Saturday, February 12, 2011

Escape from the Textbook Notes

My notes from the Escape from the Textbook Conference stream.  All times are Eastern.

12:16 We're getting started.  On time (essentially).  I like it!

12:18 "There was a time when, in Algebra II, we tried a new textbook every year, and nothing worked."

12:22 Jo Boaler takes the podium.  Her credentials seem very appropriate for this conference.  I'm excited!

12:23 When students are problem solving and applying methods, they were much more successful.  Nothing new, but people need to hear this, as "most schools do not teach in these ways."

12:24 Tracking as the greatest barrier to student opportunity to learn.  I'm not sure about "greatest barrier," but I have seen it present a significant barrier.

12:26 Summer school group is certainly an interesting sample to look at.  These students may have decent motivation (they need to pass this time around!), but probably low interest.

12:30 "The Dance of Agency."  Interesting thought of math (balancing/dancing between following rules and doing interesting work).

12:31 Groups, pairs, and coming to the board a lot.  Getting up to the board and explaining their own thoughts is huge for students.

12:33 This is actually sounding a lot like the summer school course I taught -- lots of board work, journaling about the class and learning, and group work.

12:35 Worked up to "cow and fence" problems -- why didn't they start with them?  Perhaps students wouldn't be engaged enough (remembering there is low student interest)?

12:36 Student achievement in Algebra increased after summer school course (as it should in any summer school setting [should being an admittedly loaded word]).  Big thing, though: increased engagement and excitement about coming to class.  I saw this in my own summer school class, which used a textbook.

12:38 78% of students enjoyed the class a lot, and 87% found it more useful.  Is there a tie-in, though, between enjoyment and genuine helpfulness/usefulness?

12:40 Math is about various paths to a solution, not just what the teacher says.  Yes, and?

12:41 Participation and group work made this class "better" for the students.  But again, what does "better" mean, and is that our goal?

12:44 Video of class.  "Questions for your colleagues [on different groups' work on board]?"  (Laughter from teacher audience)  No questions asked, and when one group invited up, there is HEAVY reluctance.  When they were up there, though, they did talk through it.  Teacher interpreted the words into formal language, but didn't change what was said.  "Is that always going to work?"  Students aren't too phased by this question.  Applause from classmates.  If one team is right, does that mean another team (with a different solution) is wrong?  "Absolutely not."  And they are invited up to explain what they did.  Even though the other group was shown to be "right," they eventually got up to talk about what they did.  After two groups presented, "how many are willing to say both generalizations work?"  Big encouragement to students as a community.

12:53 Comments of people seem to agree that community is important, when it's built on the math.

12:55 Math classes as silent classes.  I'm guilty of this at times myself, though I try to encourage discussion and collaboration.

12:57 All sessions were started with "number talk."  E.g., 15% of 240; 24 x 8; some abstraction with math.  Collect student's methods, and share different methods with students.  Revelation to students that different methods were there.

1:02 Discussion on chat has gone to how can we get colleagues to take risks and change.  Sounds familiar. . .

1:05 Student: "first time I ever saw math."

1:10 Comments on the stream are very good.  Discussion about real-world modeling, getting students to interact, the teacher saying "I don't know."

1:13 Observation from commenters: the teacher is still dominating.  What about students working to solve the problems, instead of a teacher-guided discussion at the end?

1:20 People in room are talking about "too much teacher talk" as well.  Boaler doesn't seem to agree (it's just a snapshot, etc.).

1:23 Students back in "traditional" classroom held on to what they did in summer school, and had significant improvement in math grades (on average).  But. . .it didn't last.  In fact, it looks like it actually made it worse overall after another term.  Hmm.

1:29 Discussion about student's attitudes in the chat.  Attitude needs to be worked on before math has a chance: "markovchaney: try it when they're in high school: it's like chiseling concrete with a plastic teaspoon. :)"

1:34 I might stop updating the blog here as Twitter is taking over, and I only have so many browsers and hands.

1:37 #mathchat is frozen, much as #engchat was frozen the other day.  Bollocks.

