This summer, I moved from my New York City public high school to an independent, all-girls school (teaching middle and high school) in Los Angeles, CA. My new school is dramatically different, but amazing! I’m so excited. The Head of School at my new school is framing this year using Gratitude. So, in the spirit of gratitude, I want to shout out some of the amazing MTBoS people and ideas that have helped make this transition as smooth as it could have been:
- Julie for sharing all of her amazing middle school activities. Thanks to her, I’m blowing away my co-planners! Army men, stickers, etc, etc, etc = AMAZING LESSONS!
- Julie for sending me amazing colored pens that I used to write colorful notes to all my advisees!
- Elizabeth, forever my teaching soul-mate, for inspiring me with Talking Points this summer and sharing all those wonderful resources.
- Sam Shah, my DH! His amazing virtual filing cabinet and other ideas just blow me away.
- Thank you cards (that Sam pushed me to buy!) that allowed me to express my gratitude to those co-workers who helped me in these first few days and build lasting relationships with them.
- Mattie for sending a hilarious dubsmash video that made me giggle after an exhausting, emotional day.
- Alex Overwijk for inspiring me to cover all my walls with dry-erase boards. It’s SO GREAT!
- Mary Bourassa for sharing with everyone here amazing Which One Doesn’t Belong site. I think my new math dept colleagues are impressed by this resource!
- The outstanding MTBoS friends I have made who checked in on me, made me laugh, sent good vibes, or helped me choose a spirit animal. As warm and supportive as my new school is, I needed all of you to get through the past week and a half. Without you all, I would have been crying at my desk at least five times this week.
One of the last sessions I attended at TMC15 was on Vertical Non-Permanent Surfaces. The amazing Alex Overwijk talked about how he covered all his walls with dry erase boards (non-permanent surfaces) and made students stand (vertical) and write their work/solutions/ideas daily in class. Basically he would randomly pair or group students and send them to the board to work on a problem. Not only was this amazingly engaging for students, but the research behind it blew me away:
Let me first explain a few things:
Vertical vs. Horizontal – basically means standing versus sitting in groups and writing on desks.
Permanent vs. Non-Permanent – permanent surfaces would include poster paper and worksheets, where marks are more permanent, whereas non-permanent surfaces would include chalk or dry erase boards.
The first three rows (not including the number N of groups) – show (1) how long it took students to get started on a task, (2) how much total time the students spent working on the problem or task and (3) how much time it took until students started writing some math notation.
The last six rows – students were scored on a scale from 0 (bad) to 3 (amazing!) for various qualities/actions seen during their work time.
Notice how non-permanent surfaces seem to make a HUGE difference in how fast students get started and how well they participate. The vertical version on non-permanent surfaces is slightly more effective in the different attributes and students tend to work longer on average.
As I sat sitting in this session (which was amazing!) I had flashbacks to my student experiences in 11th and 12th grade. I had the same teacher for PreCalc and Calc. Her name was Ms. Barile, and she made us all stand up and solve problems in pairs or groups on a very regular basis…and I loved it! Somehow in the years the have passed and the mounds of research and observations I’ve experienced, I completely forgot about how important this was to me as a student. Ms. Barile knew it all along. Now I want to do this with my students!
Some nuggets from TMC15:
- Exit ticket with student name + a grade = a quiz, not an exit ticket
- Give feedback before a final grade. Once student see the grade, written feedback is invisible.
- Arithmetic & math differ like spelling & writing. (Thanks Avery)
- Debating brings attention to the mathematical process
- Focus on the structure (roles, routines, etc) takes away the pressure of doing the math
- Vertical non-permanent surfaces (peterlilijedahl.com)
- What if you put the teacher desk in center of room…why do I even need a desk?
- Work on non-permanent, summarize by putting one good exemplar in notebook
- Teaching is not brain surgery, it’s harder. The anatomy of most brains is the same. The anatomy of most classrooms can vary greatly.
- We must share ALL our lessons
- Care about your students as much as Fawn
- We as teachers are all trying, to the best of our ability, to have students reach the best of their ability.
- Does cold-calling have value or should I avoid it?
Shooting out a quick post of some of the gems of cheesemonkeysf, my co-presenter, my teaching soulmate and my friend.
- The quality of student talk is the #1 predictor of group work success.
- Say just enough, no judgements
- Focusing on structure (rather than content) frees our minds/calms our nerves
- (In September,) The students are going to become our community. We’re just not there yet.
- As math teachers, “we understand why there’s a second column in the proof”
- “If you really believe everybody can do math, you have to accept everyone”
She always inspires me!
Been having a lot of discussions with coworkers (as dictated by the admin) and friends (as comes up in natural discussion) about working with our struggling and special education students. My school’s scores have been on the rise on most testing measures. However, the numbers have remained stagnant for our many of our weakest or most struggling students. My admin is posing a focus question, asking what can teachers do to help these students grow and succeed. My coworkers (who are admirably hard-working and enthusiastic) have valiantly taken up the charge and have been sharing best practices around topics like scaffolding, co-teaching/pull-out, chunking, differentiated grading, etc. However, I’m concerned about this approach being too teacher-centered (perhaps a result of the teacher evaluation) instead of being more student-centered. Let’s not just ask teachers what more they should be doing to make class easier/better for the most struggling students (not that that isn’t a good thing to ask). Let’s get students to grow independent of teachers, to be aware of their struggles and seek out the appropriate help they need.
