MCC Math and Tech Workshop

This week I'm at Maria Anderson's Math and Tech Workshop.  I'll try to update this post as we go through the week.  There's a large Explorers group and I'm in the Adventurer's group.

Monday Morning

Adventurers brainstormed the following for discussion.  So look for more on this this week.

• Wolfram Alpha
• Attention-Getters
• Textbooks: cost, open source
• Geogebra
• Vyew
• Student interaction
• Twitter/texting
• Math Ed Research on Tech

Resources:

• Textbook cost: article in NYT 
• Math Ed Tech Research: CITE Journal, which has different topic areas, including math.

Social Media:

• Use Facebook pages for students.  They like the page and get those updates rather than your updates.
• Go over privacy settings with your students.  They are often ignorant of the reality. Check your own.
• Linked In: limited use, like a modern rolodex.
• Twitter: internet equivalent of drinking from a firehose.
• Twitter is more collegial.  Follow people who have worthwhile info to you, get nearly instantaneous feedback, hashtags to organize.
• Twapper Keeper (love that) to archive tweets.
• Twitter is a completely public space.
• Math Blogs: a node on Maria's MindMap of Spicing Up Mathematics

Monday Afternoon

Finally got time to play with Scratch.  I'm wondering about it as an activity directly for students, for preservice teachers, or as an instructional design tool to make activities.  Here's my first - kind of like pidgin Logo.




Learn more about this project

The end of the afternoon is working on Mathematica. It has developed quite a bit in the 15 years since I've last used it!

Workshop and Responsibility

For a presentation at Michigan Council of Teachers of Mathematics 2010.  It went pretty interestingly - teachers really focused on the idea of choice.  There was a lot of interest in thinking about student responsibility.  Quite a bit of interest in the parallel with learning language and the Conditions of Learning.

It's hard to believe that I haven't written more about workshop here.  The idea is transferred from the workshop structure used in elementary literacy teaching.  This presentation, though, is more about the importance of having a structure that aligns with your beliefs about learning, and how that supports students to take more responsibility for their own learning.  I'm not big (nor is my co-presenter) on telling others how to do things, but we do want to share what we've been doing, why, and how it's working out.

It's my first Prezi, so... sorry!  Handouts are after the prezi. (Direct link to the Prezi site if that's preferred.)

Workshop and Student Responsibility on Prezi

Main handout, includes our contact info and references, and 4th and 8th grade low stress sample workshops.

Overview of the Workshop Structure as we practice it, with some of our motivation.


Workshop Connections

Handouts with sample workshops

• In-class 1:  Powerpoint Presentation on Lesson Planning
• In-class 2: Two of them: Patterns review and division algorithm
• Homework 1: Two of them:  work on a project and a review assignment
• Homework 2: Two reading workshops

Anything I forgot?  Just write me.

Elementary Homeschool

It has a been a couple of years since I really looked at what was available for elementary homeschoolers, but a recent question has me looking at this again.

The main focus has got to be curriculum, but that's a difficult question.  Many of the pointedly homeschool curricula are drill and kill to the extreme.  For example, one homeschooler who reported 132 practice problems per lesson.  This post is not going to be for those who are looking for that.

What to teach?  
The core standards are definitely the wave of the next decade.   Many states are going to have exactly these as content objectives and most states will be close.  There are still too many objectives, and too little attention to process, but it's a place to start.  The NCTM standards are practically venerable, now, but still the best guide to worthwhile content that there is.  The NCTM Focal Points would have made a better start to a common core, but still could help a homeschooler know what to center on.

