Common Core and Sketchpad - DeKalb High School Math

I love what I get to do. This week I was invited to DeKalb High School to work with my former Math Department colleagues. What a great time!

After a few minutes of letting my computer download newest drivers for the SMART Board 800, we were off and running. (Note: if the green status light on the SMART Board pen tray is flashing green, you probably need to update hardware drivers for the SMART Board. My computer actually did this on its own, after I checked the SMART Hardware Settings in the Notebook Tools.)

Like most schools, DHS is hard at work integrating Common Core Standards into math classes. One topic being re-emphasized is transformations in the plane, representing them with physical tools and software.

Bisect an angle with compass and straightedge	Bisect an angle with Geometer's Sketchpad

We will use Geometer's Sketchpad to investigate translations, reflections, rotations and dilations, but first we begin with a review of basic constructions, with SMART Notebook software's compass and straightedge tools. It takes some practice to do this at the SMART Board, so don't try it for the first time in front of a classroom of students. It is a good visual when students are also using paper, compass and straightedge. Compare those constructions with the use of full circles in GSP. It's a good thinking exercise.

Now to really exploit the power of dynamic geometry software, we look at translations, reflections and rotations using Geometer's Sketchpad. These commands use rigid motions to create congruent figures or superimpose a figure onto itself. Students need to know precise definitions of basic geometric figures (segment, angle, circle, etc.) and congruence of figures. "Two figures are congruent, if and only if there is a transformation or combination of transformations that causes one figure to be superimposed onto the other."

Show properties of isosceles triangle with GSP	Reflect rectangle with GSP

What type of questions should be asked to verify that students are grasping these concepts?

• What types of symmetry exist in the given figure - line symmetry, point (rotational) symmetry?
• Where are lines of symmetry in the figure, those that cause the figure to be superimposed onto itself? Do all figures have this symmetry?
• Where are centers of rotation in the figure, those that cause the figure to be superimposed onto itself? Do all figures have this symmetry?
• What properties of the figure are shown from the reflections or rotations that superimpose the figure onto itself?
• What transformation shows two given figures are congruent? Is there more than one way to accomplish this?
• What happens when the line of reflection moves?
• What happens when the angle of rotation changes?

As students become familiar with geometric definitions and methods of GSP, you should ask them how to create more complex figures.

• How do you use a triangle to make a parallelogram? Is there more than one way?
• How do you make a rhombus? Can you do it using reflection or rotation? 
• Can you use these transformations to create regular polygons?

To see more ideas, you can turn to online videos and tutorials. There are some features in Sketchpad Version 5 that are not in Version 4, but you can usually accomplish the task with a few more steps.

Enjoy!

YouTube playlists and videos

Sketchpad in the Classroom playlist by Key Curriculum Press

Sketchpad - Common Core Curriculum videos by Key Curriculum Press

Free Webinars by Key Curriculum Press

TeacherTube Math videos

Common Core State Standards Initiative

The Common Core State Standards Initiative defines what students should understand and be able to do in mathematic and English language. It determines what you will teach, but not how you should teach it. There is still a lot you need to think about in your teaching.

The key shifts called for in mathematics education are
1) greater focus on fewer topics,
2) coherence, linking topics and thinking across grades and
3) rigor, pursuing conceptual understanding, procedural skills and fluency, and application with equal intensity.

Illinois adopted the Common Core in 2010, beginning full implementation during the 2013-2014 school year. These standards are high and emphasize depth over breadth to improve student success and preparedness for college and careers. For example, according to the Common Core State Standards for Mathematics, "some of the highest priority content for college and career readiness comes from Grades 6-8". [p. 84]

There are many consequences to these changes. Number 3 above is a great shift. I remember when I took an undergraduate stats class in college - a long time ago - before there were hand-held calculators in general use. There was much emphasis on computation and not much opportunity for real application. It is different now with the tools of computation. Teaching the important application of probability and statistics is now possible, allowing the calculator to crunch the data. Having the opportunity to discuss and analyze results is important.

This past year I tutored two students in college-level elementary statistics. Both colleges required purchase of a TI-84 graphics calculator which has powerful statistics and probability tools. These two students, however, experienced very different situations.

One teacher embraced the tools of the calculator. He showed the mathematics and how to use the calculator tools. With the calculator he was able to use real applications which led to more discussion and better understanding. The other teacher never got past the computations. After students had already purchased it, she told them they didn't really need that calculator. Any calculator that would do the arithmetic would do. She was unwilling or unable to exploit the tools of the calculator. I showed the student how to use the calculator to build the tables that she had to copy to her paper and how to use the calculator functions to check her computation answers. That student had to worry more about memorizing formulas and writing a lot of intermediate arithmetic steps. I don't think most students in that class really understood why stats was valuable for them to learn.

