Categories
reflection

Does content matter?

A few month ago, Andrew Hacker wrote an opinion piece in the New York Times called Is Algebra Necessary? that made quite a splash in the math education community. In a few words: students are failing at learning algebra, which teaches you skills that most people never use directly and given that there is no evidence that those reasoning skills are transferable, it seems that passing algebra won’t add anything to your life anyway (except for engineers, mathematicians and other professionals who actually use algebra). Given that the world does rely on a lot of mathematics, Hacker suggests that we instead focus on quantitative reasoning, arguing that at least those skills will have a very clear use in people’s life.

What I find interesting here is that the discussion always revolves about content. This view keeps traditional education centred on informational knowledge. There are a few studies (see [1] for example) that attempt to see the differences between teaching for content coverage or content depth that indicate that there might be more to gain from depth than coverage. If that is true, how far does a discussion on content really matter? At the same time, why don’t we find evidence of that transfer more easily?

I firmly believe that education research allows us to improve the way we teach, at the same time, we might need to take into account the fact that this discipline is fairly young and still faces many challenges to inform us on how people learn. In the light of the world of possibilities that Ken Robinson famously created in his TED talks and books, I would like to take a step back and ask myself how much content actually matters. Aren’t we promoting an old industrial-type educational system by maintaining the discussion at the level of the content? Is the problem really about algebra or quantitative reasoning? Or is it elsewhere, beyond informational knowledge?

[1] Depth versus breadth: How content coverage in high school science courses relates to later success in college science coursework – Marc S. Schwartz, Philip M. Sadler, Gerhard Sonnert, Robert H. Tai – Science Education Volume 93, Issue 5, pages 798–826, September 2009

Categories
Curriculum

The learning outcomes debate in mathematics curriculum

More than ever, the question “what to teach?” is taking a central position in the debate on mathematics education.

Not even a year ago, Sol Garfunkel and David Mumford wrote an op-Ed piece in the New York Times titled how to fix our math education? In which they invite us to “imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering.” Of course, the opposition to those ideas is still vibrant; as Alexei Sossinsky illustrates with a recent piece in French titled “Applied Math in school? No!” And to counter the traditionalist point of view, Garfunkel and Mumfor suggest that the current belief that pure mathematics teaches useful abstract reasoning skills might be similar to the old belief that studying Latin improves literacy skills.

All in all, this occurs to me as a problem of learning outcomes. What do we want our students to learn about mathematics? How are we going to resolve between providing tools for all citizens and creating a fertile environment for future generations of scientists and engineers.

Categories
conference IBL

15th Legacy of Moore conference, a debriefing

I just spent the last few days in Austin, Texas, discovering a community of math educators at the 15th conference on the legacy of R.L.Moore. What is this conference about? What did I like about it? What did it make me think about? And what new question did this open?

What is this all about?

The Moore method (initiated by Robert Lee Moore in 1911 while he was at the University of Pennsylvania) is a teaching design: take a small class of 15 to 20 students, give them a list of problems and a glossary of the relevant and necessary definitions they will encounter while solving the problems. Then, ask them to work on the problems at home and come back to class prepared to share what they have. Class time is then spent having students present their solutions and having their peers critique it. The role of the teacher is to facilitate the whole process, never to give an answer or explain a solution.
This method is today understood as part of a larger teaching model called IBL (for Inquiry Based Learning) which promotes having students making sense of concepts themselves in a structured communal environment facilitated by the instructor.

What did I like about it?

This conference is mostly the meeting of a community of practice. Teachers practicing some form of IBL from all over the US (and a few Canadians) gather and exchange stories, tips, ideas, difficulties, successes and failures. Senior practitioners offer to mentor instructors at the beginning of their journey mastering this type of teaching; education researchers report back on the scholarly evidence they have accumulated; but mostly, people are here to meet and share their passion. When in your own institution, you sometime feel alone and estranged, attending such a conference is invigorating!

What influence did the conference have on my current work?

David Steinberg and I are working on a one-term course on professional development for TAs in our department. Among other thing, our goal is to design a course which allows our participants to become autonomous in their development as teachers. The IBL model offers an effective framework to develop such an inquiry and highlights specific items to consider. In particular, I am now more attentive to how we will structure our learning environment and scaffold the proposed activities. I will definitively post more about the development of this course later in the summer.

