Saturday, April 16, 2016

Mathematical Practices at Play


Standards for Mathematical Practice
Today Dave and I presented at the National Council of Teachers of Mathematics Annual Conference in San Francisco. We were most fortunate to be joined by three Grand Valley State University elementary teachers in training. Our presentation focused on finding opportunities to support the development of the Standards for Mathematical Practice with math games as a shared context between teachers and students.





In our session, participants got hands-on practice playing some simple but challenging math games.


Lauren, Megan, & Kaileigh
also affectionately
known as "Larry, Moe, & Curly"
to the #MTBoS


Lauren, Megan, & Kaileigh shared some their research around the Mathematical Practices from a GVSU Department of Mathematics capstone project with our participants.



Here is a PDF of the session PowerPoint, which includes links to resources and a list of materials needed for each game. Click here to download the procedures and any of the game boards/hand outs that do not have a copyright.
http://www.hand2mind.com/

We also want to shout out a big thanks

to ETA Hand2Mind for their support by providing manipulatives for our presentation!

Thursday, August 7, 2014

High Fidelity Teaching: Understanding the Significance of Stereotype Threat in Mathematics

Engagement is an essential element to learning. Why is it so difficult to engage some learners --especially in mathematics? This interactive session will focus on strategies for engaging all learners for optimal learning with special consideration given to ‘stereotype threat’ and ‘fixed mindset’ as potential barriers to engagement in mathematics, particularly for diverse learners.

Why do students not engage with mathematics in the U.S.? Many explanations exist:
  • Students just don't care and/or aren't motivated
  • Parents don't care
  • Students lack ability
  • Poor teaching methods in schools/universities
  • Foundational knowledge is lacking
I provide an alternative to the common themes above: Stereotype Threat and explore the following:
  • What is Stereotype Threat Theory?
  •  Fascinating research
  • Who is affected? 
  • What are the effects of Stereotype Threat?
  • What can we do about it?
Here is the link to my presentation for Michigan Council of Teachers of Mathematics 2014:

http://bit.ly/MCTMStereotype
 

Friday, April 25, 2014

Why Do They Leave?


From the Carnegie Foundation for the Advancement of Teaching
The revival of a push for the regulation of hundreds of teacher education programs was announced today by Education Secretary Arne Duncan. Duncan's plan relies on the false assumption that teachers are leaving the profession due to poor teacher preparation programs. He appears to be relying on anecdotal evidence for this assumption:
"Virtually every school I go to, I ask teachers whether they were prepared when they first entered the school or the profession," Duncan said. "There's often a good deal of nervous laughter," he said, before teachers confess that they were nowhere near ready for the job. (Politico, April 25, 2014)
Duncan is either drawing the wrong conclusion from these exchanges, or not asking the right follow-up question--what was missing? Extensive research points to the problem, and it's NOT because teacher preparation programs haven't prepared new teachers. The Carnegie Foundation for the Advancement of Teaching released a comprehensive report in March 2014, Beginners in the Classroom: What the Changing Demographics of Teaching Mean for Schools, Students, and Society that addresses the question of "why do they leave?"

According to this report, "a raft of research points to the problem". The references for this body of research can be found in the report itself, so I won't list them here.

Here are some key quotes:
"It's not money, or a lack of it, that's causing most teachers to leave. Rather, the primary driver of the exodus of early-career teachers is a lack of administrative and professional support." (p. 5)
 "Teachers abandon charter schools at especially high rates." (p. 5)
 "Too few principals spend time in classrooms, support teachers in their dealings with parents, and do other things large and small that buttress teacher morale." (p. 5)
"The biggest reason teachers leave is because they are working in a dysfunctional structure. If you put good people in a bad system the system is going to win every time." (Jesse Solomon, p. 6)
Duncan needs do his homework and examine the research.

UPDATED: 8-10-14 Teacher attrition costs the U. S. up to 2.2 Billion annually, Michigan schools up to 59 Million annually. From The Atlantic, Why do Teachers Quit?

UPDATED: 4-1-15  From an interview with Richard Ingersoll of University of Pennsylvania: "Most turnover is driven by school conditions." From NPRed, March 30, 2015: Revolving Door of Teachers Cost Billions Every Year

Monday, April 14, 2014

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.


Saturday, March 22, 2014

You've Probably Seen This on Facebook

"Old fashion" way vs. the "New" way
Fear, Uncertainty, & 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, & 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.



Friday, February 21, 2014

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 
https://drive.google.com/file/d/0B06To2Ie9XHOeWZhY2VsVDhkYWs/edit?usp=sharing

Friday, January 31, 2014

Pete Seeger in my Classroom: Abiyoyo

Iconic American folk singer Pete Seeger passed away this week, on Monday, January 27.  In 2006, one of my first grade students introduced me to Pete Seeger's retelling of the South African folk story and lullaby, Abiyoyo.  

Abiyoyo originally appeared on Seeger's 1958 album for children, Sleep-Time: Songs and Stories, and most recently on the Songs and Stories for Little Children CD.


I'm not sure how I missed this classic during my childhood and that of my children, but I did. Anyway, from 2006 on, I used this story every year in my classroom. I introduced it during the first week of school and we replayed it often throughout the school year. We would just listen to the  story 5 or 6 times, then I would introduce the book and read it aloud a few times, we would choral read it together, and sometimes we would listen to the CD and follow along by turn the pages of the book. I had multiple copies of the book available for independent reading and a listening center. My students loved this story--it is both terrifying and calming.

My students loved comparing and contrasting the language in the print version and the oral language on the CD. We had discussions about the characters, what word "ostracized" meant, and the meaning of the story. And, the CD version was the perfect thing to put on during the last 10 minutes of the day--especially after a stressful day; my students would lay back on the carpet and just listen. The repetitious lullaby chorus is so soothing!
abiyoyo, abiyoyo, abiyoyo, abiyoyo,
abiyoyo, ya yoyo, ya yoyo
abiyoyo, ya yoyo, ya yoyo

A few years ago, I found this episode from Reading Rainbow, with Pete playing his banjo and telling the story and added this video into the mix.

Rest in peace, Pete Seeger, your legacy lives on!


The activities mentioned above are compatible with many of the Common Core English Language Arts Standards for 1st Grade (and possibly other grade levels as well):

Speaking & Listening: CCSS.ELA-Literacy.SL.1.2

Reading: Literature: Any number of the standards here