At Twitter Math Camp, I gave two presentations. One “My Favorite” on using the engineering design process in math class, and a second on 3D printing in math class. Here are my resources:
Using the Engineering Design Process in Math Class:
3D Printing in Math Class:
Get out your calendars and mark them now! Twitter Math Camp 2017 is being held from July 27th-30th at Holy Innocents’ Episcopal School in Atlanta, Georgia.
Having just returned from my 4th Twitter Math Camp (TMC) experience in Minneapolis, I feel the need even more to book my entire summer plans around this camp. I like to spend time in the summer with my family and friends; go to the beach; read a book for fun; nap; go to the drive-in, etc. But I also NEED to spend four days in person with my MTBoS family. The people and sessions at TMC invigorate my passions and spirit and convince me that I can conquer anything in the upcoming school year.
I can’t possibly recap everything I took away from TMC16, but here are some of my favorite takeaways. I hope they become some of your favorites too! Grab a drink, there are a lot 🙂
Favorite Pre-TMC Outing: After arrival, I adventured to the Minnehaha Falls with a small group. The weather wasn’t the best, but we had a fabulous time exploring the falls and walking to the confluence of the Mississippi River and Minnehaha Creek.
Favorite New Desmos Calculator Feature: Desmos now has audio capabilities for visually impaired and blind students. Use Command F5 for the voice option, and Option + T for the audio trace. Desmos will read the expression being typed, and then play a graph used a pitched audio representation. Kudos to Desmos for striving to be fully accessible to all users!
Favorite New Desmos Activity Builder Feature: Card sorts! Ask Desmos and you shall receive! By turning on the “Labs” option once you’re logged into Desmos, you now have the option to build card sorts within the activity builder platform. I made a cart sort for Quadratic Equations, and I can’t wait to make more and then also steal from the crowdsourced list. My group loved that we can input card sorts already created; ask students to sort in more than one way; narrow responses by asking for a specific number of cards in a pile; and ask students to analyze why someone else sorted the cards a different way. The possibilities are truly endless, and you can check out the card sort bank here.
Favorite Passionate Educator Title: Chief Evangelist. In her keynote speech, Sara VanDerWerf challenged us to become “Chief Evangelists” for our passions in math education. Sara said, “Sharing your best with others who can benefit is a responsibility and opportunity that falls to everyone” and “To be good at evangelizing, you’re gonna have to practice.” You also need to prepare mini-elevator speeches for each of your passions so you’re ready to share, and tweak them depending on your audience (students, parents, teachers, leaders). I’m going to spend some time this summer narrowing down my list of math education passions to figure out what I want to advocate for.
Favorite Dorm Life: While not all aspects of Dorm Life at Augsberg College were glamorous (looking at you, shower stalls), I had a complete ball living with some TMC-ers for four days. Waking up and having morning bathroom chats about math ed, doing the wobble in common areas late at night, and watching the bachelorette with a huge crew were all completely memorable TMC experiences.
Favorite ELL Strategy: The snowball activity is a great way to get students writing, reading, and speaking in math class. Have students answer a prompt on paper, crumple up the paper, and throw it somewhere in the room. Each student then finds a new paper,
reads the response, and either 1) Adds a new idea 2) Contributes 3) Corrects something
written. After going through the cycle three times, ask students to share ideas out loud
from whatever paper is in front of them. It’s anonymous, non-threatening, and fun for students. And again, it provides them with an outlet for individual think time, following by writing, reading, and speaking. Priceless.
Favorite PD Strategy: To assess participant’s understanding during professional development, I highly recommend using the “Filling in Circles” strategy modeled by Michelle. Start by identifying the key concepts of the session, or in our case, the barriers to implementing responsive stations. Then, have participants continually reflect on the topics and fill in the circles as their learning and understanding grows. Facilitator is able to see what topics need to be discussed more, and participants are able to ask better questions about what they want/need to know. Very easy and very powerful.
Favorite Mapping Tool: Popplet. Use it as a mind-mapping tool or to help students think/learn visually. We used it to map skills and identify gaps.
Favorite Restaurant: Pizza Luce! I had Baked Potato pizza both times we went there because it was just SO GOOD. They were also very accommodating of our large groups.
Favorite Shared Experience: Jonathan talked about how he created a shared
experience in his school by creating “Varsity Math” for his calculus and statistics
I’m on the team!
students. He branded them with shirts, stickers, and inspirational speeches; and the kids just LOVED it. They bought in. They felt like they were part of a special community… because they were. Jonathan even graciously invited all of TMC16 to join the team. How can we create shared experiences for the students in our own communities?
Favorite JLV Reminder: In Jose Vilson‘s keynote speech on “TMC16, Race, and What We’re Not Talking About,” he challenged us to lead hard conversations and be okay with feeling uncomfortable. He also reminded us that we have students who are much more capable of talking about this stuff than we are; often because they have less filters. He told us to “get out of their way” but provide an outlet to let it happen. This was a much needed reminder for me, because I often feel like I should/need to have all the answers, so when I don’t, I avoid the conversation. I know I need to work on this, and my students can probably help me. Watch Jose’s keynote here.
Favorite “Getting Triggy With It” Activity: Kristen led an excellent session on how to make trig and the unit circle not a mystery. Grab all her resources here! My favorite activity was using one triangle drawn on patty paper to construct the unit circle. Simple approach but nicely shows how all the key points are determined.
See Rachel’s tweet for pictures of activity in action:
https://twitter.com/rdkpickle/status/754408434456485892
Favorite Verb: Edmund Harris and Chris Shore reminded us that modeling is a verb. It’s something kids should be doing, not something given to them. Modeling is a: Creative. Active. Process.
