## Sunday, November 19, 2017

### What Was He Thinking?

A few days ago I gave my kiddos this problem:

We had been reviewing percents and so I tossed this on to a quiz.  I figured they would use either a proportion or change the percent to a decimal first and then multiply.

However, one young man wrote this: (this is my handwriting, recreating what he wrote)

It was 9 p.m. by the time I got to his paper, so I just wrote:  "I think you know what you are doing, but I cannot follow your thinking.  Will you explain it to me?"

The next day I got together with him and he explained it to me.  It was a simple piece of brilliance.

"First of all," he said, "you have to ignore this."  He pointed to the proportion.  "I was just thinking about stuff."

"Oh, good," I said, relieved.  "You DO know that those are not equivalent, right?"

"Yeah, yeah.  So I knew that 8 of every 100 kids were sick.  So in 600 kids that would make 6 groups of 8 kids, or 48 kids.  Then that also means that in a group of 50 kids, there would be half as many kids sick, so instead of 8 kids, that would be 4 kids.  48 kids and 4 kids would be 52 kids out sick."

I nearly melted.  I absolutely LOVE it when kids have these great ways of seeing things.

We also worked all week (in our warm ups and review questions on homework) on taking 10% of a number in our heads, which led to taking 20%, 30%, and even 15% in our heads.  One kid asked if we could practice more on finding out how much tip to leave at a restaurant, which also led us to a discussion of why we leave tips, what it means to have a living wage, and the types of bills their parents have to pay.  It was an amazing week with those students!

## Saturday, July 22, 2017

### A Message for TMC First Timers

To all of you who are headed out to Twitter Math Camp (#TMC17) for the first time:  hang on to your hats... you are in for the ride of a life time!

First of all, I will not be attending this year, so I am sorry I won't get to meet you in person.  There are many reasons for this (two other times away from family already this summer, being chief among them), but also because one of the great things about TMC is the intimacy of it.

Deciding to keep the numbers down means more interaction among more people.  I was blessed to attend this most fabulous of professional development 3 years in a row (thanks to the administration in my school, who supported me professionally and financially), and met some fabulous people with whom I stay in touch via Twitter.  I wanted to make sure I wasn't going to take up a spot that maybe should go to a first timer.

So, First Timers:  go for it! Jump in and learn and share.  You have a lot to contribute, so don't be shy (this coming from a MAJOR introvert).  Be sure to tag along when someone announces a bunch of people are going to dinner.  This is how I met Brian Bushart (@bstockus) and Meg Craig (@mathymeg07).  OR hang around the hotel lobby or restaurant, which is where I got to meet Sarah Martin (@Sarah3Martin) and Max Ray-Reik (@maxmathforum).  Max!..... whose book I had just finished reading on the plane, and who eventually came to my school. He helped me change the way I teach: a small adjustment which has resulted in BIG changes in the way my students and I learn and share.

I even got to meet some of my heroes (and was brave enough to ask for pictures):

But more importantly, I had the opportunity to meet people who live in my geographic area so we could get together for fun and for brain storming!

I hope in the near future, more of this great professional development at TMC will be video taped so others can benefit from it!  (Yes, @cheesemonkeysf, I sure would like to see your morning sessions at TMC17!).  What an amazing library of professional development that would make!  But be sure to visit the wikis and the archives from previous Twitter Math Camps.  They are full of fantastic materials and ideas.

This school year is going to be a real challenge for me.  It is the end of July and I still don't know what courses I will be teaching.  Because of some dual enrollment courses, I will no longer be teaching my favorite Honors Pre-Calculus classes (I don't have the requisite majors/Masters), and may end up teaching some courses I have never taught.  My teaching load will also be increased.  AND we have two new staff joining our math department, to whom I will want to be sure to be available .