I keep coming back to what someone brought up as the analogy of the crutch. Suppose you break your leg. You know it hurts and you can’t walk. You see a doctor. He gives you a crutch and a timeline for getting back on two feet. If needed, there are even physical therapists who can work with you to help you build up the strength to walk on your own. The end goal is that you can proceed without crutches at some point in the near future.
What I’m afraid of is that instead of offering crutches, some teachers are building ramps everywhere. The entrances are now easier for everyone (no more stairs! yay!), but the stairs are completely covered over. No one is learning or developing skills for climbing stairs, and if those stairs appear in the future (on a state exam, in a college class) the students are not prepared. We have made life too easy for students. (I think a lot of this mentality comes from the teacher evaluations being focused on the teaching part of the classroom and not on the learning. Students are not being considered as part of the equation on how well a lesson goes.)
Going back to the crutch analogy, I see a few key features:
- The Need. Students have to be aware that they need crutches/that there is a problem and they are not capable of moving forward. I have heard so many of my favorite teachers talk about the importance of failing. I think it is important to have moments where students see their struggles/see what they can not yet do…but done in a supportive/nurturing way, with someone who can help them set goals for overcoming the obstacles.
- The Discussion. Students have to be told they are getting crutches/scaffolding with some introduction or discussion. I find some teachers make scaffolded worksheets for their struggling students without telling students that there are different versions. I fear that some students don’t even realize that they are dealing with anything different, and never set goals to become more independent. If students don’t know they are using crutches, will they ever aim to walk without them?
- The Goals. Doctors tell patients the number of weeks they will be on crutches. Why don’t teachers set a timeline for struggling students? I don’t want to rush our students or cause them anxiety, but I want to work with them to set reasonable timelines for becoming more independent.
- The Removal. At some point the crutches have to be taken away. A student has to keep working at it, and there are specialists (like physical therapists) who can offer extra support. However, the student has to let go of the crutches in order to move forward, in order to become the most successful version of him/herself.
I’ve been playing with the sequence of my Alg2/Trig/PreCalc-ish class over the years. I’ve mostly been traditional, teaching Trig in the spring in a large chunk of maybe 8 weeks or so. This year I tried to mix things up, set up more spiraling, and find a more ideal balance. One of my goals at the start of year was to find a unit that was challenging and “new” enough to students to get them ready and focused on my class…and I think I found a sequence that works for me!
I started this year with a 5-6 day “unit” on Factorials, Permutations and Combinations. I thought that this was a nice introductory topic that both didn’t require a whole lot of previous knowledge and also avoided repetition/review of concepts from other math classes. (At my school, they don’t see anything with factorial, P, or C until my class.) It has been an amazingly improved first week/first unit, and here’s why:
- My class is special. Starting with factorials, a pretty much new concept/notation to my students, made my class “feel different.” It’s not just another year of more algebra stuff. Students felt that they were actually learning a new topic, and they worked very hard to learn the material.
- Anyone can do this. Along with #1, this topic is both new but attainable for anyone who puts in the effort. I snuck in some initial discussions on growth mindset with this.
- SBG. Having a topic that is not a repetition of anything in Alg1 helped me to explain Standards Based Grading and my quiz/quiz-retake policy in a way that students totally got. They now understand what a Learning Target is.
- Abstract Thinking. Talking about n, n-1, n-2, etc, allowed us to have discussion about what these terms mean (in the sense of previous term…setting them up for success with sequences) and work in the abstract. This is the first class where students focus a bit more heavily on generalizing/abstracting with variables and not just working with the concrete (plugging in numbers).
- Proof. I can introduce proof with relatively simple topics, setting students up for success later as we do some proving throughout the course, especially with trig identities! Today, we proved that nCn = 1 always and nC1 = n, something the students understood from the a few concrete examples and could make sense of the relatively easy proof. Students were evening thinking of their own extensions, like does it work for P?
- Graphing Calculator. Working out n!, Permutations and Combinations can involve a lot of multiplying. Isn’t it nice that the Graphing Calculator already has these functions?! Having this unit at the start of the year and teaching these calculator functions made having a TI-84 (or some such graphing calc) imperative! Students are no longer slow to get their calculator and develop the routine of bringing it to class.
- Grouping Expressions. Solving problems like word arrangements might involve a solutions such as 9!/(2!3!). When students see this written as a fraction, they don’t write the parentheses, but when they put it in the calculator without grouping the denominator, they get the wrong answer. This was a great time to review the importance of Order of Operations and correct grouping in the calculator!
- Debate! Lastly, I usually start the year with a week or so of logic because it’s a natural way to introduce my debate strategies and protocols. However, after a few days of learning P and C, I introduced the debate protocol (claim + warrant) as a way for us to debate whether a problem is a P or C or neither (starting the discussion of “none of these” being an answer from the start of the year!
So with this one unit I was able to set the tone for the year and stress a lot of routines and common errors that have come up over the years. We now have a starting point to refer back to each time one of these topics comes up!
I was convinced by a presentation at TMC14 this summer to create my own website. I wanted to not only create a place for professional contact/information, but one that my students could easily find with links to all sites and info related to my classes. After a few nights of work, the site is now active! There’s lots still to come, but feel free to check it out and send me feedback, cool ideas, or anything you’d like!
It’s live: www.luzniak.com