Favorite Physical Activity: Sara graciously brought her Backwards Bike to camp, and let me ride it as much as I wanted. If you’re not familiar with backwards bikes, watch this video. Even though I came home with several bike battle wounds, I had an absolute blast trying to ride this thing. Even after just a few times, I felt like I was making progress and coming up with new strategies to try out. Now I’m off to find someone to make one for me.
Favorite Project: Sam shared a project he does with students called “Explore Math” so they can explore math outside of school and see its beauty. He wrote about the project on his blog and shared the website he asked students to explore. It’s a “low stakes, high reward” activity. Some kids will do the bare minimum, but others will take it to levels that Sam wasn’t even expecting. His recommendation is to keep it open, keep the mini explorations mini, and don’t compare projects.
Favorite Pre-Assessment: Don’t have one yet, need to make them! Michelle led us through an eye-opening morning session about identifying the gaps in students’ understanding and then using
responsive stations to address those gaps using differentiation. I’m excited to follow Michelle’s instructions to create appropriate pre-assessments. There should only be one skill per question and as short as possible. Focus on what pre-skills students need to know in order to be successful with new content, don’t worry about the would-be-nice-to-know. The goal of the pre-assessment is so you can figure out where students are at, and provide them with learning opportunities if they don’t know, and learning opportunities if they do know (enrichment). Elissa wrote a great recap of the entire three days.
Favorite Call to Action: Tracy Zager‘s keynote speech titled “What do we have to learn from each other?” was inspiring and community-driven. She stressed that we need to stop pitting content and pedagogy against each other; we need to stop pitting elementary and high school teachers against each other. Neither of these things is productive for our community. We all have an important role in building our students’ conceptual understanding, and we need to work together to get it done. Tracy’s call to action is to analyze whom you are following on Twitter, and make sure you have a variety of contacts you can reach out to for support and to ask questions. Watch Tracy’s keynote here.
Favorite Fraction Problems: After Tracy’s talk, I pushed myself to attend Brian Bushart‘s session on fractions: a place I knew I would feel out of my comfort zone as a high school teacher. One of the reasons Brian said fractions are so hard for students, is due to practices that simplify or mask the meaning of fractions.
By finding a common denominator, you aren’t comparing fractions anymore. You’re now only comparing the whole number numerators. Cross multiplying is an example of masking; you’re getting rid of the fractions and comparing whole numbers. This masks the fact that you’re still comparing two fractions. Neither of these strategies takes into account the size of the fractions and therefore rob students of sense making. Brian then shared a bunch of strategies for how to deal with this, and I will lead you directly to his documents to learn more.
Favorite Fraction Big Idea: Another huge idea that Brian threw at us is the difference in how whole numbers and fractions are treated as adjectives and nouns. Look at the slides below for comparison.
Whole Numbers:
Fractions:
I’ve never really thought about it this way before, so this was a *mind blown* moment for me, and others at my table. Many students don’t actually gain enough understanding about fractions to realize that fractions are actually numbers and can be represented on a number line. They get stuck at adjectives (1/2 a cake) instead of moving onto nouns. This is where we need to get!
Favorite “Make It Stick” Strategy: In her session, Anna talked about the various ways she uses strategies from Make It Stick in her classroom. My favorite strategy she discussed was Calibration. The goal is to “replace a subjective experience or feeling with an objective gauge outside ourselves.” It stems from the “Illusion of Knowing” in that we think we know something, but really we only have a familiarity with it. The book recommends providing more opportunities for students to test themselves, review again, and test again. Quizzes need to be low stakes. I chose this as my favorite, because it ties in nicely with my morning session theme of helping students to fill in gaps.
Favorite Dylan Kane Confession: Dylan Kane‘s keynote speech titled “More than Resources” was one of the most honest and open talks I’ve ever heard. Dylan’s confession that he thought he was doing a good job when he started, but then realized he could be doing much better, really stuck with me. His big lesson learned was: “My intuition isn’t very good, because we see what we want to see.” Dylan was stealing all the great resources from the MTBoS, but realized that great resources do not equal great teaching. He challenged us to think about what will specifically work with our own students; and deliberately practice what we want to get better at. I haven’t come across a video of Dylan’s keynote yet, but you can access his resources here.
Favorite Upcoming Books to Read:
Tracy Zager: Becoming The Math Teacher You Wish You’d Had [Expected: December 2016]
Denis Sheeran: Instant Relevance, Using Today’s Experiences in Tomorrow’s Lesson [Expected: August 2016]
Favorite Song: Greg answered a call from the twitterverse to write a song about the cubic formula. He answered with the most epic sister act version ever… enjoy:
Favorite Student Quote: I know what you’re thinking, there were no students at TMC16 
so how can I have a favorite student quote? Well, in Annie‘s flex session on “Mathematicians: More than just white dudes” she shared this student quote: “Are there any mathematicians like me?” This question led to her creation of the Mathematician’s Project, where she showcases one mathematician every Friday (as long as they aren’t an old, white, rich, dead man) in order to show her students that anyone can be a mathematician. She includes their name, date of birth, ethnicity, background biography, major accomplishments, and math specialty. She even polled her students to see the types of people they wanted to learn about, and had students write their own mathematician bios. The shift in her classroom culture was unmeasurable.
