First Day of School Idea?

At the NCTM National Conference back in April, there were a variety of speakers that challenged me to think about what it means for students to be mathematicians. Two in particular stand out to me as I look back. Christopher Emdin discussed how school mathematics denies students’ learned experiential mathematics, especially using the examples of “bars” (rapping) and learning to cook. Tracy Zager spoke about how to help students do math more like mathematicians. Her daughter’s ideas about what is means to do math were inspiring. These ideas have been spinning around my head over the past few months and when I saw a recent post on Twitter asking how we can set the tone on day one for the rest of the year, I got to brainstorming how I can make some of my typical beginning of the year routines fit more into this theme of helping students to think as mathematicians.

This idea is not completely developed, but I thought that the process of writing it out might help to solidify it as well as clarify my intents. Something that is important to me throughout the year is that students can identify patterns and consider what those patterns might mean. I want my students to have confidence going into the year that this is a skill that they already have experience with.

What I am considering is that rather than telling students about myself, they are going to look at some objects and pictures in order to draw conclusions about what they think is true about me. I could do this by having stations around the room or making up bags that get rotated around to table groups. A group of students will look at their objects in order to determine what they think is true about me. I might give them a simple sentence frame to help them make sure that they are backing up their statements – “We think that Ms. Stuckey ______________________________ because ______________________________.” For example, rather than telling students that I like hiking and that I traveled to Glacier National Park over the summer, I could set out my hiking shoes and backpack, my map from Glacier and maybe a few photos.

Is this mathematics in the strictest sense? No, but being able to look at “data,” find patterns in that data, and being able to justify an argument are all very mathematical skills and ones that I hope to be able to promote throughout the year. I don’t know whether I will end up actually doing this with my classes this year, but I would love to hear from others about how they are starting the year out setting the tone of encouraging students to be mathematicians (and to show that they already are).

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June #MTBoSBlog18

Despite the fact that my last post declares that I am determined to keep up with #MTBoSBlog18, the end of the school year got the best of me and I skipped April and May. I am hoping that I will be able to use this blog as a reflection and brainstorming tool throughout the summer to help keep me motivated and thinking about next year.

For now I will start with one thing that I am proud of and one thing that needs some rethinking for next year, but both are connected to relationships.

I am proud of the relationships that I made with my students this year. My gut feeling is to hedge that statement or make it softer somehow, but I’m going to just leave it there. I am not a loud, gregarious teacher filled with stories and jokes, but I think that my connections this year with students have stemmed from little opportunities to make conversation and to see them as people who are far more multi-faceted than being a Geometry student. I know that when I started teaching I read a bunch of books that advised greeting your students in the hallway every day. I just wrote it off because I needed to get ready for the next class. The past year, at the very least, I have said “Hi,” “Good morning,” or “How are you doing today?” to every student, every day. Before my fourth block class, I also have some students who stand there with me. I mean, its not with me – with me, they want to see who else is walking by, but that is another time where I get to connect with them and there is no expectation of talking about Geometry at all. Some of them even ask me how my day is going. Has that little gesture made all the difference for all of my students? No, but I think that it has made a difference for me – to remember who they are outside my classroom (even though its just the hallway) and that there is so much more to each one of them than their score on a Geometry test could every tell me.  There are times where I wonder if I am too soft on my students and not enough of a “disciplinarian,” but I think that the ways that I show that I care about them as human beings outweigh that one extra Geometry problem that they could have solved if I had just told them to put away their cell phone and get down to work (which certainly does happen plenty of times as well). As I look forward to the 2018-2019 school year, I hope to continue to find ways to see my students for who they are in all the parts of their lives.

While I felt like my relationships with students was a strength of this past year, I felt that my classroom community overall needs some work for next year. While I am grateful that my students were not hostile or rude toward one another (to my knowledge anyway), in general it seemed that if they were not assigned to be working with their chosen person or persons, they just preferred to work alone. Some ideas that I have to address this dynamic are:

  • More intentional community building during week 1 – I’m not quite sure what this looks like yet
  • Changing seats more frequently (visibly random groups)visibly-random-groups-vrg
  • Possibly changing my seating arrangement from pairs into 3s (see above)
  • More stand and talks 

Any other suggestions for me?

I am grateful for the cyclical nature of teaching that allows for embedded times to reflect and respond. In many ways it feels critical because of the intense environment of the school year that at times can stifle the necessary work of considering what has gone well and what needs some work moving forward.

 

March #MTBoSBlog18

I am new enough to blogging that being inspired to write each week feels overwhelming. I was not able to keep up with the Sunday Funday challenges back in August and September, but I am determined to keep up with the once a month #MTBoSBlog18 challenge. I even have it in my Google calendar to help me to remember to brainstorm ahead of time. I was feeling a little bit uninspired about this month’s post, but nonetheless, I was able to come up a few highlights from my most recent Geometry unit on right triangles.