Doing Math

The toughest thing for a homeschooler is the same as for a school teacher - shifting from a weak tea vision of math being grinding calculations to a rich frothy mug of math as an active way of thinking.  The key to this transformation is best exemplified in the NCTM Process Standards.  Center your time spent in mathematics with the student engaged in:

• Problem Solving.  The big one.  Working on finding answers to questions when you not only don't know the answer, but you also don't know how to find the answer.  The trying and finding of methods to investigate is the heart of mathematics.
• Representing.  Making, interpreting, translating between and choosing ways of showing and displaying mathematical information.  Numbers, equations, functions, tables, charts, mind maps, written descriptions, pictures, diagrams, physical enactments, etc.  Typically this is the biggest support to problem-solving, and one of the key means of differentiating in mathematics.
• Connecting.  Seeing how what you know, mathematical information, and the real world relate and what they can tell us about each other.  Many problem solving strategies boil down to
• Reasoning.  Following connections in a particular direction (forward or backwards) or examining the strength of those connections.  Answering why and how does this work questions.  One framework for this is a) Making sense b) Conjecturing c) Arguing (which includes Proving).
• Communicating.  Sharing or recording what you know.  Strive to be clear, coherent, complete, correct and consolidated.

These can also be used to evaluate curricula, activities or problems.  If the materials do not offer opportunities to do these processes, they will not support the teacher or student in doing math.

Curricula
My favorite curriculum, bar none, is Contexts for Learning Mathematics.  Excellent activities, literacy integration, and student and teacher support.  I use these materials with my preservice elementary teachers.  Issues are price (though they are almost half off right now), and focus on number to the exclusion of geometry.  So a little bit of supplementary materials might be needed.  Strong on pre-algebraic thinking and reasoning though.

Second choice, or for the whole span of content objectives would be Investigations in Number, Data, and Space.  There's an option for online access to games for practice, too.  Unfortunately, it can be a daunting task teaching it for someone who might feel shaky on the math themselves.  If you want quality activities, and are willing to explore along with your student(s), this might be the series for you.  Unfortunately it is priced like college textbooks, $420 for a year's worth of teacher books.  You can buy by unit to supplement another curriculum.

An interesting option is the relatively recent translation of the Japanese curriculum.  They're available by grade level or the overview.  It does not cover all of our objectives, because the Japanese have a more reasonable curriculum, but it definitely covers what's important.  There are workbooks, too.

The cheapest option I've seen that has some value is the Jump Math program.  It's a bit worksheet centered, so you would have to supplement activities and problem solving, but there's a try at conceptual focus and it's a start.

Sue Van Hattum  thinks it's worth looking at the Mathematics Enhancement Programme (it's English) - and I'll be looking at it.  (You can always trust the Math Mama.)

Resources

• A membership in NCTM gets you access to the standards and the journal of your choice.  Probably the single greatest resource for learning about the math, the teaching of the math, and finding worthwhile activities.  The Calculation Nation games are free to all, though.
• NRich.  Best single source for math problems I know.  Searchable by topic, filterable by grade level and challenge level.
• Let's Play Math.  Terrific blog of Denise, a homeschooling mother.  Resources, links, activities, discussion.  Also maintains a collection of Mostly Free Math Resources.
• Homeschool Math is run by Maria and is also worth a look.
• Me - write with questions and I'll help however I can.

Wishing Well
Good math teaching is the same wherever it happens - it's supporting worthwhile and significant student learning.  My main advice would be to try to transfer from the areas where you feel your teaching is strongest.  Science, reading, etc.  What's making that work, and how would it look in math?  Emphasize making sense.  Don't you and don't let your student do anything just because.  Connect with other teachers (blogging, commenting, or tweeting) and discuss your teaching.

Jonah the Math Teacher

If he thought being a prophet was a tough gig...

OK, prophet's probably still tougher.  Pastor, too.  But math teacher is up there.

Warning:  This is probably over-synthesis on my part.

