1 - Scholarship

I was hired out of discipline. As a result of becoming deeply interested in math education, I almost left grad school for mathematics with little time left. My advisor, the brilliant Nigel Higson, counseled me to finish writing as I was so close, and who knew what doors it might open. As usual, he was right. I finished, traveled and returned to the old family business of running a bed and breakfast on Mackinac Island. In the next year I got to teach for a semester in the Island school, got married and traveled again. I was intending to go to Chicago with my wife (her school) and looking into getting certified when Ed Aboufadel, a friend from undergraduate school, called about being a visitor at Grand Valley. What an opportunity! Within weeks, Char Beckmann had me involved in an Eisenhower grant at a Grand Rapids middle school, I was teaching 221 and 222 (math for elementary teachers) and two different algebra classes. I applied for both tenure-track searches that year, math and math ed, but my heart was clearly in one place, and, somewhat amazingly, they hired me for the math ed position.

The difficulty was that I now had an academic position in a field where I was a novice. I began seeking out opportunities to teach in K-12 classrooms and work with K-12 teachers, and read mountains of colleague-suggested articles. I didn't feel qualified to write for these colleagues, initially, and when I did feel like I had new things to contribute, I was mortified by the idea that I'd be espousing something that I would have moved past by the time it saw print. An early attempt at a new bit of math ed research, an assessment of van Hiele levels for use in preservice classrooms, was (I think properly) categorized by a colleague as unfit for print.

This state of affairs bothered me quite a bit, as I valued the work I found in the journals so highly; it felt more than a bit hypocritical that I was not writing for them. At its heart, to me scholarship is about acquiring new understandings and sharing them with your community. I began to share more frequently with area teachers in inservices as professional development and at local conferences. More recently, I discovered the world of education blogging and this felt like home. It allowed me to work on a wide variety of things in a short period of time and to share them quickly and efficiently. Never having been a K-12 teacher, it's imperative for me to spend time in the classroom, and the blog has been a good way of sharing those experiences and the activities that I field test. This has improved my teaching of teacher preparation classes immeasurably.

Distribution

Blog (Numbers from August 2011)

I am not trying to claim here that my blog is particularly well-known or impactful. The numbers I'm about to share are dwarfed by the most popular math education blogs, such as Dan Meyer's (6000 Google Reader subscribers) or Kate Nowak's (1400 subscribers). I have a blog page that collects some of the best writing from these teachers.

mathhombre.blogspot.com has 150 subscribers in Google Reader, and 30 Blogger followers. I currently average more than 2000 unique visitors a month which includes more than 300 returning visitors per month. (This is excluding the weird spike - about 10,000 hits - that the blog got for Pi Day 2011. To this post which was mostly a joke about having 2 pi day instead. That goodness there was a decent pi activity, also.) The blog is and will remain ad-free, with a Creative Commons 3.0 license. (Everything is freely reproducible and modifiable for any non-commercial use.) Google says I average about 2 posts per week, and this summer I made my 175th blog post. Some are short and silly, but some are longer and more involved descriptions of activities or teaching ideas. I recently started a Tumblr for the short silly stuff, or for more permanent-than-Twitter links to resources to share, so that the blog can focus more on sharing professional work. Being able to share my classroom work on a frequent basis with a wide audience has helped the work I put into my lessons be more worthwhile. And some of the things I would not have thought to share otherwise; for example, the anchor chart posts are some of the most popular I have ever done.

Blogger statistics.

Statcounter statistics.

