Think: The Five-Letter Word Game

Linda taught me this game when I was visiting her in Muskegon. She just called it "the five-letter word game." I thought it needed a name, and Think is as good as any.

Preparation
Each person thinks of a five-letter word with all five letters different, and writes it down in a hidden spot.

Goal
Guess your opponent's word.

Play
The players take turns offering a five-letter word (all letters different), as guesses, and as clue-gathering. If the guess is not the right word, then the opponent tells how many letters are right.


The game is similar to mastermind, but there's no information about where the letters go. (So you could get all five letters right, and still have the wrong word!) It's not a math game, but it is a logic game, and I think logic and math are twins.


Example
I'll share my guesses:
STOMP 0 (No letters right. Great. I can cross all of those off my alphabet where I'm keeping track.)
BLAND 2
QUOTE 1
FLASH 2
DIRTY 1
TRUCK 0 (Now I know 9 letters that aren't in the word.)
VOWEL 2
EXITS 2
QUICK 1
LARDY 2
BINDS 1
NIGHT 2
LINER 3

Would you have picked other clue words? Do you have enough information from these clues to guarantee any of the letters in the word?

Calculus: Planning My "Standards", Calculus Skills to Master & Mini-tests

I don't like the term 'standards-based grading' (SBG), because it reminds me of standardized tests. But I like the ideas behind it, and it's the term used by most of the teachers who are grading based on the goals they have for student learning. (Hmm, would 'learning-based grading' be any better? I like it better, but maybe it loses something for others?)

I know that most people who use these methods have more "standards" than I do.  I thought about all of the content of each course, looked at what's been on my tests, and portioned it out into what I have been calling mastery tests, though I think I'll start calling them mini-tests. I came up with 15 (later 17) for calculus. (Precalc has 16.) Each time I give a test, it includes about 4 of these mini-tests. Each one gets a grade, and can be retaken. The ones I'm willing to make lots of version of, I allow students to retake in my office when they are ready to show mastery. (Below the skills list is a description of how to show they're ready to retake.) The ones I can only make a few versions of, we schedule a time for them all to do the retake together. They get at least two chances on each mini-test and the final and as many chances as they want on quizzes.

Here's what I've been handing out on day one for the past few semesters, along with the syllabus. I fine-tune it each semester:



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Calculus Skills to Master

The test portion of your grade will be based on the 17 mini-tests described below. You will have more than one chance on each of them. On the mastery tests marked (RA), you may do the retake any time (in my office, after showing me your retake packet). The other retakes will be scheduled for once before class, on a day we arrange as a group. Use this sheet to record your grades.

Problem-Solving

You will have multiple chances to solve one problem that requires problem-solving skills. (Each test will have one of these, and there will be a few available during the final.)

Unit 1: Exploring the Idea of the Derivative

·            Definition (RA, as oral exam)

·            Tangent (RA)

·            Graphs

·            Rate of change (from a table of data)

Unit 2: Derivatives of Polynomials, Limits, Trig functions, Products & Quotients; Graphing; Optimization

·            Derivatives (RA)

·            Limits

·            Graphing Polynomials (RA)

·            Optimization

Unit 3: Composition, Exponential Growth, Implicit Functions, Related Rates

·            Basics (RA)

·            Graphing with Limits (RA)

·            Implicit   

·            Related rates 

Unit 4: Anti-Derivatives, Area, Volume

·            Anti-derivatives  (RA)

·            Area

·            Graphs

·            Position, Velocity & Acceleration

Unit 5: Volume

(No mastery test, but this will appear on the final exam)

Notice that graphing appears repeatedly. Graphing is a great way to visualize functions. Each graphing mini-test will cover different skills.

Retake Packets

For the mini-test or quiz you wish to retake, you will do the following for each problem you got wrong:

1.     Re-do the problem you got wrong. If you aren’t sure how to do it correctly, get help (from me, a tutor, or a friend). Once you are sure you have it right, think about what mistakes you made on the test, and explain what you did wrong.

2.     Find 3 problems (in the textbook or one of our supplemental texts) like the one you got wrong, do them, and check your answers. If you needed help to get these problems right, do more. Keep working until you can get 3 right on your own.

3.     Email me to request a retake appointment. When you come, be ready to show me a packet with the test on top, including your revisions and practice problems for each problem you got wrong.

Linkfest, part 3

Making Math

• Simple Sonobe (Sonobe units are used for multi-piece origami constructions)
• Weaving the Three Times Table
• Fractal App

Interesting Questions from Classrooms

• Circles Rolling on Circles
  
• From Graph to Equation (See the last question on this post.)
• On 'wait time' in Calc II (Wait for it... he talks about words before he gets to the math. This guy is brave. I can't imagine waiting "a few minutes" for students to answer a question.)
• Games for Complex Numbers
• Analyzing a Sonic Boom in Calculus Class

Education Politics

• Who Gets to Graduate?
• Women in Science
• Does Math Teach Higher Order Thinking Skills? (Not necessarily...)