But I will not be alone. In addition to the great math faculty at my school, I have a huge Professional Learning Community in the Math Twitter Blogosphere (be sure to go explore it!)  I may be shouting out for help along the way.  Thank you, in advance, to members of MTBoS past, present, and future, for your help!  I will be reading your tweets and posts (especially during TMC 17 time).

One final piece of advice:  Go forth and have a blast, First Timers!

## Sunday, January 8, 2017

### My Math Autobiography

Once upon a time, math and arithmetic was fun for me.  I enjoyed it, I found it easy and fun.

Then integers happened toward the end of junior high school.  And suddenly nothing made sense.  Well, that isn't TOTALLY true.  Multiplying and dividing integers had a very simple pattern: easy to catch on to, but adding and subtracting integers?   Why not just teach me Chinese....while speaking Russian?  That's how much sense it made to me.

And my teacher had only one way to "explain" it... using a horizontal number line.  Being spacially dyslexic, this was the worst possible way for me.  It was his ONLY tool.

When I got to Algebra 1, I was supposed to already be fluent in this integer-speak.  I learned process quickly.  I absolutely understood how to do and undo.....except I couldn't add or subtract with those integers!  I was just guessing!!!

Midterms came.  I studied so hard: practiced by doing and re-doing old homework assignments and tests.  Our teacher called us up to his desk during silent work time to "stage whisper" our exam grade to us.  I didn't hear him say "C" a grade I was expecting...it wasn't an ssss sound.  Could all my hard work have paid off?  "Excuse me?" I said.  His reply came through loud and clear, and in the silence all could hear him say:  "D.  As in Dumb."

I wanted to die.

I was truly crushed.  And for a while, I was convinced he was right.  But I knew I was good in other subjects, REALLY good, so this just didn't make sense that I was Dumb in Math.

I muddled through that year, and Geometry was better.  I think I saw all those proofs as puzzles.  But then I got an Algebra 2 teacher who asked me if I could read (I asked for help on several word problems everyone else was too afraid to ask about).

I snapped.  I was done being called stupid.

"Yes, Ma'am, I can.  There is a sign down the hall that says "Guidance" and I think I will take myself down there."  This from skinny, timid Tina  The whole class fell silent as I gathered my books and bag and left.  I had never, ever done such a thing in all the years we had been in school together.

I deposited my stuff in Guidance, told the secretary I would be right back to see my counselor, and then went to my Assistant Principal's office to let him know I had just walked out of my math class.

"Come in, Tina," the Assistant Principal said.  "What seems to be the problem?"

"Well, I just walked out of Mrs. O's class, Dad, and I wanted to let you know.  I was not disrespectful, but I did walk out and will serve whatever detention she or you feel I should get for that.  But I will not go back to that class.  I am going to Guidance to have my Algebra 2 class switched.  You can talk with her and let me know what my consequences are."

Dad nodded, told me to go on my way and he would talk to Mrs. O.  He asked me to close the door on the way out.  I was nearly in the hall when I heard him erupt in laughter.

It was a long, slow climb back to some semblance of confidence in my math ability.  Some decent college experiences helped, but I still stayed away from math as much as I could.

I was trained to teach reading, and it was because of students with learning disabilities who came to me for reading help that math and math education returned to my life. Turned out many of my tutees also needed math help.  These students all struggled with concepts I had struggled with.  Together we came up with ways that helped them or I would think and think and think of how to make this more visual or more hands on for them.  Sometimes they showed ME things that someone else had showed THEM.

In the end, it was my students who made me a better math student, and eventually a better math teacher.  I am forever grateful to them, as my students continue to challenge me and make me grow.

## Wednesday, November 9, 2016

### In My Own Little Corner

It has been a difficult two weeks.

I have been told what goals I have to fulfill for my two year "self-evaluation" period, and I attended a meeting where a we were scolded for half an hour over several things that did not pertain to me. At the end of all this, I had to help students: some of whom were feeling unsafe and afraid before the election, and some of whom were feeling unsafe and afraid after the election.  Not an easy task when I, too, am feeling unsafe and afraid.  It puts me in mind of how I felt after 9/11:  I just want to gather up my most beloved family, find a little hidey hole and block out the big nasty world.  I am SO grateful for a long talk with my sister who loves and supports me, who understands this visceral need, and who expresses it so eloquently.

