Better Questions

betterquestions

It is week three of #MTBoS Blogging Initiative and the focus is on questioning.

Last week I visited a 5th grade classroom in my district and had the opportunity to sit down with the children and talk to them about their work.  As a former Algebra I & II educator, I was very much at home, up to my elbows in visual patterns, input-output tables, and graphs using Desmos.

In grade 5, the learners interact with multiplicative and additive patterns (y=ax and y=x+a).

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Though I appreciate teachable moments to support learners as they inquire about the math beyond the scope of their current class, I am always hesitant for them to jump to the abstract before they have a grasp of the concrete, pictorial, tabular, and graphical representations.   This is where the questioning came in.  At this table, shown in this picture below, you can see the pattern growing (with a hexagon in the middle and triangles added each stage).

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In the picture you can also see the input-output table.  When I first sat down with the group, their x-column and y-column was complete (indicating the stage number and total number of shapes used to create the image).  The children were attempting to use guess-and-check to complete the process column.  Though eventually they arrived at the correct expression for the relationship, this method is not efficient nor transferable.  In an attempt to direct them back to the visual pattern, I asked:

How is the 6 from your expression shown in the pattern of shapes?

After a long silence, the response was not what I expected.

It was just random luck.

So, I directed them to use words to describe the pattern in the shapes.  Stage 1 has a hexagon and 6 triangles.  Stage 2 has a hexagon the 6 triangles from before and 6 more.  Stage 3 has a hexagon, 6 triangles, 6 triangles, and 6 more triangles.  Then came the ah, ha!  And one child said it:

The repeated addition of the 6 is multiplication.  6x means adding 6 each time!

What a response!  But, what about the 1?  Remember, this is beyond the scope of this class.  But, since the students created their own visual patterns, there was not safety net to keep them from creating a pattern of the form y=ax+b.

Next, I asked:

If this is Stage 3, this is Stage 2, and this is Stage 1 (pointing to the visual pattern), what would Stage 0 look like?

No hesitation.

There would be 1 hexagon.  1!  That’s where the one came from!

So what about the graph?  They entered the table and equation into Desmos and again, without hesitation, announced proudly, the 1 is where the graph starts!  Yes – the initial condition, the y-intercept, yay!  And if 1 is where the graph starts, then that must be where the pattern started.  In no time we were talking about the coordinate points from the table on the graph.

And that is why I love Algebra.  Oh, and that these children in elementary school were using Desmos and airdropping images on their iPads of the visual patterns they created.

My Favorite

myfav

It is week two of #MTBoS 2016 Blogging Initiative and I am excited to share My Favorite!

My favorite app for sketching is Paper.  I have used this app for a few years now to document my learning at professional development conferences and key notes.  Many of my sketch notes are linked on my blog here.  I am beginning to embrace the updates which include photo annotation and a Think Kit.  I was a fan of the app before these enhancements because it was so simple.

I have pasted a quick sketch below of a concept in upper elementary mathematics (additive patterns in tables and graphs) I made using Paper.  Notice how I jumped over to another favorite of mine, Desmos, and grabbed a screenshot (saved to my camera roll) to embed in my sketch.  I also used the Think Kit to create the squares and quickly duplicate them.

Using Desmos rather than hand sketching the graph supports the importance of precision in mathematics and allows me to verify the accuracy of my equation.

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One Good Thing

It is Week One of #MTBoS 2016 Blogging Initiative and I have great news!  My book, Collaborative Inquiry and Educator Professional Development is available on iBooks!  Knowing the topic for the first blogging prompt, I found myself on the lookout for one good thing.  I actually made a list of good things today as I encountered them (rose-colored glasses and all), but they were out-matched by the wonderful email from the iBooks team I received this afternoon.

Here’s a summary:  Utilization of the inquiry model (ask, investigate, create, discuss, and reflect) with teachers provides opportunities for positive change in schools.  In comparison to traditional professional learning, the inquiry model establishes teachers in an active role in designing and experiencing learning.  Teachers work in collaboration with peers, exploring and reflecting on new knowledge and making a commitment to a change in practice.

So, check it out!  That’s my one good thing!

