Tim Pelton, firstname.lastname@example.org
Leslee Francis Pelton, email@example.com
University of Victoria
May 18, 2016
Helping pre-service teachers learn how to teach mathematics is a challenging, but enjoyable task. In this paper we discuss how we fortify our lessons with online resources and share some of our strategies to encourage student engagement and learning.
We have abandoned required textbooks in our classes. While they may be useful occasionally, we don't teach by them and they are a burden on underfunded students. We recommend to our students that want a textbook for reference—that they purchase an older/used edition of one of the many quality textbooks through an online bookseller. In place of a textbook, we offer a curated collection of online resources relevant to each lecture and make them available through CourseSpaces (the LMS that our university employs). You may choose to incorporate a textbook in your program—but including videos may still be very worthwhile
In preparation for each lesson, we review our goals and previous notes, check our existing collection of resources for broken links and content coverage/quality, and seek out additional resources to refine the collection and incorporate new ideas. Some of the resources are professional journal papers that provide students with research-based evidence and support confidence-building in such research; a few are websites with mathematical content, lessons, or interactive exploration tools; but the majority of resources are videos. Videos are often multifaceted, but typically include components such as: classroom routines and practices; teacher reflections; mathematical contexts, processes and explorations; and student interactions.
We have observed that a keen student may be willing to devote up to two hours in preparation for each lesson, with good students typically allowing themselves about one hour to prepare for a lesson and note that busy students often do not find any time to devote to preparation at all—relying instead on classroom learning and follow-up review of resources as needed to complete assignments and prepare for their practicum experience. To make class work, and to ensure that all of our students are moving toward mastery of content and pedagogy, we strive to find a way to motivate every student to review the resources that have been shared, and ensure that these resources are available to our students for an additional year following the course.
Reflecting on our practice
Our practice of using online resources has been developing for more than a decade and although it is still imperfect several aspects of it are worth sharing. We are always striving to expand our own understanding and to find better ways to help our students prepare to teach mathematics. Resources are selected to enhance each student's 'well of experience' and to provide a foil to support discussion, exploration, discovery, and sense-making in the classroom. Students are also encouraged to own the responsibility to understand concepts and processes and challenged to create learning objects that might be used in the classroom. Video resources are among the most powerful resources we use to supplement our classes and we like to create our own video examples to complement found resources and model our ideals and expectations.
Find and share effective resources
With respect to the resources we select, we have several objectives:
- Create an easy way for students to access an organized collection of relevant video content
- Accurately present mathematical ideas
- Motivate positive teacher-student and student-student interactions
- Emphasize sense-making and problem solving
- Model effective representation and communication
- Demonstrate the negative effects of 'telling'
- Model resilience and perseverance
- Encourage the development of mathematical power.
- Reduce math anxiety
- Inspire curiosity, thoughtful risk-taking and confidence
- Share counter-examples to promote discussion
- Many sources—e.g., www.edutopia.com www.teachertube.com www.vimeo.com www.youtube.com www.khanacademy.org www.mathsnacks.com
- Prescreen everything—is it consistent with the message that needs to be communicated?
- Find an app that lets you capture and replay video offline
Challenge our students
In our readings, classroom activities and assignments we aim to challenge our students to:
- Appreciate and learn from what is available
- Avoid "learned helplessness"—be in control
- Be prepared to summarize and paraphrase what was shared
- Discuss and learn from each other by sharing perceptions and related experiences
- Transfer ideas from the video content to classroom practice with complementary activities
- Ask questions, seek resources, make connections and share new learnings
- Seek out opportunities to explore challenges, problem solve, and discover real mathematics
- Create explanations, learning objects and lessons to support their peers and their students.
- Anytime/anywhere consumption—share the link and students can view when it works for them
- Any speed—2x for quick review; 0.75x when it is tough; pause and re-play when I have to think it through
- Available for review and to meet individual needs, Available support for supporting learners (tutors, parents, peers)
- Short, focused video combined with questions and activities form useful learning objects
- Provide a menu of learning objects supports self-directed learning by allowing learners to focus on that which they need or want to understand most
- Classroom discussions and activities can be supported by short (or even very short) selected clips
- More in-class activity time, and 1:1 time can be made available when 'teacher-talk' time is reduced
- Teacher created videos support confidence building—you are more than a selector of content, you have ideas to share
- Identify key points, concepts and processes that you can restate in another way
- Expand upon ideas and provide additional clarity
- Demonstrate a positive attitude and effective habits
- Model and animate processes to support sense-making
- Share visual representations that are helpful and meaningful
- Keep your videos short and simple—1 or 2 minutes is great
- Production value is far less important than clarity and accuracy
- Even talking heads, screencasts and narrated powerpoints are fine if they are clear, succinct and engaging
- Have a question or goal as your focus
- Scripts and storyboards are your friends
- Edit out pauses and speed up playback to a normal rate
- Insert break-points (questions, discussion pauses) if it is a longer video
- Creation is a problem solving activity
- Keep it focused—point to other videos for tangents/excursions
- Try rapid prototyping—limit retakes and keep it real
- But remakes are fine too—if you have a better way—share it
Also check out another website we have created to encourage folks to create and share their understandings on video using an app called Explain Everything: www.explainingunderstanding.com