Monthly Archives: June 2018

Don’t try to remember, try to figure it out

Often I see students I’m working with struggling to recall something, and drawing a blank.  Usually they remember that they had seen an example of the process that would help them with their current math problem and they’re trying to remember exactly what it was, and how it starts.  When I see this, the advice I give is, “Don’t try to remember.  Try to figure it out in a way that makes sense to you.”

I think this has two advantages.  For one, I feel like I am more likely to remember something if I am actively playing around with related information, rather than trying to recall by brute force.  Often if I start doing something, anything, on a problem, it will jog my memory and I will suddenly remember what I had forgotten.

Also, of course, I feel like the process of trying to figure out a problem anew – especially one that is somewhat familiar – deepens the understanding and helps build a quicker recall the next time a similar problem is encountered.

I mentioned this to a friend of mine, and she said she refers back to this mantra even when trying to remember simple things like where she put something or the name of something.  She runs through related information, often talking through it aloud, and that process helps her find the right mental pathways that lead her to recall the information she was seeking.

I’d be interested in hearing everyone’s thoughts about memory and recall.  What techniques work for you?  Do you think your own memory has been a strength throughout your life or has it been something you’ve struggled with it?  What helps you commit mathematical knowledge to memory?  Is it different for you than learning other topics or types of information?

The Power of Habits

Today I’m rebooting my writing habit after taking a few days off while we were on the road for Seattle Pride.  I planned to take a break on those days.  I had noticed that the habit was starting to feel easier, so I judged that the break would not be fatal to the habit.

I was reflecting in a conversation today about how different it is for me as a tutor to work with families who already support habits compared to those who don’t.  Last year I worked with a learner who played piano and whose mother I gathered supported her regular practice.  It was easy for her to add a new habit of working on her math curriculum daily and as a result she moved through the material very quickly.  This was despite the fact that she had medium to low interest level in math.

On the other side, I’m working with a learner who finds math quite enjoyable, but who is struggling to work on it as regularly as he would like to.  We are experimenting with habit formation strategies to see what works for him.  I think it’s a valuable process for him to go through, as he’ll be able to use what he learns in many areas of life.  But not already having that habit program online ready to reproduce for a new endeavor has limited his pace over the years.  (Despite that, he has a high skill level and ready intuition in math, I think due to his high interest level).

I was remembering back to how my mom dealt with swim practice when I was growing up. Whenever I would complain that I didn’t want to go she would remind me that I had the option of quitting at the end of the month, but that since we had signed up and paid for it, skipping practice was not an option.  She would remind me that I always had fun once I got there.  I very rarely missed practice and as a result achieved a high level of success.  My achievements reinforced my commitment to regularly attending practice and to working my hardest while there.

I think people perceived me as completely internally motivated and probably didn’t pick up on how my mom was supporting me in this way.  I was certainly in a different mindset than some of my teammates whose parents pushed them to continue swimming despite their desire to quit.  And of course my experience was also softer from those teammates who were inconsistent in attending practice, for whatever reason.

The key, as is often the case, seems to be finding that sweet spot between too much choice and too little.  Between too much structure and too little.  It can seem great to be free to do whatever you feel like doing all the time.  But isn’t one way to achieve that to train yourself to want to do the things that support your goals?

Teacher Trade Podcast

I recently uploaded the first episode of my new podcast “Teacher Trade”.  I had to push through a bit of a learning curve getting Audacity to do what I wanted, but by the end I found the editing process to be kind of fun.

In this post I’ll talk a little about my concept for the podcast and how I came up with the idea.

In one of his TED talks Ken Robinson tells the story of a dancer who discovers that there are other people in the world like her who have to move to think.  I find that I’m the sort of person who sometimes has to talk to think.  At times, when I’ve needed to work through a lesson plan idea, I’d call up my parents and just sort of think at them for a half hour or an hour.  Thankfully, they are the sort of parents who happily put up with this sort of behavior.

This self-knowledge was useful, but the break-through came after I became familiar with the practice of co-counseling.  In the practice, people trade off holding space for one another to facilitate emotional discharge and healing.  (If you’re curious about the practice here’s the website for Allies, the organization I’m involved with).  The thought struck me that emotional discharge wasn’t the only thing I could use a trading partner for.  Trading time to talk about lesson planning, and think through my learning process about my work with students would be a great deal for me.

