Necessary Conditions: Quality Tasks

Before taking my current position, I worked at a STEM magnet school. Few things put me on the course to my current pedagogy as much as my time there did and tasks were a really key part of that. I did a lot of stumbling through the dark, experimenting, and seeing what worked (and failing forward when things didn't). I often feel like the idea of implementing tasks is one of the most intimidating to teachers- how can you give students all this time when this image makes us all feel so personally attacked:

And math teachers aren't wrong- a poor quality task is not worth the time it takes to implement it. That's what I really appreciated about the treatment of tasks in Necessary Conditions. Quality is king. 

Quality Tasks

Ideas I’m Implementing/Saving for Later:

• Tasks don't just allow for creativity- they should rely on it
• It's so easy for kids to hide behind rote, low level learning in many traditional classrooms. If they can regurgitate it back to you, GREAT! They can even do it with the numbers changed?! AMAZING! But those same students often cannot think around a problem posed differently or see when their knowledge might be necessary. They think math relies on memorizing processes and then implementing those "when the question looks like this" and who in their right mind would want to study THAT? Real world problem solving involves creativity that is intrinsic to true mathematics. I want to prioritize that in my classroom more. 
• I loved this quote from the book:  "If you deny students the opportunity to engage in this activity- to pose their own problems, make their own conjecture and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs- you deny them mathematics itself" (p.59)
• Two solutions from the book for this: 
• tasks that are primarily student generated 
• tasks that have a singular solution that can be arrived at through a multitude of solution methods 
• Curiosity is key
• Tasks should naturally spark curiosity- building engagement and buy in. I had 2 favorite suggestions from this section of the book:
• Solicit Predicitions! Start with one that is obviously too low and one that is obviously too high, then a best guess. These get students to think about what their results should and should not be- sense-making and allowing them to justify what they think. 
• "Steeped in Dissonance"- cognitive dissonance is such magic in the classroom. It gets kids thinking, wondering, trying to explain (or argue against!). This phrase gave me that warm, fuzzy feeling all over. You have to let kids sit in their dissonance a little to let them process when something is counterintuitive to them.
• Access is non-negotiable
• We talk a lot about "low floor, high ceiling" tasks in math ed and for good reason. If every single student in your class can't access the meaning of the task in some way, they have no way to be curious about it, much less get started. 
• One suggestion from the book for sussing out the level of access is asking students to restate the task on their own. This is so simple, but brought me back to my time at the NYC Math Lab. Kids will explain to you what THEY understand, whether that's what you want them to or not. It's my job to find where that knowledge is anchored- what they DO know, instead of what they don't. Again, let them talk. Strategies after empathy. 
• Simplifying tasks can lead you down a more complex road in the end
• I loved the discussion of simplifying what we ask- not only to extend access to more students, but also to open up the doors of creativity. It set off a lightbulb in me....I have been in a graduate cohort for the last 1.5 years that partnered with NASA and I couldn't figure out why so many of the NASA resources felt "off" to me. Here's an example about radiation in astronauts.

https://www.nasa.gov/sites/default/files/files/SMIII_Problem28.pdf

• It's got good bones- I like the real world applications and the use of data. But I've often felt like these feel "forced" to me- like a person said "HEY! There's math in this! I bet we can make this seem interdisciplinary!" Last year I started trying to open up my tasks more and it made a huge difference. This was my favorite- discovering the derivative. I asked me kids "What's the actual instantaneous velocity of a marble at this point?" and made them figure it out. It being open ended allowed them to ideate, test ideas, fail, and learn. It wasn't just a bunch of steps they were following because I asked them to do so. They were answering a big question in a way they saw fit. My goal this year is to simplify more. 
• There is task inspiration everywhere! 
• I loved the practical suggestions the book gave for adapting existing tasks. Textbook writers take a lot of time to write application problems, but they're often too scaffolded or too contrived. These tasks- which often rely on simplifying, as discussed above- help transform a meh question into a great task:
• Start with the answer
• Remove the steps and sub-problems
• Make the problem one of optimization (hellooooo, calculus)
• Choose your own problem
• Blur or withhold critical information
• Move from application problems to authentic experiences
• Keep fighting the good fight, even when kids fight you back!
• Sometimes you just need to hear this. A student that I taught 2 years ago and who graduated this year wrote me a card at the end of the year thanking me for not giving up on teaching the way I do, even though he fought me on it daily. He said it took him being years removed from it to realize the impact it had had on his ability to think. So for any of you fighting the good fight, keep fighting! 

Questions I’m Pondering:

• What are good strategies for a student who really struggles with accessing at-level tasks? Especially with open enrollment in classes?
• What are more resources for upper level tasks? Who wants to share some with me (hint, hint ;o) )? 
• What are the best ways to balance tasks with timing in an AP course, where you are already missing a month of instruction?

Last day tomorrow- effective facilitation & wrap up! 

Necessary Conditions: Academic Safety

On the list of tasks I wanted to accomplish this summer, reading Necessary Conditions by Geoff Krall was near the very top. My lofty goals of reading one book per week was quickly put on hold when I started my 2 week research fellowship in a pharmaceutical lab and spent all of my leisure time reading about protein-protein interactions and enzyme-linked immunosorbent assays (I really know what those are now…more coming on that experience later in #MTBoSBlaugust). As soon as I got back on track, though, I couldn’t put Necessary Conditions down. I don’t think I’ve ever read a book that felt more resonant with my own aspirations of pedagogical practice in my classroom. I spent the first half of the book pausing the music in my earbuds and reading excerpts to my husband across our table at the coffee shop, followed closely by spending the second half of the book filling the pages with scribblings and practical ideas.

