Friday, August 28, 2015

Summer Reading #2: Switch

Wow, this week has passed rather quickly. It's the last week of holidays before we head back to school to prep for students to return. (But, don't be jealous if you have already returned to work; in order to make up for the late start of school this year, we are shaving off holidays during the school year, ie. the buffer days that used to exist in between terms, which I would have probably rather kept.) Since I am nursing a foot injury (plantar fasciitis on both feet, sigh...), I did some planning, read some books, and hung out with the hubby*. It is so luxurious to be able to have lunch and coffee dates with my husband during the week! I love it.

*The hubby works from home.

Anyhow, I thought I'd jot down some notes about Switch, which is written by Chip and Dan Heath of Made to Stick fame. Switch is a book about how to initiate change in other people or in a system, when people's natural inertia is to resist change. I wanted to read this book because I think that as teachers, we are constantly trying to change our students' approaches and attitudes towards their learning. In our minds, there is a vision of what an ideal student does, and we are striving to move all of our students a bit closer to that model. For example, for me, an ideal student is always actively engaged and reflective of their learning. They are always asking questions and trying to draw connections between topics. They are risk-takers, communicators, and they have a deeply rooted growth mindset. The ideal student does not necessarily always enter the class with all of the skills from previous classes ( fact, sometimes they can be missing significant skills...), but they have a big, open heart, ready to take on feedback and to re-tool their learning processes as needed.

The book outlines a deceptively simple framework for initiating change, and then it illustrates the use of this framework through a variety of almost unbelievably successful stories. The framework is basically this:

* Motivate people emotionally. In order for someone to change, they have to want to change. You don't motivate people using numbers or research, because our intellect is not what causes us to change; you have to find a way to give them a vision and trigger their emotions. Sometimes, this can mean helping them to envision or build a new identity, because we tend to behave in a way that we wish to see ourselves. (This is a silly example, but have you ever wanted to buy something from a store that looks really stylish, but whose clothes are not very flattering on you? You're subconsciously trying to assume the identity of the type of person who would shop at that store, and you're shifting your behavior to match that identity. Another example is how Geoff and I started composting. In Seattle, it's part of our collective identity because the city provides infrastructure and even a small financial incentive to compost, as compost-collection costs less than regular garbage. Now that we have grown to see ourselves as composters, we can't seem to break the habit of looking to compost everywhere, even when we're away traveling. It has changed our behavior permanently!)

* Give clear directives and "shrink the change". Once you get people on board emotionally to change (which, I know, isn't easy), you have to give them clear, achievable, and black-and-white goals in order for them to get started and feeling successful. The example given in the book is that instead of telling someone to "eat healthy", to say instead to "drink 1% milk." This clear health directive has completely shifted the way America now consumes milk. When you script these directives, think in terms of something immediately achievable, although you can link it to a longer-term vision that it will hopefully pave way to. Give the brain a reason to follow the change and give it also a clear path to follow.

* Follow the bright spots. Change is hard and change takes time. Instead of focusing on what isn't working, look for what is working and highlight those consistently. Find ways to duplicate the success until it creates a positive momentum. For example, are 70% of the kids turning in their projects on time? Praise those kids and ask them to share what strategies are working for them to help them stay ahead of schedule.

* Shape the path. Are you making it as easy as possible for people to create and maintain the change? For example, if your students are not in the habit of doing homework, are you posting homework online and giving them organizers in order to help them ease into the habit? Are you finding ways to create a positive group culture wherein the norm is to do homework? If the change you wish to see is kids volunteering to speak in class, are you providing a structure wherein it's the norm to speak up?

I liked the book, but what I would like to hear is what other teachers think are challenging changes to institute in their classroom, and how we can use this framework as a lens to help us think about transitioning students into more successful learners over time. For example, one incentive that I want to try this year is the ability for the class to earn "homework passes" by showing consistency in completing homework. It's not so much the homework that I care about, as much as I care about them doing and thinking about math consistently outside of the classroom and really attempting problems when I am not there by their side. I figure that if I start with an incentive system, over time the learning will hopefully become its own reward, and I can wean them off of "homework passes." But, in the mean time, it can help me to shrink the change from "be a more proactive learner" to "try your homework", to help the kids who don't already have good study habits to start to build them.