Okay, I'll admit this next image is just fun. I love seeing visitors come from crazy places. (Crazy in the sense that they're reading a west Michigan blog.) It's more of a statement about how interconnected the world is than anything else. This image is a map of my most recent couple hundred visitors (late August 2011).InservicesAn inservice usually means a professional development session for teachers in the field, or inservice teachers. I'm fairly active in giving inservices, though I am more selective about them now. The inservices I've done this year for GeoGebra have had a good amount of traction with teachers because they have been self-selected. (Math in Action and Michigan Council of Teachers of Mathematics presentations have a similar impact.) Teachers are interested and immediately looking for application. In administration-initiated inservices there is a fairly serious obstacle in teachers' experiences with past irrelevant, mandated professional learning. The best answers to this that I have found have been using video of children the same grade as the teachers', actually working with demonstration lessons with the teachers' students and materials that impact the teachers' own mathematical understanding in a way that is accessible to the students. I've worked with 15 distinct groups of teachers, schools and intermediate school districts in the last 6 years. Collaborative work on some of these with Esther Billings, David Coffey and Pam Wells has been very rewarding.

One of the most interesting sequences of these inservices was work with Grand Rapids Public Schools. Work on Loretta Konecki's Urban Teacher Development Grant led to contact with Brian Gamm and Ena St. Germain, a couple of innovative teachers at Burton Elementary School. That led to a series of workshops for the school on teaching mathematics for problem solving, which led to developing an instructional model with Brian and Ena. The district piloted the program the next year, which led to work with 3 other elementary schools. That work led to the district adopting Everyday Mathematics, a curriculum which supports problem solving much better than their previous, irregularly used curriculum. Very satisfying to have good work with a couple teachers turn into something which benefited all the students of such a large district.

Presentations

I have presented only twice at national conferences, both for Association of Mathematics Teacher Educators with GVSU colleagues. Esther Billings, Dave Coffey and I have submitted presentations on the Workshop Model multple times to no avail; possibly because it is not so much research as practice. I am active at our two principle local conferences, Math in Action and the Michigan Council of Teachers of Mathematics, presenting 16 times at those two conferences in the past six years, as well as miscellaneous others. The Michigan Reading Association presentation was particular fun, as the teachers were very interested in reading-math connections, a topic that is dear to my heart.

Content

Scholarship of Teaching

The first area that I work on constantly is being in the classroom with K-12 students. I have had many opportunities through work with teachers, but also through volunteering in my children's classroom. The last two years I have worked extensively with Jeff Schiller at Ferry Elementary School and expect that to continue.

A terrific project with Dave Coffey and Rebecca Walker (and early discussions with Stephen Burton) has been the introduction of paired placement for our student teacher assistants. The motivation was to extend the benefits of cooperative learning to our preservice teachers at their moment of greatest challenge. The response in terms of student teacher accomplishment, relationship with cooperating teachers and every measure of the quality of placement that we can think of has been terrific. It's not perfect, but the issues that have arisen pale in comparison with the challenges of the previous system. Instituting this had made a real difference for our students. In terms of dissemination, this is probably the area we need to consider the most. The situation defies the typical research protocol in terms of amassing enough numbers for statistically significant data, and would require doing single placement for a significant portion of our students for a true comparison. An important part of the dissemination, though, has been the support and interest of the College of Education, which is considering this as the model for all TAs.

The area that Dave, Esther and I have presented on the most is the Workshop Model. Adapted from work in literacy education, particularly by Brian Cambourne and Lucy Calkins, and encouragement from Kathy Coffey, it is a flexible framework that encourages connections and reflection, which are both shown to have long term and significant impact on learning and retention. It can be seen as a small shift from a Launch-Explore-Summar

ize model, with more emphasis on connections and reflection. One of the strongest aspects is that it can be used with homework as well, encouraging these processes as habits. I believe the workshop to be progressively stronger over time as students who have had two or more classes that used this structure seem to be more independent learners that make better use of their time. This condition of learning of responsibility has been a real challenge to me as a teacher. This is an area that Esther, Dave and I intend to write in when time allows. We have presented it to the department, the university (via FTLC), and statewide math (Michigan Council of Teachers of Mathematics, MCTM), college-level Scholarship of Teaching and Learning and reading (Michigan Reading Association) conferences.Student Scholarship

I have had the good fortune to mentor three students in significant work. Cindy Groenink worked on a Summer Student Scholars project to support students that were the hardest for schools to support because of No Child Left Behind. In schools that over-respond to the need to make adequate yearly progress, the students who are just passing or just failing the Michigan Educational Assessment Program (MEAP) tests receive the most attention. Cindy designed activities for the lowest achieving students and made several that could also engage higher achieving students with a game structure. She presented this work at Math in Action and the MCTM conferences.

