*By Benjamin Braun, Editor-in-Chief, University of Kentucky*

It has been one year since *On Teaching and Learning Mathematics* launched, so it seems an appropriate time for reflection. As I re-read the 36 articles we have published over the past twelve months, five prominent themes emerged that I will discuss below: teaching practices; bridges between K-12 and postsecondary education; expanding visions of mathematics education; the voices of students; and research, communication, and policy. If you have not had a chance to read all of our articles during the past twelve months, or if you have done so and would like to revisit them from a new perspective, this is my guide to the first year of our blog.

**Teaching Practices***.* One major theme of our blog over the past year has been the importance of interactions between students and teachers, particularly in classroom settings. From reflections on experimenting with varied pedagogical methods, to descriptions of interesting activities for students, to consideration of the role of broad student learning outcomes, the following articles provide many ideas that teachers can use to create quality interactions and engagement with students.

- Jerry Dwyer, Transformation of a Math Professor’s Teaching
- Benjamin Braun, Teaching Practices Between and Beyond All Lecture and All Student Discovery
- Art Duval, A Call for More Context
- Ryota Matsuura, The Hungarian Approach and How It Fits the American Educational Landscape
- Priscilla Bremser, Teaching Mathematics Through Immersion
- Oscar Fernandez, Helping All Students Experience the Magic of Mathematics
- Benjamin Braun, Assessment in Postsecondary Mathematics Courses
- Elise Lockwood, Reading Articles in Mathematics Education — It’s Not Just for Prospective Teachers!
- Janet Barnett, Dominic Klyve, Jerry Lodder, Daniel Otero, Nicolas Scoville, and Diana White, Using Primary Source Projects to Teach Mathematics
- Priscilla Bremser, Taming the Coverage Beast
- Benjamin Braun, Famous Unsolved Math Problems as Homework

**Bridges Between K-12 and Postsecondary Education**. What happens in K-12 education is important to postsecondary mathematics teachers for several reasons. Since postsecondary students are products of the K-12 system, what happens at the K-12 level has a clear impact on postsecondary mathematics education. Postsecondary mathematics educators have influence on the K-12 system, since K-12 teachers receive specialized mathematics content instruction in postsecondary classes. Further, core mathematical ideas and concepts transcend the K-12 to postsecondary divide, providing rich ground for making mathematical connections at all levels. The following articles address aspects of these issues and more.

- Art Duval, On Being a Friendly Mathematician
- Diana White, The Role of Mathematics Departments in the Mathematical Preparation of Elementary Teachers
- Sybilla Beckmann and Andrew Izsák, Why is Slope Hard to Teach?
- Dick Stanley, Proportionality Confusion
- Art Duval, One Reason Fractions (and Many Other Topics) Are Hard: Equivalence Relations Up and Down the Mathematics Curriculum
- Hung-Hsi Wu, The Mathematical Education of Teachers Part I: What is Textbook School Mathematics?
- Hung-Hsi Wu, The Mathematical Education of Teachers Part II: What are We Doing About Textbook School Mathematics?
- Elise Lockwood and Eric Weber, Some Thoughts on the Teaching and Learning of Mathematical Practices

**Expanding Visions of Mathematics Education**. Many of our articles emphasize the need to expand our vision of what it means to teach, learn, and use mathematics. Some of the following articles explore ways in which students’ and professors’ expectations of each other and themselves affect mathematical teaching and learning, while others meditate on the purpose and utility of mathematical knowledge and learning.

- Elise Lockwood, Striking the Balance Between Examples and Proof
- Keith Weber, Mathematics Professors and Mathematics Majors’ Expectations of Lectures in Advanced Mathematics
- Audrey St. John, The Power of Undergraduate Researchers
- Carl Lee, The Place of Mathematics and the Mathematics of Place
- William Yslas Vélez, Mathematics Instruction, an Enthusiastic Activity
- Priscilla Bremser, The Liberal Art of Mathematics
- Reinhard Laubenbacher, You Can Do Anything With a Math Degree

**The Voices of Students**. An often-neglected aspect of mathematics education is the reality of the experiences of our students. The following articles were written by students about their experiences, good and bad, providing teachers with a window into the world of mathematical learners.

- Morgan Mattingly, Transformation of a Math Student’s Learning
- Sarah Andrews, Justin Crum, and Taryn Laird, We Did the Math! Student Perspectives on Inquiry-Based Learning
- Sarah Blackwell, Rose Kaplan-Kelly, and Lilly Webster, Community, Professional Advice, and Exposure to New Ideas at the Carleton Summer Mathematics Program
- A.K. Whitney, In Math as in Dance, Don’t Miss a Step, or Else You May Fall

**Research, Communication, and Policy**. The final theme that stood out to me in our articles is the growing importance of postsecondary mathematics education research, communication among participants in the mathematics education community, and the impact of policies affecting higher education. Postsecondary mathematics education is in a state of transformation, and the following articles give a sense of how this transformation is manifesting itself with regard to how we understand learning, how students experience mathematics courses, and expectations for mathematics departments at institutions of higher education.

- Estrella Johnson, Karen Keene, and Christy Andrews-Larson, Inquiry-Oriented Instruction: What It Is and How We Are Trying to Help
- Priscilla Bremser, Do Mathematicians Need New Journals About Education?
- Diana White, The First Two Years of College Mathematics: Reflections and Highlights from the CBMS Forum
- Benjamin Braun, “The Time Has Come”: Highlights of the 2014 AMS Committee on Education Meeting
- Martha Siegel, Creating the 2015 CUPM Curriculum Guide
- Karen Saxe, Collective Action: Why the Future is Brighter for Undergraduate Teaching in the Mathematical Sciences

To conclude this article, I would like to thank the other members of the editorial board and our many invited contributors for the time and effort they have invested in this blog. All of our articles go through an editorial review process, meaning that every article we publish goes through multiple feedback/revision cycles. I have greatly enjoyed reading these contributions and watching our readership grow. I am looking forward to seeing what the future will bring!