There are great resources for learning about and applying Common Core standards to your teaching.

The official site of Common Core State Standards Initiative (CCSSI) includes standards adopted state by state and information for parents. http://www.corestandards.org/

Illinois State Board of Education Common Core: http://www.isbe.net/common_core/default.htm

Illinois Common Core Standards Resources: http://www.isbe.net/common_core/htmls/resources.htm

At the National Council of Teachers of Mathematics site enter  free common core in the search box to find online resources without cost. You can also go to the their Core Math Tools homepage for downloadable pdf documents of sample lessons and Java-based tools. http://www.nctm.org and http://www.nctm.org/resources/content.aspx?id=32702

The Mathematics Common Core Toolbox site is "a resource designed to support districts working to meet the challenge and the opportunity of the new standards. It includes tools and instructional materials that help you to better understand and to implement the CCSSM [Common Core State Standards for Mathematics]. http://www.ccsstoolbox.org/

Happy Teaching!

Mathematics Illuminated

Do you know how many riffle shuffles it takes to get an ordered deck of cards into a random order, or that it has something to do with symmetry? (I know - what is a riffle shuffle?)

Do you know how/why Neptune was discovered? Do you know to what the phrase "sensitive dependence on initial conditions" refers or what Jules Henri Poincare discovered in the late 19th century that influences our weather forecasting today?

I enjoy looking at different selections of free online courses from Open Culture, The Best Free Cultural and Educational Media on the Web.

Today I was browsing through some of their math options (under the Sciences heading, look for Mathematics). One that looked interesting was Mathematics Illuminated, a 13-part series looking at the big picture and how mathematics has influenced our knowledge. Before I left the web site, I had watched the videos on Symmetry and Chaos - where you can find the answers to those questions I posed at the start of this post.

The site suggests this course is for adult learners and high school teachers, and graduate credit is available. However, I can't help but think it might be great for those high school students who are motivated by relevant content in their classes. The videos are informative and interesting, with accompanying online textbook, interactive activities, participant and presenter documents. It's all very well done and very accessible.

This course is part of the Annenberg Learner, whose "mission is to advance excellent teaching in American schools through the development and distribution of multimedia resources for teaching and learning." Their course videos exemplify excellent teaching. They focus on the teacher and students both as a learners, such an important concept in our today's educational environment.

http://www.openculture.com/freeonlinecourses
http://www.learner.org/courses/mathilluminated/
http://www.learner.org

SMART Training and Professional Development

Great Youtube videos for learning to use the SMART board. See more SMART resources on my SMART Symbaloo at

http://tinyurl.com/janetteachessmart

Great fun with NIU Math Education Students

Today I had the privilege of working with Northern Illinois University Math Education preservice students. These students are observing and working with teachers and students in middle school and high school math classes. They will soon be engaged in full-time student teaching.

What an outstanding bunch of energetic and enthusiastic young adults! We had a great time working with SMART Notebook Collaborative Learning software and learning best practices for integrating this great tool into the math classroom. Stress not just how to do something on the SMART board, but ask why do it and how does it help students learn.

Their NIU teachers/coordinators are Mrs. Renee Olsen and Mrs. Bonnie Kersten. You could not ask for two more dedicated and excellent instructors. I taught with both of them in my tenure at DeKalb High School and always admired their passion for teaching and their skill at getting the best from their high school students. I can see this is what they now are doing at NIU.

What an opportunity these new teachers will have in classrooms - today and tomorrow. Technology in students' hands can do so much to make learning relevant and powerful, while giving teachers  responsibility to address that power and make it productive. Here are some web sites that might help you get started.  http://tinyurl.com/matheducniu With so many avenues to learning today, so many ways to collaborate and share, it is an exciting time to be a teacher.

Good luck to all of you - Kim, Courtney, Carrie, Janet, Lindsay, Dylan, Branko, Brian, Raghav, Nick, Mike, and Abbey!!! Have a fabulous student teaching adventure.

Good luck, NIU pre-service math and science teachers!

When I retired from my job as a full-time secondary math teacher, I guess I wanted a bit of a rest. I wanted to spend more time with family.

I also thought I would finally spend some time learning more about using new technology in classrooms. Weird, huh? Most people would probably want to step away from those things that had consumed so much time. But I do still love learning new things and sharing.

