8 Mathematical Language Routines

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
• Information Gap
• Co-craft questions
• Compare & Connect
• Discussion Supports

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!

Nacho Problem

What’s a problem that’s not yours? Nacho Problem!

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.

Finding Problems

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

Results

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?

Summer Presentations

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.

I’m Back!

Well, it’s been a hot 🔥 minute since I’ve written anything on here. I’m not exactly sure where to begin so I think I’ll just jump right in with what’s new. But before that let me reintroduce myself. I’m a lot of things but primarily a teacher, author (The EduProtocols Field Guide Math Edition), and creator of MathReps. More recently, I have started embroidery, bread making, and homemade vanilla extract.

In no particular order:

• The MathReps Facebook Group continues to grow
• I’ve been doing a lot of work creating new MathReps for various grades
• EduProtocols Plus has launched and has included me in the fun!
• Jeremiah Ruesch and I have launched our EP+ Math Show
• I’ve been terrible about posting my resources after presenting. I will be better at that. I’ve already updated my presentation page to include Spring CUE. Go me!
• I’ve created a course for EduProtocols Plus on implementing MathReps

I intended this one to be a quick reintroduction/catch-up post. I will write more soon about some of the amazing things that I experienced at Spring CUE 23! Quizizz was amazing and loving the new updates – that’ll be one post on its own. There was LOTS of LOVE ❤️ for MathReps during the conference. It felt like it was mentioned or highlighted everywhere from sessions to hallway discussions to the vendor hall.

I would like to thank Kyle Anderson for inspiring me to blog again. He too took a hiatus, although a shorter one than myself, and is now back at it!

92%, Say What?

So what’s the big deal with 92%? A lot when it comes to having 3 weeks off and the likelihood that none of my students practiced their multiplication facts.

Monday was our first day back after winter break. As we do every day, we practiced our math facts using the Fast & Curious Eduprotocol. I had an anticipated drop from our usual 96% – 98%. I predicted, to myself,  it would drop to around 89%.  I wasn’t too concerned as I knew that they could easily get it back up to our normal within a week.

Well, to my surprise, my class scored 92%. Seriously, I was happily surprised that they really didn’t lose as much as I had feared. YES! The continuous rep practice has worked. The facts are sticking.

I was so giddy, I needed to write this quick post to celebrate the success my class is finding. I was sold before, but now I’m a believer for life!

Resistant

I will admit, I was reluctant to use any sort of ‘timed tests’ for math in my classroom. The research does not support it. However, my students were sorely lacking in their multiplication skills, a skill they should have mastered by now. At conferences in September, I spoke with each parent about the need to practice at home and easy ways they could help their child. After a month, there was little improvement. THEN, I had a conversation with Jon Corippo.

Jon suggested I use the Fast & Curious Eduprotocol with math facts. I knew he had convinced Cori Orlando to try this with her 3rd graders previously. She balked at first then became a believer. I still held out. He gave me the same spiel he gave Cori. I begrudgingly tried it. It felt too much like timed tests. At first, the kids loved it; it was something new. But then, they kept asking for it day after day. This lasted a while. Several months later, they STILL beg for it.

Does It Really Work?

Simply put, yes. The data speaks for itself. In the beginning, we were averaging around 56% as a class. That’s 56% correct on a 10 – 20 multiplication question quiz. As a class, we could only score 56% on a quiz. And some quizzes we were a bit lower (48%). YIKES! Within two months, as a class, we score between 96% and 98% no matter the quiz I give them. That doesn’t mean that I still don’t have kiddos who are struggling, I do. I still have kiddos who take an incredibly long period of time to complete it. Some day, I have to end the quiz before everyone can finish. But let’s face it, going from 56% – 96% is a drastic difference. I’ll take it!

My Process

I use Quizizz, a computerized gaming review system. It’s a mouthful but if you’re familiar with Kahoot, it’s very similar. I choose a multiplication quiz. No need to make your own, just do a search and you’ll find one. Set up the quiz in classic mode and have the students sign in. On day 1, we take the quiz twice. The first time is cold, we write down our score (Quizizz is great that it’ll average your class score for you), review the questions, then take it again. We keep our first score then we record our second score to see how much we’ve improved. For the rest of the week, we take the same quiz. If our score goes up, which it should, we erase the last high score and replace it with the newest score. We repeat this process with a different quiz the following week.

Because students can consistently score in the 90% range on the first go-around no matter the quiz, I only do the quiz once on Mondays. I have some added bonuses you can read about.

Cheating

I have teachers ask if students cheat: help each other, start the quiz over again, tell another student the answer. The answer is yes. But I don’t care. The kids who are getting the answers are clicking the correct answer and reinforcing it. Those that take it again are practicing twice as much as everyone else. It’s really a win-win.

I’m a Believer

Based on all that I have seen in my classroom, I am now a believer in this protocol. The kids still love it months later. The information is transferring. The data doesn’t lie. Even if you’re still reluctant, give it a try. I did and so did Cori!

Fast & Curious Teams

In the first Eduprotocols Field Guide by Marlena Hebern and Jon Corippo, they describe one of my favorite EduProtocols: Fast & Curious. I use this daily and the kids love it. Recently, the website I use, Quizizz, made some updates and they are AMAZING!!

First of all, the students are loving the ‘teams’ play. We don’t play teams each time, but when they play it creates a fantastic bonding experience with the groups. The app places students into 4 teams randomly. Now, add in the newest feature: redemption question. This means that if a student gets a question wrong they have a chance to redeem themselves by trying to answer it again. There are so many reasons that I LOVE this feature. Immediate feedback, better retention, and not a ‘gotcha’ situation.

NOTE: There are a few other new features that have enhanced the app. Check it out at quizizz

If all that wasn’t amazing enough, I have implemented ‘Classroom Economy’ in our class this year. One of the bonuses we agreed upon was 100% (on selected items like quizizz) earns a student \$50. So the stakes are even higher and more fun. What my class does with this information and teams is beautiful. They sit in their teams and help one another in order to get 100%. If someone on the team needs help, it’s freely given. They are also aiming to get 100% as a class (this comes with a \$100 bonus for all).

They don’t think I see or hear what’s going on. I do, of course, and I how could I ever stop such wonderful energy?

EduProtocols + Hyperdocs = Dream Lesson

I have been in school for 2 weeks now. On week 3 I decided to jump in with Social Studies lessons. I have been doing a Hyperdoc, Google My Maps lesson on Native American Regions for several years. Each year I tweak the lesson. This year was no different.

2 minutes before class, I revised my lesson once again. As I was walking the class back from lunch I was retooling it in my head. This year, I was going to have the students do an Iron Chef AND THEN have the students create a group My Map to record information. Brilliant!

In years past, students were given the hyperdoc, took notes, and then created the group My Map. This worked, but always took waaaay too long. This time, we completed the first region in 2 days! Do they have the information and understanding that I’d like? No. However, I can now do other projects to help solidify this information. Again, more interesting and fun.

Another advantage of doing the Iron Chef Protocol first is that the student heard the information several times BEFORE digging into the task. It really was so much more enjoyable, at least on my end, this year. I’m sure that the hiccups we encountered will lesson we continue this process with the other regions.