, I wonder”, though it’s a good reminder that I need to be intentional about planning this into my lessons, daily if possible. I may spend more time with Algebra I because there will likely be more students in those classes who think “I can’t do math”.

Hmm, I thought I had more resources to put here, but just #PushSend.

[1] I do think I forgot to hand out the syllabus one year. They sat in a stack in the corner of my room until I used them for scrap paper halfway through the year.

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End of the Year

As I’m getting ready for next year, I realized that I need to have closure on this past year.

Last summer (2016) my family moved back to Maryland from New Mexico and because of that, I needed to find a math teaching job. I was hoping for a high school position, but according to the county math specialist, it was a strange year because no HS math positions were opening up. They asked, and I said that I was willing to teach middle school, and before I knew it, I was teaching 8th grade math and Accelerated Algebra 1!

It was a big transition for me for several reasons: private to public, Christian to secular, high school to middle school; Precalculus, Physics, Chemistry to 8th grade math. In both schools I was fortunate to teach a very diverse group of students, though the makeup of the diversity changed[1].

One of the biggest changes was having an new boss/principal (who ended up being really awesome!) I didn’t know whether I would be allowed to continue my bizarre Standards Based Grading gradebook.

How I Graded This Year

Because of this, I graded differently in Algebra (where I was the only Algebra teacher in the school) than in 8th Grade Math (where I taught alongside an experienced teacher).

In both classes, we had quizzes/tests every Friday, for consistency, and the content of the assessment depended on where the students were in their understanding.

In 8th grade math, students could do quiz/test corrections, like I’ve done in the past, but there were not really standards in the gradebook and each quiz/test was one grade[2]. Classwork was a big chunk of the grade (~25%?) and by the end it was really just me grading their warm-up sheets weekly on effort.

In Algebra, I graded them out of 100, but they really could only usually earn multiples of 10 (50, 60, 70, 80, 90, or 100). Quizzes had fewer than 10 questions and I just took 10 points off for each one they got right (so getting 4 out of 6 right would be an 80). That was 95% of their grade and the other 5%, just like in the other class, was HW.

Where I’m Going

Next year, I’m going up to High School, and I’m moving to the local High School where my children will eventually attend one day!

I’ll be teaching two sections of year-long Algebra 1 and one section of Precalculus each semester.

Once again, I’m moving into unknown territory: I don’t know what the principal will allow. At least I’m a little more familiar with the gradebook, though I know it can’t do SBG the way I want it to (like ActiveGrade!).

One added challenge is that my “year-long” Algebra kids will really only have me for a semester because they switch all their classes around. So they’ll likely have two different Algebra 1 teachers. Also Precalculus is a semester course, so I’ll have a new batch in the Spring there too.

That means the weirder my grading policy, the more time I’ll have to spend explaining and the longer students will take to adjust to the new setup.

How I Want to Grade Next Year

I know I want to go back to more SBG than I did this past year. I need to have students see that grades are communication, not rewards/punishment. I need to give students second chances. And I need my classroom instruction to be driven by the focus that SBG brings. I need to work on what this looks like, so first up, I need to find well organized standards that are “just the right size”.

I also intend to flip the classroom. So much of my Algebra class left positive on that aspect of the class, more than I was expecting!

I also want to create a class website again. I used Google Classroom this past year and it was very effective for the middle school students, but it’s too difficult to find previous posts (even with the tagging system)[3] and the organization that a website brings is so helpful.


[1] In NM, 70% of my students were Native American, compared to in MD, roughly 1/3 of my students were African American and 1/3 of my students were Hispanic.

[2] Except for one time near the end of the year where I gave them a large quiz and wanted them to see that they were two different topics. I also wanted to reward them because I thought it was going to be a quiz that they’d do really well on. They didn’t. Oops.

[3] I still can’t believe that you can’t easily search within a Google Classroom yet. Makes no sense.

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[DITL] 5/22/17

6:00 am

Woke up at my usual time. It feels like it should be the end of the year, but we have 3 weeks of school left, so I’ve got to figure out how to motivate myself in order to motivate my students to try through to the end. This week is exam week at my last school, so it would already be the end of the year if we had stayed in New Mexico.


7:52 am

Students start coming into class and the morning lesson from admin is to vote on rising 6th and 7th grade students. It does not make a lot of sense for my 8th graders to care about the election, but they care more than I thought the would, so I appreciate their efforts.


8:40 am, 1st & 2nd period, planning

We have a diversity training. I already heard this from my “First year teacher” course, though it is new to most of my colleagues. The best time in the 45 minute session is 3 minutes where they ask us to share something meaningful with our colleagues. I wish we could have more time set aside for just that because we can learn so much more from personal stories.


10:20 am, 3rd period, Merit 8th Grade Math

The students are unfocused. There are always 5 different conversations going on at once and they are unable to stay quiet for more than 2 minutes at a time to listen to my explanation of what we’re doing today. It’s become my roughest period by far. A few students have their phones out and I struggle to ask them to put them away. After five minutes some of the phones return. I know at least one student is having a bad enough day that he might go off if I take his phone again. I decide to ignore him and his phone this time. [1]


In this class we did a “hand squeeze” activity, where students stood in a circle and we timed how long it took them to squeeze each other’s hands all the way around the circle. The goal was to create (in Desmos) a scatterplot with a strong positive linear correlation: the more people in the circle, the longer it should take to go around. Here’s a Desmos graph to go along with some of our data (I couldn’t convince everyone in the class to stand up and be willing to hold hands).


