By Taylor Martin and Ken Smith, Sam Houston State University
A good educator must facilitate learning for a classroom full of students with different attitudes, personalities, and backgrounds. But how? This question was the starting point for a new Faculty Teaching Seminar in the math and statistics department at Sam Houston State University. In the conversation that transpired, we looked to identify the most important components of creating a class culture that best enables us to achieve learning outcomes. What are our goals? How do we get the ball rolling each semester? How do we get our students on board? Read on to find out…
By Benjamin Braun, Editor-in-Chief, University of Kentucky
While one important component of successful teaching and learning is what happens inside the classroom, an equally important component involves decisions made at the administrative level that impact our classroom environments. A challenge that mathematics departments face is to make successful arguments for resources that support high-quality programs and courses for our students. Such arguments are often bolstered when the activities of a department are placed within the context of recommendations from professional societies.
In this article we survey a selection of recent reports and recommendations related to courses in the first two years of college study, with the goal of providing an overview of these reports for faculty and department leaders. It is worth noting that most of these were created with grant support from the National Science Foundation (NSF). There are at least seventeen professional societies involved in mathematics education efforts, of which six are represented in these reports: American Mathematical Society (AMS), Mathematical Association of America (MAA), American Statistical Association (ASA), Society for Industrial and Applied Mathematics (SIAM), American Mathematical Association of Two-Year Colleges (AMATYC), and National Council of Teachers of Mathematics (NCTM). Continue reading
By Priscilla Bremser, Contributing Editor
Many college and university students do volunteer work in local communities, and can learn valuable lessons in the process. The term “service learning” refers more specifically to service activities that are integral parts of academic courses. It can sometimes be difficult for mathematicians to envision how such projects could be included in their courses, especially courses focused on “pure” topics; for example, I have difficulty imagining how one would include such activities in Abstract Algebra. I have found myself, however, teaching courses in which service learning made sense, and I’ve implemented some service-learning projects with varying outcomes. Below I share some lessons I’ve learned in the process. Continue reading
By Art Duval, Contributing Editor, University of Texas at El Paso; Kristin Umland, Associate Professor, Department of Mathematics and Statistics, University of New Mexico (on leave), and Vice President for Content Development, Illustrative Mathematics; James J. Madden, The Patricia Hewlett Bodin Distinguished Professor, Department of Mathematics, Louisiana State University; and Dick Stanley, Professional Development Program, University of California at Berkeley
At the 2016 Joint Mathematics Meetings in Seattle this past January, an unusual mix of mathematicians and mathematics educators gathered for an AMS special session on Essential Mathematical Structures and Practices in K-12 Mathematics. This was the fourth consecutive special session at JMM organized by Bill McCallum and other folks at Illustrative Mathematics that focused on work in mathematics of mutual concern to mathematicians, mathematics educators, and K-12 teachers. The theme this year was inspired by a conversation between Dick Stanley and Kristin Umland about ratios and proportional relationships, and the talks were selected and ordered to highlight the development of mathematical ideas that are both upstream and downstream of this terrain.
Academic mathematicians are able to describe mathematical ideas in an efficient way. Across specialties, they share tools of language and habits of communication that have been shaped in order to facilitate the exchange of abstract knowledge. One purpose of the special session was to apply this cultural skill to selected topics in K-12 mathematics. The participants sought to create clearly expressed and easily understood descriptions of topics that are rarely developed clearly in the K-12 curriculum, such as measurement, number systems, proportional relationships, and linear and exponential functions. Although many people have been working in this area in recent years, much more needs to be done.
By Johanna Hardin, Pomona College, and Nicholas J. Horton, Amherst College
As statisticians in mathematics departments, we have both spent many department meetings, departmental reviews, and water-cooler conversations discussing the merits of various different curricular decisions with respect to the calculus sequence (“Why not take linear algebra before calculus III??”), upper division electives (“But those classes are needed for graduate school!”), and number and order of courses required for the mathematics major/minor. Recently, more of those discussions have related to critical components of the statistics curriculum, and how courses from mathematics ensure that statistics students have a solid quantitative foundation. These kinds of conversations reinforce the fact that there are strong connections between mathematics and statistics, and these connections can and do affect decisions about undergraduate curricula.