What new question opened up?
The greatest challenge of the IBL model is to apply it to capstone, service courses with large enrollment (or more pragmatically: calculus). There is no clear consensus on how to do this. A sub model called POGIL (process oriented guided inquiry learning) originally developed in chemistry seems very promising. I’ll explore and will report back later on.

Overall, I’m extremely satisfied by what I got from attending this conference and warmly recommend it. And on top of all the above, I also got to discover Texas and read “How learning works: 7 research-based principles for smart teaching” published by educators at Carnegie Mellon. Expect a post about this shortly.

Categories
SoTL TA training

Standards for TA training

At the TA training Community of Practice meeting last month, Catherine Rawn treated us with four references from the scholarship of teaching and learning. Instead of letting me give him a copy of these papers, my coworker and friend David Steinberg invited me to post them on my blog (and since I didn’t have one, led to the creation of this one).

Each of these papers offers specific points to consider when thinking about a TA training program and we all enjoyed a great conversation based on those during the meeting.

In their paper, Eison and Vanderford [1], offer five guidelines for self-assessment:

  1. GTAs should be provided with a substantive orientation program designed to facilitate their introduction to both their department and their teaching assignment.
  2. GTAs should be provided with a comprehensive set of written materials that assist them in their initial teaching efforts.
  3. GTAs should be provided with periodic, discipline-based, instructional skill-building training programs.
  4. GTAs should be observed in action periodically in the classroom and provided with appropriate feedback.
  5. GTAs supervisors should meet regularly to design collaborative strategies which enhance the effectiveness and efficiency of GTA training activities in the department.

In the Lueddeke [2] paper, we are offered four areas demanding high priority in GTA training:

  1. Tutoring in seminars, workshops, field trips and practicals.
  2. Traditional and interactive lecturing (including IT).
  3. Assessment and marking.
  4. Classroom management: special considerations (e.g. student diversity and special needs) and problems (e.g. plagiarism, discipline).

The seven principles for good practice in undergraduate education by Chickering and Gamson [4] have been around for a while and remain pertinent in the context of TA training. Good practice:

  1. Encourages contact between students and faculty.
  2. Develops reciprocity and cooperation among students.
  3. Encourages active learning.
  4. Gives prompt feedback.
  5. Emphasizes time on task.
  6. Communicates high expectations.
  7. Respects diverse talents and ways of learning.

The chapter written by Shore [4] offers a literature review of best practices and also includes suggestions for data collection.

Look at my own department and its current TA training program in the light of those suggested standards gives many insights in both what has been already accomplished and the amount of work that still needs to be done. I’ll leave those thoughts for a later post though! Thanks again to Catherine for facilitating that meeting and sharing these resources!

References

  • [1] – Eison, J., & Vanderford, M. (1993). Enhancing GTA training in academic departments: Some self-assessment guidelines. To improve the academy, 12, 53-68.
  • [2] – Lueddeke, G. R. (1997). Training postgraduates for teaching: Considerations for programme planning and development. Teaching in Higher Education, 2, 141-151.
  • [3] – Chickering, A. W., & Gamson, Z. F. (1987). Seven principles for good practice in undergraduate education. American Association of Higher Education Bulletin, 39, 3-7.
  • [4] – Shore, C. (2010). Assessing the effectiveness of GTA preparatory activities and programs. In W. Buskist, & V. A. Benassi (Eds.), Effective college and university teaching: Strategies and tactics for the new professoriate (pp. 181-187). Thousand Oaks, CA: Sage.
Categories
general

Welcome to badadia

Hi and welcome!

My name is David Kohler, I’m a 5th year PhD student in mathematics here at UBC. I was born in Geneva in Switzerland, where I grew up and obtained my MSc at the Ecole Polytechnique Fédérale de Laussane (EPFL). Since then, I expanded on one of my favourite hobby: teaching. I’ve been involved in numerous programs now on campus and my goal is to start sharing some of my thoughts, discoveries, failures, successes and adventures here!

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