Favorite Icebreaker: Amy taught us an amazing new icebreaker that I can’t way to play with my students when school starts called “Go Ahead – Break the Ice.” Break students into small groups, and give them three minutes to collectively come up with a favorite book, movie and game. Then, have students list all the ways they came to the decisions they did. This leads into a great discussion on group norms and how to work with other people. Some of the decision-making strategies were: “strong arming, time pressure, majority rules, brainstorm, survey, throw out ideas until they stick, pickiest gets the choice, narrow the choices, help those who aren’t speaking up, make sure everyone has a voice, etc…” It was a really fun activity to get to know your group, and have time to talk about group dynamics.
Favorite Day of the Year: Hannah loves celebrating birthdays and she shared some great ideas for celebrating in the classroom. She does birthday shoutouts on the board and buys cheap birthday seat covers. She sees increased positivity in her classroom culture and her students love it. She also uses birthdays to talk about what is and is not a function:
Favorite My Favorite: I can’t really put into words out much Glenn means to me in this community. Watch his talk here, and be as thankful as I am that he didn’t turn around.
Thank you to everyone who helped make my experience at TMC16 an amazing one! Much MTBoS love ❤
And of course, the end of camp song and dance:
For the final week of the Explore MTBoS challenge, I am going to share my lesson on Absolute Value Functions written in piecewise notation.
Learning Target for Students: I will be able to write the equation of an absolute value function using piecewise notation.
At this point, we have spent many days graphing absolute value functions from tables and directly from examining the vertex form equation. We have also discussed the characteristics of absolute value functions.
When students entered the classroom, this warm up problem was posed to them:
I chose this problem as our “throwback” because I wanted students to recall how to find the domain and range for a relation, since this skill would be necessary for today’s lesson involving the domain intervals for the pieces of the functions. After giving students a couple minutes to think about their answer, I switched up the problem so that the third segment had an arrow at the end; this allowed us to talk about how the domain and range would change if the line continued on forever.
At this point, I gave each student his/her own graph (I quickly removed extras once I had taken attendance for each class period. Only one class had an odd number of students, so I partnered up someone who been absent for 2 days with another student.) Here are the 20 that I pre-made:
I asked students to examine their graph, and briefly examine the graphs around them. What is similar about your graphs (linear, slopes, restricted domains)? What is different (slopes, y-intercepts, equations)? Students copied their own graph onto this sheet, in the box labeled: “My Linear Function.”
Students wrote the equation for their line, and determined its domain. Then I told students that right now, they were alone. Their graph was alone. But that somewhere out there, it has a perfect match. I showed students how if they folded the graph at the x-value of the domain interval, they would be able to line it up with another classmate’s graph, to create a new function. I directed students to find their match, and sit with their new partner.
Original graphs:
Post folding:
With perfect match:
Students then shared everything they knew about their original line with their partner, and transferred the new information into the box: “My Partner’s Linear Function.” At this time, I asked students to recall earlier in the year when we studied piecewise linear functions, and how they were able to write the equation of each line segment. We talked about how they had not noticed that an absolute value function could be thought of as a composition of two linear pieces, until this moment. We talked about how easy they found it to write the equation for their individual piece, and it wasn’t much different adding in their partner’s piece. Students combined all the information to create “Our Absolute Value Function” and made observations about the two different forms the equations could be written. Most students recognized the the connection between the y-intercepts from piecewise notation as being the distance from the vertex (h units away from k).
When we tried another problem, I gave out yellow post-its so that students could hide part of the function, and focus on one line at a time. Some students prefer to use colored pencils to highlight the different pieces, so I also encourage this option.
I had every intention of giving students this exit ticket at the end of the period, but time ran away from us and I didn’t want to cut our earlier conversations short.
This is the second time I’ve attempted this activity, and I would do it again next year. I love how student pairs are determined by who is their perfect match, which gets my students to work with someone they usually don’t, and they know it’s completely random. I love how it’s close to Valentine’s Day, so we had a silly time with the idea of the Perfect Graph Match. I love how each student physically started out with only one line, and then did some paper folding to pair them with another. I love how this visual representation really shows the separation of the pieces, and that it’s a shared experience we can refer back to during the rest of the unit. And I love how it starts by activating students’ prior knowledge about lines, and how they could use that information in this new setting.
Would love to hear any feedback about this lesson, and if you try it in your room, please let me know how it goes!
Week 3 of the MTBoS Blogging Initiative corresponds with midterm week at my school. Reviewing for midterms is not a task that I particularly like.
It’s tough to find the balance between refreshing minds or reteaching skills. Based on my review of our last unit test, I wasn’t convinced that my students truly understand the differences between systems of equations and systems of inequalities and their solutions. So I created this basic comparison:
At this point, we had never placed two similar systems graphs side by side in this manner. We reviewed writing the equations and inequalities together, and then I asked students to make a list of all the similarities and differences they noticed. Students were given 2-3 minutes to write this on their own. Here are some of their responses:
I then asked students to share aloud: “What similarities and differences do you notice?” This question was okay. The responses were okay. But something just didn’t feel right. I didn’t want to put these graphs in a specific context; I wanted students to go back to the basics and see the similarities and differences for what they are; but the discussion was flat, and I wanted more energy…
First period ended and I had some time to think about how I would fix this before I taught the lesson again. I remembered the blogging prompt to write about questioning, and specifically, asking better questions. And then I remembered what Chris Luzniak taught us in his Twitter Math Camp session: “Make the question debatable.” It was my own a-ha moment!
I did everything the same the next period, except for one key point. After giving my students individual writing time, I asked:
“What is the BIGGEST similarity you noticed?
What is the BIGGEST difference you noticed?”
