NCTMNOLA: Playing with the Common Core

NCTMNOLA participants playing one of the games

This past week, I had the pleasure of presenting, with my husband Dave, my workshop Playing with the Common Core  at the National Council of Teachers of Mathematics (NCTM) Annual Meeting and Exposition in New Orleans. The official Twitter hashtag for this conference is #NCTMNOLA. I encourage you to check it out.

Shared Context

This workshop focuses on using a variety of games to establish a shared context within the classroom. Having a shared context provides teachers with an opportunity to develop narratives, or stories, based on the context so they don't leave learning to chance. At the same time, all of these games address both the CCSSM Content Standards and the Standards for Mathematical Practice. 

These games are excellent for use throughout the school year because they intertwine most of the content standards in Operations & Algebraic Thinking (OA) and  Numbers in Base Ten (NBT) for grades K-2. Each of the games can also be modified for other grade levels, either up or down.

Resources

For the slide presentation and "procedures" for each of the five games that were played click on the link below:

NCTMNOLA Playing with the Common Core (slide presentation and other resources)

Some of the games we played are copyrighted. For those resources, click on the links below:

Part-Whole Bingo, came from Contexts for Learning's resource Games for Early Number Sense. Scroll down to the "Year-long Resource Guides" and you can download a resource summary.

Roll-A-Square was adapted from Investigations in Number, Data, and Space®, 2nd grade module "Putting Together and Taking Apart: Addition and Subtraction"

How Many More To . . . was adapted from Carolee Norris' Focus on Math Blog

My original Playing with the Common Core session from GVSU's Math in Action 2013

Please feel free to contact me if you have any questions! My contact information is on the last page of the slide presentation. I'd also love it if you would leave a comment.

You've Probably Seen This on Facebook

"Old fashion" way vs. the "New" way

Fear, Uncertainty, and Doubt

 

UPDATED 9-19-16 See other math educator's explanations for this and similar photos here, here, here, here, & here. Also check out this link for an explanation regarding the
5 x 3 homework problem that was marked wrong.

The photo on the right has been all over Facebook the past few weeks, posted by folks opposed to the Common Core State Standards. It really is a very simple and clever way to really scare people and attempt to make the Common Core State Standards for Mathematics look really confusing--even ridiculous! In fact, it's an excellent example of the Fear, Uncertainty, and Doubt (FUD) strategy used in the corporate world and in politics to spread negative or disinformation in order to influence and/or coerce others.

 So, what's going on here?

The "New" way is actually not new at all. It is, however, a really terrible and confusing representation of a very old method (note the copyright of 1916) that's also called the "counting up", "shopkeeper" or "Austrian" method of solving a subtraction problem by addition, or counting up to find the difference. Indeed, it's how I learned to count change back to customers when I worked in my father's pharmacy a very long time ago.

Is there a better representation or mathematical model?

The creators of the above photo chose to use a confusing representation or model of this method. I know my eye was quickly drawn to the numbers in the vertical box and it took me a bit to refocus on the actual horizontal equations before it made sense to me. The open number line model below provides a visual model that's easier for me to understand the equations in the photo, using the same numbers and counting up strategy used in the photo:

 

In the above open number line model, I've shown the strategy of counting up to the landmark numbers 15, 20, and 30, then on to 32. This is is how I might have counted back change to a customer as a novice. Students modeling how to use landmark or "friendly" numbers (5s and 10s) might show their thinking much like this.

In the open number line model below, I've illustrated the same problem using  a "jumping tens" strategy. This is how I would have counted change back to a customer as I became more experienced. Students might also model this way as their conceptual understandings develop.

UPDATE 3-27-14: I don't mean to imply that students should be taught or required to solve  the problem 32 - 12 by counting up or by using the open number line, nor should they be required to solve the problem using the equations in the "New" way. There are more efficient strategies that could be used for "32 - 12" and  models other than the open number line that could be used to create a visual representation for the "New" way.

Common Core or FUD?

The mathematics represented in the "Old fashion" way vs. the "New" way photo above have nothing to do with the Common Core. The Common Core does not prescribe that students use the method depicted in the "Old fashion" way photo, nor does it require that the strategy or counting up be taught. The Common Core is not a curriculum and does not require any particular teaching style or method. The Common Core does require students to have a flexible and conceptual understanding of the relationships between numbers and operations before they apply the "traditional algorithms" (also known as the "Old fashion" way).  Along with the Common Core math content standards, the CC also seeks to develop positive mathematical dispositions through the Standards for Mathematical Practice, below.

What parent would not want their child to have well established number sense and a solid conceptual understanding of addition and subtraction, including strategies such as "counting up"? Don't we want all students to develop Mathematical Practices like those in the illustration on the left?

To be sure, there are some concerns with the Common Core. I worry that administrators, curriculum specialists, and teachers will not receive the professional development needed in order to effectively implement them. I worry that some standards may be in the wrong grade level, but believe that will get worked out in due time. I also worry about the excessive high stakes testing that is consuming valuable instruction and learning time, the results of which are being used to inappropriately evaluate teachers--even though it's not really a part of the Common Core.