Monday, August 24, 2015

Summer Reading #1: Thanks for the Feedback

OK, web, I am back! I had a fabulous summer. My husband and I did a big trip! We started in New Zealand and ended in Iceland, covering a total of 12 countries in 60 days, so it was quite a sprint.

Anyhow, I have been doing some summer reading after returning from our trip. I had picked up two professional books prior to the start of the summer, but didn't get around to reading them until I got back. (Traveling with a smallish backpack made carrying paperback books unrealistic, and as it turned out, it was hard to find places to reliably charge our phones while staying in hostels, so I did relatively minimal digital reading also while away!) I thought I'd jot down some notes about the books I read, as the books were very useful to me!

One book I read this summer is called Thanks for the Feedback, and I had picked it up because I wanted to get better at hearing and parsing through feedback myself, as well as giving feedback effectively. I highly recommend the book! It was a great lesson in thinking about nurturing my own growth mindset, because how we receive feedback has everything to do with our own growth mindset. The book, for me, contained a lot of valuable information regarding why hearing negative feedback is challenging and how we can frame our minds around this more effectively.

To give you a small taste of why I really liked the book, it talks about how sometimes someone we really don't get along with would try to tell us what they think about us. They would probably present it at the wrong time and in the wrong manner, and you can easily, based on many legitimate reasons, write them off and think to yourself that what they have to say does not apply to you, and that they're in the wrong for X, Y, Z reasons or disqualified to give you feedback for M, N, R reasons. Well, the book encourages you to put aside all those factors and to ask them questions about why they feel this way. Dig further into the data that they're looking at. Do they have information that you don't have? Is their role giving them a reason to consider other factors that are not on your radar? Instead of deflecting negative feedback as is tempting for most people to do, embrace it actively and ask probing questions in order to start a conversation. In the end, you don't have to accept all parts of their feedback, but the first step to growing is to understand where they are coming from, particularly because the people you get along with the least are most likely to offer you an honest look at yourself.

The book also talks about examples of when someone we are in a close relationship with tries to give us feedback. While reading this, I related this in my mind to my husband, who from time to time tries to give me critical feedback about something in my personality that he thinks needs some work. The book talks about how people often react to this by essentially redirecting the conversation to include a new thread about how you are also dissatisfied about something that the other person does. I know I'm certainly guilty of this, and the book gives specific strategies about how to tackle this type of impulse / conversation trainwreck to guide it towards a productive conversation, wherein you focus on one conversation at a time and really try to hear the other person's point of view.

One of the things that I really liked also is a diagrammed model in the book about how our own behaviors are invisible to ourselves. We, as individuals, are only aware of our intentions and the impact that we intend to make, but we have no visibility into our outward behaviors (particularly our micro-movements and our body language) and their impact on others. On the flip side, the people who are experiencing our actions have no visibility into our intentions, even though both parties think that we are seeing the full picture. For example, I am only aware of what I say to my students and why I am saying it, but I'm not aware of how it is coming across in the moment and whether it has the intended effect. This is why getting feedback from our students is very, very important. It helps to close that feedback loop and to make sure that the messages that I hope to send are actually aligned with the messages that the students are receiving, particularly when it comes to my instructional choices and what I think are important aspects of their learning!

The book also helped me reflect upon how I give feedback to my students! The book distinguishes between feedback forms that are evaluation, coaching, and appreciation, and gives examples for why it can cause a lot of frustration for the receiver if they are constantly missing a certain type of feedback. It also talks about the importance of giving feedback in the manner that a person prefers to hear it. So, one of the things I will do this year is to find out, from each student, how they prefer to receive feedback. I'll have to think about how best to phrase this, but the book has some good suggestions for probing questions.

Wow! It is turning out to be a fairly hefty entry here, particularly because I have gone for so long without posting much at all. I'll come back and talk about the next book tomorrow, but if this quick summary sounds intriguing to you, I highly recommend checking out Thanks for the Feedback as written by Douglas Stone and Sheila Heen. Worth a read and worth taking notes!

Wednesday, March 25, 2015

Circumference of the Moon

So, as a follow-up to Erastothenes using geometry to calculate the circumference of the Earth, this week I plan to go over how we can use the ratio to Earth to calculate the circumference of the moon!