That slight change in questioning is all it took to completely change the dynamic between class periods. All of the sudden, I had at least half the class waving hands in the air to share their opinions. The gist of what students were saying was the same between the different periods, but this time the students were more convincing and provided more evidence for their statements. I wondered if this reaction would continue throughout the day, and it did. All of my other classes had the same level of enthusiasm when I asked them for the biggest similarities and biggest differences.
Today’s experience reminded me that one easy way to ask a better question is to make it more debatable. Check out Chris’ Global Math Department Webinar for more strategies on how to do this!
For Week 1 of the Exploring MTBoS blogging initiative I decided to document one day of my life. Although I’m just posting about it right now, this day occurred last Thursday (1/14/16).
5:11 am Alarm goes off. Hit snooze.
5:20 am More snoozing.
5:29 am Get up and get ready. Orange juice is my morning power beverage. Check email/facebook/twitter while eating my cereal. Forgot to pick out an outfit the night before so I waste a good ten minutes staring at my closet. No food in fridge for lunch, that means I’m buying today.
6:20 am Put out trash and leave for work.
6:28 am Arrive at school. Check mailbox and help a substitute teacher find her way.
6:32 am Arrive in classroom. I am amped up for today! We are doing one of my favorite lessons and following it up with a Desmos Activity Builder lesson that I can’t wait to try. I make some last minute edits to the activity, and queue up all the browser tabs I’m going to need for the day.
6:50 am Students start entering the building and my classroom. I immediately get bombarded with demands to know how many jelly beans are in the container. I refuse to tell them.
They know the winner is going to be announced today, but not until 7:25 am I say. Last minute guesses are welcome. Students hang out in homeroom, play board games, and experiment with my Eno board which is now up and running.
7:20 am Homeroom officially begins. Take attendance. Two students absent. They’re going to be sorry they miss today’s lesson.
7:25 am The bell rings to go to first period, and without speaking, I simply go up to the white board and write down the correct number of jelly beans: 1472. Students from the other two homerooms next door come in to see the answer. There is yelling; they are excited! They still don’t know why we are playing guessing games.
7:29 am This is the 1st of 5 times I am going to do this lesson today. I teach five sections of STEM Honors Algebra 1 to 9th graders. It will get better as the day goes on, as I observe and adapt to how my early students respond to it. Today is the first day of our unit on Absolute Value Functions. The beginning of the lesson can be found here, minus the project part (they’ll get this later). After we dissect the jelly bean situation, I show them this Estimation 180 problem, and we guess again. I take predictions for the shape of the graph and this time they think they have it all figured it out. The shape will be a V, but skinnier! No, wider! No, a check mark! Because there are fewer under-guessing options! We are on to something:
At this point, they are ready to explore and play around in Desmos on their own/with a partner. This was my first attempt at duplicating someone else’s Activity Builder and using it in my room. Overall, I was pleased with how it went, but would definitely make adjustments for the future. Some students finished early. I wish there were more challenges, such as what happens when you throw in negative signs. I tried to throw this question in as the day went on, but it didn’t work because I had already made a class code. I also wish I had a question about the absolute value vertex form equation with h and k. So that students could be more specific when they described how the function transforms. Here are some of their descriptions:
We ran out of time at the end of class to debrief (my fault), and we don’t have class again until Wednesday (1/20), so to be continued!
8:17 am Period A ends. 4 minutes passing time. Run to bathroom. Head to STEM colleague’s room for our common planning period. Our big Winter STEM Expo is tomorrow, so we are doing last minute prep work. Edit presentation rubrics and chat with 10th grade team about last minute details.
9:12 am Period C begins. Algebra 1 take 2.
10:05 am Period D begins. Algebra 1 take 3. Four students actually leap out of their seats when the number of sweethearts in revealed.
10:53 am Lunch! Rush to teacher’s cafeteria and order my turkey wrap. Ask for cookies too. Get a slight look of disapproval when I reject the offers for pickles, apples or carrots as an additional side. No, just cookies please. I already have lettuce and tomato in my wrap. Eat lunch with math colleagues. Discuss our losing the powerball last night.
11:22 am Period E begins. Algebra 1 take 4. By this time of the day, we have some cheaters. Students from earlier have given away the answer, but I weasle out some confessions and we move on with the activity.
12:21 pm Period F begins. Algebra 1 take 5.
1:08 pm Period G begins. My prep. Finally. It’s been a great day but I’m exhausted. Today’s lesson was a high energy one. I always try to show the same enthusiasm with my last class as the first, but sometimes it can be difficult. Check personal email. Finish editing STEM rubrics. Take care of emails. Chat with STEM Director.
1:55 pm School day ends. Go to advisor meeting about upcoming school-wide dance. Return to classroom. Approximately 40 students have elected to stay after school to make trifold posters and last-minute changes to their STEM projects. My coworker has been supervising all of them while I was at the meeting. Spend afternoon giving advice on projects and printing, printing, printing for them.
3:55 pm Write passes for the late bus and start kicking kids out. They are nervous but ready for tomorrow. Here’s a video released after the Expo!
4:15 pm Say good-bye to final students. Clean classroom.
4:30 pm Pack up and head out. Run errands. Sit on couch. Breathe. Check email/facebook/twitter. Make dinner. Have plenty of time to write this blog post… but don’t do it. Take the night off. Watch an episode of the Blacklist (okay, okay, three episodes).
10:00 pm Bedtime.