Shelby Vogg was a very independent student who worked on describing, understanding and designing interventions for math anxiety for a senior honors thesis. She also presented her work at Math in Action and MCTM, andI've been able to share it with several teachers since then in addition. Danielle Snow had a more personal seniors honor thesis project. After student teacher assisting, she was interested in comparing traditional teaching and inquiry-based teaching for herself, and did a good job getting background, assembling resources and trying out the different modes of teaching. This year I'll get to mentor a third honors thesis with Cassie Becker, a very strong student from whom I expect a lot.

One of the ways I have been trying to help get students involved is by presenting with me at Math in Action. The last three years (2009, 2010, 2011) I have had 20 students present games. The structure was inspired by a presentation Feryal Ayalont organized with several faculty at different tables and the participants rotated through. Each student (or sometimes a pair) will present a particular game for 10 minutes and then get a new group of teachers. It gives the students practice in presenting the game, and introduces them to many area teachers. Typically the students are presenting my designs, but a few have taken it on themselves to find a modify a game on their own. All are responsible for their own presentation of the game. This past year Nick Smith co-designed a game, Honeycomb, with me based on his idea.

I enjoy more informal mentoring of students, also. I supported several groups of students with materials, activity advice and games for Char Beckmann's MCTM Adventures with Mathematics. Teaching courses for the graduate MS Ed program has led to informal thesis/project advising with four of these students, with that turning into extensive work with two of them. One of the things the blog has done for me is to give me a place to share student writing as guest posts; response from students and readers has been positive about these.

Games

I have always been interested in games, and see that interest as connected to mathematics. When considering deeper issues of how to share the potential engagement in mathematics, in the way that engagement in reading and writing can change students' lives, I keep coming back to games. Many of the experiences when I have seen students with a distaste for mathematics be extremely engaged in problem solving have been during a game. In graduate school I had the good fortune to get to know and live in a house with Richard Garfield, who has gone on to be a world famous game designer. (Albeit, as famous as a game designer can get.) This served as quite a mentoring on game design, and exposure to more games than most people will ever have the chance to play. So far I've created over 50 games for math content from preschool through Euclidean geometry, with most being elementary and middle school number games. Some games are for skill practice, some are a context for gathering data, and some are to illuminate a mathematical structure. The blog has a page to gather resources on many of these games at http://bit.ly/mhgames. I've expanded on a few examples to give a flavor of this work.

• Eleusis Express is an adaptation I have made that has had some life beyond my use. It came to the original game designer's attention, and he helped to popularize it with players of his game Eleusis. It's gone on to be published in The Games Bible by Leigh Anderson. The game is an excellent context for discussing both inductive reasoning and problem solving with high school or college students.

• Fraction Catch is a good example of a game that gives practice at a skill while working on the concept of benchmarking. The original game design was for middle school, but the linked game is a variation for elementary school that simplifies by using more common fractions. The pictorial representation on the fraction cards allow kids to play before they have formal fraction algorithms.

  • Decimal Point Pickle is a good example of a game adaptation that made the game more fun and effective. Esther Billings had a game (from Nimble with Numbers by Leigh Childs and Laura Choate, Dale Seymour Pub., 1998) in which students pulled a number and placed it on a path, eventually wanting to fill in the path in order. I changed the game to be played with playing cards, and used the card color to make it feature variable length decimals, as comparison of these numbers is difficult for 5th-7th graders. The excitement level with the game was on a different order with these changes as was the learning from the students.

