I have been on a journey to educate myself on the 8 Mathematical Language Routines (MLRs). While they were designed with Multilanguage Learners in mind, I find that they are just good teaching. So what are they?
Stronger & clearer each time
Collect & display
Clarify, critique, and correct
Compare & Connect
So what does each one entail? Well, rather than sit and explain, I’d rather give you a resource that does a far better job breaking it down. It’s also one of my favorite resources.
Part of my deep dive allowed me to align Math EduProtocols and these MLR’s. Doing this has my mind working on how to incorporate more MLR’s within Math EduProtocols.
With all this in mind, I have begun to curate some resources for teachers. I break down each MLR and give links to activities. It’s not a comprehensive list, so I will continue to add to it as I find more. If you have something that should be added to the document, let me know!
I have the honor to go into a 3rd-grade classroom in my district. Each time I am in there, the teacher has an inspirational quote posted. This isn’t your everyday quote. No, this teacher organically connects these quotes to social-emotional learning (SEL).
As you can see, the teacher is helping the students to have a healthy mindset about previously made choices. Not only does the teacher write these words, but demonstrates them to the students daily. The students are also reminded that mistakes are okay but in an authentic voice. It’s one thing to tell students, but it’s another thing to experience the compassion and encouragement to be gentle with oneself.
I have learned so much from this teacher. And hopefully, you learned a thing or two as well.
This post will be slightly different from most, but related to teaching nonetheless. Back in September 2022, a friend reminded me of a promise I made: I would run the Big Sur International 11-miler. In case you are wondering, yes, I run regularly. HOWEVER, I am slow and generally only run 5K races. I run most mornings, but no more than 2.5 miles. Getting up any earlier is way too difficult. So, being a person of my word, I signed up for the race. The race is held in April each year.
After signing up for it, in September, I vowed I would train to run this 11-mile race. I started off strong with a training routine. Then I purchased a new treadmill. This amped up my training. Along with the new treadmill, in early December, I started using a new app that accompanied this treadmill.
I realized I was a bit behind in training, but still had plenty of time to make it up. I was doing well until I wasn’t. You see, the time from January to mid-April just sort of flew by. I was still running, but not increasing my distance. Then, it was a week before the run and time had run out. So by this time, I was a bit worried. My running partner had told me since I signed up that we would mostly walk. Maybe that’s why I didn’t have a sense of urgency.
The night before, we went up to Monterey to easily catch the bus in the morning. While waiting for the race to start we decided to run all downhill grades. And that is exactly what we did. I’m not going to lie; by the time I got to mile 9, I was proud of how well I was doing and in a little pain. Yeah, I should have done a bit more training. Finally, near the end, I realized I could finish in under 3 hours. – Go ahead and laugh here; my dad did. – Anyway, I was very proud of myself, and we beat my running partner’s time by over 10 min.
My point behind all this is that I never, in a million years, thought I’d start running let alone do a (nearly) half marathon. And as I crossed the finish line, I thought to myself, “I really can accomplish the things that seem undoable. Mile by mile, step by step, no matter how difficult or daunting a task may seem, I can do it”
I know that there are mixed feelings regarding creating California Missions. I’m going to focus on the positive. I work with a fourth-grade class in my district. The teacher went “old school’, her words, not mine. She had the students create physical models.
Now before anyone is concerned about equity, I assure you all student creations were created equally. How? Students created them in class with teacher-provided materials. She provided the cardboard, basic dimensions, paint, rulers, and scissors, while she hot-glued the walls together. Some students did bring in some extra decorations and happily shared them with others. Check out some of their work
Clearly, these were all student created. In order to get ready for this project, they did their research. The students began by learning about the colonization of California and the role Missions played in changing it. Then each student researched a mission: its history, founder, indigenous people, and its current use. They then produced a slideshow to present to the class. There was a lot of learning that occurred before this culminating activity.
All in all, I was blown away by their work. They did an amazing job and each student was proud of themself.
The opinion heard around the internet. On Meghan Trainor’s podcast, Workin’ on It, she spoke with Trisha Paytas. She and her guest began speaking about schools. Megan stated that she was homeschooling her children. They also brought up issues like school shootings. Then, things took a turn. Trisha began talking about bullying. This led to teachers bullying kids. Which led to Meghan saying, “Fuck teachers, dude.” Without hesitation, without stuttering, and with her whole chest.
Needless to say, this didn’t sit well with teachers. Look, we know that not every teacher is amazing. We recognize that we are human and have bad days. We acknowledge we have made mistakes. We also apologize, stand in front of bullets, buy food and supplies for our students. To be so easily and quickly dismissed was hurtful. What’s even more hurtful are the hundreds of people who also feel this way about teachers.