So, the idea for Teacher Trade was hatched.  Plus, even though I’m trying not to take on extra projects while I focus on launching Pixidoku, I figured that this is something I would gain efficiency from.  The thinking would have to get done one way or another, but this way I could share it with another person and other teachers who want to listen to us thinking aloud.

I hope that it might become a larger collaborative project with many teachers sharing their thought processes about their teaching.  Let me know if you would be interested in doing an episode with me, or hosting one of your own!

We are disappointed…

I got negative feedback from a parent.  I ran across it unexpectedly.  The sheet with learner and parent feedback was sitting in a pile of papers and it caught my eye as I was digging around looking for something else.

“We, as parents were disappointed…”

My heart sank and my stomach clinched up.  Why am I so sensitive to one little piece of criticism?  I have been delighted over and over this year by the positive comments about me, my classes and my teaching.  Yet that one little comment rings so much louder in my ears.

I want to accept it with calm, and appreciation.  I want to let it inform how I refine my classes in the future without having to doubt my entire self-concept as a teacher.

The comment was about the structure, or rather, the lack of structure in my Puzzles & Mindbenders class.  There were no “learning objectives”, it said.

My thoughts react with defensive retaliation.  People don’t learn because of learning objectives!  People learn because they are interested and focused, because they are engaged with something that challenges them.  It builds confidence and new ways of thinking.  And different learners need different learning objectives!  Even if I had the time to formalize objectives for each learner, would that really enhance my ability to guide them significantly?   Aren’t learning objectives simply a way to make it appear that learning is happening, regardless of whether it actually is?  Aren’t we in a non-traditional setting precisely so we can avoid this kind of song and dance and focus on what really matters?

But, it may be that my classes can use more structure.  Maybe homeschoolers don’t need a class to have plenty of opportunity to work on puzzles they choose.

Actually, though, I think of the value of a class like my puzzles class as similar to the value of a practice group for swimming or running.  Sometimes there is focused learning around technique.  But most of the value comes from building up your muscles and developing muscle memory.  It is much easier to work hard and practice regularly if you have a practice group.

Puzzles and Mindbenders is exercise for your brain.  It gives learners a chance to work hard at puzzles that are the right level for them.  They are building up the circuits in their brains that allow them to think logically, creatively and carefully.  They are learning persistence and gaining confidence.  Perhaps I can communicate this objective more clearly in the course description next year.

Just a note at the end here – if by some chance the parent who authored the comment happens to be reading – this kind of feedback is essential and welcome.  Please keep it coming!

A Review of “Calculus By and For Young People”

Calculus By and For Young People by Don Cohen is one of my most frequently used resources these days.

I use this book mainly for two types of learners.  The first group are those interested in math for it’s own sake and who are working at a fairly advanced level for their age.  The second type is any math learner who could use a playful and fascinating way to master fractions.

I love so many things about this book.  And it’s not just me.  Much of what I find delightful in the book matches what kids love and are drawn to.

Kids love the idea of the infinite.  I mean…. who doesn’t?… but for those young minds the fascination is fresh and all the more captivating.  It is tragic to make these fascinated and inquisitive learners wait all the way until college, by which time many of them have been tortured by far too much algebra drudgery, to discover the magic of the infinite mingling with the finite.  Through working one-on-one with kids himself, Don created a series of explorations that are accessible to anyone who can do basic arithmetic.  They guide learners into discoveries of infinite series and limits.

Kids enjoy finding patterns and often find them more easily than adults.  This book takes great advantage of that, leading the learner to discover patterns in numbers and in the world.

Kids love solving puzzles.  A main section of the chapter on functions relies on two fascinating puzzles – the peg puzzle, and the Towers of Hanoi – for exploring different kinds of functions.  It’s great because kids get to solve the puzzles first and then discover that there is a mathematical pattern underlying the moves they have been making.

