MATH ISW

This article contains ISW Materials

What is the MATH ISW?

The MATH ISW is an Instructional Skills Workshop (ISW) specially developed for graduate students and postdoctoral fellows at the mathematics department. It has been designed by and for mathematicians, with mathematics-specific content and an emphasis on transferring instructional skills to the classroom.

A workshop group consists of up to seven participants and two facilitators. Each day, facilitators lead discussions on major topics in mathematics teaching (e.g. "Learning Objectives in First-Year Calculus"), and participants design and deliver three "mini-lessons" followed by a variety of feedback. It caters to individuals new at teaching as well as those who wish to refresh and enhance their skills. Due to the interactive nature of this workshop, participants must be comfortable communicating verbally in English. Participants benefit from practicing skills and sharing ideas in a cooperative environment. The workshop consists of teaching practice, theory application, and topical sessions specifically relevant to the teaching of college mathematics.

Why take a MATH ISW?

• Taking an ISW will help you be reflective about your own teaching. It will provide a vocabulary for talking about and assessing teaching, as well as practical advice on planning and delivering lessons.
• An ISW will also form a strong part of your teaching portfolio; it is an internationally recognized certification.
• The ISWs offered by the Mathematics Department have additional benefits: they foster a teaching community in the department, introduce you to like-minded colleagues, and provide a rare opportunity to discuss mathematics teaching intensively.

Below are some comments from past participants in the Mathematics Department ISW.

• I would recommend this workshop to others because talking about teaching — just like talking about mathematics — is how we learn to teach better. This ISW provides a medium to accomplish this.
• Such a big difference from when we started. This was interesting, but more importantly, useful.
• The facilitators brought peer-level participation and discussion which was highly valuable. The community formed here will hopefully endure.
• This was a great experience, with lots to take away and apply!

The facilitators

There are six trained facilitators in the mathematics department:

• Dr. Warren Code (Science Teaching and Learning Fellow)
• Dr. Djun Kim (Skylight Research Fellow)
• David Kohler (graduate student)
• Dr. Fok-Shuen Leung (faculty)
• Michael Lindstrom (graduate student)
• Thomas Wong (graduate student)

Theme Session

The MATH ISW has developed a unified concept of theme sessions under the broad notion of constructivism.

Learning Outcomes

Participants will be able to

• elucidate ideas of student centered teaching and learning and apply them to their own classrooms
• give examples of active learning strategies and techniques and describe benefits of such approaches
• engage in reflection about their practice and imagine adopting this as a component of their professional practice. (feedback, continuous improvement, peer feedback, community of practice)
• be able to engage with elements of constructivism to analyze their teaching and learning experiences and apply the theory to their practice

Aspects of Constructivism

• learning by incorporating new knowledge with existing
• new knowledge, as it is incorporated, may lead to inconsistencies - these manifest as “misconceptions” which eventually requires a rebuilding of the model
• people are sense/meaning making machines
• there is an emotional content of knowledge
• learning is a social / relational (mediated) process; knowledge is socially constructed (e.g. importance of language in explanations, making meaning)

Theme sessions outline

• Day 0: What is effective teaching?
  • pretest for remaining sessions
  • hope to detect potential misconceptions
  • engage in a reflection on effective teaching (reflective practice)
  • focus on what they are looking for
  • use to do goal setting
  • serve to individualize topics
  • bring in emotional investment in the topcis suggested
  • illustrate social process
  • we illustrate that “effective teaching” is socially constructed

• Day 1: Questioning
  • our goal: engage in first three points of “constructivism” in a way that is informed from Day 0 discussion
  • emphasize individual meaning making
  • illustrate honing in on misconceptions, using questions to guide learners to new conception
  • model effective questioning
  • provide an expanded vision of what questioning is and what it allows; the purpose of using it.
  • local post-test - what did you gain from this session on questioning

• Day 2: Classroom management
  • really a discussion of the social nature of learning
  • goal for participants: ideas for setting up learning environments; specific classroom management techniques
  • participants will be able to give examples of how social constructs manifest in teaching and learning
  • discuss different framings of the “enterprise” of the classroom

• Day 3: Active learning
  • posttest of the process
  • discover active learning activities that they can apply in their classrooms; be able to discuss the benefits
  • rationalize the benefits of active learning by referring to the principles of constructivism
  • engage with frustration w/ t&l situations; re-examine through the lens of constructivism

Lesson plan for Day 0: What is effective teaching?