Our Geometry team had made the decision this year to not teach the distance formula, but only to teach it as an extension of the Pythagorean Theorem on the coordinate grid. We reviewed the Pythagorean Theorem within the first month of school, but as we entered our unit focusing on right triangles, I wanted an activity to practice on a graph once again. I love soccer and many of my students love soccer, so I was inspired by this tweet: Untitled

I  wasn’t able to recreate this in my classroom, but did the best I could on paper. I had fun incorporating current soccer players into my soccer story. I follow US women’s soccer more closely and my husband helped me out with some of the Premier League players. I used this with my Geometry Lab students and this was a great start to build up some confidence in a unit that can be very difficult.

The main component of our right triangle unit is introducting students to trigonometric ratios. Entering into planning for this topic this year, I was wondering if I typically make the jump too quickly from identifying the different ratios to solving for side lengths and angles. I wasn’t sure what else to do, but I ended up on this post from Pam Wilson. The post is from 2013, so I think I may have been in an #MTBoS rabbit hole. Thank you to whoever had linked me there. I had just recently cut out a whole bunch of little cards for another activity, so I decided to turn her work into a Desmos card sort. I was really pleased with how quickly my students were able to pick up on the differences between sin, cos, and tan.

The final challenge in our right triangle unit is setting up word problems with the angle of elevation and angle of depression. By this point, I was really pleased with how well my students were doing with solving problems with trig ratios, but I knew that setting up the pictures was going to be a challenge. To try to isolate the skills, I set up this 2 part worksheet. Before they started, they folded it on the vertical line so that they were only looking at part 1. In part 1, their goal was just to draw the picture and since there weren’t any numbers, they weren’t trying to jump ahead. We used 2 colors to identify the angle and side length that would be given in part 2. We marked with color on the blank and in the picture. Once we got to part 2, they used their color coding to quickly identify where the values belonged in their pictures and then went about solving the problem. Drawing the pictures was still a challenge for sure, but this did help to ease the difficulty a bit. I may try this structure again with other types of word problems as well.

February #MTBoSBlog18

My Honors Geometry textbook includes a significant number of always, sometimes, and never questions. I like these questions because I think that they inspire good discussion and deeper thinking into a variety of ideas, but by this point in the year, my students are starting to get tired of them. In thinking about ways to structure these discussions and change it up a little bit, I came up with this activity.

I have 3 corners of my classroom labeled with always, sometimes, and never. Rather than just having students go to the corner that represents their answer, I pass out playing cards before each round. If they have a face card, they are a “decoy” and they need to go to the corner that represents what they think is not the answer. If a student gets a number card, they just go to the corner with their answer. The purpose of the decoys is to alleviate the “Oh, Sarah is always right, so I’ll just go where she goes.”

Once students are in place, I give each corner the chance to give their argument. Any students who are persuaded by an argument can move. The other thing that is interesting about having the decoys is that they are forced to try to think about an argument that might make the wrong answer seem correct. After all arguments have been given, I ask the face cards to show themselves. Hopefully the decoys are the only ones remaining in the incorrect corners.

I did this activity this week with both regular and Honors level Geometry students using this set of quadrilateral questions from Lisa Bejarano (thank you!). If you would like to try always, sometimes, never questions, asnmath.blogspot.com is a great resource.

January #MTBoSBlog18

I tried something new yesterday. We had a snow day, on the day immediately preceding my Honors Geometry midterm exam. I knew that some of my students would be trying to use this “extra” time to brush up on things and I was brainstorming ways that I could support them. I decided to offer two Instagram Live study sessions, each for an hour. I had very low expectations, thinking that maybe 5 students (out of around 60) might join me. The school that I used to teach at did “online days” in cases of inclement weather and I had offered Google Hangout sessions (just chat), which I think only one student ever took advantage of. It felt very low risk. Worst comes to worst, I was just going to video myself working on my computer.

My first session I had scheduled for 11:00-12:00, notifying students via Google Classroom and Remind. Pretty immediately, I had 5-10 students with me. If you are new to Instagram Live, it basically just allows you to send a live video to your followers (in this case, I made a new non-personal Instagram account) and throughout the video, viewers are able to comment. For the most part, students used the comment feature to give me problem numbers that they wanted to discuss, but they were also able to add follow-up questions if I hadn’t answered their question. During my first video, I had my phone on a stand using the front camera. I’m not much of one for selfies. If I was, I might have remembered that the front camera reverses the image, which is a problem, if you are, for example, writing in a notebook. I wasn’t working out long problems, mostly just reminding students of concepts and formulas, so it didn’t feel like a huge deal, at least to me. At the end of the session, Instagram told me that my video had 19 viewers. I was pretty pleased.

I also offered a second session from 3:00-4:00. I did try to remedy the camera issue by propping my phone on top of 2 small boxes, but then I needed to hold it in position. During this session, all students could see was about a quarter of a sheet of notebook paper. More boxes would have been better. I did have fewer students during this session, but also some repeats.  By the end of the session, there had been 12 viewers.