I just finished rereading Under the Unpredictable Plant by Eugene Peterson for a book group.  (Link to Google Books, which has the first 40 pages.)  It's a book about vocational holiness.  For many of the teachers I know, teaching is a vocation.  It's literally what we were called to do.  So the book applies on that level.  On another level, pastoral work and teaching have lots of connections, so it applies there.  But on a metacognitive level, Mr. Peterson wrote a 200 page think aloud about how he worked his way towards living his vocationally meaningfully.  He parallels this process with the book of Jonah, from the Old Testament, a story about a guy who is definitely struggling with his vocation.  It's an interesting book regardless, possibly essential for Christians or Jews and maybe Muslims (Jonah is in the Qur'an), and should definitely be required reading for vocational workers.

Mr. Peterson breaks Jonah's story up into four parts.

The first is the journey to Tarshish.  God tells Jonah to go to Nineveh, an ancient and future enemy of the Israelites, and he does not want to go.  So he heads in the opposite direction, to a mystery destination full of romance.  Mr. Peterson connects this with careerism.  Before we begin, or in our fantasy moments, or before we leave to take another job, we may indulge in the fantasy of teaching.  Stand and Deliver, or Glee, or a classroom full of attentive, willing students, or the couple students whose lives are turned around by our near miraculous intervention.  I have those days and years, for sure.  The solution to this is to stay.  Teach my students that I actually have.  These guys who were complete duds and still haven't read the article/done the homework/even tried it.

The second part is the storm and the belly of the whale.  Jonah is asleep on the ship, despite it being in a life and death battle with a storm.  Somehow, this is when jonah recovers his vocation, and he tells the sailors to throw him into the sea.  This is when the big fish swallows him up.  In the whale, Jonah amazingly prays a song of praise, made up completely of lines from the psalms.  (Maybe a whale, maybe not, depending on your view of many things.)  Waking up is seeing our students for who they are and claiming them.  Mr. Peterson connects this with the need for askesis.  (This is a Greek word for athletic training - cf. Wikipedia - he uses because the idea of ascetic has some really strange stuff attached to it now.)

Askesis involves finding a mentor (or mentors) and devoting yourself to training.  That maintenance is the big thing.  Regular participation.  Peterson found he couldn't get that from the institution or the congregation, and started reading Doesteyevsky, and other classics.  He makes quite a point out of not doing what the congregation asks for, as that leads to golden calf moments.  (Not good, wrath of God situations.)  But the worst barrier by far is ego.  When I abstract teaching too much, I'm forgetting the students.  If I'm thinking about teaching in the abstract, or even focusing on what I'm doing instead of what they are learning, it gets in the way of teaching.  Sometimes terminally.

For me, askesis is the colleagues who challenge me, the reading I do, and, maybe, this online community.  Dave and Esther seriously help me monitor and think through my practice.  Reading Debbie Miller and Ellin Oliver Keene is seriously challenging.  Trying to find teaching connections to other reading (hence this post!) is also helpful.  And blogging and twitter... well, I think it helps against the incredibly strong pull of isolationaism that teachers face.  It is so easy, on most days, to close our classroom door.  Especially the weirder I get teaching.  At the end of the semester, when students are working mostly independently, and I'm sitting and watching them... I get some looks.

Peterson describes that a practical askesis has a rule, or a structure, that is supported by disciplines.  For him, his rule was a cycle:  worship with the congregation -> praying the psalms -> individual recollected prayer -> praying the psalms -> worship with the community.  It's a real question to me what a practical rule or structure would be for teachers.  The workshop structure is central to my class; is it some variation of that?  For him, the pslams are where you learn how to pray.  Where do we learn how to teach?  Maybe that's our teaching frameworks?  So for me the rule could be:

The rule would be supported by teaching disciplines.  What do you see as the disciplines which improve teaching practice? 

The third part of the Jonah story is Nineveh.  He finally goes to meet the people he's supposed to reach.  He's obedient.  He walks a day's march into the city, not even just shouting the message in through the gate.  Peterson connects this with getting to really know his congregation for whom they are, and differentiating his work with them based on where they are.  He describes being pulled into being either a messiah or a program director.  The messiah is looking to help, and never allows struggle.  The program director recognizes strengths, and plugs people into service whether that would be good for them or not.  It was easy to recognize both of these traits in my own teaching.  The solution to this is what he calls eschatology.  This is usually used to refer to study of the end times, but Peterson uses it to talk about being goal-oriented.  As teachers, if we keep the learning goals in mind and combine it with authentic assessment, we'll see our real congregation and stay as their teacher.