There was an apology. After the backlash, after the podcast was edited, after the podcast went through production. But an apology was given.
Why is it so easy to trash teachers? Why are teachers expected to be superhuman? Why is it encouraged to give students grace, which we should, but not extend that same grace to teachers? Why am I now expected to understand that being shot while teaching is a ‘hazard of the job’? ⬅️That one is absurd!
I know the answer to most of these questions is politically motivated. But can we PLEASE leave politics out this? We are all doing our best.
Back to Meghan
We appreciate your apology. You say that you weren’t talking about all teachers, but felt good enough with what you said to keep it in the published podcast. You say you respect us. You say you fight for teachers. How? How do you fight for us? I’ll admit that you may and I just haven’t seen the reciepts. I’m open to seeing what you have done. Will you now take up inititives to fight for our, and our students’, safety? Many times, I have told my students, “If you are really sorry, your behavior will change.” Many teachers will be watching to see if your behavior changes, Meghan.
It’s that time of year, Test Prep time. Which makes me think about using EduProtocols for Test Prep. One great one that really promotes deeper thinking and understanding is Nacho Problem. This was created by Ligia Ayala-Rodriguez. It’s a fun way to do error analysis with your students. I have done this with students as young as 7.
One of the advantages is that you begin by telling the students the answer is wrong. This seemingly takes the pressure off. I like to have the students talk it out the first few times. I guide them along the way to help set the expectations. Just like in an ‘Analyze the Error’ on the test, students are expected to express their thoughts in writing. This can present an additional challenge if they haven’t exercised this skill. I’m not saying we should do this solely to prepare for the state test; the benefits of students being able to do this go far beyond that idea.
How to Get Started
As a class, they are presented with a Nacho Problem. We read and analyzed the problem together; starting with “What do you notice?” and “What do you wonder?” I explicitly tell them the answer is wrong and that we must find where I went wrong. I have found that looking at the question and working out the problem allows us to focus on the process (that the problem is asking us to solve) rather than the arduous task of finding a mistake. Once we work it out together, and later independently, students can then go back and compare their process with the original (wrong) process. It makes it more obvious where the original problem solver went wrong.
The written explanation can be the most difficult part. When I started doing problems like this, students would explain, in an addition problem, “I started in the ones and added 8+7. I left the 5 in the one’s place and regrouped the 1.” While technically that is true and we as teachers understand, that’s not showing an understanding. That is why practicing the structure of Claim, Evidence, and Reasoning (CER) is so important.
Claim: Ms. N. did not draw a quadrilateral. Evidence: The student example with explanation. Reasoning: Definition of a polygon and Ms. N’s error.
One of the easiest ways to collect incorrect problems is from your class. Whether you use exit tickets or collect information from the day’s lesson, you have a plethora of options. When using student errors, it’s advisable to use a common mistake by many students. Done early, this can correct any misconceptions before they become habits. Ligia suggests using mathmistakes.org
Teachers and students alike enjoy this math EduProtocol. Students find it ‘fun’ to find the mistakes. Teachers report that it takes little time to begin implementing in their classes. Doing this a few times a week can really improve understanding. Let’s face it, students LOVE to point out teachers’ mistakes.
If you use this, I would love to hear how it went. What changes did you make? How have your students improved with error analysis?
Recently I had a teacher ask me about some review games. Bingo is always a hit so I went on the search for a 3rd-grade Geometry Bingo game. Sadly, I couldn’t find what I wanted. Which then led to a search for Bingo card creators. I was not about to sit and recreate 25 Bingo cards. I like to use my time a bit more efficiently. And that’s when I found it! My Free Bingo Cards
This awesome sight creates simple Bingo Cards. They have several ready-to-go, broken down by categories. There is also the option to create your own. I opted to create my own. The process was simple. I plugged in all the words the students were to review. I then pressed one button for the program to create 30 unique Bingo cards. I did play around with it to see if I could insert images via copy/paste. No such luck. That was okay; I had a backup plan. The program also created a sheet for me to track which words were used and calling cards. I opted NOT to use the calling cards.
What did I use instead of the calling cards?
Instead of the calling cards I created a wheel on Wheel of Names. This was part of my backup plan: I used images. I could have also opted for the definitions, but I felt the images were more engaging and less repeating. This game was a big hit!
If you’re a 3rd-grade teacher and would like to play this here are the cards and here is the wheel.
If you’ve never used Wheel of Names before, you’re going to love it! There’s no need to guess where the spinner landed. The program tells you which one. Then you have the option to remove the selected item from the wheel to avoid mishaps.
This summer, I will be presenting at two academies for EduProtocols. My sessions will have a math emphasis; shocking, I know. So this past week when I was asked to come up with titles and descriptions, I struggled. I wasn’t feeling it. Luckily, a friend called before I could toil for too long. I relayed to her my lack of motivation at the time, and she came up with some catchy titles.