Other coolness

• Analyzing the Game of Go
  
• Statistical Noise in Reporting
• Links for Statistics Teachers
• Don Cohen, Math Man, Interview As He Ends his Career

Linkfest, part 2

(Saved from the drafts bin...)

• These gifs are making the rounds on Facebook. I'm putting the link here so I can find them later.
• Henry Segerman makes fascinating mathematical artwork using 3D printing. While honing the description of the piece we'll be featuring in Playing with Math, I can across his 100 prisoners and a lightbulb paper. The puzzle posed seems impossible, but...
• Here's a much easier puzzle from 9gag (found on Facebook).

Linkfest

Hour of Code
Skip Counting with Manipulatives
 

Puzzles and Games
Skyscraper Sum puzzles (from Tanya Khovanova)
Geometric Construction puzzles (from Henri Picciotto)
Chomp (I haven't beat it yet...)
Just Make 10 (harder than 2048 for me, easier for some of my friends)



 (Wondering about Playing with Math? The book will be out within a month or two. I sent in corrections to the page layout proofs yesterday. Another round of corrections, last round on the index, off to the printers, and we're done.)

Monday Linkfest

I think my energy for blogging will return once the book (Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers) is done. I haven't even been reading the blogs on my feedly list regularly. I had to stop to get focused on the book this summer, and then I guess I just wanted a break. I caught up yesterday and today. (My Veteran's Day gift to myself.) Now I need to make a list of everything lovely that I found...

• I often enjoy Gary Antonick's NumberPlay column (each Monday). I especially like logic puzzles, so solving this one should be fun.
• Polar curves in nature... I wonder if the math might help explain the shape?
• This "which would you pick" question is a great intro for expected value for statistics.
• GSWP describes lots of different kinds of critical thinking.
• Fawn Nguyen is brilliant. This is a place-value puzzle that got her whole class thinking hard. 
• I love the Mighty Girl profiles I see on facebook. I wonder if this book they recommend is good: Infinity and Me
• A good article on Steven Strogatz in the classroom, which mentions some very interesting free curriculum.
• Hmm, I wonder if my son would try this maze puzzle, called Ogleboro City ... I'll print it out and see.
• I've played with this problem a little. I want to play with it more. Dan Finkel took the basic problem and posed a bunch of variations. Facinating! It might lead to another math circle topic...
• These gifs are making the rounds on Facebook.
• Henry Segerman makes fascinating mathematical artwork using 3D printing. While honing the description of the piece we'll be featuring in Playing with Math, I can across his 100 prisoners and a lightbulb paper. The puzzle posed seems impossible, but...
• Here's a much easier puzzle from 9gag (found on Facebook).

And I'll end with a request. Would someone please teach me to use a slide rule? I know it's a totally archaic skill, but I think it would help me explain logs to my students.

Making Assumptions

What do you think of this shirt? (Facebook keeps showing me an ad for it.)

I think the message it sends about math is very wrong. Part of how we do mathematics is by showing that something must be true, or figuring out that it's false. Even though the Collatz conjecture works for every number up into the billions and beyond that, we still don't say we know it's true, because we don't have a proof.

We don't assume we're right. In fact, I think mathematicians may be more willing than others to question their own assumptions.

Caclculus II: Parametric Equations

Last week I realized how much hand-holding my calc II students needed so they could get started with parametric equations. Most of them are very weak in trig. Many of them aren't sure how to get started when they're doing something new with graphing.

So I slowed down. But I also wanted them to do more exploration and experimenting. On a whim I gave them the typical assignment to draw something using parametric equations (or polar graphs). It can be anything, be creative. I don't have a particular assignment yet.

Sometimes (for some students) less is more. One of my students emailed me with a question, I replied, we went back and forth with over a dozen emails, and he produced this loveliness. I've included a screenshot below, but what he did is animated, so click on over to Desmos.

Wow! I hope his enthusiasm inspires the rest of them!

All You Need Is ...

(from the facebook meme, pictures removed)

[.docx here.]

If We Knew How to Trust

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If We Knew How to Trust

we see the amazing effort

young kids put into learning to walk and talk

(this work is their play),

and we know they are capable

of miraculous feats of learning.

if only we knew how to trust

their ability to continue learning

just as powerfully and miraculously,

maybe we could build a school system

that would honor every child’s fierce desire

to master the world’s skills.

their differences would no longer sort them

into good, mediocre, and bad students,

but into artists, scientists, poets, musicians, mathematicians,

writers, inventors, leaders, organizers, and more.

and each child would be many of these,

their differences adding to their strength as a community,

their school an ecosystem of learning.

written by Sue VanHattum, inspired by Lisa Cooley, 2014

[And here's another poem on what schools could be.]