Little Kids Math - Scary!

Recently my job description has changed a bit. Because of the ongoing financial challenges that almost everyone in education is dealing with, my job description has changed a bit. Currently, I am work with middle and high school math teachers. Soon our primary math specialist will be leaving due to budget reasons, leaving me as the math specialist. Scary!

My personal experience in the classroom is limited to middle school and up. I am certainly not a math expert, but feel I have a pretty good handle on the content of middle and high school math as well as understand enough about the students to be helpful. The thought of being in a classroom of 20+ 6 year-olds, makes me want to run away screaming. The closest experience that I have to working with such a group of kiddos is playing with and being Dad to our 4 year old son. Not really what one would look for during the hiring process.

In order to ease my anxiety I have been studying the content of the elementary grades. I will tackle classroom management strategies later and will be relying on my wife's experience as a 2nd grade teacher, the expertise of some friends, and my PLN to get a handle on how to maintain control of an elementary classroom. 

So far I have spent 2 days learning about computational fluency with K-2, read most of "Introduction to Problem Solving by Susan O'Connell, written a detailed 1st grade lesson on adding and subtracting, and closely studied the 4th grade math standards. I have learned a bunch and really am amazed at how much I have enjoyed this learning experience. What I find most fascinating is the idea that the standards really do seem to be addressing some challenges that I have personally experienced with high school students. I often observe such gaps in students understanding of the structure of numbers that it interferes with completing more complex tasks. So many patterns and relationships exist within numbers that one could spend a lifetime discovering new patterns. Pretty cool and amazing stuff. I really do see how the AZCCRS emphasize helping students learn how numbers work together.

Another thing I have enjoyed is being able to read the standards and actually understand what they are asking for students to be able to know, do, and understand. Ever read the AZCCRS math standards for high school? It's kind of like watching Jeopardy for me. 90% of the time I have no idea what the question (or I guess answer) is looking for, but recognize something about 10%. The high school standards are super dense and difficult to read. It takes a very focused effort and some review to make sense of these standards. Perhaps it is because of my experience and knowledge, but the elementary standards seem pretty straight forward. It makes me smile!

I get really excited when I see what students are doing in the lower grades because it will be such a benefit to the students as they encounter more difficult and complex topics. Understanding what the equal sign means and how numbers can be decomposed, rearranged, and put back together is an invaluable skill that can not be emphasized enough.

Although I am nervous about my credibility with elementary teachers I am very excited for the chance to learn from them and expand my knowledge about teaching math to students of all ages. Can't wait to see what is next.

Use Desmos for Least Squared Lines and Regressions

Graphing calculators are great. They do everything that I have ever needed plus a whole bunch of things that I have never needed. They certainly have their place in the classroom. However they have their limitations. Students can find the navigation frustrating and it is sometimes really hard to see the graphs. Zooming in and out can be cumbersome and finding key points quickly requires a less than simple process.

Enter Desmos. If you haven't used Desmos take some time to mess around with it. Desmos is a web-based graphing calculator. It's a great tool and easy to learn. A couple of weeks ago I had a few spare minutes during a tutoring session. The students were working on determining the least squared line of a set of data using TI-83 calculators. The students were struggling with changing the viewing window and finding the equation of the least squared lines. I turned to Desmos to provide some clarification.  A quick search confirmed that Desmos does regressions. Beyond that you can put the data, the line (or parabola, or whatever) and the residuals graph on the same coordinate plane so that students can really see the relationship between the two. Here's how.


Step 1:
Enter the data. This can be done as a series of ordered pair or by adding a table (To add a table click the + at the top left of the screen and then choose "table.") If you have the data in a spreadsheet, simply copy and paste it into Desmos. Desmos will automatically put the data into a table for you.

Here is the data that I used.

Length	Time
53	1.43
63	1.53
73	1.67
83	1.76
93	1.93
103	1.98
113	2.08
123	2.21
133	2.28
143	2.38
153	2.43

And here is what it looks like in Desmos.

Notice that you can not see the data. 

Step 2

To see the data, simply zoom out or click on the wrench to access the graph setting where you can choose the viewing window by adjusting the minimum and maximum values for the x and y-axes. Watch the video to see how to do this.

Here is what my graph looks like now.

Step 3
Now we are ready to find the least squared line. Since the graph appears to be linear I will do a linear regression.
Enter the following equation into Desmos

y₁~mx₁+b

This tells Desmos to pull the data from the table. The "~" indicates that it is an estimate. After this is entered the least squared line will be visible and information about the correlation will be displayed.

It appears at this point that the line closely correlates to the data. The r²value is very close to 1.

Step 4

To confirm that a linear model is the best fit for this data we can use the residuals graph. To create the residuals graph first simply click the "plot" button under residuals in the information about the least squared line. Boom! The residuals plot is automatically created and a column with the residuals is added to the table.

If we look closely at the residuals plot it appears that all the points at the end are below zero while the points in the middle are above. This would indicate that perhaps a linear model would not be good for lengths outside of our data set.