The lesson idea came from my colleague John. I fleshed it out to scaffold it for my kids. It looks like this, and it ties in nicely both with our school's Grade 9 science curriculum (which teaches astronomy for all of next term), and our current circles unit. I plan to use this lesson the day after our basic circles quiz, when a few of the students will have family members visiting our class. (At our school, this is called Grandparents' Day, even though it is quite possibly not the grandparents that are coming.)

I'm excited!! I've never done this lesson before, but I like how it revisits perpendicular bisectors and makes them seem useful in application.

Addendum 3/26/15: I prepped for this lesson today and it REALLY BOTHERED ME that I got the estimate that the Earth's circumference was about 2.5 times bigger than that of the moon, when in reality it should be about 3.6 times bigger. I did some more digging and worked out a ratio to find out how big the Earth's shadow would be by the time it reaches the moon, and I think it's 9200 km in diameter at that point! That makes my ratio make a lot more sense, because this is only 2.6 times bigger than the moon!!! Go Geometry!

Saturday, March 21, 2015

Geometry to Algebra Transition

Our school is trying out a new thing this year (one that I think is fabulous). We're re-shuffling 9th-grade kids' Math classes for the last 8 weeks of school this year, depending on whether they intend on taking Algebra 2 or Precalculus after finishing Geometry this year. The classes in our last term of the school year will prep the kids for transition into their choice of algebra classes for next year, and we'll assess them at the start of the term, end of the term, and again at the end of summer to determine whether their achievement and commitment-to-hard-work together seem to predict success in their choice of classes (particularly those intending on skipping Algebra 2), in order for us to advise them and their parents about whether they should be working over the summer, and what seems to make sense for their course placement. In prepping for this transition, we are including lots of algebra into our current circle unit to help kids "warm up" in thinking about algebra skills.

Below is what I have so far. The kids are definitely hitting their edge, but I am able to motivate them by explaining that quadratics is the next logical thing for us to practice, since we have done already a lot of work with lines and systems this year. Even those who have taken Algebra 2 in Grade 8 and who are intending to take Precalc next year did not have an easy time solving for points on a circle, so this is great stuff for all of them!

Here is my intro to circular equations, which most of the class is about finished with. Following it, I plan to spend a few days doing this, which is a modified version of a worksheet that two of my colleagues had created. We want the kids to get familiar with circular vocabulary (as preparation for Calculus) and to do some algebra practice involving circles, but besides it, we're not too attached to teaching all of the circle theorems, since we only have 7 more school days left of this term. I am excited to see the kids' transition to algebra after all the work we've done with them this year in terms of problem-solving. I hope it'll pay off when they get to Algebra 2 or Precalc next year!

Sunday, March 15, 2015

Some Calculus Worksheets

I took some time during the previous school term to observe some of my colleagues, in order to educate myself about the ways in which they encourage inquiry in their classrooms. Among other observations, I enjoyed seeing how the other Calculus teacher (who is about 20 years more experienced than me) structures his worksheets to always circle back to applications and interpretation of answers. Since my visit to his classroom, I have been working on modifying my handouts from the previous year in order to put in more application into every concept.

Here are two of them: I used this to help kids wrap their minds around basic integral Calculus applications, and this one reviews some algebra skills from earlier this year, plus introduces the necessity of going in between algebra and the graphing calculator sometimes. The problems are not ground-breaking, but I think they've definitely helped to break up the skills practice, so I'm happy to share them if they might be useful to someone else.

From earlier months of this year, one thing that I did that totally helped with teaching Related Rates is that I first taught implicit differentiation with respect to time, and formally assessed students on this skill, prior to starting Related Rates word problems. (Sorry if this sounds obvious; it wasn't that obvious to me last year, teaching Related Rates for the first time!) Here is how I introduced implicit differentiation, using the analysis of non-functional relationships as a premise. After this, I had the students do some pure skills practice in converting geometric formulas to differential equations with time as the domain, before introducing my scaffolding for related rates problems and the many related problems I took from Bowman last year. I felt really good about this sequence of skills this year, because I noticed that it really made the problems more accessible to ALL students (as in, by the time they got to the word problems, they were really only focused on parsing the word problems process, rather than simultaneously struggling with the algebraic skills of differentiating implicitly). I recommend trying this, if your students get baffled by Related Rates problems.

I am also trying to place a general focus on vocabulary and communication this year. I've been doing this in all classes by giving the kids a list of essential questions at the start of a unit, and then having them journal their responses to those essential questions throughout the term. For example, for our current term in Calculus (which is short, only about 5+ weeks), I gave the kids the following questions. The questions are a mix between related rates (which we did at the start of the term) and intro to integral Calculus.

