Engaging Learning

Changing Paradigms: Engaging Students in New Learning Spaces & Contemporary Contexts

In our presentation at GVSU's Faculty Teaching and Learning Center's 19th Annual Fall Conference on Teaching and Learning, David Coffey and I explore the idea of engaging students in learning. Because engagement is an essential element for learning, we focus on three key questions:

What does engagement look like in our classes?

How do we support learners in engaging with our discipline?

What factors might interfere with learners' ability to engage?

Dave's part of the presentation addressed the first two key questions. Since he has blogged a number of times on engagement, I direct you to his previous blog posts, which can be accessed by clicking on this link.

I addressed the third key question, What factors might interfere with learners' ability to engage? You can find our PowerPoint presentation here, and also on FTLC Scholar Works website. I will provide links to resources throughout this post.

During fall semester 2012, I was teaching at GVSU as a visiting professor. I was teaching two math for elementary teachers courses (MTH 221 & MTH 222) and one remedial course, MTH 097, elementary algebra, for incoming freshman. The course for my doctoral program that semester, on diversity and social justice, started several weeks into the semester. Let me just say, I believe in serendipity.

I was surprised at the number of pre-service teachers in the math for elementary teachers classes who expressed their dislike for math, in fact some clearly had math anxiety. Even though I was challenging their paradigm for what it means to do, learn, and teach math, many were trying to engage with the learning. The students in the remedial algebra class, however, were down right hostile. Thankfully, in my grad class, I learned about several factors that were most likely contributing to what I was witnessing in my classes: stages of cognitive development, stereotype threat, and mindset.

The stages of cognitive development established by Piaget typically leave off at about age 12. In his seminal work during the 1960s, William Perry looked at the cognitive development of college students and identified additional stages that begin to develop around age 18. His stages distinguish students' attitudes toward knowledge (epistemology). The first stage in his scheme is defined as Dualism/Received Knowledge. Students in this stage exhibit dichotomous thinking, i.e., right or wrong, black or white, and are authority dependent.  Marcia Baxter Magolda (and others) have further refined Perry's work. This gave me some insight into my 097 students, but it was not sufficient.

Claude Steele's research on stereotype threat provided further insight. Stereotype threat is defined as the threat of being viewed through the lens of a negative stereotype, or the fear of doing something that would inadvertently confirm that stereotype. He documents his research and experience in his recent book, Whistling Vivaldi (you can also listen to an NPR podcast here). Anyone that is a member of a group for which negative stereotypes exist can be effected by stereotype threat. For example, minorities in all subject areas, women in math, and white men in sports. Minority women in math often experience double stereotype threat. My insights were expanding; my 097 class was predominantly minority women. Now I was really wishing I had known about these issues before the semester started.

That led me to the work of Carol Dweck on what she calls "mindset". People with a "fixed"mindset believe that their basic qualities, such as intelligence, are fixed and not malleable. On the other hand, people with a "growth" mindset, believe that those basic qualities, including intelligence, can be developed. Fortunately, a growth mindset can be taught and developed. Click here for an excellent graphic summarizing Dweck's mindset theory. Developing a growth mindset can help students (and adults) progress through the stages of cognitive development and significantly reduce, if not eliminate, the effects of stereotype threat. Carol Dweck's book Mindset is a must-read resource. You can listen to a brief interview of Carol Dweck here.

MindsetWorks.com and ReducingStereotypeThreat.org are excellent resources for those interested in learning more about these subjects.

I welcome your comments, shared experience, and suggestions. I will be writing more about all three of these topics in the next few weeks, so please check back for more.

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.

                                                                *   *   *   *   *  

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

Nitpicking??

Really?? Do Sal Khan and his supporters really understand where the word "nitpicking" came from? I know it's used informally as an adjective to suggest that one is looking for small or unimportant errors or faults. But I also know nitpicking, literally, is critical for student success.

Almost a month ago two math education professors from Grand Valley State University released a video they made satirizing one of the Khan Academy videos on multiplying and dividing integers. They highlight both mathematical and pedagogical concerns.

If you want to see the entire history, check out this Storify page by Audrey Watters. If you're wondering "what were these guys thinking??", check out these blog posts by Dave Coffey*.

Khan's initial response was to pull the video in question and post an updated video. He also commented on Justin Reich's Education Week blog post entitled Don't Use Khan Academy without Watching this First:

We at the Khan Academy really appreciate the feedback from you and your colleagues regarding videos that could use improvement.

But, a few days later he was quoted in a piece by the Chronicle of Higher Education:

. . . so it's kind of weird when people are nitpicking about multiplying negative numbers.

What really struck me in Khan's comments to the Chronicle, was the word "nitpicking". He's not alone in suggesting that those who find errors in his videos are nitpicking. Many comments made by Khan supporters also suggest these two professors are nitpicking and, just today, Teach for America had a blog post that also dismissed critiques of Khan Academy videos as "nitpicking".

Picture Courtesy: Medline Plus

Nitpicking is, unfortunately a very common occurrence in elementary schools. Over the years, I have had a number of students who reported to the office daily for nitpicking. It was the only way we were able to keep them in school, because in Michigan, students can be in school with nits, but not with live lice. If you don't get rid of the nits, AKA nitpicking, the live bugs hatch, multiply and spread to others.

So, maybe it's a good idea that someone is "nitpicking" Khan Academy videos. If Khan doesn't find and correct the little, seemingly unimportant errors (nits), the millions of viewers that he reports watch his videos from around the world may find they've developed critical misconceptions, kind of like having the nits hatch into live bugs.

*Full disclosure, I am married to Dave Coffey. Don't let the lame satire fool you, he's really a nice guy. :)

Read at the Beach!

Read at the Beach is an annual March is Reading Month tradition for 1st graders at my school. Of course the end of March is usually too cold to really go to the beach, so we turn our cafeteria into the beach with a little imagination, some beachy props, and great calypso music by our own technology director, Jeff Grossenbacher. (Also of Two Dudes in Flip Flops and Island Breeze fame!) Jeff gets us started with a reading of The Jolly Mon by Jimmy Buffett and his daughter, Savannah Jane.

Then, the kids are off to "read at the beach"!

 

Writing Process

A few years ago, Su Palmer was assistant superintendent of curriculum for my district. She introduced me to writing workshop, "draft books", writing demonstrations,  Dancing With the Pen, Smith and Elley's (1997) How Children Learn to Write,  Effective Literacy Practice. I couldn't get enough. As I began to develop my understandings, I made significant changes in my teaching practice and watched my students grow as writers.

After serving as superintendent in a K-8 school for a few years, Su is now teaching at the college level. She visited my classroom last week to observe my students during our literacy block to get a feel for the realities of the classroom.

She reminded me of two key components of effective writing instruction:
1) make the writing process explicit
2) follow the writing process all the way through to publishing

And, she reminded me of the value of collegial conversations.

My students have been doing lots of pre-writing, drafting, revising, and some editing all year. But, somehow in our busyness, publishing had taken a back seat. The reality is, it's not easy to squeeze in publishing without making it a priority. So, to help make the writing process visible and explicit, we made this chart as a class and have it posted in a prominent place. And, I've started publishing student writing--my goal is to confer with at least 3-4 students each day until each student has one published piece over the next 2 weeks.