Desmos is not the only way to create this plot. However, the ease of use makes it a good tool for teachers to use when discussing graphs and data. Being able to quickly create graphs can help teachers lead great discussions with students. These graphs can also be saved and shared with students through email or share a link to your graph. Click the link below to see the graph I created for this post.

https://www.desmos.com/calculator/ihn6qvicng 

Enjoy and happy graphing!

Force a Copy in Google Docs

A cool trick that I just learned and has made my life easier. There are times when I want to have participants create their own copy of a Google Doc. This can be a cumbersome experience for those that are just starting with Google Docs. I can imagine with younger students, this can also be a bit of a challenge and take some training. I do not have access to classroom and it really wouldn't be very practical to use in most circumstances. Forcing a copy has helped me overcome some of these hurdles.

1. Open the document

2. In the address bar change "edit" to "copy"

3. Create and send short link

When the link is opened by someone else they will see a screen similar to the following. They are forced to make a copy to their drive in order to open the document and you are ensured that no one can make changes to your original document.

EdTech Summit Arizona - Google Apps For Education - 2015 Version

Today is my first day back to the office after an amazing two days at the AZ EdTech Summit featuring Google Apps For Education. I have been looking forward to this event for a long time. It certainly didn't disappoint. I laughed, got choked up, learned some things, talked to some great people, met some people from my PLN (Rodney Turner) in person for the first time, learned some more, and have been thinking about the experience since I left. I had a hard time sleeping last night because I was so excited about all I have learned.

Now it is time to try to make sense of and record (before I forget) some of what I have learned. Alas - some of those nuggets of greatness have already been lost. Maybe not forever, but at least as I write this.

This year I am going to write a top 5 list (complete with links) of what I personally found most compelling/interesting/thought-provoking. Hardly any of it will directly relate to the teaching of mathematics and may not even strike a cord with some who are reading. Instead, this is my attempt to capture some personally relevant thoughts in the hopes of passing on some inspiration.

1. "Change the World" - Juan Deluca - 

Juan closed the conference as the closing keynote speaker. He related personal experiences and his appreciation for being in the position that he is today. He is currently working on a project which will be putting devices in the hands of hundreds of thousands of students. Pretty awesome in my book. He will personally be participating in something that will affect thousands of students. His final message was that today's teachers and today's students are going to change the world. He shared some examples of what students had accomplished in his class when they were allowed to create freely without restrictions. I believe that  we need to move out of the way and let students use their creative powers to solve problems that they are interested in. Juan shared the work of a student who completed a design project of a school building that was in need of an update. The student used research, creation, and presentation techniques to create a design that was "green" and student friendly. The ideas were presented to the leadership along with ideas from the professionals. "And guess whose design was chosen?" Juan teased. "The professionals." He answered. Of course that really doesn't matter. That student probably learned more valuable skills from completing that one project than they would have learned from an entire year of lecture. These are the opportunities that not only change the lives of our students, but lead to real change in our world.

2. "Tweet Your Ideas - Or at Least Share Them" 

During the conference I was Tweeting away any takeaways or "ahas" that I was having. And to my surprise people were interested. I have received more Twitter traffic over the last two days than I have in the last year by simply using #gafesummit and sharing what I thought was interesting. It would take me years to share these thoughts if I had to do it through conversation and PD training events. My ideas have reached thousands of people. I'm sure many of these will totaly ignore my ideas and thoughts but that's not really the point. Some will make use of what I shared. This in turn may help some student who may some day "Change the World." Good enough for me.

3."Hire or Fire" - Brian Hamm 

Brain really opened my eyes to the idea of controlling your on-line presence. In the last two years I have made great strides in creating an online presence. I have a Twitter account, G+ page and Google Site along with this blog. Admittedly, they are not the greatest social media accounts, but they are a start a lot of ideas are work are displayed. The greatest take away for me was the impact that on-line presence can have. Our students do not think of the impact that an inappropriate Tweet or post can have on their future. Research Justine Sacco to see one example. On the opposite side, if students create a positive online presence it can positively impact their future. Many major colleges (if not all) are using online presence as part of the application process. Some people get hired based on their online presence. Watch the video below for an example of how this can be done. 

4. "G-docs Top 3" - Rachel Wente-Chaney

#1 Google Docs are collaborative #2 Use the "Comment and Chat features #3 Use Revision History - If you use Google Docs you probably already know about these. However, I thought it was worth sharing. Rachel also clarified for me, how I can explain to people (without overwhelming them) why Google docs are more effective than other word processors.

5. "Soul Fuel"
I really need conferences like this. At times the negativity and the mundane day to day events can cause me to loose some momentum. Conferences like EdTech AZ Summit help me regain my momentum and remind me that change is happening and there are people like me who are excited about education and what is happening. It reminds me that politicians and media don't have to be the loudest voices in education. Teachers and administrators are doing great things every day and teaching our students what is really important. What is really most important isn't always covered in a standard (not that these aren't important).

I love the EdTech AZ Summit, I love Google Apps for Education, and I love sharing what I learn with anybody that is willing to listen to me or read what I share. I can't wait fo EdTech AZ Summit 2016. Can we register yet?