This first session of our constructivism module serves two main purposes: it engages participants in a reflexion about the criterion participants have for evaluating teaching; and it pre-tests the participant’s understanding of how people learn.

Lesson plan (30min)

Ahead of the session, participants are asked to take the teaching perspective’s inventory (TPI) (available at http://teachingperspectives.com/) and send us their raw scores (actually we didn’t have the time for that, so we ask them to have the scores with them).

(10 min) We begin the discussion by asking the participants what they think makes for effective teaching. We list those elements on a flip-chart.

(5 min) We then ask them what they thought while completing the TPI. Did they feel their answers were mostly constrained by their personalities or by the discipline?

(5 min) We ask them if they feel comfortable sharing their personal results, if not, would they agree to do so anonymously (to do this, we hand them a cue card and have them write their scores, sub-scores included). We display those on a black board (or flip-chart) and see the diversity of teaching perspectives.

(10 min) From there we discuss what they see, what questions they have, what they would like to explore. This will lead to the creation of their goals to the ISW.

Notes for facilitators

• Questions should aim at broaden participants perspectives while asking them to be more precise about their conceptions about teaching and how people learn. Any important question, misconception or dilemma should be recorded for further use in this module.
• This lesson plan follows the CARD model.

Lesson plan for Day 1: Questioning

The goal of this session is twofold: discuss three aspects of constructivism (we are meaning making machines that is we create mental models, we incorporate knowledge to our existing one using our mental models, and faulty models create unnoticed inconsistencies (or misconceptions) that require a new model to make sense of once surfaced) and discuss the use of questioning in teaching.

Lesson plan (30 min)

(5 min) We first brainstorm the purpose of questioning. We list that on a flip-chart. This should lead fairly naturally to a discussion about how people learn and asking the learners to expose their thinking.

(10 min) We collect on another flip-chart the three points of constructivism (mention above) under the title “how people learn”. Participants are asked to provide relevant examples for each of those 3. We make sure to insist that all this together means students who make “bad” mistakes are convinced it makes sense somehow.

(13 min) From that background, what will improve our questioning skills? Make sure to conclude or highlight that good questions need planning.

(2 min) We conclude and distribute the handouts about questioning.

Lesson plan for Day 2: Classroom management

Lesson plan (60 min)

(10 min) We discuss what is classroom management, how it applies, what are common experiences about it; outlining the notion of the classroom as an environment which requires explicit rules and expectations to function. Activity

(15 min) “In groups of 2, create a poster on a flip-chart to present the assigned content. Your mission will then be to present that material to the others in a few minutes.”

The two topics are:

• Tuckman’s stages of group development (we refer the participants to the wikipedia page which mainly describes the first four stages: forming, storming, norming, performing).
• Bain’s Natural Critical Learning Environment (using Bain’s book and asking participants to focus on aspects of this notion pertinent to the classroom management).

(15 min) Each group present their poster and its content. We follow this by a short round of clarification questions. Reflexion

(15 min) Given the activity and what was presented, “what does this tell/say/inspire us about classroom management?”. Thoughts and ideas are recorded on flip-chart paper. Documentation

(5 min) Each participant is asked to continue their reflexion individually and document it by writing on cue cards or in their binders.

Notes for facilitators

• This lesson plan follows the CARD model.

Lesson plan for Day 3: Active learning

(soon)