Kids love being silly.  Scattered throughout the book are playful tidbits.  1/2 is sometimes called “one-twoth” and the chapter on functions is entitled “On Thin Spaghetti and Nocturnal Animals”.

Kids like to be challenged.  The depth of this book is incredible.  You will be hard pressed to find anyone who will have trouble finding a difficult task.  At the same time, no one who can do a little arithmetic will find the easiest challenges to be inaccessible.

There’s a lot more I could say, but go look at the book, it will speak for itself.  Feel free to ask me questions about my experience teaching with it!

Writing habit update

Still going strong on the writing habit.  I’m on day 7, and I’ve only missed two days so far due to being on the road all day.  I’m pretty proud of sticking to the habit on Saturday and Sunday despite being at a camping event.  I could have easily rationalized my way out of those days, but I didn’t.

The thing about the habit at this stage is that it feels really hard.  When I form the intention to pull out my laptop and write I get filled with deep reluctance, almost dread.  It’s amusing from where I am now to think about how hard it feels.  Once I get typing it doesn’t feel so bad.  But damn, new habits are hard in this first week.  I hope it will feel better in week two.  It probably didn’t help that I had those two days on the road.  Now that we’re back I should be able to have more consistency which hopefully will make it start to feel a little easier.

Anti-adultishness

Last Wednesday I did 8 hours of filming for the Pixidoku Kickstarter video.  Going in I had a decent idea for the intro segment.  The kids added their own ideas and made it way better.

Here was my idea: Someone is working on a Sudoku puzzle, looking a little bored or tired.  They get handed a Pixidoku puzzle and look surprised and delighted.

I thought it would be pretty good.

Here’s what the kiddo’s did instead:

A girl is working on a Sudoku puzzle, looking a little bored.  She let’s out a big sigh and lets her head fall down on the desk.  Then, as she goes back to her solving, tiles begin to fall from the sky onto her puzzle.  She grabs at them looking confused and bewildered as more and more Pixidoku tiles rain down.  Looking at the camera, she asks, “What is this??”.  Three more kids holding Pixidoku puzzles lean into view and say, “It’s Pixidoku!”

Brilliant.  Great job everyone.  I am so delighted by how that scene came together and can’t wait to see how it turns out.

And here’s the main take-away for me.  You see, when I first heard the idea about the tiles falling from the sky, I must confess I was pretty skeptical.  I figured we’d try it, it wouldn’t work out, and we’d move on and try something else.  But we had time to give different ideas a shot.  I am so glad that I didn’t let my skepticism impulses trample on that beautiful moment of creativity.   It is important that my aldultishness does not get in the way of youthful creativity and experimentation.

Way to go you guys, you rock!

Writing habit: Engage!

I’m done with my lesson planning projects for the school year, so with a little more time on my hands its time to start a new habit I’ve been looking forward to acquiring for a while.  I want to write at least a little bit every day.

I’m doing a few things to set myself up for success.

I waited to get started on my habit until I knew I would have time every day to devote to it.  Habits are hardest in the first couple weeks, so it’s important to minimize other difficulties.  Being pressed for time makes it harder to stick to a habit early on.

I also made sure that I can easy log in to my blog from both my tablet and my computer.  I ended up having to put a little time and effort into this because my password manager wasn’t working quite right.  But I went ahead and did that extra step today because I know that having flexibility will also be important in the early weeks of forming my habit.  If it’s hard to log in to my blog on my tablet that’s one more internal excuse that will make it more difficult to stick to my habit.

I’m starting a simple tracking system for my habit so I can see my progress and get that little psychological reward every time I stick to my habit.  It’s on my small paper notepad that I take everywhere so it is always handy and always easy to scribble in.  Every day that I write I’ll draw a little star on that day’s box. When I drew today’s star I let myself enjoy how it felt and colored it in with pencil to make it look all nice. Yay for stars!  I put a big circle around the 28th day.  That’s about how long habits take to form so I know if I stick to it until then it will get easier.

There is so much I want to write about all the time, but currently I don’t write regularly at all.   I can’t wait to be writing all the things!  Hooray for successfully completing day one.

I’d love to hear from you in the comments.  What habits have you formed purposefully?  What works for you?  What is hard?