  • How are "implicit differentiation", "chain rule", and "related rates" all related? Illustrating this with a simple algebra example may help to clarify your thinking.
  • Take one of our Level 2 or Level 3 Related Rate problems from class and explain/describe, step-by-step, how you are able to find the missing information.
  • What is integral Calculus? Describe a couple of situations where this concept is useful.
  • Choose an exponential function of the form f(x) = a*e^(x - k), by assigning values for a and k. Estimate the area underneath the curve of f, from x = 0 to x = 5, using a total of 10 rectangles. Show both left-hand sum and right-hand sum, and draw labeled diagrams to show what your numbers mean.
  • Show, step-by-step, how you would calculate the enclosed area that lies between two functions f and g, where f is a quadratic function of the form f(x) = ax^2 + bx + c and g is a trigonometric function of the form g(x) = m*sin(n(x - k)) + p, where the value of n is not 1. You get to choose the parameters a, b, c, m, n, k, p to start, but make sure n is not 1.

Students have shown a varying degree of enthusiasm about the journal assignment, even though I have been doing it since the start of the school year and explaining periodically its purpose. Part of the purpose of this journal is to get them to record, in their own words, examples and explanations to important concepts, so that they can have a succinct set of notes for future years. Another purpose is for me to see what they write periodically, so that I can informally gather information about common misconceptions for the topics that we have finished learning, and clarify them with the class. As it turns out, however, the naturally reflective students are thoroughly utilizing the journal to dialogue with me about their understanding, and the rest of the kids see it as a drag to have to keep revising their explanations until the end of the term, so the work that I receive is kind of a mixed bag in terms of quality. It has been a somewhat tough sell, but one that I think is important, because from time to time, students would comment on how they notice that by answering questions in their journal while learning the concepts (instead of putting it off until the end of the term), their understanding improves in real time. Do you do something like this in your classes? How do you drum up enthusiasm for such a revision-based assignment?

That's it for now! My Geometry students are wrapping up their 3-D project, which is very interesting as per usual. They have some really neat designs this year, which I might share at some point. Algebra 2 kids are knee-deep in thinking about the domain and range of different function types, and thinking about transformations on the various functions. It is nice to hear them go, "Ooh, ahh..." as they realize that they can connect information from different types of functions. Not much to write home about, but a productive time of the year nonetheless!

Saturday, March 14, 2015

Hello, World!

Sorry, web, I have been away! It has been a busy few months.

Geoff and I went to Hawaii in December, followed by some busy weeks at work for both of us while shopping in our off-time for a house. In February, I went home to visit my parents, and almost immediately afterwards, my in-laws came to stay with us for 10 days in our 700-square-foot apartment. They have just left, and Geoff and I have finally begun planning for our big summer trip. This summer, Geoff plans to take off 2 months from work and travel with me. Tentatively, we will start in New Zealand, then go through Philippines, Indonesia, South Korea, Japan, Estonia, Russia, Greece, Italy, Germany, England, Ireland, Iceland before coming home to Seattle. Our house's closing date is still set for the end of March, so in the mean time, there are just a lot of things keeping us busy. Hence, the radio silence...

But, I have been reminded recently that I have a blog! Through the grapevine, two friends of friends have mentioned this blog to me. Funny, small world. So, let me think about what I can put on the blog that is worth sharing. Stay tuned.

Friday, December 12, 2014

A Fun Lesson on Similarity

This term, I have been mixing in some old Geometry lesson material into my current Geometry class, now that we're no longer doing purely Exeter problems. It has been so much fun!!! My kids are delighted every time I throw in something that I had used and liked in El Salvador. It makes me very happy to observe.

The last couple of days, we have been doing a fun little similarity activity on the Geoboard, that I had made back then and then revised for this year. See it here. I am using it to introduce similarity, as a lead in to special right triangles and right-triangle trigonometry. The kids are having so much fun with rubber bands that they don't realize I am sneaking in significant learning.

I still like the Exeter problems for their incredible richness, but balancing them out with other modes of learning is the way to go,  I think! 

PS. This has been a good teaching week. Two of my low-confidence students who have been working their BUTTS OFF for weeks each got an 100% on their requiz. HOT DAMN! I'm so, so proud!