Over the past couple semesters, I have had the pleasure of working with math and science pre-service teaching students. I think back to those days when I was a new teacher. (Most of the parents of these college kids were babies at that time or not even here yet.) Two of my very good friends and former HS teaching colleagues are teaching these students at Northern Illinois University. They were excellent high school teachers, and I respected both of them for their subject knowledge and dedication to teaching.

My underlying messages to these new teachers - More learning takes place outside of the classroom than inside. Much of what you learn about using the advantages of technology you will need to learn in your own time. You are teaching at a very exciting time, yet with many challenges. Keep your passion alive.

One thing I do to help is sharing web sites that should help them get started. Good luck to these future teachers. The future is bright!

http://tinyurl.com/scienceeducniu
http://tinyurl.com/matheducniu
http://tinyurl.com/janetteachessmart

(Symbaloo is a great tool for sharing collections of web sites. One of those tools that every students should know about.)

SMART Notebook and MS Powerpoint

Do you have Powerpoint presentations with information that you would like to work into a SMART Notebook? Maybe there are images or text that you don't have time to recreate.

You can import these Powerpoint files directly into SMART Notebook using File/Import. However, there may be a slight glitch. I attempted this using SMART Notebook v. 10.8 in Windows 7 and MS Office 2010. I had saved the Powerpoint presentation as an PPT 2010 file, the default file type. The SMART Notebook translator was unable to import the file.

To get this to work, I had to save the Powerpoint file as a Powerpoint 97-2003 presentation file instead. After that, the import worked like a charm. For the most part this was not a problem, since importing these files to Notebook loses the animation and special effects used in Powerpoint. At least all the text and images came across nicely, and I can add the animation and special effects available in SMART Notebook.

Do you have SMART Notebook files that you need to pass on to a Powerpoint user? You can export the SMART Notebook file as a Powerpoint file. Open the file in SMART Notebook. From the File menu, choose Export..., then Powerpoint. Each page of the Notebook file is exported as a Powerpoint 97 slide. Again, you lose the interactivity from Notebook, but can add these effects in Powerpoint. Any interactive Java objects are left behind and replaced with blank space on the Powerpoint slide.

You don't have to completely redo those presentations.

QR Code Ideas

sites.google.com/site/janetteaches/

QR codes are finally showing up in lots of places, posters, magazines, web sites. Sometimes they direct you to a vendor's web site, sometimes to contact information, sometimes to special offers. I think they could be a useful addition to the tech integrated classroom and tech-savvy teacher.



A QR Code (it stands for "Quick Response") is a  two-dimensional  "bar" code that can store a web site's URL, plain text, phone numbers, email addresses and pretty much any other alphanumeric data you want to communicate. You need a scan app to access the code. Just launch the app, center the code image in the viewer guides and get to the info coded in the image.



So how do I see this used by a classroom teacher?

Review answers

How about coded answers to a math review? Scan the code at the left.

Maybe you have iPads in the classroom or students have smart phones. You might have different stations around the room, where QR codes are used for instructions. No one knows what to do at the station until they get there. Scanning the QR code of the URL with the device (iPad, iPhone, etc.) takes them directly to the web site, without having to fuss with getting the URL typed correctly.

You can scan a QR code being projected to a large screen or from a computer screen. If the camera can focus the image, it can read the code information.

Consider a student doing research in the media center. As they find web sites to use in research, have them create a QR code for the site. This is simply an image, so it can be stored or included in a document as desired. QR codes might be incorporated into a presentation done by students.

Have some fun with this tool. Put your contact information or your teaching schedule into a QR code. Print these on handouts or cards that you hand out to parents. If they don't know how to use the QR code, consider it a teachable moment and help them along.

The QR code is standardized, so any code-scanning app will be able to read any code image. QR codes have been used in other parts of the world for a few years and are finally getting more attention in the US. In theory, you can store up to 4296 characters, but with larger amounts of data the image resolution becomes important. Keep it well under the max character count.
<>  </><></> <>  </><></>

www.qrstuff.com

A web site that I have used successfully to create QR images is QRStuff.com. http://www.qrstuff.com/
At this site, you can create any type of QR code, then download the image. Print the image on business cards, web pages, paper handouts or post it to web pages or online profiles.


The scanner app I use on both my iPhone and iPad is called simply Scan. It is extremely easy to use, activating the QR code automatically once the device camera focuses in on the code. Scan, Inc. was founded by three friends in their college apartments in January 2011.

scan.me