If you want to read about other past days, check out these posts:
Take 1 – November 15th, 2012
Take 2 – November 18th, 2013
Although I just returned “home” from a California adventure that included visits to Santa Cruz, Big Sur, Anaheim, Los Angeles and Claremont… I actually felt like I was home while attending this year’s Twitter Math Camp (TMC). It has become my must-attend event of the summer, and I plan the rest of my break around it. Doing math and talking about math with such passionate and inspiring educators propels me into the new school year on high speed. Next year’s camp will be held at Augsburg College in Minneapolis from July 16-19, 2016 and you can bet I’ll do anything in my power to attend.
It always take a bit of time to wind down from TMC; it’s information overload in the best way possible. But it’s unreasonable to think that I will return to my classroom in 5 weeks and implement everything I learned. These are my largest takeaways from TMC, and “my favorite” memories/quotes/highlights, that I wish to carry with me during the year.
Favorite Disney Picture(s): Pre-TMC, I spent a whirlwind 16 hours at Disneyland and California Adventure Park with Casey, Connie, Nicole, and Meg. We mapped our course through the parks to maximize the number of rides/attractions we could see in one day. And of course, when we weren’t tweeting while waiting in line, we talked about teaching math.
Favorite Price is Right Group: It’s a very long process of signing waivers, getting nametags, and being interviewed by producers for a potential spot on the show, but in the end it was worth it to check this item off my bucket list. We cheered and yelled prices at the contestants, and you can watch how it all played out on November 2nd!
Favorite Morning Session: I made the decision to attend Elizabeth and Chris‘ morning session on “Creating a Culture of Exploratory Talk” and it was the perfect decision for me. I have been attempting to hold better classroom discussions, but this session provided me with specific strategies/structures to use with my students to get them to have richer conversations. I have selected Elizabeth’s Talking Points Activity as my #1TMCthing, so I will be writing another blog post about that in the next couple weeks. In the meantime, here is our morning session wiki page, and here is one of Elizabeth’s posts about Talking Points.
Favorite Debating Activity: Table Debates. During the exploratory talk session, Chris shared his numerous activities for bringing debate into the math classroom. He shares many of his strategies on his website. An argument is comprised of two parts: a claim and a warrant. You can turn almost any statement into a debateable question by adding words such as: best/worst, always/sometimes/never, most, weirdest, biggest/smallest, etc. When students are table debating, they are given a problem or situtation, and two possible opinions on the topic. They must state their argument for the opinion on their side of the table. This is my favorite strategy because students might not always agree with the opinion they are given. However, they need to figure out a strong argument to support that opinion. I feel like many of my questions can be easily rewritten in this format, so it shouldn’t be too difficult to implement this activity this year.
Favorite Must-Watch TED Talk: In Fawn’s keynote, she shared a quote from Rita Pierson’s TED Talk: “Kids don’t learn from people they don’t like.” I’ve come across this TED talk before, but never actually watched it… until now. The quote nicely highlights Fawn’s recommendations for good teaching: fast (in terms of returning emails, feedback, etc); fair, friendly, firm, and funny.
Favorite SMP Posters: During his talking on Teaching the 8 Practices, Chris shared his SMP posters and had us analyze them. Chris boils down all the CCSS into two words: Thinking and Communicating. The posters all have the same format and are designed specifically for our students. My favorite part of each poster are the questions in the bottom left corner. These are questions that not only can our students ask themselves to determine which practice they are doing, but we as teachers can ask them as we develop lessons and tasks.
Favorite Jumping Picture: Taking jumping pictures while traveling is kind of my thing, and I found a jumping partner in Connie. She shared my general enthusiasm for just having the best time ever no matter where we were, and it resulted in epic pictures like this one (the burgers were great too!)
Favorite Math Mistakes Activity: Andrew’s session on Math Mistakes and Error Analysis provided me with a great opportunity to analyze the value of mistakes and how we can use them to help our students learn. My favorite activity of Andrew’s is when he gives students a handout like this:
Every problem has a mistake. Every problem. Students must analyze the structure of the problem to build their conceptual understanding, based on what is currently incorrect. Students must fix the mistakes once identified and justify their reasoning. Read more about this activity on Andrew’s blog.
Favorite Good Teacher vs. Great Teacher Distinguishing Feature: Ilana Horn’s keynote titled “Growing Our Own Practice” was inspiring and informative. Among sharing many discoveries found during her studies, she shared three key features that differentiate between the good teachers and great teachers she observed: Teacher Agency, Empathetic Reasoning, and Ecological Thinking. My favorite among these is Teacher Agency. Ilana emphasized that great teachers state their problems as actionable items. The example she shared is how a teacher views the problem of a student finishing his/her work early. A great teacher does not discuss this problem as having fast vs. slow kids. A great teacher discusses this “problem” in terms of the task itself, and the value of finding group-worthy tasks that engage all levels of learners and include extension possibilities. As I start a new school year with another new principal, I want to remember this mindset: how can we take a problem and turn it into an action item?
Favorite New Desmos Activity: This is actually a trick. I can’t tell you about my new favorite Desmos activity because it hasn’t been released yet. But Eli gave the TMC crowd a sneak peek, and let me tell you, it’s amazing. It will change your teaching life. Stay tuned, it should be released sometime next week.
Favorite Data Table: In his session on Vertical Non-Permanent Surfaces, Alex shared this data table from Peter Liljedahl’s research:
Hopefully this convinces you to head to your nearest home improvement store and purchase some shower board panels if you haven’t already!