One of my reflections on these two sessions is how different it felt for me to have students seeing my face and notebook versus just my notebook. During the first session, when I could see my own face, I felt much more confident that I was engaging and explaining things in the way that made sense. During the second session, when I could only see my notebook, I didn’t feel as connected to my explanation. Obviously, if we were in person, there would be body language, etc. that I would be gauging as I worked with a group of students, but in both of these cases, the only interaction was via the comments. I’m not sure if there was some kind of “placebo” effect of viewing my own face on the screen and reading my own body language, which then affected how I perceived my students to be feeling.

While it was an interesting experience and helpful given the circumstances, in some ways it also goes against part of my teaching philosophy. I was the presenter and students were only there to ask questions. Students were able to just be passive learners and receive the information rather than truly interacting with it. Earlier this month, my district’s math coordinator sent out the article “Never Say Anything a Kid Can Say,” which I was familiar with, but is nonetheless a good reminder. Students’ work yesterday was to review for a midterm and for most students, they could have said a significant percentage of what I said, but the difficulty was in putting together the pieces. This form of interaction made me do a lot of the work that my students are already capable of doing.

I’m still thinking about the balance of the personal (my face) versus the function (my notebook) and other circumstances where this form of student/teacher interaction might be helpful and/or appropriate. Has anyone else ever used Instagram Live?

When a test isn’t so great

What to do when a test isn’t so great? In the most ideal teacher world, it would never happen, perhaps because you are just that good and are able to push and challenge your students exactly all the right amount so that they can each perform to the best of their abilities on your test. Also, we theoretically as teachers should have indicators of how things are going, like the formative assessment strategies that we should be utilizing each day. But what happens when the formative assessment seems okay, not great, but okay, and that test just really needs to happen before Winter Break? It seemed like it was all going work out. Students worked hard on the review, some stayed after school to get extra help, etc. Then you grade the test and you realize that no, you rushed things and maybe that new strategy that you were trying maybe wasn’t the best for this particular group of students. What do you do?

The issues that I want to balance are: needing to reteach content while not taking up too much time and not wanting to drastically impact their grades close to the end of the semester. What is the best method to include some elements of re-teaching, having an additional grade represent what they know now, and take a reasonable amount of class time? Additionally, how does all of these thoughts apply to the students who did do very well?

Here are some options that I have considered:

  • Hand each student back their test. Let them use their notes and/or classmates to fix their errors. Move into heterogeneous groups for a group re-test. Their two test grades could be averaged.
    • Pros: This could be completed within one class period. Group work could provide them with the additional support that they need to be successful.
    • Cons: Their grade may simply reflect who they were grouped with rather than any knowledge that they have gained.
  • My typical test retake scenario is that they must complete test corrections before they can retake a test. Students do not tend to take the time to do this and then get frustrated that I will not let them just retake the test. Perhaps taking a class period to do a quick re-teach and then class time to work on test corrections before offering an optional retake could allow the retake to be more accessible to more students.
    • Pros: This option seems to leave the most room for the students to opt in/out.
    • Cons: This requires a higher level of individual motivation than the first option.
  • In combination with a little bit of re-teaching, do some variation on “My Favorite No” by picking out some key errors from the test to have students work on either individually or as a group. This error analysis could either be graded or I could follow it up with a short re-quiz.
    • Pros: Whereas test corrections may leave students floundering with their own mistakes, they may have a different viewpoint if they are looking at someone else’s work.
    • Cons: Is error analysis enough to demonstrate additional content mastery?
  •  Curve the test now and re-teach the content immediately before the unit it is prerequisite to.
    • Pros: Kicking the can down the road makes things easier right now.
    • Cons: I would rather deal with the mistakes while they are fresh(ish) in their minds. While Winter Break is long, March is even further away.

In addition to this list, I also have many things that I am thinking about in how to teach this unit better next year and how this experience affects how I teach these kids throughout the rest of this year. In this space I am just considering what I need to do in the next week to rectify this most immediate issue. I definitely look forward to hearing any ideas or suggestions that anyone may have, while also feeling some trepidation as this is definitely the most vulnerable that I have been in this space.

Holiday Flags

Inspired by this video about Nepal’s flag’s construction being outlined in the Nepalese Constitution, my Honors Geometry teammate and I were tossing around ideas about how this might connect to our Honors Geometry content. We had a day between a unit test and the beginning of Thanksgiving break, which obviously is not a great time to begin new content. We wanted to be festive, but productive and decided to assign a holiday flag project. Students needed to include at least 4 geometric constructions, have a holiday design of their choosing, explain the connection between their design and their holiday, and include a write-up of directions that could be used to duplicate the flag. See here for the rubric that I developed in order to communicate expectations and then grade the flags. There were lots of Christmas trees and snowmen, but there was a nice variety as students considered what was important to them. The last student example shown here was made to show his family’s celebration of the Iranian spring holiday, Nowruz.

Overall, I was very pleased with their work on this project. I gave them about 2 hours of class time, spread over two days, but almost all students used additional time outside of class in order to finish. It was a nice way to wrap-up our study of the basic constructions and have students consider how different constructions could be combined.

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