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
— 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!!
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.
- 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!