The final part is the unpredictable plant.  In what is the least known part of the story, Jonah has finished his message and goes up to a hill above the city.  To watch it be destroyed.  God even grows him a shade plant for his comfort.  When God takes away the shade plant, Jonah loses it.  Argues with God, complains repeatedly, and whines that he is angry enough to die.  Jonah rejects the mess:  the city has repented, Jonah doesn't accept this and doesn't know what to do.  Peterson points out that pastoring is essentially a creative activity, and that requires mess.  Easy to apply that to teaching.  "In any creative enterprise there are risks, mistakes, false starts, failures, frustrations, embarassments, but out of this mess - when we stay with it long enough, enter it deeply enough - there slowly emerges love or beauty or peace."  It helps in this to have a simple statement of what it is that you are called to do.  For me, it's something like "Support students to learn how to learn."  Math or math teaching is the context, but not the mission.

The Jonah story ends open to interpretation - the Inception of its day.  Will Jonah see his mistake or die from his anger in rejection of his calling?  I'd love to imagine him descending back into the city, meeting his class where they are.

PS> I'm always interested in comments, but this really felt like going out on a limb for me, and I would especially be interested in if it was worth your reading or not and why.

Growth Model

Dweck.

Last summer, my colleague Dave Coffey's summer reading revolved around the idea of a growth mindset and its relationahip with learning.  Carol Dweck is the most often cited researcher in this field.  There's a pretty good piece on her and the related research in a recent Chronicle of Higher Education article.  Some of her ideas have been popularized by Daniel Pink.  (Jamie Feild Baker has a post about that connection.)  There's a commercialization of her work by Brainology, that seems to be based on proving to students that this brain research is true by showing them it's how their brain works.  (Brainology is also on Twitter, it turns out. Not bad linkage.)

The oversimplified summary of the research is that people's growth is limited by their own assessment of their possibility for growth.  People who think ability is fixed find it hard to grow.  People who think it's possible to grow find it hard not to.

My response was to try asking Dr. Dweck's questions of my future teachers and see what happened.  It was definitely interesting, and the discussion of the growth mindset idea was definitely a great discussion.  But there's always so much to do, that I just let it slide.

Recently Sue Van Hattum (aka Math Mama Writes) posted that she was thinking about it also and put up a sample questionaire.  I dug up the one I had given last fall to send her, and then started thinking about making it more math-centered.  And that's what I wanted to share today.  I merged them with some mathematical process questions I had used before, and a few other math attitude chestnuts.  I am more and more convinced that assessment and evaluation is where I need to concentrate so that I can teach my actual students and not figments of my imagination.

Dweck's original questions (2 forms)

Implicit Theories of Intelligence Self-Eval.v2 by goldenoj

Modified for math

Implicit Theory of Mathematics Learning by goldenoj

Web Roundup

Well, I've made the Twitter jump.  I want to try twitter in classes this fall, and that means I need to be a user.  So far it has been interesting, and it's a slower fall down the rabbit hole than I expected.  Follow me as @mathhombre.  I would recommend it, as it has linked me to several interesting resources, and hasn't taken much time.  There's a whole social aspect I really don't get yet, but I'm a bit of a misanthrope.

A Reston Kid has a nice collection of math blogs to start with, all people who are on the mathteachers twitter list.

For example, Jim Knight tweeted: 35 web 2.0 educational resources.  Some are no brainers, some charge, but I found several new ones of use to me. 

Kate Nowak tweeted the MathFail website where the image at the bottom came from.