11:10 am, 4th period, Honors 8th Grade Math

This used to be one of the class I had the hardest time getting them to focus, but now they’ve done pretty well for the last several months. Phone calls home to this group really help and I’m staying in daily contact home with at least one of the students.


In this class we’re doing our end of year stats project. This involves finding two things to compare to each other via a scatterplot and creating a few questions for their classmates to answer.


12:00 pm, 5th period, Algebra

My Algebra students took their PARCC test (part 1 of 3) this morning and are taking part 2 in the afternoon. Since this is during their lunch time, they had to have their lunch during 5th period, so they just hung out and ate in my room. One student said “this is the best class of the year!”


12:50 pm, Lunch

Three students came into my room for “tutoring”–however, for these three regulars, they just hang out in my room. We got to have a discussion about various topics, such as religion (since they ask), friends, and family.


1:23 pm, 6th period, Honors 8th Grade Math

Just as before, we’re doing the stats project. I walk around the room, but this class has a harder time figuring out what they’re doing.


2:13 pm, 7th period, 8th Grade Math

This class is not as loud as 3rd period and we get much farther in the “Hand Squeeze” assignment. We just need to discuss the conclusion, but they’re ready to start the next assignment!



The end of the day bell rings and I go through my after school routine. Here’s my current checklist:


The email addresses are students that I contact daily, blurred out for obvious reasons.

I get to go home about 2 hours after the students are done. Tonight I need to grade Friday’s quizzes, figure out lesson plans for tomorrow’s Merit classes, and sign up students for tutoring who didn’t take the quiz on Friday.

Just 13 more days to go!


[1] I ended up making a positive phone call after school. I hope to hold it up to him tomorrow and point out that I could have called about his phone being out, but I want him to succeed. I need to keep trying to build relationships even if we’re in the last 3 weeks of school. This also helps me to feel that I haven’t given up on him: I ignored his lack of effort in class, but didn’t ignore it after school and won’t tolerate more than one day of being angry as an excuse.

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[3 Act Lesson] Sandboxes: Volume of Cylinders (& Spheres)

In middle school we only get 47 minutes, which is not enough time for the 3-act lessons I had gotten used to (coming from 90 minute blocks!). After a 5 minute warm-up, and 5 minutes of going over HW, that leaves no time for a lesson. But today I think I was able to get all three acts in, so I wanted to share my success!

We’re doing volume of cylinders, cones, and spheres in 8th grade math right now.

Act 1

Me: Spring break is next week, and here’s my Spring Break plans.

Image result for sand box

Students: You’re going to the beach?

Me: Nope, I’m going to build a sandbox for Benji (my 2-year-old). What do you think is the most expensive part of the sandbox?

Students (in unison, surprisingly): The Sand!

Me: Right, so forget the wood for now because I have enough scrap wood that I can probably build the frame without buying any wood. My wife and I are trying to decide between a 6’x6′ and an 8’x8′ sandbox.

Student: 8’x8′ cause it’s bigger, duh!

Another Student: But that would cost more!

Me: What do you need to know to find out how much more it would cost?

Student: How much all the sand costs.

Me: Right. You don’t buy “one sandbox worth of sand” at Lowes. It comes in bags.


Eventually they get to needing (1) how much is in a bag (0.5 cubic feet worth of sand), (2) how deep is the sand in the sandbox (6 inches), (3) how much each bag costs ($4.25 is what I found at the local Lowes).

We did the comparison together because we were so short on time. If we had a block period, then I would have let them struggle instead, but I wanted them to get to calculating volume of cylinders in context instead. The work I write on the board looks something like this:


18 cubic feet

36 bags

$153 is the total cost for a 6’x6′


32 cubic feet

64 bags

$272 is the total cost for an 8’x8′

We have a brief discussion answering “why is $272 nearly double $153 but 8′ isn’t nearly double 6′?” Unfortunately I pointed this out to them and had to start the discussion but it’s something that I feel is important enough for me to “artificially” bring up.

Act 2

Now I want you to get one large (4’x2′) whiteboard for your table, one marker, and make a cost comparison between a 6′ diameter circular sand box and an 8′ diameter circular sandbox. Go!

Image result for sand box circular

The students did a really good job (we’ve been practicing finding the volume of cylinders).

Here’s some of their work (I’m sharing the more legible ones)


Act 3

As students finished, I gave them this challenge problem:

“Suppose the silo at our farm is filled with sand. How many 8’x8′ rectangular sandboxes could we fill with all that sand?”

I draw a picture of a silo (hemisphere sitting on a cylinder) with cylindrical height of 20′ and overall diameter of 10′. As you can see from the pictures above, some students did pretty well at that problem, too!


The students were really interested in my spring break plans. The “builders” of the class liked the idea of figuring out how to get ready to build a project, even if it was just buying sand. The “caretakers” of the class like that I was doing something for my 2-year-old. Get enough of the students on board and they all really take to it, and I was fortunately that this happened here. Here’s the google slides I used for the lesson.

How would you improve it? Alter it? Thanks for any and all feedback!


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