Measures of Central Tendency: Range, Mean, Median, and Mode. Halloween Edition!

You and your friends go Trick or Treating, and decide to pool all of the candy and divvy it up evenly when you get back home. You get 23, 27, 18, and 26 pieces of candy.
- How many pieces of candy will each person get?
- What MoCT is this?
- What are the other measures?

Right before you leave the house, your Mom tells you to bring your little sister along with you. Ugh! But, all of the neighbors thought she was so cute that she was raking in the candy. She got 45 pieces of candy!
- What will happen to each of the MoCT? Will they stay the same, increase, or decrease? By a lot or just a little?
- Will each person, including your little sister, end up with more or less candy?

After the first house you visit, you run into a classmate of yours, who tags along for the rest of the night, but doesn't get any candy himself. (All of the pillowcases at his house were in the laundry.) At the end of the night, he asks to get half as much candy as everyone else.
- How do you distribute the candy between all of the people?
- What expression can you write to show this?

I'm one month into my second year of tutoring math at an urban high school, serving almost all ELL students. Now that I have a degree and a year of school-specific experience under my belt, there are some aspects of my tutoring that I want to improve.

1. Spiral Review daily.
   Our official curriculum has built-in review days, but they are designed to target only the skills that we taught that past week. I've been slowly creating review cards with questions from every topic we've studied so far, so I can pull them out and let students choose a random card (skill) to practice.
2. Teach note-taking and note-using skills.
   Even if my students are technically placed in 9th or 10th grade, due to possible interrupted schooling, many of them are not used to "doing school", or what they need to do other than just sit and learn in order to succeed in high school. With some of my younger students, or those with major organizational issues, I write out a set of notes as the lesson goes on, and tell them, "Make your notes look like mine." Then, as we accumulate more lessons in their notebooks, I encourage them to look in their notebooks for answers before they ask me.
3. Create cumulative vocabulary sheets.
   I'm still undecided whether it'd be better to create a long list of words at the back of their notebooks (or on a separate sheet), or to make an outline before each section with the words and phrases written in, with space for them to write definitions and translations, and show examples. The latter worked excellently last year for the Algebra I unit on linear equations, so I might try that again this year, even if it requires more upfront work on my part.
4. ELL support, even for English speakers.
   By the nature of this particular high school, every student in the academy is enrolled in an ELL class along with their content classes. Even if the students are comfortable with spoken, social English, all of them need help practicing the academic language structures that will let them be successful in their content classes, and eventually be able to transfer into one of the other academies (that isn't specifically designed for newcomers and ELLs). These techniques could include writing sentence stems into their notes; encouraging students to discuss problems with each other in English or Spanish and responding to them in English; and pre-teaching the vocabulary needed for an upcoming section.

As the year goes on, I also intend on keeping detailed notes on how I teach all of the different topics, and what did/didn't work for various students. Even though I can remember most of the techniques for myself the next time I see that topic, my notes could possibly help some of the new tutors this year and in the future.

This isn't directly related to teaching, but I bet I can find something relevant to say about it.
As of the past two weeks, I've been taking a free, online college course called "Principles of Economics for Scientists." I'd somehow managed to never take any sort of Econ course before, and this one is a great response to my hesitation about the subject relying too much on discussion of human nature and the sociology aspect of things. (While I do respect both of those approaches as valid, neither of them would have helped me make intuitive sense of this new subject.) As it happens, the "for Scientists" part of the course title roughly translates to, "for people who know and understand Calculus", which squarely includes me.
(Ooh, I figured out the connection to teaching and learning!)
In this class (at least so far), the professor is using Calculus as the lens through which he is teaching the fundamentals of economics. Therefore, for the intended population of students, there is a basic level of math needed in order to comprehend the material of the course. We are not doing math just for math's sake; we are using it as a tool for something else. Without a conceptual and practical understanding of calculus, the professor would have to take a more convoluted approach to teaching the exact same topics, probably resulting in students appreciating the material less.
This is equivalent to the pedagogical idea of "learning to read vs. reading to learn," the transition that all Language Arts teachers encounter in their respective grade levels. Once students can physically read a text out loud, what do they get out of it? How will the skill of reading translate into a truly functional literacy?
These same questions can be asked of math: "learning to do math vs. doing math to learn." Many secondary math classes spend all of their time teaching and learning sequences of math skills that build upon each other, with the promise that students "will need to know this later on." But for students that have no desire to continue in math or science classes, that later time never comes. I see myself as a perpetual student of math, but I've realized that while some math is universally necessary in participating in adult life, and other math is elegant and interesting in its own right, some topics are useful not just for the sake of doing math, but rather as a tool for understanding other topics, spread far and wide across the human quest for knowledge.
Every math teacher gets asked the question, "Why do we have to know this? When am I ever going to use this?" In response, think further than just the upcoming test, and even further than the next few courses in the school's sequence. Math is pervasive, and we need to convince our students that there is a bigger picture to the subject, that stretches far beyond the classroom.

Life update, since the last post:
- Completed my Math major.
- Started and finished my student teaching (MS and HS), and my Secondary Education major.
- Graduated from college =)
- Became a certified Secondary Mathematics teacher in two states so far, working on the third.
- Taught my two summer classes for the 2nd year, and got asked back for my 3rd 2013 summer.
- Currently working as a full-time math tutor at a HS in urban Massachusetts, and job-searching for next year.

Hoo boy!

What's been on my mind lately:
- Do I want to start my classroom teaching career in an urban, more difficult-to-manage school, or in an "easier" suburban environment?
- How will I measure the success of my students mid-year and at year-end?
- What can I do to increase my students' retention of math content from week to week, other than just in basic skills?
- What else can I do this school year to improve myself as an educator and thinker, and make myself a more marketable teacher candidate?