#LoveTeachingChallenge - Why I Work in Education

In the midst of much negative attention and feelings toward education, there is so much good that is happening in schools everyday. It seems the only time that schools are on the news is when something negative happens. Meanwhile in every single school across the country great things are happening. Teachers are creating supportive, exciting, safe, and effective environments in which kids are allowed to do what they do best: learn, share, and have fun.

I am not on the front line of education anymore. I am not doing the heavy lifting anymore. I do not face the challenges that classroom teachers face. However, I do support teachers. I am there as a resource and hope that my efforts help teachers be more effective in supporting the learning of their students. I know that teachers are often the most influential adult in a student's life. This is why I stay in education.

Luckily, I do have the opportunity to work with students in some capacity. I tutor high school students who are in a residential soccer program. Mostly I work with the students on math, but will give any subject a shot.

I love it when a student comes into tutoring frustrated and worried that they do not understand their math assignment. Often they will say they have no idea what they are doing and have little hope of ever "getting it."

I love this not because I enjoy watching the students struggle, but because I know it is another opportunity for me to see that "light bulb" moment. It is another opportunity for me to show students that seemingly impossible tasks, can be overcome and understood. Over time, I see these students show incredible growth and some even learn to like math. I love hearing, "I never liked math before. But now that I understand it, I like it." These are the moments that keep me going back. These are the moments that I remind myself are happening in classrooms all over Pinal County and the reason that I try my best to provide teachers with relevant and useful information.

I believe education is something much different than most professions. I would say education for most people is what life is about. It is connecting with and helping students discover themselves and grow into whatever it is they wish to be.

Blogging - Leaving Pieces Behind

I am writing this blog in response to Todd Nesloney's #EduLS Week 5 challenge. The assignment is to write a blog entry. For some it will be their first ever blog. For others this week's assignment will be part of their regular routine. For me, it falls in the middle. Blogging isn't something I do everyday or regularly, but something I have done sporadically. I have contributed to two blogs, this blog and Banana Daiquiris and Life Lessons. This blog is for my "professional life" while BD & LL is more personal. I am one of several (and certainly not the most entertaining/creative/cleaver/consistent/funny) contributors to BD & LL.

Back to the point. As I thought about the topic for this blog post, I read through some previous posts and a thought started to develop. There are lots of great reasons to blog. Jon Harper mentions a few of these in this video introduction. I find that blogging is a chance for me to think through some of my disjointed thoughts and attempt to make them understandable and relevant for others. As I read and reflected I also took a moment to look at my blog data. My blog is not followed by many people (actually only 1 and I think he was guilt-ed into it). However, by the magic of the inter-web and social media, my blog has been viewed 595 times. Certainly not very impressive and not even close to what more popular educational blogs see in one day.

Still I can't see this as a bit impressive. My first post was on March 21, 2014. In a little less than a year my little dinky, experimental, rambling, inconsistently contributed to blog was looked at 595 times. Not too bad. Granted some of these were friends and family, some were certainly repeats, some were probably even accidental. Still, it means that 595 times someone was exposed to what I had to say. I can somewhat confidently say that even if only half of those visits were from viewers who were somewhat interested in the content and took the time to read all or part of a post, my thoughts were shared with another human being around 300 times. That's pretty cool! And just maybe of half of those times - 150 times someone read something what I wrote and considered it. And just maybe a quarter of those instances (around 37 of those times - I should have used an easier number) someone thought further about or talked about or actually made a change to something that they do in their classroom or with their own children. Well that's pretty cool. And all I had to do was take 15 minutes and write some thoughts and post them to the magical inter-web. Pretty awesome stuff.

And how does this all relate to the title? I began to understand that writing a blog is like leaving little pieces and bits of information behind. And what's so impressive about that? Pretty simple. We all look for information on a particular topic daily. What's cool about blogs is that any time someone goes to the Google and types a question or topic into the search bar, there is a chance that that person will come across what you wrote. My job is to present PD to educators. I love my job and hope that I make a difference for students. However, I know that there are times when I present on a topic - let's say task-based learning for instance, and those that I am presenting to (or some of them) are not quite ready to use the information to make change in their classroom. Unfortunately this information may be lost. And lets face it 99.9% of the time they will never look at the materials given to them ever again. But then later (maybe 1 year, 2 years or 5 years later) they say, "Wow, I can really see how I could use task based learning to help my students understand _______________. I just wish I could find that stuff that one guy gave me." That's were the internet, including blogs, teacher pages, etc are great resources. They are little pieces of information left for others to find when they need it and when they are ready for it.

Now do I know if anything that I write makes a difference to anyone? Not really. But I think the odds are with me. Especially if I continue to blog, read blogs, consider their ideas, share their ideas, blog some more, post some more resources etc.

Happy blogging and thanks again to Todd Nesloney for putting us all to the #EduLS challenge! Maybe someday I will make his, or someone else's list of favorite blogs! And be sure to check out BD&LL. I like to think we are somewhat entertaining and will make you think about some things you never thought you would think about. Besides, we'd all like to be famous. And the only way for that to happen is if people like you read our stuff. Enjoy!