Very few tests are well designed, but I believe the AP Calculus exam is a pretty well designed and consistent exam. One thing that amazes me is that in 6 Free response questions (FRQs) they test a majority of a course. While that is great for the test, it isn’t good for teaching. It makes it hard to use these items in class in the fall continuously, but I want students be familiar with the format and types of questions asked way before they could confidently complete an entire AP Question. I’ve watched my previous iterations of Calculus struggle with the FRQs, but never implemented a system to “train them” because I always started in the middle of the year. This year, my first full academic year of AP Calculus, I’ll be implementing FRQF’s -> Free Response Question Fridays to address that gap.
Every Friday, students will work on an actual AP FRQ (even if they aren’t computing answers to all the parts). I casually had read of Polya’s How to Solve it and his 4 step problem solving strategy on the #MTBoS, but hadn’t implemented it rigorously. I sat down this week and read it (well…I read the first two sections and skimmed the dictionary….). I planned on implementing Sarah Carter’s S.O.A.R. acronym – which is how I’ll be introducing it to kiddos in August. (P.S. I made some nifty INB notes for SOAR last year, hung a kite in my room…and never referenced it again after September. Hence the deliberate planning this time around).
Speaking of giving credit to where credit is due, in my internet search to find something like an AP Calc version of this AP Stats FRAPPY resource, I found this problem solving guide by Florida DOE “Research Based Strategies for Problem Solving in Mathematics” (PDF). They break down all four parts of the process and have activities and prompts for each of the areas. I’ve taken some of their ideas as I’ve written my FRQF’s.
I’ve written the first month or so of my FRQF’s – focusing mostly on Polya’s first step in the process – understanding the problem. The first involves mostly just ensuring that students know what the problem is asking and understanding the situation. We’ll be breaking down this year’s ridiculous Volume problem (#5). Problem not included, because College Board be CRAZY.
Students are answering questions like these:
- Summarize what this problem is about in your own words.
- What do the variables r and h stand for?
- What are the units to describe this funnel?
- What is the height? What is the radius?
- What are the restrictions on the values for h?
- What is the shape of the cross sections of the funnel?
I’m hoping that by focusing on the thought process behind answering questions like these by May we’ll be able to let our knowledge shine instead of being bogged down by words.
P.S. Interested in looking at FRQF’s? Comment or tweet at me (@jakewinfield) and I’ll share my work. I’d love feedback too 🙂 Since I’m using AP Released Items I’m erring on the side of caution.
I’ve been reading Robert Cialdini’s Influence for the past couple weeks which is about how we are designed to comply with certain requests. I read this tonight and am blown away and had to blog to think through this:
Studies have shown that, compared to other classrooms in the same school using the traditional competitive method, jigsaw learning stimulated significantly more friendship and less prejudice between ethnic groups. Besides this vital reduction in hostility, there were other advantages: Self-esteem, liking for school, and test scores improved for minority students. And the white students benefited, too. Their self-esteem and liking for school went up, and their test performance was at least as high as that of whites in the traditional classes.
Cialdini PhD, Robert B. (2009-05-28). Influence (Kindle Locations 2955-2958). HarperCollins. Kindle Edition. [emphasis mine]
I’m blown away by the consequences of this study he summarizes way too briefly. I can decrease hostility by having students get information from one another through the jigsaw method (where each person in a group is responsible for a different part of a passage or problem). WHAT!?!?! Oh, and test scores will increase for everyone?!?!
This to me asks so many questions:
+ Is it any cooperative group work where you have to get information from “teammates” that would have this outcome? What other kinds of assignments could add onto this impact?
+ Why haven’t I been told this before when I’ve been introduced to the method many, many times?
+ Could jigsawing reduce fighting between students (or even groups of students like gangs) at school? Or, if not reduce fighting at least promote cooperation in classrooms?
+ What impact could a dedication to this one cooperative learning strategy have on my school?
+ Are there great examples of jigsawing in math classrooms out there? I can think of some ideas (different problems or parts of problems in each group or possibly reading a text/problem).
I’ll definitely be spending some time jigsawing all year because there look to be huge benefits. We’ll see what happens!
Aside: Cialdini cites the study and another study on group behavior in this part of the text. I can find the reference for you if you’d like – its a little hard on the kindle.
The Book: Do I really have to teach reading? by Cris Tovani
This book was recommended to me before I began TFA Institute in 2012 by one of my favorite High School teachers. In fact, it is her copy of the book I read….I’ve been meaning to get hit back to her forever but just got around to it…..whoops. I ferociously read it in 3 hours at Panera this weekend – a wonderful advantage of summer 🙂
Tovani gives plenty of reading strategies and examples on how they can be implemented in the math class. For example she described a double entry diary with the quote or fact on one side and a reflection or explanation of its importance on the other. One main thing that stuck out to me was her explicit calling out of math teachers who probably complain most about reading. As a math teacher we have to teach how to read word problems. Math teachers will read all the way through a problem then identify the given and what is needed, including variables. I do this without thinking – I have to remember to teach that explicitly. The book was full of strategies and hints. Tovani also includes plenty of examples from her classes which make it such a quick, beautiful read.
To be honest, i picked this off my shelf to get it off my to read list. I didn’t expect much out of it but did get quality info. I know that I am also responsible for teaching reading now – the PARCC test requires that my students can read and break apart complex problems like never before. I will have to teach students what that means and how to do it. I also think Tovani provides some insight to keeping students involved with a text.
My favorite thing I am certain to implement are her conversation calendars. Relationships have always been a weak spot for me so by creating a structure to build and maintain relationships and dialogue is wonderful. It is also simple and gives students immediate feedback on the days work and their effort.
(I just re-read this to get it out of my edit que and have picked up so many other things that are so important: group work, my goal of implementing text sets slowly [sub work in part])
Once I start creating strategies to dissect PARCC problems I’ll be sure to come back and skim this post and my top secret google docs with more notes.
The book: Instructional Coaching: A Partnership Approach to Improving Instruction by Jim Knight.
This text was highly recommended from the former 9-12 math coach, our consultants and even a random math specialist I met at AVID’s conference. I had high hopes that this would be the one-stop shop to figure out what I was going to do as a Math Coach.
Knight is a leader on academia about Instructional coaches (ICs) and how to make them most effective. He bases his model on partnership – not on authoritative rule. Knight says that by asking questions to the teacher about the teacher’s goals you are more likely to get buy in (which I whole-heartedly agree with). With the focus on a partnership, ICs must focus on relationships and be positive with their teachers. Finally, Knight believes there are the “BIG 4” of coaching – what are the 4 things ICs can help coach with. They are Behavior, Content, Direct Instruction and Formative assessments. In his book he includes some strategies for each of these areas.
I am pretty underwhelmed by this text. Maybe it is because I had just finished “Leverage Leadership” by Bambrick-Santoyo a week before which aligns much more with my needs or just all of the hype I’ve heard. Maybe it is because my job will include more administrative duties than ICs with his definition. Maybe it is because Knight consistently reinforced what I’ve already been told: Relationships with people make things happen. Period. And even though I’ve heard it a million times, my biggest take away is still that I need to focus on relationships to create sustained success. I also like how Knight broke down the four things ICs should focus on and gave solutions to each. That could be helpful come fall. I also picked up on his preference of the word “visit” over “observation” which I’ll definitely implement next year in my schedule I’ll be sharing with teachers. Visits are much less intimidating and are informal – which my visits will be. These big take-aways will supplement my plan I created after reading Leverage Leadership.