But in my own little corner, in 207, we continue to do fun and challenging math.  Thanks to Alex Overwijk at SlamDunkMath we have been playing with bicycle rims to learn about radians, arc length, and such.  Go visit him!  He is the MAN!  And thanks to my son and daughter-in-law who spent a rainy afternoon taking all the spokes out of 7 bicycle tires!

Here are some pix:

 G. really gets "into" her work!

 M and crew just "hanging" out.
We have a shortened week because of Veteran's Day, so we'll have to play with these some more the next time we get together (I see these students only every other week because we are a vocational school).  We will have only 2.5 days together next cycle, so...not sure how much we can get done.  But it is a safe place where students can work together to explore and to learn.

This is my own little corner.

## Saturday, October 8, 2016

### #Star of the Week!

Meg Craig (@mathymeg07) is one of those people who make your heart sing.  I have learned so much from her and she shares her materials, thought, ideas, and encouragement so freely.

Last summer she announced that she would be perusing the Math Twitter Blogosphere and Twitter to find teachers who are doing cool things.  This week she chose several, and I got to be one!  If you click on the #Star of the Week button, it will take you to Meg's post.

Dear Meg,

Thanks for your kind words.  More importantly, thank you for the encouragement you ALWAYS give and for the humor that goes with it!  We love you, Meg!

Yours Truly,
Tina and the rest of the MTBoS !!

## Wednesday, October 5, 2016

### Getting Past Those Hurdles!

Algebra 1 and introduction to functions:  I have never liked how I did this before, so I scrapped everything and borrowed some stuff I had done when I introduced polygons (developing definitions).

The link to the slides is here, but let me explain what I did at the end that seemed to make a huge difference in my students' ability to interpret a graph of a function.  They can easily tell me this is a function (because I always start this unit by doing Hiker on the TI84 which uses the motion detector and they have to recreate some graphs I have created).

I started by showing this graph and asked them to share out some notices.

Then instead of doing wonders, I asked them to sit quietly for a moment and come up with a plausible story for what was going on in this graph.  I let them share out stories, and they had to be able to account for what was going on in the various parts of the graph.  We recorded a bunch of plausible stories.  Some of the stories included manufactured goods, car races, people walking, etc.

After we were done, I tapped the screen and gave them one additional piece of information:

We went through our stories and starred the ones that could still be plausible now that we had this additional information, and talked about how this domain or input information made some stories work and some not.  We went through the remaining stories to be sure the various parts of the graph still made sense.

Then I gave them one more bit of information:

We went through our stories and starred the ones that made the cut, given this new information.  We were left  with just 2 or 3, and it was getting hard to keep talking about the Solid Line, Dotted line, and Dashed/Dotted Line.  I revealed one more bit:

Ah, yes. SO much easier when we are given a key!!  We went through the various stories left, accounting for that horizontal piece and the place where A and B cross.  They still were voting for a car race, a trio of people walking, and a running race.

I asked what this graph was still missing.  It took them WAY longer than I expected, but finally one of my most quiet students threw his hand in the air and shouted:  "A TITLE !"

In triumph we showed this slide and there was a chorus of "OH!"s and some fist pumping:

Then I asked them to sit and write the story of this graph,  And they were spectacular.  We had spent so much time already thinking about causes and effects, they were able to do this SO much better than ever before.

But ONE of my Algebra 1 classes (small, mostly guys) kept saying NO WAY could any one run 400 meters in 60 seconds.  They kept thinking about the length of a football field and just refused to believe that these numbers made sense.  I had to put them on hold so we could finish the writing.  I even told them if they had to change the 60 seconds to another number, I was okay with that, as long as it got incorporated into the story.

