mathcoachblog

A New Start for The Blog?

So, the name of this blog is “MathCoachBlog”. I picked the blog name about a year-and-a-half ago, as I was working in my district’s curriculum office, and hoped to use this forum to share ideas, resources and experiences. I treasure the opportunities I have had to share with others, the kind feedback people have given me about many of the activities, and the many friends I have made through this blog and twitter.

But here’s the thing: I’m not an academic coach anymore. After 2 years working with some great people in my office, I have chosen to go back to the classroom. This was purely my decision, and I am looking forward to implementing many of the ideas and resources I have been encountered in the last 2 years. I’m thinking of it as a mid-career re-set, and in some ways I am more energized to teach classes than I ever was before.

But the blog….keep the name? Change the name? Keep it? Change it? We’ll get back to that….

This week, I had to set-up a new classroom for the first time in a long time. I was in the same room for 13 years before, and had to pack a lot of stuff when I moved into an office. So, time to dust off the cobwebs, think about what’s important, and do some moving-in. Here are some elements I like to have in my classroom. What are some neat things you like to have to create a positive classroom culture?

I like to tell a lot of stories in my class, think about anecdtoes from previous years, and keep in contact with as many former students as I can. For AP Statistics, the “Wall of 5’s” has always been a topic of conversation, and a goal for many students who strive to eventually be “immortalized”. It’s a nice hook the AP classes. Thanks to my colleague Joel, who kept the wall alive the past 2 years, and has now made a duplicate wall for his classroom.

Wall of Fives

Along the same lines, I like to have lots of pictures from previous years around. Many of these are from our annual Stats Fair, and are great conversation starters.

Stats Fair

The Wall of Badges: more chances to talk about my experiences as a Siemens STEM Fellow, an AP reader, and conference junkie.

Badges

Cool art. Escher works always generate buzz. Now with 100% more Legoes!

Escher

T-shirts from math contests our math club has attended provide just the right amount of geek-pride.

Shirts

And finally, the oragami art a graduate made for me is the best gift ever, and gets it own spot in the room. Special appearance by John McClain – a “Secret Santa” gift.

Oragami

So, about the name of the blog… Since I announced my return to the classroom, I have had lots of conversations with colleagues in my department, and know I am blessed to work with many fantastic people. Sometimes we don’t agree on things, and that’s healthy. And I’m thrilled to be able to implement so many of the great new things I have learned, and continue to share them out to you. So, I’m no longer a coach in my district, but I think that, in many ways, I way wind up being a more effective coach to my friends online through the sharing of classroom ideas. So, MATHCOACHBLOG LIVES ON!

Also, it’s sort of a pain to change the name,….so there ‘s that.

Tags classroom

Middle School Statistics

Globe-Trotting With Random.org

Post author By Bob Lochel
Post date August 13, 2013
No Comments on Globe-Trotting With Random.org

The Common Core places increased imporance on statistics in middle school, beyond the tasks of creating simple data displays often encountered in middle-school texts. The new standards require that students be able to describe distributions, compare samples to populations, and design simulations:

CCSS.Math.Content.6.SP.B.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered
CCSS.Math.Content.7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

It’s all great table-setting for AP Statistics down the road, and working with authentic, interesting data. In this activity, students use an online resource to perform a simulation in order to find the proportion of the earth’s surface covered with land (as opposed to water). This is not a new activity, as a number of teachers suggest using an inflatable globe and some classroom tossing to reach estimates. But I think the method below uses some web tools in a novel way, and encourages some authentic geography discussions.

GATHERING SOME INITIAL IDEAS

Before diving into any simulation, I like to gather ideas from my students, to see if they have any initial estimates or backround about the problem. Using sites like Padlet or TodaysMeet are great for encouraging and archiving discussions and participation, or you can go old-school and just record initial estimates on the board. Asking an initial questions like: “Do you know the percentage of Earth which is covered by water” to start the discussion. The start a discussion of sample size: “Would it be better to sample 20 points on earth, or 40 points, or 100 points? What factors would be part of your decision?”

COLLECTING DATA

In this simulation, students will sample a random point on the earth’s surface, record whether the point is covered by land or water, and repeat for a given sample size. For this, we will use the site Random.org, which generates random events, mostly things like numbers and dice, and their Random Coordinate Generator, which chooses a random location on earth and displays it using Google Earth.

Google Earth

The site works quickly, and the water/land data can often be determined without issue. It is also easy to zoom in and out to take care of those “close calls”. Quite a more accurate measure than the thumb-check data from the inflatable globes. Very few issues arose in my trials with this method, but the biggest snag is Antarctica, which is land, but often appears light blue on Google Earth. Also, a few rare occasions produced a data point above the North Pole on the map, which I discarded. For your class, have each student generate a sample of size 10, and look at the proportion of land hits. Below, I did 10 trials for 4 different sample sizes:

Samples

The next steps depend on the sophisitcation and grade-level of your class. But in general, we want to know which sample size provides the best estimates. How do you know? Have students write explanations which defend a particular sample size.

Multiple sources (Circle graph from ChartsBin,NOAA Information) verify that about 29% of the Earth’s surface is land. Do our trials verify this? How often were our trials within 10% of this 29% mark?

Within 10%

As more data is collected, free site like StatKey can be used to generate appropriate graphs and statistics.

StatKey

FOR AP STATISITCS

I see this as an improvement of an existing AP Stats exploration, and opening activity for Confidence Intervals for proportions, and extension into the behaviors of CI’s. For those playing along at home, here are the calculations for 2 standard deviations (Margin of Error) for my given samples:

2sds