My Blogging Journey (so far)

I am proudly serving as a #MTBoS Mentor and preparing for the January/February Blogging Initiative.  What better time to reflect on my blogging journey (so far)???

I am also participating in my own district’s professional learning opportunity (led by our team of Digital Learning Coaches) Find Your Voice Through Blogging. I am very thankful for this team to support educators in our district to tell their story, reflect on their teaching, and contribute to the great knowledge base on the web.

For these reasons, I have recently given my blog a much needed re-vamp (thank you WordPress for the awesome themes!) and kickstarted my writing again.  Though I have two blogs (one is more blog-like and the other is used for information dissemination), my WordPress blog is my focus recently.

Blog #1: A Greater Impact

In the summer of 2015, following the most impactful opportunity of my career, I was ready to establish my own personal/professional blog.  I chose WordPress for a few reasons:

  1. A Separate & Different Site

Since I had already established the CISD Mathematics blog (see Blog #2 below) as a Blogspot, I wanted a site that was clearly (to me and potential readers) separate.

2.  A Challenge to Learn

WordPress was new to me and I wanted to challenge myself to use something new – to learn to navigate and utilize the tools and settings.  I am a Lead Learner (I borrowed this term from somewhere and love it!) and strive to model continuous improvement, thus making this a great opportunity to learn!  I am still learning the potential and power of WordPress.

3.  Research led me to WordPress

I read this post from Vicki Davis about why she chose to move her very impressive site from Blogger to WordPress.  Clearly she invested time and consideration into her decision and I respected that.  Also, some of my favorite bloggers are on WordPress: Jon Orr, Michael Fenton, Graham Fletcher, Ian VanderSchee, and Dan Meyer.

 

Choosing my blog name and corresponding site name (A Greater Impact) was a lengthy process (it’s my personality to agonize over such a decision).  My recommendation to someone struggling with pulling the trigger is to write down all of your ideas and carry that paper with you for a week.  Each time you think of anther idea, add it to the list.  At the end of the week, start marking out the ones that don’t speak to you.  Test the others on WordPress (or your chosen site) to see if they already exist.  Then, set a deadline for yourself and go for it.  It really isn’t that major of a decision (except it is because unlike the theme and background image, this cannot be changed).  Thank you to the MTBoS for these tips.

The first post was easy – ADE Institute 2015.  Wow.  The rest is history.  Well, it’s math, but you get it.

Blog #2: CISD Mathematics

I have a Blogspot I use for Mathematics updates in my district (http://cisdmath.blogspot.com/). Using MailChimp, information I post is automatically delivered to the email boxes of recipients within CISD at designated times/days.  I have it set up to deliver at 7:00 am on weekday mornings following any posts I create.  Details of this blog were thought through carefully – from the title, the image (official district logo) and the font of the word Mathematics (our mascot is a Cowboy).  My decision to house this blog on Blogger was a simple one – we utilize Google for Education in our district and I am modeling for my campus administrators and educators.  And, I can log in through Google, so there’s one less username/password to remember (bonus!).

I utilize the blog to post information not best suited for email.  Some posts contain professional learning opportunities, updates from our state education agency (TEA), or process updates from mathematics initiatives.  I recognize the importance of multi-faceted communication efforts and I try to share information in many ways if it is important for my constituents to know about it (spoken word, written communication, digital media, social media, etc.).

I recognize I have room to improve upon this blog, but getting started and establishing consistency were some of my first priorities.

Recommendations

  • Read the eBook 10 Habits of Bloggers that Win by Vicki Davis (if you sign up for her mailing list, she’ll send you a DropBox link via email).  Any tips I could share are beautifully articulated in her book.
  • Use images (photos you take are best, but Pixabay.com is good, too.) and embed links (be sure to check the “open link in a new tab” so readers can easily navigate back to your post.
  • Read other blogs for research purposes.  Why do you prefer certain blogs?  Is there something about those blogs that you would like to replicate in your own?
  • Ask for feedback.  Reach out to your PLN via Twitter or colleagues down the hall to let you know what is working/not working about your blog.  A fresh set of eyes provides new insight.
  • Continue to improve.  Don’t be afraid to venture into uncharted waters (like I did with WordPress) or try a new theme to solve readability or organization problems.