Favorite Debriefing Partner: At the end of every day, Rachel and I would meet up for the walk/drive back to the hotel, and immediately begin sharing everything that happened during the day. It was one of the times of each day that I treasured most. We needed that time together to gather our thoughts and really process everything we learned/experienced. Since we didn’t end up attending a single session together, we were able to double our information intake. Thank you for being the perfect roommate, Rachel!
Favorite Piano Bar Song: Sweet Caroline. John requested it, someone else vetoed it, more money was thrown into the pot, and then we had an epic singing contest between both sides of the room. We owe a huge number of thanks to PianoPiano in Claremont for entertaining us each night.
My Favorite My Favorite: Matt shared his strategy of using music cues to help students “become self-directed learners.” I won’t go too in depth because Matt graciously wrote a very extensive blog post about it. Within his post, you can find a google folder with all the music he uses, and a list of the cues in which he uses music. I would like to try implementing 2 or 3 of these this year, but I am definitely overwhelmed trying to figure out the technology to make this happen in my classroom easily. If I can get it working, I know I want a music cue for: “Take out your chromebook, go to student desmos, type in the class code.”
Favorite Quotes:
Thank you to the TMC volunteer planning committee! This special conference would not exist without all your hard work, and we are all better teachers because of it!
After attending Twitter Math Camp 2014 in Jenks, OK, I immediately flew to Hilton Head where I joined my family on vacation. While lounging by the pool, I had a lot of time to reflect on this year’s camp. It still ranks as the best professional development experience I have ever had, but I often struggle to find ways to articulate why TMC is so special. Prior to attending, whenever I told someone I was going to a Twitter Math Camp, the person laughed and made a joke about nerdy math teachers.
So I changed my story: “Me: I’m going to a math conference. Them: Oh cool, hope you learn a lot.” And I hated myself for those interactions. Why does everyone else think a math conference is acceptable to attend, even cool, when I (and I’m sure most TMC attendees would agree) that Twitter Math Camp is by far the coolest “conference” a math teacher will ever attend? But it’s because they don’t understand. I know that I shouldn’t take the easy way out by changing my story, and I’ve promised myself to never do that again. I want to help people (especially math teachers!) understand and appreciate what everyone in the MathTwitterBlogosphere (MTBoS) has created together. The comparison to an actual overnight summer camp might actually help the most. At TMC, you attend sessions of interest to you, listen to inspiring speakers, eat every single meal with your fellow campers, play games (some math some not) during free time, explore your surroundings, and stay up way past your bedtime. After four days, you are exhausted; you are inspired; you are passionate; you are reflecting; you are questioning; you are bonded. Luckily, the conversations that begin at TMC don’t have to end at TMC. Throughout the year, we will continue chatting on twitter, blog posts, text messages; so if you’re out there lurking, jump in and join the conversation, then join us at Harvey Mudd College next summer.
In the same spirit as last year, I will recap some of TMC as a series of “My Favorites” (in no particular order).
Favorite Airport Reading: Powerful Problem Solving by Max Ray. I wanted to read this book last summer but never got around to it. I’m now four chapters in and devouring it. Max writes about problem solving strategies directly connected with the standards for mathematical practice. He shares numerous activities you can do with your students tomorrow and shares actual samples of student work/classroom conversations.
Favorite Standard for Mathematical Practice: In Steve Leinwand’s keynote, Shifting Our Mindsets and Our Actions from Remembering HOW to Understanding WHY, he referred to SMP #3 as the “Trojan Horse” and the “Most important 9 words in the CCSS.” I would have to agree with Steve on this one. SMP #3 = Construct viable arguments and critique the reasoning of others. Students must be able to communicate their findings and respond to the conclusions of others. This is a practice that must be taught explicitly and will be one of my goals for this school year. I plan on echoing Steve, and demanding that students “CONVINCE ME” of their conclusions.
Favorite Game: Andy Pethan introduced me to the game, Q-bitz, during Wednesday’s game night. There are three different challenges where you have to recreate patterns out of cubes faster than your competitors. As someone who loves math and wants to be on Survivor one day, this game is right up my ally.
Source: Amazon
Favorite Opening Day Activity: John Mahlstedt tells his students how awesome he is on the first day of school by sharing facts/pictures about himself. It’s a way for students to learn that you’re not only a teacher, but a human too, and a fun one. I usually have students try the matching activity below, but normally I simply share the answers at the end of class. This year, I’m going to enhance this activity with John’s suggestion of making a slideshow with pictures to show my students rather than just telling them about me.
Favorite Lunchtime Adventure: During lunch one day, a group of us found Gameday Popcorn on main street and had a great time testing all the flavors.
Favorite Morning Session: Writing Real World Lessons with Mathalicious. Karim and Matt led a fantastic session on the creation process of Mathalicious lessons: “The narrative determines the standards, not vice-versa.” This was so interesting to me because I feel that most of the time, when my colleagues and I are discussing an upcoming topic/unit, we are doing the vice-versa. Ex. Tomorrow we have to teach solving systems of equations by elimination… how should we do this? Mathalicious lessons are conversations about a really interesting topic that needs math to answer the question. That’s why the lessons are so authentic and engaging. Our group spent time proposing thought-provoking questions, discussing their authenticity, and attempting to write a sample lesson out of our ideas. The experience was extremely rewarding and although it’s time consuming, I hope to bring this practice back to my own planning time.
Favorite Cupcake Locale: Smallcakes. Delicious.