• Linear War is a game that is in the early phases of design, as I need a class with which to pilot it. (I've used it with inservice teachers that know the content already, which has shown some promise to the game, but that is different than the intended audience.) In this game students construct their own deck of cards, consisting of graphical representations of lines, and then compare characteristics. I think the game would be better as a unit game, as students learn various concepts of linear functions and then use the game to practice, eventually having the full game at their disposal. It brought up interesting cases that even gave the more advanced students something about which to think, so I wish to keep investigating the game.

• SPQR is an example of a math game for math majors. I wanted students to practice evaluating complex logical statements, but those exercises can get dry, which makes it a perfect context for a game. It was also successful with some students at getting them to observe the behavior and characteristics of AND, OR and NOT operators in a way they were not getting from static examples or logic tables.

Technology

GeoGebra has become a real focus for some of my work in teaching and professional development. It is a powerful, dynamic mathematics software package (geometry, algebra, statistics and now some Computer Algebra System capability) that is free and open source. I've successfully integrated it into my classes and this year started introducing and training teachers in its use. Some of my personal GeoGebra work is collected on this page; as with most things my emphasis is on developing activities for use with students and for teachers. We have a baby-GeoGebra community, with our first attempt at a website and a brand new Google group.

The past two years I have been the mathematics consultant for Andrew Topper's and Sean Lancaster's Content-Focused Teacher Inquiry Group (CFTIG) for Allendale Public Schools as they have shifted to becoming a 1:1 school district - that is, every student from 6th grade on has a laptop. We had alternate months inservice sessions that worked on specific teacher needs, shared uses of classroom technology, and discussed implementation issues. They summarized some of their learning in a Google document. Part of what this experience taught me was that I needed to address technology differently for teacher preparation. Much of the technology they were using I had never tried: interactive whiteboards, ExamView, student monitoring software, Moodle, etc. Nor did I feel that we were preparing our preservice teachers well to figure it out on the fly.

This is part of what led to Paul Yu and I submitting a National Science Foundation Transforming Undergraduate Education in Science grant, and then resubmitting it. As we prepared that, Asli Ögün-Koca, a colleague from Wayne State University, directed us to Technological Pedagogical and Content Knowledge research. (See TPACK.org for more information.) This points to the need to both use technology proficiently in preservice teacher preparation (or inservice teacher professional development) and also intentionally address the learning of new technology and discussion of how to evaluate its impact on students. This supported my work with the CFTIG and changed my teaching.

I regularly (about 1/3) classes have students bring laptops to class for use while learning. As I shifted from Geometer's Sketchpad (a beautiful program, but pricey) to GeoGebra I have learned the value of free applications. The ability for teachers or preservice teachers to have the software on any computer and have access to it for their students is crucial. Some of the principle tools I use are GeoGebra, Wolfram|Alpha, and Google documents, but there are many more. We also use the laptops and classroom computer for access to different types of problems (like Toast; post is actually on creativity for teachers), and I've started having students generate some of this kind of content themselves (like the Graphing Stories). I write on technology topics for things like tech for new teachers or iPad use. I've educated myself by attending Maria Anderson's Muskegon Community College Math Technology Bootcamp and recorded my learning, as well as returning to help with it the next year. I also try to work out some math/tech details to share with the blogging community, for example LaTeX and Google gadgets.

This past summer I had an opportunity that combined several of these interests. I worked with Alejandro Montoya, a computer science grad student, on developing, implementing and testing a game that he designed with Char Beckmann. The game, ParabolaX, is an iOS game for investigating graphs of quadratic functions. It's an example of a class of games called "serious games" that have specific non-entertainment goals while still striving for fun and playability. While he was not able to gather enough data this summer to prove his results conclusively, the preliminary results were promising. It was an excellent opportunity to work with Jonathan Engelsma and the GVSU Mobile Applications and Services Lab, and to see where educational games might be headed. I wrote up some connections I made while doing this work between general games and the mathematical practice standards from the Common Core.

Conclusion

I value connections and synthesis highly, and am happy that I have finally found a way to integrate and share my scholarship and teaching through the blog. It has helped me be a better teacher, served as my own reflection and journal, and connected me with a world-wide network of colleagues as well as been a way to disseminate the work.