1:39 Discussion of standards and politics, and who has control.  Assessments don't test "extra content," but there's "still a lot of content to be covered."

1:42 Twitter's back.

1:45 End of Jo Boaler's presentation.  Sparked a lot of good conversation.  Notable: video database of good teaching methods and of good student collaboration?  That seems to be needed.

2:02 Paul Zeitz talking about math circles.  Get excited!

2:06 His first job brought him close to suicide, because he felt like such a failure.  Oddly encouraging to new teachers going through difficult experiences.

2:07 "Math is good for it's own sake." -- Paul Zeitz

2:08 "Math class should be more like field biology, shop class, and sports."  "The thing about sports is not harsh competition, but gentle competition."

2:10 "Math is the investigation of problems.  My definition of a mathematical problem is in contrast to an exercise.  An exercise is something you already know the answer to."

2:12 "Anything that facilitates investigation is good."

2:13 Math circles -- "club" atmosphere.  This idea is an import from Eastern Europe.  "We are the elders of a tribe."  Using this as folklore analogy, and it's an oral tradition.

2:16 Using games that have competition, but are mathematically open-ended.

2:17 "We're not composers [as teachers], we're performers."  Yeah, perhaps.

2:21 Zeitz models a game he would use, an animal taking-away game.  I missed the introduction a little bit.

2:22 Sage fills me in: 7 kittens and 10 puppies (for example), and each student may take away as many puppies or kittens as they wish, or the same number of each.  The student to rescue them all (have 0 of each remaining) is the winner.

2:25 Math circles now: do this on the board, and teacher challenges someone who will lose.  So everyone is seeing a game being played for real (after they have tried and played with it).

2:29 "When you know you've lost, that's the next step to winning."  And it provides the motivation to succeed.

2:32 Zeitz tells the group they will master the game today, but doesn't tell them how, then has them go to work on it.  The game: 16 pennies, each player must take away between 1 and 4 (inclusive).  The player to take them all away wins.  chatlog:

2:32 chadtlower: I take away 1 -- leaving 15
2:33 BrianWyzlic: I'll bite -- I take away 3, leaving 12.
2:33 chadtlower: I take away 3 leaving 9
2:33 BrianWyzlic: I take away 4, leaving 5.
2:33 chadtlower: gg
2:34 sageparade: anyone else? 
2:34 sageparade: I will let you go first!
2:34 chadtlower: lol@sage -- played this before?
2:34 sageparade: yes!
2:34 sageparade: ok, I'll go first.
2:34 sageparade: I take away 1 leaving 15
2:35 chadtlower: I take away 1 leaving 14
2:35 sageparade: I take away 4 leaving 10
2:35 chadtlower: gg
2:35 BrianWyzlic: What would be great: show this chat log to middle schoolers.
2:36 BrianWyzlic: Why did we know the game was over at 5?  Why do we know, then, at 10?

2:40 Zeitz breaks down the strategy, using color coded numbers:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

2:43 Changing the game to a graphical, vector-based game (the dog/kitten game).  Interesting, and has engagement, but where's the connection to a standard state curriculum?  It's there, but how do we guide the students to it?

2:46 "The great thing about us is we get to be stupid, and then we learn from our mistakes."  Common theme that's been coming up a lot.

2:49 Participants go to work on finding the graphic "oases" (green or safe points to give your opponent).  It all comes back to working backwards and finding the pattern/strategy.

2:54 Infinite diagonal (slope of 1), horizontal, and vertical lines of desert from each oasis.  Then looking at the deserts it creates for the opponent.  Good math here.  Is there a function that represents these oases?  Students will be curious.

2:56 The points are about differences between kittens and puppies.  So to get to them, for example: if a difference between them that is 2, then just go down to (3,5) or (5,3), and you'll win soon.

3:00 Turns out the oases are found using Fibonacci.  Dang, that's cool.  If you list the difference first, you will have 3 consecutive Fibonacci numbers with the difference, kittens, and puppies.  Well, almost -- (8, 12, 20 is not Fibonacci, but 8, 13, 21 is).

3:03 The audience is really excited about the mathematics behind this.