Favorite Formative Assessment Explanation: John Scammell shared more than 60 formative assessment strategies that you can easily implement in your classroom. He kindly shared all of them here, but it’s how he described formative assessment that actually stuck with me the most. John said that formative assessment must be risk free. If you put a grade on it, or enter it into an online grading system, it’s no longer risk free to a student or parent. Formative assessment should be all about providing feedback. One easy suggestion is to use a highlighter to mark the last spot a student’s work was right. Another is to mark a problem with a + (better than previous work), – (worse than previous work), or = (equal to previous work) sign. And my favorite method he shared, was to actually classify a student’s error. Many students get frustrated when something is marked wrong, and they immediately think they don’t understand anything. It’s important to differentiate between whether an error is a conceptual misunderstanding or calculation mistake.
Favorite Ice Breaker: Bob Lochel discussed Meaningful Adjacencies as related to the 9/11 Memorial in NY and how a similar connection activity with tv shows can be used in your classroom. He provides a very thorough explanation on his blog post.
Favorite Phone Holder: Glenn Waddell taught us an ingenious way to use a smartphone as a video camera in your classroom. 1) Make a vertical slit in the bottom of a paper coffee cup 2) Insert smartphone 3) Record
Favorite Dan Meyer Quote: “I want to profit off what you know.” – Dan Meyer
In Dan’s keynote address, he shared tons of data on tweeting and blogging math teachers. He’s interested because he knows that great ideas are being shared, but no one knows about them. He wants to know about them. And so do I. When you post/tweet your great ideas, my students get to benefit from them. It’s okay to be selfish here, because the more students that benefit, the better it is.
Favorite Dan Meyer Slide: Dan shared a graph comparing a blogger’s velocity (posts per week) to number of subscribers. He said he’s interested in the individuals in quadrant 2, those who post infrequently, but have many readers. After examining his data, it appears that my blog falls in quadrant 2. I post infrequently because I’m afraid and therefore selective. Afraid that what I’m offering won’t be as good as what other people are offering. So I’m choosy. I like to post activities after I’ve done them so I know if they worked or not, and so I can edit them before posting. I try to include any part of the activity that is downloadable, so you can take it and use it tomorrow. I post when I want more than the 100 students on my roster to benefit from something fun. Maybe this is why some of you are following my blog, if you have other insights, please let me know. But in the meantime, thank you for reading!
Favorite Desmos Update: In his keynote, Eli Luberoff assured us that Desmos would be free forever. This is incredible news. Desmos has created API partnerships and has financial security to ensure that we will never have to pay to use this online graphing calculator. All teachers and students can benefit from this resource, so if you haven’t played with it yet, stop reading and go to Desmos now. Also, be sure to check out this new digital math lesson from Dan Meyer, Christopher Danielson, and Desmos: Central Park (and the other four lessons on Teacher Desmos).
Favorite Roommate: Rachel and I bonded over being teachers at the high schools we went to, Algebra 1, True Detective, Richard Linklater films, quiet time, beer choices, traveling and so much more. Check out her blog here and let’s convince her to post more this year.
Favorite App: Pam Wilson introduced TMC to Plickers and our classrooms will never be the same. Each student responds to a multiple choice question by holding up a unique bar code. The teacher uses a smartphone to scan the room and the responses are graphed/recorded automatically. I see myself using this as a quick formative assessment at the end of class.
Source: @approx_normal
Favorite BBQ: Elmer’s with this fun crew. Thank you Jason for treating us!
Favorite 3D Printing Resources: John Stevens and I talked about using 3D printers in the math classroom. We are going to have several 3D printers at my school next year and I want to do something awesome with them. If you have any advice, please share with John and me!
Favorite Book Recommendation – Justin Lanier plugged the books How Children Learn and How Children Fail by John Holt. Justin’s takeaways: 1) Look Around 2) Teach Crazy 3) Trust Children.
I know there’s a lot of TMC awesome-ness that has been left out of this post, but I could never write about everything that I learned, because it would take forever. I owe a huge shout-out to all the TMC14 organizers for making this happen and providing us with this incredible experience. Thank you to everyone I met, and I hope to see you all again next year 🙂
Not sure about you, but I’m pretty glad March is over. Nothing terribly awful happened, but I, and most of my school, seemed to be in a funk. Our normal schedule was changed constantly due to MCAS tests and class scheduling meetings for next year, and we didn’t have a regular day of classes for most of the month. Everything just seemed to be harder than it should have been. Therefore, I wasn’t really tweeting, and definitely not blogging. When I lurk on Twitter, I favorite tweets and then immediately forget about them. I decided it would be worth it to see what hidden gems I have recently favorited. Here are a few standouts:
1) Graphtv: The site provides you with a graph of the ratings for your favorite tv shows based on episode ratings from IMDB. I think my students would love this site because they can choose any show that is interesting to them. This would be perfect during our Linear unit in Algebra 1, so I’ll have to wait until next October/November to put it to good use.
Here’s my favorite show, Homeland:
2) 3-Act Handout: This is definitely going to be handy when doing one of Dan Meyer’s Three Act Lessons, wish I had come across this form a long time ago!
3) Math Munch writes about 2048: My students and I are obsessed with the game 2048. We challenge each other to games during homeroom in the morning, and I just knew they would love to hear more about the game. Students who have already beaten 2048 were psyched to find new versions to play.
4) Why Am I Teaching This?: @Approx_normal started this site as a way for teachers to connect regarding those frustrating topics we teach but sometimes aren’t sure why. I hope educators keep contributing to it because it has the potential to be extremely valuable.
5) Robert Kaplinsky’s Problem Based Search Engine: The search engine allows you to quickly find awesome problem-based lessons and is a must to have bookmarked for all math teachers.
https://twitter.com/emergentmath/status/429069163626110976
Last year I wrote about a day in my life for the #DITLife Challenge and I was psyched to read that this week’s Explore #MTBoS Week 7 Challenge was to do it again. So here goes…
5:11 am Real alarm goes off. Hit snooze.