But, don't fall for the FUD. Be informed, read about the Common Core State Standards for Mathematics. Click on "download the standards" and read them for yourself. If you see something you don't understand, ask your child's teacher or someone who does. It's highly likely someone is trying to scare you.

Please post your comments, I'd love to hear what others think about this.

High Fidelity Teaching

High Fidelity Teaching: Fine-tuning for Engaging Learners in Mathematics

It's Math in Action time again! This year my presentation theme is High Fidelity Teaching: Fine-tuning for Engaging Learners in Mathematics and looks at Stereotype Threat and Mindset. The slide deck is at the bottom of this post. Here is a link to a Google Drive folder with resources:  http://bit.ly/MIA14-hft

We know engaging students with mathematics in the United States is difficult. According to Jo Boaler and the Carnegie Foundation for the Advancement of Teaching, 50% of students are in 2 year colleges and 70% of those students are in remedial math classes, essentially repeating high school math. Only 1 in 10 complete those remedial math courses, the other 90% leave college.

We can't wait until college; we must engage students as early as possible!

How can we work to engage students at an early age with mathematics? My presentation addresses three topics that can help with "fine-tuning" instruction to impact student engagement:

1) Intentional teaching practices that work to develop positive mathematical dispositions, such as implementing the CCSS-M Standards for Mathematical Practice (developed from the NCTM Process Standards & Adding It Up--if you don't like the CCSS-M, use one of those sources);

2) Awareness and prevention of Stereotype Threat; and

3) Intentional teaching that promotes a Growth Mindset.

Click to view 

MCTM 13 Playing with the Common Core

Wonderful, flexible participants!

This week I had the opportunity to revise my presentation "Playing with the Common Core", and present it at the Michigan Council of Teachers of Mathematics Annual Conference (MCTM) in Traverse City. One of those revisions was co-presenting with my husband and GVSU mathematics educator, David Coffey.

Other revisions included changing the schema activation, refining the focus on the Standards for Mathematical Practice from the Common Core State Standards for Mathematics, reducing the number of games during the activity, and adjusting the final organizing and integrating activity. And, since I just finished Thinking Collaborative's Adaptive Schools training, I added some things I learned about being a better facilitator.

Luckily, my worst fears--that no one would attend our session, the desks in the room would be the old fashioned slanted type, and that Dave would talk too long--did not come to pass. Instead, we planned for 30 participants and had 70+ in a room designed for about 32! We made some on-the-spot adjustments and were so thankful that our participants were all extremely flexible and understanding. I thank all of you again.

Here is the link to my Dropbox folder for this presentation. Directions for all three games are in the folder, as well as my PowerPoint slides, CCSSM Content Standards for K-2 and the CCSSM Standards for Mathematical Practice. Several of the game items used in the session are copyrighted and therefore are not in the folder. Links for additional games can be found in my original post Playing With the Common Core. If you have any questions about any of the games, please contact me directly via email.

Playing With the Common Core

AL Abacus for Race to 100

This past Saturday, I presented at Math In Action 2013. This conference for K-12 mathematics teachers is hosted every February by Grand Valley State University.  My one hour session (view my PowerPoint presentation here) was Playing With the Common Core. Here's the outline of my lesson plan for the session: 

Objective: The learner will explore using strategic early number sense games as a context for intentional instruction.

Schema Activation:  (10 min) The role of context in intentional instruction. Read aloud the first page of Grandma Eudora's T-Shirt Factory from Contexts for Learning Mathematics. Briefly highlight within the story contexts for the 5 & 10 structures, use of a "T-chart" as a place value mat, and finally composing and decomposing two-digit numbers. Participants turn and talk about the role of context in instruction.

Focus:  (10 min) Review the Common Core State Standards for Mathematics (CCSSM) Content Standards & CCSSM Standards for Mathematical Practice (SMP) for grades K - 2, with emphasis on the SMP.

Activity: (20 min) Session participants explore and play the following Early Number Sense Games. Click on the link for a materials list.

• Roll-a-Square
• Part-Whole Bingo
• Race to 100
• Exchange Game
• Make 20
• Tens Go Fish

Reflection: (20 min)  Reflect on the games you played and write your own scenario anchored in the context of one of the games you played. Special focus on the Standards for Mathematical Practice.

Don't leave learning to chance--you can center your instruction by setting up a scenario around a game that has been a common shared experience by the students in your classroom. This can be done with individual students, in a small group for intervention, within your mathematics workshop, or even whole group. Examples:

• Race to 100: (Content Std: Count by 10 from any number; SMP: Mathematical structure) "Remember when we were playing Race to 100? Let's say I'm on 14. What if I rolled three tens in a row? Where would I land at the end of each turn?"

• Part-Whole Bingo: (Content Std: composing & decomposing numbers; SMP: Problem Solving) "What if I just rolled a seven and all of the towers with seven are filled? What could I do to be sure to use all seven of my cubes?"

From a teacher perspective, write a short narrative scenario that you can use in your classroom related to both a CCSSM Content Standard, and more importantly, one or more of the Standards for Mathematical Practice that is anchored in the game(s) you explored.

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