Author’s Note: Later in this post I will share some video clips of interviews with students that I have uploaded to my YouTube channel. When you get to the end of each clip come back to this site. The other video clips displayed on the screen at the end are something YouTube does but have no connection to the topic of this entry.
I have been blessed to have an ongoing ability to interact with fellow Teachers of the Year (TOY) from around the country ever since I was named Oregon’s TOY in 2007. As an example, last year many postings on this blog were about lessons that were inspired by my participation in the Mobile Learning Institute. I flew to Washington D.C. in the summer of 2010 along with 15 other fellow TOY to participate in this institute sponsored by Pearson Learning Group, Nokia and the Smithsonian.
This year, we are taking advantage of participating in webinars sponsored by the Center for Teaching Quality and CCSSO to provide professional development opportunities to our group. Our first webinar had as guest speaker, Marc Tucker, currently the executive director of the National Center on Education and the Economy and a leader of the standards-driven education reform movement for many years. In this webinar Mr. Tucker shared some of the findings from his new book, Surpassing Shanghai. This book was published by Harvard Education Press in September of 2011. It explores the question, “What would the education policies and practices of the United States be if they were based on the policies and practices of the countries that now lead the world in student performance?” The research on the highest performing countries was performed by a team assembled by the National Center on Education and the Economy, at the request of the OECD.
Even though I was only able to participate after the webinar had been aired, I still found this to be a very worthwhile and thought provoking discussion. I will share a few of my “aha” moments from this webinar in upcoming blog posts. The first “aha” happened as I was listening to the following discussion around one of his findings, that high performing countries had teachers who were very involved in acting as educational researchers. Lesson study in Japan is just one illustrative example. Here’s a small excerpt of a conversation among several of the folks participating in this webinar.
“My biggest takeaway was this ‘Action Research’ focus–several countries said their most effective PD is having teachers do their own classroom research, which is very rare here outside of teachers’ colleges.” Justin Minkel, Arkansas TOY, 2007
“Imagine what pre-service teachers would learn from a classroom and school culture like what Justin is describing.” Sarah Henchey, 6th grade language arts teacher from Orange County, NC and a virtual community organizer for the Implementing Common Core Standards project team
“I wish teacher evaluation would have a lot more to do with the kind of research teachers conduct in their classrooms.” Sarah Wessling, 2010 National TOY
“So do we need to sell ourselves to Schools of Education? Do we need to share with them all of the research opportunities that we offer?” Sarah Henchey:
“Just the simple idea of coming up with a compelling question, then observing students closely and talking with them to answer that question and share what I learned with other teachers is very thrilling to me. I do that informally each year — For example, this year I wondered what impact home libraries would have on my students (who tend to have between 1 and 10 books at home), and I designed a project to provide them with 40 books each over the course of two years, and kept track of the impact through interviews with kids, surveys for parents, DRA data, etc. If I could share that project widely, it could make a huge difference for teachers with lower-income students.” Justin Minkel
This discussion was very exciting to me because I believe it is at the heart of the classroom-based action research project I have been working on for many years now. The project is an investigation of the interview screening questions teachers at my school and I have been implementing and tweaking over the last several years. As you know if you have been following this blog, I have begun to share some of the many things we’ve learned about how young children think and work toward solving math problems. Along with my thoughts, I am also sharing snippets of video clips of interviews I’ve done with students at my school to illustrate some of the more interesting things we’ve found out.
The blog entry last month shared some of what happened when we asked students some counting questions. This entry will expand on the topic of counting up into first and second grade. As you may recall, we asked kindergarten students to count objects as part of the screening interview questions. First we wanted to see if students were able to conserve and count on. If they demonstrated an ability to do either of those two things, we then asked them to count a set of objects. We also checked to see if they were starting to visualize sets of numbers with a referent such as ten frames. We showed them pictures of sets of items in tens frames to see if they could quickly recognize the number of objects in the set. If they could do it for sets up to ten we extended by showing them two frames for the numbers 11 through 20.
Many students were able to easily see up to 4 in a set. This fits with the theory of young children being able to subitize somewhere around 4 objects. Subitizing, coined in 1949 by E.L. Kaufman et al., refers to the rapid, accurate, and confident judgments of number performed for small numbers of items. Students with strong number sense could chunk smaller groups within a larger set for numbers greater than 6 or 7. The kindergartner shows that she is able to easily do sets up through 7 but she called all the numbers larger than that 6.l
The second child on the video is a first grader who demonstrated the other end of the continuum where students are able to recognize sets of objects even beyond ten by understanding how to chunk tens and ones together. This in turn is an important precursor to place value skills that we will discuss in an upcoming blog.
We learned about other developmental benchmarks along the way. In our last entry we discussed benchmarks for conservation, counting on and one to one correspondence. In first grade we extended the question about counting forwards to find out whether students could also count backwards and count objects backwards (a foundational skill necessary for subtraction understandings).
View the Counting Backwards Video:
I look forward to sharing more of these video snippets in upcoming postings. I hope they will illuminate much about how young children think about math and how they are informing us to think about the best ways to teach students based on what we now know about what they can do and where their gaps in understanding are.