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
 

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 

Early Number Sense

One in five adults in the United States is functionally innumerate; they do not possess the mathematical competencies needed for many modern jobs.  (Geary,  Hoard, Nugent, & Bailey,  2013).

In the three sections of MTH 222, Mathematics for Elementary Teachers II, that I'm teaching this semester at Grand Valley State University, my students are learning about research-based games that help elementary students develop number sense and gain a conceptual understanding of place value. An article in the Education Week blog Inside School Research features the results of a longitudinal study published in the current edition of the online journal, PLoS ONE. The study found that number sense is a better predictor of students' later math achievement than counting or other speed-based measures. The authors go on to conclude that "first grade number system knowledge predicts seventh grade functional numeracy" (Geary et al., 2013). As teachers, we must be prepared to assess and evaluate our student's early number sense. And, more importantly, provide appropriate intervention experiences that immerse our students in rich experiences that expand their early understandings of the relationships between numbers.

So, tonight I was doing a Google search for games that promote number sense--in particular a game called Part-Whole Bingo from Contexts for Learning Mathematics Investigating Number Sense, Addition and Subtraction. I came across a blog post I wrote on 'Mrs. Coffey's Classroom Blog' a few years ago when I was teaching 1st grade at Edgewood Elementary school at Fruitport Community Schools. What a wonderful surprise!

Here is the photo I posted on that blog on February 26, 2010.

I'll be using this game, as well as a few others, in my presentation at the  Math In Action 2013 Conference this Saturday at GVSU and introducing it to my pre-service teachers in class next week.

Geary DC, Hoard MK, Nugent L, Bailey DH (2013) Adolescents’ Functional Numeracy Is Predicted by Their School Entry Number System Knowledge. PLoS ONE 8(1): e54651. doi:10.1371/journal.pone.0054651