Upcoming Events

Algebra Project/Young People's Project Working Conference, May 18-20, 2012

The Stanford Tizard project showed that it is possible to reproduce the benefits of the Cui approach on a modest scale: in single classrooms and in a small school. One of its important objectives was to develop strategies and tactics to scale these benefits to whole school, and ultimately whole districts/local authorities/school groups. In studying how to do this Sociality, managers of the Tizard project have closely followed the work of the US Algebra and Young People's projects.

A working conference, jointly sponsored by the Educational Testing Service, Princeton University, the Young People's Project (YPP), and the Algebra Project (AP) is being held on May 18-20, 2012. The following abstract is taken from the prospectus for the conference by kind permission of the organizers.

``The AP and YPP projects build on the legacy of the work of Mississippi SNCC (The Student Non-Violent Coordinating Committee) for voting rights. Organizing for the right to vote in the early 1960s was not radical per se, doing so in the ‘60s for sharecroppers in the Mississippi Delta was. Likewise enabling high school students to graduate on time ready to do college math for college credit is not radical per se, to do so for students who enter high school in the bottom quartile is. Reaching those students is a game changer for them, and a game changer for the academic profile of the schools they attend.

``In the Algebra Project’s work with these students, a pattern is emerging. Participants can reasonably expect that students in the lowest quartile who remain in the Algebra Project cohort program through the tenth grade will continue to take four full years of high school mathematics, and graduate from high school on time prepared to do college math for college credit. This “reasonable expectation” comes out of the past 12 years’ work of the Algebra Project, YPP and a network of people, organizations, colleges, universities and schools.

``The Algebra Project has developed classroom strategies to help high school teachers transform mathematics learning for students in the lowest quartile, using instructional materials developed through NSF funding. This requires related teacher preparation and ongoing support; this also requires alternative or additional forms of assessment of student learning, and consideration of how we can best interface with the implementation of current and new state standards such as the Common Core State Standards for Mathematics (CCSSM). In addition, the scaling-up from individual classrooms to whole schools will require many new teachers. Thus, there is a need to rethink and restructure pre-service teacher preparation programs so that these teachers emerge ready to facilitate experiential STEM classrooms using AP pedagogical strategies.

``The YPP has developed after-school strategies to help Algebra Project students orient their youth culture to leaning. This requires developing and deploying entry-level knowledge workers: College Math Literacy Workers (CMLWs) and High School Math Literacy Workers (MLWs), who engage AP high-school students as well as elementary students in learning math through games and experientially-based activities.

``The purpose of this conference is to conceptualize the work needed to expand the AP/YPP model from individual classrooms to whole schools and search for network-wide consensus about the different dimensions of this work. For more information contact ben@algebra.org.''


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Recent Events

Wednesday 4th April 2012 11:00-12:30

ATM Annual Conference, Swansea University, Wales

Ian Benson on Experience with the Cui Curriculum

``Progress in mathematics is not merely a progress from easy exercises to complicated exercises, from short theorems to long ones. It should be a progress from the concrete to the abstract, from the particular to the general, from diversity (many little patterns) to unity (fewer,larger, patterns), from the comparatively unstructured, to the comparatively structured.'' A. G. Sillito paper to the Scottish Education Committee, Mathematics Syllabus Committee, April 1963 cited in Mathematical Reflections: contributions to mathematical thought and teaching written in memory of A. G. Sillito, ed ATM, CUP, 1970

``If the value of mathematics in education lies in process rather than product, then we have to revise radically many notions of what is important in school mathematics.'' Dick Tahta, Idoneities p28 op cit

Gattegno maintained that we can exhaustively identify the awarenesses needed in any domain and redefine teaching as the activity which leads students to cover this ground for themselves without missing any essential steps and without wasting time. To this end he developed the Cui curriculum and popularised it in his Mathematics textbooks. This session is based on seven years experience of re-introducing Cui to English primary schools. We will follow sample lessons in which students and teachers work algebraically before studying number, and explore the mechanisms for sustained student performance improvement. For more information email SuStrange@atm.org.uk
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Saturday 25th Feb 2012 10:00-16:30
2nd Meeting ATM Science of Education Group

The idea of this group is for us to commit to work within the theme of 'Science of Education' (a phrase coined by Caleb Gattegno). The group will meet each term and the work of the group might lead eventually to a 'product', possibly a publication of some type. This first meeting focussed on imagery and its role within various areas of mathematics. Attendees were invited to submit a brief note inspired by the session at this blog. The agenda for the second meeting is under development.

