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Contents |
[edit] Research Projects
[edit] SimCalc MathWorlds®
Here you can read of the ongoing work of the SimCalc MathWorlds project funded by the Institute for Education Sciences, US Department of Education, July 2007-June 2011
- Use of SimCalc MathWorlds by local teachers
- Translation of SimCalc MathWorlds® into other languages. Visit Internationalization_Efforts
[edit] Early Algebra
[edit] Famous Author Series
During the course of the academic year 2008-09, we will be studying various scholarly works each month and recording the meetings. Please feel free to join the seminar on-line. More details are posted here.
In this section of the Wiki, participants of the seminar can post their thoughts.
Wednesday 15th October 2008 at 4-5pm
Article: Unpacking Pedagological Content Knowledge: Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students Author: Heather C. Hill, Deborah Lowenberg Ball & Stephen G. Schilling Reference: Journal for Research in Mathematics Education, July 2008, Volume 39, Issue 4, Pages 372-400 Download Article: [1]
Famous Author Series Academic year 2007-08
[edit] Interdisciplinary Colloquium Series
Please feel free to post your reflections of the talks in this series. Streaming videos of the talks can be found on our [2] website. Even if you could not make the talk but have viewed it on-line please feel free to add your thoughts. We are especially interested in contributions from research students.
Academic Year 07-08
Formulating Measures: A Step Toward Understanding Modeling in the K-12 Curriculum Dr Judah Schwartz. Wednesday 7th May 2008
Talent Development and Social Justice: Amicable Agendas or Conflicting Constructs Bharath Sriraman. Wednesday 2nd April 2008
Foundations of Algebra in the Elementary Grades Susan Jo Russell. Wednesday 5th March 2008
Generalizations in the Early Grades: Algebraic Structures for Young Children Dr Barbara Dougherty. Monday 10th December 2007
Perspectives on Dynamic Geometry Nick Jackiw, Friday 16th November 2007
From Symbolic Cognition to Digital Environments - a Long Term Perspective Dr Luis Moreno-Armella, Friday 26th October 2007
[edit] 1st Foundational Issues in Mathematics Education Symposium (March 20-21 2008)
Thursday March 20th
Thursday evening dinner
Side discussion about 'objectivity' and 'truth'
Friday March 21st
Morning Round table Discussion
5 grand challenges for the 21st Century
Preliminary Set of Foundational Issues
- New forms of communication and participation - (verbal and non-verbal, e.g. gesture) in the classroom particularly the changing role of identity
- The roles of technology in changing the means and purposes of Mathematics Education
- The roles and nature of proof and justification across Mathematics Education from kindergarten through graduate study
- The issue of the best way to account for students understanding and personal meaning attached to mathematical knowledge (either concepts, know how, skills, etc)
- Plausible curricular futures in Mathematics Education – Trajectories for next generation Standards and beyond (across and within topic areas)
- The changing nature of the mathematics of change and variation in the computational medium – complexity and dynamical mathematics
- The historical evolution of representation in mathematics and its deeper impact
- The nature of the capacity for change at the individual, school, district and regional levels and how these capacities interact - {please replace with international nouns}
- Social, cultural and political impacts on change based upon new innovations in mathematics education and the learning sciences
- Conditions that support having an impact in the real world
[edit] 2nd Foundational Issues in Mathematics Education Symposium (November 20-21 2008)
AGENDA
Group 1 Teaching & learning of complexity - notes below
Group 2 Technology Subgroup Scribblin's
Group 3 Role of Teacher Professional Development notes
Thursday 20th November 2008
9.00 – 9.30 Coffee & Regrouping
9.30 – 11.30 Three Plenary sessions with Q&A
11.30 –12.00 Planning specifics of afternoon sessions (group structure, aims and objectives)
12.00 – 1.00 Working lunch beginning preliminary thoughts
1.00 – 4.00 Breakout groups around major themes – see notes below
- Complexity-Breakout-Group
- Technology Subgroup Scribblin's
- Role of Teacher Professional Development notes
4.00 – 5.00 Regroup: Report back to group and synthesize work in preparation for tomorrow
6.00 – 8.00 Dinner Buffet at Stephen’s house including members of the Kaput Center, UMass Faculty and Admin
Friday 21st November 2009
9.00 – 9.30 Coffee & Regrouping
9.30 – 11.00 Whole Group: Share data from individual projects, structure what a final resource might look like (issues of impact, need, resources)
11.00 – 2.30 Breakout to working/planning groups (inc. Working lunch)
- Day 2: Complexity-Breakout-Group
- Day 2: Technology Subgroup Scribblin's Part 2
- Day 2: Teacher PD notes
2.30 – 3.00* Re-group to plan next steps (Farewell if some folks need to leave early)
3.00 – 5.00 Working Group to discuss action plan (e.g. proposal for publisher)
6.00 – 8.00 Dinner at Elizabeth’s, Fairhaven for those still around
- We leave this as an option for folks who need to leave to catch flights in the evening.
