I arrived in NYC today with Bob Heal, Jim Dorward, and Patricia Moyer-Packenham. Tomorrow we are making a presentation titled “Using Virtual Manipulatives to Support the Development of Mathematical Understanding” at the Teachers College, Columbia University. Daniel McVeigh has been an advocate of our work with the NLVM for a number of years and arranged for us to come out.
In my part of our presentation I plan to talk about Teacher Training and Curriculum development. Here are some links I plan to use / reference:
- Overview of the eNLVM
- eNLVM eModules
- Curriculum development / teacher training case study
- How to rite good applets
- eModule research materials
- Transformation of Functions (example observations)
- Probability and Relative Frequency (example of simulations)
- What’s My Line (example of reinforcing group discussion with hands on experience)
- Patterns, Relations, and Functions (example of adapting by adding questions)
- Digging Dirt (example of open-ended, manipulative supported, grounded instruction)
- THEORY FOR AUTHORING TOOLS THAT SUPPORT TEACHER ADAPTATION OF MATHLETS
- Presentation on the eNLVM
- When Teachers Reuse and Remix Interactive Online Resources
- Interesting Interactive Math Websites
Teacher Training. A process I have used with teachers:
- Demo a lesson
- Discuss / critique the lesson together based on a rubric
- Have teachers observe students while the lesson is taught
- Debrief the experience
- Revise the lesson
- Reteach
Training Goals. My goals are for teachers to learn:
- Content knowledge
- Instructional strategies
- Familiarity with using high quality materials
- Where to find high quality materials
- Material evaluation / selection
- Help them enter a community
- Implementation issues
- Barriers / workarounds
- How to adapt existing resources
- How to evaluate student learning
- Processes for continuous improvement
Developing Interactive Math Curriculum
When developing curriculum, one of the first thing designed are the elements and structures of design and the processes of design, whether they be ad-hoc or structured. Curriculum design structures include time, learning outcomes, content models, instructional strategies, messages, representations, and media elements such as pages, displays and controls. Important design activities include:
- analyzing content,
- identifying desired learning outcomes,
- recognizing common student errors and difficulties,
- developing an overarching design,
- using design tools that allow for quick inexpensive prototyping and iteration,
- putting off expensive development as long as possible,
- using modular approaches,
- expert review,
- testing with real users,
- iteration
Considerations for Designing Interactive Math Curriculum
The design of interactive math curriculum should take into account the affordances that the medium can offer. These include efficient rich, dynamic, and linked representations, exploration, simulation of physically in-accessible situations and events, guided practice, immediate feedback, easy revision, recording sharing and replay, collaboration at a distance, linkages to real-time data, data sampling, and complex computation.
Contexts of Use
- Group presentation – projection, activity, discussion, worksheet
- Classroom station
- Computer lab (self-paced, pairs)
- Home work (self-paced)
Three Levels of Adaptation
- Activity instructions (via web or worksheet)
- Problem sequence (via web or instructions)
- Virtual manipulative (via configuration or code)
Multi-Disciplinary Teams
- Mathematician – Make sure the concepts / content / terminology / representations are correct
- Instructional Designer – Translate ideas into concrete technology designs
- Programmer – Develop virtual manipulatives
- Educator – Instructional sequences, strategies and types of activities
- Classroom Teacher – Access to students, anticipate student responses, guide implementation
Some Observations
- When an interactive model is on the screen, students ignore the text
- Text must be short and to the point
- Questions that require responses can help focus attention
- Transitions (going to lab, setting up equipment, getting people started, etc) waste time and need to be taken into account when designing experiences
- Always test out exact usage before going live and check again in the morning
- Developing virtual manipulatives is expensive
- Leverage existing manipulatives
- Choose areas where the impact will be greatest
- Teachers are much more likely to adapt than create activities
Posted on February 20th, 2009 by joel
Filed under: conferences, math education
Good luck to you all. Have a great time.