🍸The Mixology of MathReps – MathReps
Wheel Of Word Problems – Word Problems with Random Emoji
Playing with Parts – 8 p*ARTS meets word problems
🌶️🌶️ Spicey Solutions to a Bland Curriculum – Nacho Problem
👩🏽🍳Chef’s Kiss – Sous Chef
Frayas for Ya Playas – Frayer and, honestly, my favorite title
🦹🏻♂️Math is a Villain: Comic Strip Math
Then it was time to get started on the descriptions. This is where I got inspired. I doubled down on the titles and all descriptions fit that theme. I mean, check out this description for Comic Strip Math:
In a world full of villains, the fine citizens of Mathemagicalville are up against the most evil, vile, sinister one around. Master of Dark is relentless in the pursuit of conquering the city. It is up to you, the superhero, to prove Master of Dark wrong and find the errors that were made. You create the comic, find errors, explain processes, and become the hero the city needs.
Yes, Mathemagicalville is a mouthful, but the names I wanted were all taken, and so I had to become creative. When I was creating this description, I felt that I had to be very careful with my wording. The character ‘Master of Dark’ was created by my 5th-grade class at the time, around 2019. The character was created to be gender-neutral. However, in today’s political climate, with hundreds of anti-trans laws being introduced throughout the country, I want to be sensitive to this. In 2019, the intent was to NOT represent one group as ‘evil’ or ‘bad’ but to keep the focus on math while empowering ALL the students in my classroom. The empowerment came from not having the gender stereotypes that boys are better at math than girls, and by taking the gender out of character seemed like a good solution at the time. However, as I began writing the description, I tried avoiding any pronouns. I don’t want to put a negative focus on any group.
I may be overthinking all this, and I may not be. However, in cases like this, I would rather err on the side of caution. So what do you think? Am I overthinking this? Does this character need to be revisited? Do I simply avoid using any pronouns as it’s not critical to the purpose of thinking critically about math? I would love to hear from everyone, especially those in marginalized communities.
Okay, that took a serious turn. NOW if you’d like to join me in Laguna Beach or Notre Dame this summer, here’s more information. I can’t guarantee that all seven sessions will be presented at both, but I can say that MathReps and Comic Strip Math will be presented at both – if I have a say.
Google Lens may have saved the day after a series of unfortunate events. Or at least made a less-than-desirable day okay. Let me set the scene for you: it’s 4 am, all lights are off, and a sleepy teacher walks into her bathroom and steps on the ‘squishy’ rug. Said rug should NOT be squishy. This can only mean 1 of 2 things. Neither is good. Option 1: one of the dogs peed. Unlikely, as this is out of the norm for them, and it would have been A LOT of urine. Option 2: I have a leak. Alas, after opening the cupboard door under the sink, I was presented with Option 2. Oh, joy.
Fast forward to me calling the plumber after school today, he tells me that he may or may not be able to fix it depending on the problem. We agreed he would return tomorrow to fix it (or not). Side note: it was close to 6 pm and not an emergency. Fair enough, he’d been working all day. This led to a discussion on what to do if it can’t be fixed. Seeing as I like the faucet and it matches the others in the bathroom, I have little choice but to find another one. It’s a unique waterfall faucet. So a Google Search will take a while.
Enter Google Lens! What is Google Lens? It is an app that allows you to point your camera at something, like a waterfall faucet for a bathroom, and does a Google image search for that thing! So being the big brain thinker that I am, I used it to locate where it could be purchased. And Bingo! I now have the name and places where I can buy a replacement.
Google Lens can be found using your Google App (iPhone), and tap the camera icon in the search bar. On Android, open the camera app and tap the Lens icon (pictured above). There are several options, including translate, shopping, and search.
Recently I was in a 3rd-grade classroom doing a geometry MathRep. As I was walking around I noticed that one student wasn’t just writing the answer using just numbers, he was also putting it in word form. Needless to say, I thought this was great! Which then led to a discussion on different ways we could represent the answer. We talked about using tally marks, equations, and shapes.
I then went into another class and did the same lesson. Well, another student leveled it up yet again! I was having students state their answers out loud in complete sentences. As the students were being creative in reporting their answers on their paper, one girl wrote out the complete sentence! Yes! What a win. We celebrated her and her work.
Currently, I am a Tech TOSA (Teacher on Special Assignment) in my district. I love my job for so many reasons. One of which is the ability to go into classrooms and become inspired by the teachers I work with and their students.
If you are interested in this MathRep or others that are available, please head over to MathReps.com to view them all. The best part, they are all FREE! We have kinder through high school.