More generally, this is an exciting time to be in a quantitative field. The amount of data available is staggering and there is no end to the need for models that harness the deluge of information presented to us every day. Mathematicians, Statisticians, Data Scientists, and Computer Scientists will all play substantial roles in moving quantitative ideas forward in a new data driven age. To be clear, there are challenges as well as opportunities in what lies ahead, and how we move forward – particularly with respect to training the next generation of mathematical, statistical, and computational scientists – requires deep and careful thought.
The goal of this blog post is to share some of the recent pedagogical ideas in statistics with our mathematician colleagues with whom we – as statisticians – are intimately engaged in building curricula. We hope that the description of the recent developments will open up larger conversations about modernizing both statistics and mathematics curricula. Many of the ideas below on engaging students in and out of the classroom, connecting courses in sequence or in parallel, and assessing new programs are relevant to all of us as we work to better our own classrooms.
By Hortensia Soto-Johnson, Professor, School of Mathematical Sciences, University of Northern Colorado
Those of us who teach mathematics know that students struggle writing the symbolism of mathematics even through they can articulate some of the concepts behind the symbolism. Those of us who interact with children know that they struggle articulating their thoughts even though they can convey their thoughts through gesture. For example, children point to indicate what they want and touch items or use their fingers as they learn to count. It is through such bodily action that children learn to recognize three objects as the quantity three without simultaneously touching and counting one, two, three. Athletes and musicians also apply bodily actions to master their sport or instrument respectively. For example, how many times have you have seen a basketball player shoot an imaginary ball into an imaginary hoop? Consider how a piano teacher places a student’s hand on top of the teacher’s hand as the teacher plays the piano. These are just a few ways in which we use our body to learn, so why not use it purposefully to promote the learning of mathematics? Continue reading
by Priscilla Bremser, Contributing Editor
I had what seemed the perfect first full-time teaching position, in that much of the planning for Calculus had already been done when I arrived. The department chair handed me the textbook and the syllabus, essentially a day-by-day schedule of book sections and homework assignments. This being the United States Naval Academy at Annapolis, where every student takes Calculus, a lot of wisdom had gone into the schedule. I now look back at that syllabus with a mixture of gratitude for the jump start and recognition that much has changed. What’s in your syllabus? What does your institution require, and what is most important to you? What is decidedly not in your syllabus? Do you hand out a paper copy on the first day, or is it all online? How well does the syllabus reflect what you want your course to be? Continue reading
by the Editorial Board
We want to begin this post with thanks to all of our readers and contributors — we appreciate your feedback and ideas through your writing, social media comments, and in-person conversations at mathematical meetings and events. In-person conversations have been on the minds of the editors recently because we had our first-ever in-person meeting as an editorial board at the 2016 Joint Meetings in Seattle. This was great fun and gave us a chance to seriously reflect on our blog, its role in the mathematical community, and what we want to do over the next year or two. In this post, we give a brief update about a change to the structure of our blog, followed by some highlights of our experiences attending the joint meetings. Continue reading
By Elise Lockwood, Contributing Editor, Oregon State University
Solving counting problems is one of my favorite things to do. I love the challenge of making sense of the problem, the work of correctly modeling what I am trying to count, and the fact that I get to reason about astonishingly large numbers. I did not always feel this way about solving counting problems, though. For much of my mathematical career, counting was a mystery – a jumble of poorly understood formulas and equations that just made me miserable. As an undergraduate, I struggled to grasp the difference between order mattering or not mattering, what the respective factorials represented in confusing-looking formulas, and why I should care about how many full houses could be chosen from a deck of cards. My teachers at the time may have shared the sentiment nicely captured by Annin and Lai: “Mathematics teachers are often asked, ‘What is the most difficult topic to teach?’ Our answer is teaching students to count” (2010, p. 403).
At some point during graduate school (thanks to an influential professor who loved counting), I turned the corner and became more interested in understanding counting. Through lots of practice, I began to improve in my ability to solve counting problems. Since that time I have committed my research interests to learning everything I can about undergraduate students’ counting – what they do when they approach counting problems, why they struggle, and how we might help them solve such problems more effectively. Continue reading