**Tell me about yourself.**

I taught high school math for a little over 10 years, working in districts with large immigrant populations and high poverty rates. I taught everything from pre-algebra to AP calculus, but specialized in teaching students with disabilities. Sometimes that meant co-teaching an inclusion class with a variety of students and other times that meant teaching a class entirely for students with disabilities (one group all had language based disabilities, another all had significant intellectual disabilities). While I was teaching I wrote Nix the Tricks, which I think is especially important for teachers with high needs populations since all of those groups tend to get rote learning over conceptual depth because too often people (wrongly) think those kids can't learn the deeper math. I left the classroom in 2018 and spent 1.5 years working with Illustrative Mathematics to write the high school curriculum, specifically I was the lead writer for the geometry course. I've done presentations and workshops at both conferences and districts, mostly on my own but more recently for IM as well. Now I'm looking for my next adventure!

**Can you talk about some of the specific challenges to learning for high poverty student populations. How did it shape your teaching approach and philosophy?**

It's challenging to find a balance between sympathy and high expectations. It's important to consider the extenuating circumstances - kids in poverty are less likely to have access to technology so I never assigned homework that required internet access or graphing technology unless I provided graphing calculators for everyone who needed one. And it's also important to know which kids are working long hours or taking care of siblings after school. But that doesn't mean I said "oh it's okay you don't have to do this thing that everyone else does." Instead it meant that when kids said they couldn't stay after school I understood that they weren't avoiding me, and so we problem solved alternatives. I made sure to check in with kids during class, and provided times during class for anyone to choose to do a quiz retake (something that needs to be supervised) instead of the problem set (which they could do at home). But everyone was expected to learn the material and show mastery. It's like the difference between modifications and accommodations for students with disabilities - students in poverty may need some accommodations to allow them to meet the same expectations (providing calculators and alternative times) but they don't need modifications (exempting them from learning something).

**Teaching is an incredibly demanding profession and most teachers I know have cards or notes or stories from a student who said their life was bettered by the efforts of that teacher. I still have a thank you card from my student teaching days. It was from a high school junior for helping her to get her first A ever on a math test. These stories, I think, help teachers to keep motivated after a particularly difficult day, week or month. Are there any stories you’d be willing to share?**

At the end of every school year I invite students to complete a reflection on the class, their growth, and their future plans. I've saved many of those because they remind me just how much students can change in a year. Time after time students shared that at the beginning of the year they thought they were bad at math, or were scared of it, or thought that math was just about calculations, but by the end of the year they felt confident in their ability to do mathematics, with a much broader understanding of what it means to do math! One of the great things about teaching is the chance to start fresh every year. But it's also one of the hardest things. I enter summer with a group of fantastic kids who know my routines and understand my beliefs about them and about learning. But at the end of summer I meet a whole new group of kids, who I'm sure are fantastic, but most of them are unfamiliar with my routines, dubious that I believe in them, and have a wide variety of experiences with learning math. It's so hard to convince them that my way of teaching is worth the effort, but I know that it's worth the effort on both our parts because of all of those end of year reflections.

**Can you tell me about the evolution of Nix the Tricks? What’s so bad about teaching algorithms such as “Keep, Change, Flip” when dividing fractions or the “Butterfly Method” for adding and subtracting fractions?**

Nix the Tricks is entirely based in my philosophy of what it means to do mathematics. Reading a set of instructions and completing them lockstep is a skill. It's helpful for building IKEA furniture, but it's not doing math. When we only tell students a series of steps like Keep, Change, Flip, we're robbing them of the opportunity to think and make meaning. It turns out that dividing fractions is a really challenging subject to understand, I really didn't fully understand it until I was working on this book! But we can show students that the methods we use have to be consistent - so if we want 6 divided by 3 to equal 2, then we have to make sure that 6/1 divided by 3/1 also equals 2. This idea of extending what we know for whole numbers into larger number systems comes up repeatedly, for example when we study rational exponents. It's not just about telling students why the rules exist, but about convincing students that math makes sense. And they're capable of doing that sense making - using simpler cases to check a rule they don't remember. Just in case that's not convincing enough of a reason - if we ask students to memorize 20 distinct rules during a school year they may do fine on each quiz they take but come a final exam, or a subsequent course, they will be unable to remember all those rules. Brain research shows again and again that connected concepts are much easier to remember (and re-derive!) than distinct ideas that don't fit into a larger web of understanding.

**On Twitter, I see hashtags for sharing resources between math educators (#MTBoS #mathcoach #iteachmath) as well as for weekly online professional development (#mathchat #geomchat #msmathchat #ElemMathChat). How does Twitter help you to grow professionally?**

When I started using twitter it was a fantastic way to meet people who were as enthusiastic about math ed as I was. Some people were the only math teacher in their department, others like me were the quirky one in the department always wanting to try new things like bring in technology and shift instruction to be more student centered. At that point we were using the hashtag #mtbos to find each other and I was writing about my lessons and routines both for sharing with others and self reflection. But eventually I had a set of routines I liked and I was tweaking lessons rather than writing new ones. I switched to using twitter to mentor new teachers, speak up about issues I thought were important, and attempt to counteract the negative messages teachers were encountering. One way I did that was by compiling “a day in the life” blog posts. Another way was by posting #onegoodthing each day to try to remind myself and others that teaching is about the kids, and the kids are always great, even when the bureaucracy makes teaching a challenging career. More recently I started participating in #cleartheair where we read books and discuss them. These conversations aren’t specific to math but invite a broader group of educators to engage in conversations about race and equity. Usually I find scheduled chats to be difficult to follow and overwhelming, but Val Brown only posts one question every 15 minutes which gives you enough time to think and respond to other people’s tweets.

**For a math educator new to Twitter, can you recommend some good folks for them to follow?**

That’s really too hard to do, I'm going to avoid listing anyone for fear of leaving someone out and because I follow such a range of people for a range of reasons it's hard to make broad recommendations. Instead I'll recommend that people introduce themselves to me, with something about why they're joining Twitter, and then we can work together to find them some good people to follow!

**How can we best stay up to date with you?**

Tinacardone.com

Drawingonmath.blogspot.com

Twitter.com/TinaCardone

Nixthetricks.com

**Final thoughts?**

After lots of dreaming and deliberating I’m excited to announce that I’m headed back to the classroom in the fall!

I’ll be the sole math teacher at the local alternative high school. It offers all the supports that I believe every student should have, and embraces innovation.

**UPDATE. Our original interview was done this past summer and Tina wanted to pass on this update.**

So we must have done this interview during that one week I thought I was going back to the classroom! Turns out I’m coaching and researching through Lesley University instead. Things have changed a lot in the last few months!