Reston Kid (blog link) also tweeted out Frink, a "practical calculating tool and programming language designed to make physical calculations simple."  As RK notes, the documentation is hilarious.

EDIT:  Cathy Campbell (@ccampbel14) points out this great post on Twitter for math teachers.

The first Math and Multimedia Carnival post is up at Guillermo Bautista's blog.  Lots of interesting stuff.  Sol Lederman's puzzles, Maria Drojkova's educational twitter uses, David Wees building off Dan Meyer's video problems and more.

For example, an Alexander Bogomolny post at C(ut)T(he)K(not) Insights, who's hosting the next Math Teachers at Play.  I'm excited as his Cut-the-Knot (a Gordian reference?) was one of the first worthwhile math sites on the internet.  (IMHO)


Of course, if you're on vacation, more power to you.  Maybe you'd be interested in trying our new family game... C'mon, please?

Playing Math

I am, probably obviously, a big proponent of games in math.  I know on some non-research-clinical-double-blind-trial level that when I see students most engaged, in the same way that math engages me, it's as if they're playing.

I walked into a neat building in downtown Holland, MI (the kids were at a science camp at Hope College) that now houses a 5/3 bank.  The facade is beautiful, but I'd never been inside.  It was just as beautiful.  One of the tellers was talking about how they just filmed a scene at this bank for Ed Harris and Jennifer Connelly's coming movie "What's Wrong with Virginia?".  The ceiling has a fantastic pattern (idealized above) with regular hexagons and rhombi.  One of the things I've promised myself I'll think about some day is tesselations of more than one tile, and how to do Escher tesselations.

I sat down and started sketching the pattern trying to think about alterations.  These really boil down to what's the fundamental region and how are you going to move the region about the plane (or what subgroup the tessellation represents if you're more algebraic).  The fundamental region needs to be at least a hexagon and a rhomb.

That led to noticing the obvious translation tessellation, but there's also a rotation tessellation possible.  If you do two rotations and a translation, it becomes really an altered quadrilateral.  (Or, what I actually notice from making this picture is that it's a pentagon with an additional rotation on the side between R1 and T2!)  I also noticed that two of them made a hexagon tiling.  So I thought about making more interesting tilings by dividing up standard tilings into congruent pieces.  Which got me thinking about which shapes can be divided into congruent pieces.  That got me thinking about rep-tiling alterations which is another thing I've promised myself I'll think about someday.  I really got lost in the ceiling for 15-20 min when all I needed to do was make a deposit.

Why don't students play with mathematical objects?  

At this point, take 5 minutes to read this Jonah Lehrer column at science blogs about video games and our interactions with them.  

Video games used to appeal to a limited audience, like math.  More people than in math, because it's easier to get engaged.  The people who got into them could get really into them, like math.  But the Wii has changed things.  A much broader audience of people enjoy playing it.  Why?  Lehrer relates some of the neuroscience, which actually goes all the way back to William James.  (Sometimes I feel like if we had just taken a century to figure out why he, Dewey and Piaget were really saying, things would be better now.)  Someone at Emory's Education Division has assembled some great William James info.  In particular on interest and his talks to teachers (pdf).  He thought a lot about engagement and connections.

"The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal." - William James (available on a mug)

I think that games help some people see the playful nature of math, but are still not broadly accessible. Is physicality the key?  How do we  broaden the physicality of math?  This is probably a multiple intelligences question.  We played this Prism Power Game, and I shared with the preservice teachers how I had considered having them draw isometric views or just keep data for the game, instead of using blocks.  They unanimously thought it was obvious that the blocks made it more fun.  (I agreed.)

I'm very curious what other teachers do that relates to this idea of physicality, or if you think it is important, too.  Please share your thoughts!

PS>  the game!
Prism Power Game


PPS>  Math at my university actually started in William James College. Those were the days!

PPPS> Had to make a geogebra sketch of this pentagon tiling.  It's pretty cool and flexible. Be fun to Escherize.