5:15 am Hit snooze on phone alarm.
5:25 am Get out of bed and get ready. Drink orange juice and eat Honey Bunches of Oats with Almonds (same breakfast every single day) while checking email/facebook/twitter.
6:16 am Drive to school.
6:24 am Arrive at school (8th car in parking lot). Stop by main office to pick up mail and write a morning announcement about the after school Student Council meeting. Put lunch in math department fridge.
6:32 am Arrive at my classroom. Smile because I stayed later than I usually do on Friday and set it up like this:
Having my stations lab already set up for first period, and remembering that I had already updated the objectives/agenda for the day, made me so happy. It’s the little things 🙂 I logged into my computer and chatted with a STEM team colleague about our weekends.
7:00 am Met with Principal regarding a class officer issue. Solution reached.
7:20 am Took homeroom attendance. Ran to 4 other homerooms to remind students going on a field trip tomorrow to bring in their permission slips and show up on time.
7:35 am Period A begins (Algebra 1). Today was a block day so we had class for 85 minutes, normally our periods are 48 minutes. We reviewed the homework assignment, a MCAS open response question, by having the students correct a partner’s paper. Then, we did this W-R-I-T-I-N-G Equations Stations Lab. It went really well, and many students finished it more quickly than I thought they would. So I directed them to Visual Patterns… Thanks, Fawn!
9:05 am Period C begins (Algebra 2). We started class with a mini quiz on Functions (domain, range, parent function transformations). Then, we took notes on the characteristics of absolute value functions and practiced with some links. Class went just OK. I don’t love starting with a quiz and then having students take notes, but I didn’t see a way around it today.
10:30 am Lunchtime. I eat with the math department, it’s a great time to catch up with everyone.
11:00 am Period E begins (STEM Common Planning Time). We review/choose dates for our Term 2 project and update our project guidelines document. We also plan tomorrow’s project work period and finalize details for an 8th grade visit to the high school.
11:50 am Back at my desk. I respond to a bunch of emails and make a few copies. I don’t think I used my prep time wisely today… I can’t really think of too much that I accomplished…
12:30 pm Period G begins (Algebra 1). Same lesson as Period A, but the lab takes longer and no one gets a chance to play with Visual Patterns.
1:55 pm School ends. Student Council meeting begins. We run through some normal agenda items and then write letters to soldiers (a school wide service project).
2:45 pm Back at my desk. Respond to a few more emails. Received 32 throughout the day and sent 15. Pack up stuff.
3:05 pm Drive to nearby school for Administrative Internship class. Today’s topic is “What to Expect When You Move Into Administration.” I don’t know when in my future I’ll move into administration, but I had an opportunity to be part of a licensure program this fall and took advantage of it. It was great to get the prospective from educators who had gone through the same process.
5:45 pm Leave class and drive to Burlington Coat Factory. I needed a new winter coat and I found just the perfect one! Black, knee-length, belted, and with a detachable hood.
6:30 pm Drive to gym for Zumba class. Zumba! Drive home.
8:30 pm Sit in favorite spot on couch. Prepare to watch the Patriots game. Write this blog post.
I fired off the above tweet to kick off the Explore #MTBoS Week 2 Challenge. It was great fun to discover some Swedish fish lovers I was already following, and some new #MTBoS tweeps who are also Patriots fans.
But for this week’s challenge, I am going to write about how my tweeps came through for me a few weeks ago! We use TI graphing calculators on an almost daily basis in my Honors Algebra 1 class. For most of my students, this is the first time they have used a graphing calculator. On September 9th, I decided that the perfect activity for my next lesson, would be to do a graphing calculator scavenger hunt. The thought of creating this from scratch seemed daunting with everything else I had going on that day, so I tweeted the following:
Here are some of the replies I received:
https://twitter.com/jensilvermath/status/377083964864733184
Rachel emailed me her document, which I edited and turned into a scavenger hunt introduction to the graphing calculators. I’ve used Jen’s resources to help students with additional graphing calculator tasks, and found so many great links from the MathForumBooth. I am so thankful for my twitter friends!
Here is the updated document. Please comment and let me know if there are any additional scavenger hunt tasks you think should be included in next year’s version!
Fun missions & prompts, Always ready! Blogging initiation starts Jan 2017
Education and Innovation
Reflections on teaching math and striving to do better each day than the last
Reflections on teaching math and striving to do better each day than the last
Reflections on teaching math and striving to do better each day than the last
The mathematics I encounter in classrooms
Teachers Working Together to make our Struggles Productive
Are you pondering what I'm pondering?
Reflections on teaching math and striving to do better each day than the last
Reflections on teaching math and striving to do better each day than the last
Teach it. Learn it. Live it.
Reflections on teaching math and striving to do better each day than the last
Reflections on teaching math and striving to do better each day than the last
If the only tool you have is a hammer, you tend to see every problem as a nail. - Abraham Maslow
Reflections on teaching math and striving to do better each day than the last
Reflections on teaching math and striving to do better each day than the last
Running, Cooking, Life
Reflections on teaching math and striving to do better each day than the last
Reflections on teaching math and striving to do better each day than the last
Integrating Technology and Mathematics
Reflections on teaching math and striving to do better each day than the last
I have no idea why I picked this blog name, but there's no turning back now
Reflections on teaching math and striving to do better each day than the last
Growing Exponentially 