3:04 Oases are found through the floor function of the multiple of phi.  Sweet. 

3:07 Triangular/trapezoidal number problems.  "Perfect for math circle-y type math." 

3:09 Powers of 2 comes out pretty quickly -- accessible to middle schoolers.

3:16 Zeitz's pitch: "There's good folklore out there" and finding ways to help yourself and your students find those sources and work with them effectively.

3:19 Listening to him just talk and converse about mathematics and teaching is enjoyable.  This man clearly loves what he does

3:20 They're breaking for lunch.  I may or may not be back for the breakout session we get to see online.  It's supposed to come back at 4:15, until 5:30. 

4:20 They're got us set up watching The Arc of a Quadratics Unit breakout session, presented by Dan Bennett.

4:25 "Is there the culminating goal?"  Even though I missed the context, isn't that the question we should always be asking about our classes?  Is where we get to our goal?  And if not -- is that okay?  Answers may vary. 

4:27 They're working on a worksheet here, but there's nothing provided for those watching online.  This is unfortunate.  Future sessions should have some way to publish these online so they can be made available.

4:29 A large "a-ha" moment was just heard from many around the microphone.  That was kind of cool, even though we don't know what it was about.

4:34 There's a parabola opening down on the board, but is difficult to see as it's on the far board (this was introduced as a "launch problem" -- perhaps we're dealing with projectile motion here).  It's tough to know what's going on.

4:37 Sage to the rescue!  Worksheets have been posted.  It's a problem with a jackrabbit jumping over a fence. 

4:40 Video feed cut out and we missed a bit of the discussion, but the camera is in a better full-room discussion position.

4:44 New problem.  Oh wait.  Now we're on the jackrabbit problem.  But we're here for all of it, with the information.  Here we go.

4:49 Sage has offered to be our voice for questions.  That is a helpful feature. 

4:53 Some quick movement by the camera operator has helped.  We're placing coordinate axes on the problem.  We saw two possibilities -- one with the vertex on the y-axis and the ground is the x-axis, and another with the vertex at the origin.

4:57 Wally commented about using an interactive white board.  This probably would help with transformations and being able to quickly see the similarities between the graphs, and how it's just a quick translation.

5:00 In discussion: doing this in a geometry class, to look at transformations.  Not a bad idea, especially for those in geometry who haven't had algebra -- they can look at it in a geometry way, and maybe freak out less when they see it in algebra.

5:04 Talking about completing the square to solve quadratic equations always pains me.  Use completing the square when you need it, but please don't force it on a problem that doesn't call for it.

5:07 Lots of discussion about the problem, but nothing going very deep (at least to me).

5:11 Chat discussion now about students finding vertex from standard form -- calculators vs. finding a method that gives an exact answer (not just a numerical estimate from the calculator).
blaw0013: challenge students with developing a method that yields the EXACT vertex, and prove why

5:15 Give each student a camera and find something that looks like a parabola, and bring it back.  Then they do sketchpad with it as a class.  I like it!

5:17 "Ooh" from the audience as Bennett brings up a picture of a blade of grass the students brought in.

5:18 Students found "a" in the equation by using properties of symmetry and then roots.  Interesting.

5:19 Using stickies to watch video -- making video translucent, freezing it on the vertex (ball throw), and then putting that onto sketchpad.  When it's translucent, then it can be placed back over the sketchpad graph, and the ball can be seen following the graph (or not).

5:26 Bennett's wrapping up as we look at the room empty out.  There's a closing session that I won't be watching (and I'm not sure if we'll get the feed from that or not).  This has been a great day of online networking and a nice conference about teaching math!


  1. Thanks for the notes!

    By the way, her name is Jo Boaler (

  2. Thank you for the excellent notes! Waiting for a presentation as well. I really liked "The Dance of Agency" - a phrase to meditate on.

    Motivation is not sufficient to learn math, but it is absolutely NECESSARY.

  3. @Jan: Thanks for the correction. I found this out later, but apparently never made the change here. I'm on it!

    @Maria: What do we do to find the resources we need to properly motivate our students within our curricula?