FOCUS & GOALS
Our goal from these two symposium is to focus on what are some of the main foundational issues in mathematics education today and where do we see the field moving in addressing these issues. The result of focusing on this goal will hopefully yield a resource that will be of use to the field in one of many ways.
Such may include:
- A white paper/list of recommendations that the Kaput Center will publish on its website and distribute to alert researchers and practitioners of our discussions
- A scholarly article/monograph or special issue in a well-read journal/venue
- New projects
- Archive of existing resources (papers, datasets) or on-going work that researchers and practitioners can access to help establish partnerships and new projects
It is not expected that the Kaput Center will be a lead in all of the final products of this meeting. But it will aim to keep track of subsequent activities particularly in respect of the original funding (NSF).
Central Issues (for now)
In reviewing our original work and attempting to consolidate these with subsequent feedback, I present the following five themes for our preliminary discussion in conjunction with the plenary speakers.
I encourage all attendees to add to these strands with papers and critical notes prior to the conference.
The Kaput Center uses a variety of mind-mapping software and on-line tools to record ideas/reading and literature so please contact us if you wish to use alternative tools.
Please react to the following areas:
1. Ubiquity of Technology
Here are some framing questions:
- Role of new dynamic technologies in reformulating mathematical knowledge for education and vocational use
- Transparency of technology
- In what form does an affordable technology exist (i.e.. where and for whom)
- What are the new “design principles” for our educational and research practices?
- How can we explore new ways of mathematical thinking vs use technology to prop up existing practices?
- What is the role of a commercial company such as Verizon in providing the right kind of wireless infrastructure to help make our theoretical visions for accessible education become a widespread reality?
- Characterize particular ways of thinking in mathematics as a human activity
- What are the next research questions to address advances in:
- Socio-Cultural studies
- The evolution of tools and symbolic thinking
- What are the next research questions to address advances in:
2. Data Interpretation and Visualization
- How can we help children make sense of large datasets and data of the world and society around them as well as adults making sense of natural and alternative ways of formulating ideas?
- How do we make sense of understanding the dynamics of complex systems? And more so, how do we understand what and how to focus on?
- There are many ways to visualize complex datasets but we need to know what constitutes an effective set of visual tools and how we apply them to educational environments.
- How do we explain them with different epistemologies? i.e. can young children today see a patterns in relevant data and make claims about truth.
- Fundamental: What do our young children believe in when they look at data in the daily papers? Who is their expert?
- Characterize particular ways of thinking in mathematics as a human activity
- What are the next research questions to address advances in:
- Socio-Cultural studies
- The evolution of tools and symbolic thinking
- What are the next research questions to address advances in:
3. Students as co-participants in building predictive & explanatory models
- How do learners identify themselves with the mathematical “stuff” they operate with, and on, in digital environments?
- How do students identify with their work and in what ways?
- In essence, how can we develop from where students are, in thinking through mathematical ideas to, something that they identify with?
A topic that extends across the three points outlined above:
- Psychologising, socializing and formalizing
- I see a new theme that extends our March 2008 discussions and integrates thoughts from colleagues that could not make the original discussions.
- John Mason presented the following idea:
- Consider the integration of 'psychologising the subject matter' (as Dewey put it), with 'socialising (enculturating) learners into mathematical practices', with the changing 'absolutes' (as Gattegno put it) of children as they pass from early childhood through adolescents to late teens.”
- In addition Ubiratan D'Ambrosio wrote to me reflecting on our earlier themes:
- Is mathematics accessible and necessary for every human being? Rather than asking "particular ways of thinking in mathematics as a human activity" I would ask "mathematics as a particular way of thinking as a human activity …The obstacle in Math Education has to do with language.”
- John Mason presented the following idea:
- I see a new theme that extends our March 2008 discussions and integrates thoughts from colleagues that could not make the original discussions.
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