My fave response when someone asks how I could possibly spend my days with teenagers 💕 #NecessaryConditions ⁦@geoffkrall⁩ pic.twitter.com/5owRaqlm8I

— Caitlyn Gironda (@Caitlyn_Gironda) July 22, 2019

I’m not crying, you’re crying 😭😍 #necessaryconditions ⁦@geoffkrall⁩ pic.twitter.com/hybZCuGZuf

— Caitlyn Gironda (@Caitlyn_Gironda) July 30, 2019

It was a tremendous read that hits at the heart of everything I’ve learned in my experience with teens and STEM education. It left me with practical ideas I could take and adapt to my classroom immediately. It centers around developing a true pedagogy for math instruction, centered around academic safety, effective facilitation, & quality tasks. Over the next 3 days, I will be covering each one of these. First- Academic Safety!!

Academic Safety

Krall emphasizes that academic safety has 2 “levers” to which we need to attend

• Creating an accurate representation of the discipline of mathematics
• Communicating to each student and all students- with words and actions- that they have unfettered access to the discipline of mathematics

Ideas I’m Implementing/Saving for Later:

• Asking students and colleagues “What makes a good mathematician?”
• My graduate advisor treated this question as a driving force in our work with her. I was required to complete a “What Is Math?” paper- I think mine was over 30 pages- that included historical context and pedagogical applications of my views of mathematics. I’m not sure if other teachers have ever been challenged to really think about this and I know what a vital part it’s played in my own pedagogy. Cute little 2012 me even wrote my second blog post ever about it: http://givemeasine.blogspot.com/2012/11/what-is-math.html
• Helping students understand the discipline of mathematics may help “open up” the discipline to everyone as a more inclusive field, something to which they have access through their unique set of skills
• Krall suggests “reimagining the disciple” through the following mathematical experiences:
• Do math with students
• Do Creative Math
• Do Useful Math 
• Giving specific feedback to each student on which ways they are “smart” in math
•  I love the idea that kids will better be able to see themselves as a mathematician if they understand in what ways their own strengths play a role in mathematics. Krall suggests a few different ideas, but one that I really loved is the idea of going through your rosters and answering the question “In what way is this student ‘smart’ in math?” I can think of fewer more powerful “I see you” moments for a student that getting this sort of one on one feedback. I will be incorporating it into my process of getting to know my students
• Academic status should not be left to chance- assign it intentionally; Praise must be public, specific, mathematical, true. 
• Engaging more with empathy and less in a search for solutions or strategies
• I feel like I am really good at connecting with about 98% of my students. I work really hard to be an active carer, instead of just a passive carer- something addressed in the book as well. I can push my kids because they trust me and they know I’m coming from a place of belief in what they can achieve. But every year, I have one or two students who just don’t want to participate in groups or come to extra help or some other challenge for them. I go into “solution seeker” mode- maybe if I do this or that they’ll do this. And I am realizing I’d just like to slow down more and talk to them. Maybe they just need some more one on one to let them know I care that they aren’t doing x. Or they have something going on or some prior experience they haven’t shared with me yet that stops them from doing y. More listening. That’s my goal. Solutions come after empathy.
• Publicize moments of brilliance
• I think I do this, I try to do this, but I know I miss some kids. I am going to make a more structured support for myself this year to make sure I’m doing it for every kid. I will write more about that in my “facilitation” blog post. 
• Shifting the way I talk about grades
• I try to combat the “need for correctness,” as Krall calls it, often in my class but sometimes it’s hard to get students to believe you when they’ve already survived 12 years of school telling them otherwise. This description of the shift struck me: "from a diagnostic tool (yielding messages of fixed mindset) to a standard of excellence that everyone can achieve.” This makes me want to add this description to my syllabus, but also to help my students view grades this way. I’m just grappling with how. 
• I need to understand and work to preempt stereotype threats more
• One example from the book was about a 1999 study by Spencer, Steele, and Quinn. In this study, students were separated into an experimental and a control group, then given a test. In the experimental group, students were told that men and women had been shown to perform equally on that test, but the control group they were not. Men outperformed women in the control group, but not in the experimental group. Such a simple, specific message can break a stereotype threat. I want to be able to do that for each of my students, no matter what stereotype they fear. 

Questions I’m Pondering:

• How do I plan for these daily?
• How can we present the discipline of math accurately in a system that demands immediacy and achievement?" (p.19) 
• This made me think deeply about the ties to assessment and making our “talk” match our “walk.” I have worked in scenarios where I felt that I was expected to “fall in line” with the way things have always been done, even if I knew better. It tears me apart when I can’t make my talk match my walk and it’s been something I’ve been more and more cognizant of as I’ve gained experience. 
• How do students feel the most “celebrated”? 
• How do we support assessing with growth mindset in mind in a system where we cannot control our own grading practices completely? How do we help students see grades as a standard of excellence that everyone can achieve when working within those confines?
• How do we learn more about stereotype threats to groups? Where can I do more research or talk to more resources about this? 

Tomorrow- quality tasks!