Today, I grabbed them all as they came into class and told them to drop their bags we were going outside.  We walked the track and I told them that this track is 440 yards (roughly equivalent to 400 meters).  As we walked I asked them to take out their phones and google what the world record is for the mile.  (A mile is four laps around this track.)  What?  Under 4 minutes?  So about how long to do one lap?  They were amazed.

Then we looked up the record for the 400 meter race.  Roughly 40 seconds.  The world record for the 400 meter hurdles?  Only 3 seconds more!

"On Friday, I will time anyone who wants to run one lap on this track.  How many of you volunteers think you can get close to 60 seconds?"

When I got home today, I told Hubby about this.  He suggested I let them tell me how many seconds they thought they could do it in and then I give them a range that they could be within that guess.

HOLY MACARONI, Hubby!!!  You are talking absolute value equations here!!!  (He's a pastor, what do they know from absolute value equations?  Bloody genius, he is!)

So a will be their target time, the number of seconds they think they can run the lap.  And b will be the range I will give them ("You know, you have to be within plus or minus this many seconds and you can still win that candy bar.")

I will update after we get through with this, but I am beyond excited thinking how I can introduce absolute value equations, all because I wanted to introduce functions differently!

## Thursday, September 29, 2016

### Intro to Segment Addition Postulate Morphed into SO Much More!

My Geometry students are a really mixed bag of abilities.  Just shy of half of them are on IEPs and/or 504s.  It makes it challenging to be able to figure out how to get the material introduced in ways that are accessible for all learners, including those who are not native English speakers.

Today we had only 15 minutes at the end of class to introduce the Segment Addition Postulate.  I put this on the board:

(Max and Maxine live on the same street.)
My friend Max walked from his  house some distance to visit his friend Maxine.
Meanwhile, Maxine decided to walk out to meet him along the way.
 Max
 Maxine

Then I asked a student to go up to the board and draw how far Max walked.

"How far should I draw?"
"Until you think that is how far Max walked."

It was funny to watch her add a little bit more and then a little bit more. Why?  Because she would turn to me with a questioning look and I would say, "OK.  Is he done walking now? Finally she just said "Yes, he's done," and I asked a second student to go show how far Maxine walked.

I am grateful when student number 2 drew the other segment, Maxine walked all the way to where Max seemed to have stopped.  I wasn't sure how I would deal with that except to say, "Is she done walking yet? Why/why not?"

I asked a third student to put a point where the two met.

We called it P for "Perfect" (said with an English accent....I did that once and they now all mimic me! Whenever someone does something great they all say in unison: "Perfect!" with the appropriate English accent.)

Here is what we had so far:

Next I asked them to notice things in the story that they could say with ABSOLUTE CERTITUDE.  One of the notices was that P was the midpoint.  I had to intervene here and ask the student to prove it.

S: "LOOK at it!" he exclaimed.  "It's right in the middle!"
Me: "Prove it."
S: "How?"
Me: "I dunno...got any ideas?"

Someone grabbed the yardstick and measured the segments.  To make it more "real" we decided to scale it: 1in = 1 yd.

Finally I asked them to come up with some questions we would be able to answer with ABSOLUTE CERTITUDE.  These questions ranged from "Are they friends?"  (Yes b/c it says "his friend Maxine") to the one I had hoped for:  "How far do they live from each other?"

THIS question led to a spontaneous Number Talk.  I had not had an opportunity to do Number Talks with this group of students yet.  It was SO cool.  These strategies ranged from "I did the algorithm" to "I took 4 away from the 19 so that it became 15 + 15 = 30, and then added the 4 back in to get 34."

I particularly loved the very last one. It was SO cool, I made the kids stay quietly in their seats even though the bell was ringing b/c THIS young man noticed that if Max had waited and not walked the extra 2 yards, Maxine would have walked an extra 2 yards which means they each  would have walked 17 yards and he knew that 17 doubled was 34.

O be still, my heart.