We welcome people joining the group not for a one-off day but as part of a general commitment to the theme of a Science of Education and working as part of a group over a period of time. For more information email alf.coles@gmail.com.

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In Classroom of Future, Stagnant Scores?

Writing in the New York Times on Sept 3rd Matt Richel addresses the problems of introducing new technology without reconsidering our approach to learning and teaching.

Download file "Technology in Schools Faces Questions on Value - NYTimes.com.pdf" .

Writing in September's Aspect Improvement, the magazine of the UK body for school improvement professionals, I discuss Gattegno's philosophy of learning and teaching as it applies to mathematics and literacy.

Download file "Recognising Children's Mental Powers.pdf"


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Welcome to the Visible College




This afternoon, for one session only, delegates to the Association for the Teaching of Mathematics Annual Conference are invited to learn about and feedback on the progress of the tizard schools. We call our partnership a Visible College because teachers, researchers and developers work productively across organisational and geographical boundaries as self-conscious participants in the Bourbaki tradition of mathematics education reform. Gustave Choquet wrote in ``Modern Mathematics,''

``Since Bourbaki has such clear-cut concepts and is so intimately associated with the development of mathematics in our time, we can hope that a study of `his' philosophical and mathematical work ... may serve to develop for all levels of education a teaching of mathematics better adapted to the needs of our time and the level of awareness of our generation''

Gattegno built his Cui approach on the axiomatic principle of Bourbaki. So do we in recording the dependencies between Zones in algebraFirst. The figure shows progress of a cohort of 125 experimental pupils (Cui) in six years of classroom based research through the ten zones of algebraFirst and eight levels of the UK National Curriculum compared to the national norm (Tra). Visit the latest youtube video on our approach to classroom based research.





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ATM eXtra session Wednesday 20 April

This year the UK Association of Teachers of Mathematics, founded by Caleb Gattegno, is celebrating the 100th Anniversary of his birth with a special Gattegno strand. We will be presenting an eXtra session at 1400-1530 on Wednesday 20th April with the title ``Mathematics as a Language: lessons from the Tizard project.''

PREMIERING: A VIDEO INTERVIEW WITH Gattegno’s collaborator Madelaine Goutard

PRE-READING (optional): AN ONLINE REPORT ON GATTEGNO/GOUTARD FROM A TIZARD SCHOOL


SESSION DESCRIPTION:

The tizard primary schools are exploring the use of multimedia technology to overcome the obstacles to wider adoption of Gattegno’s mathematics curriculum. We introduce students to the Cui approach to algebraic writing by naming particular patterns made with Cuisenaire's colored rods. These names are interpreted as instructions for a user (or computer program) to draw images using a software tool called an algebra checker. The manipulation of the contents of a box of Cuisenaire rods is represented in software as a process of structured drawing with colour- coded rectangles we call brix(TM). Attendees will learn how to re-organise Gattegno's “Mathematics with Numbers in Colour” as a common learning procedure for algebraic and number systems. And, they will learn about the experience of teachers as researchers, such as the tizard alpha site in Devon, who have introduced the Cui approach to mathematics to their schools.

Delegates are encouraged to bring laptops to take away the software tools and textbook to try the tizard approach for themselves.

REFERENCE:

From the UK Williams report on Primary Mathematics. ``Within the primary curriculum there is a clear and logical pattern, which builds on the EYFS, through number and counting to more complex and abstract concepts in mathematics. This approach has much to offer and, where it is implemented well, builds children’s confidence so that they feel ‘at home with number’. However, some schools have developed schemes and use programmes that first stress the concrete, abstract and algebraic aspects of mathematics, and then apply them to understanding number and calculation. All the programmes of this nature that were observed to be successful invariably gave the children a considerable amount of practical experience with structured materials. For example, ‘Cuisenaire’ resources were used very effectively in one school visited by the panel, where the defining criteria for success were undoubtedly the enthusiasm and expertise of the head teacher and the staff for this approach.'' (para 220, page 61)

Download file "Williams Mathematics.pdf"

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Installing algebraLab

Instructions for installing the algebraChecker component of algebraLab have been posted here

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The Primary Mathematics

Download file "bookcoverFinal.pdf" is published by Lambert Academic Publishing.


Copies have been sent for comment to participating schools in the tizard network and for review.

The book describes the conceptual model for learning and teaching mathematics that forms the basis of algebraLab for schools.

Additional copies can be obtained from Amazon Books: The Primary Mathematics: Lessons from the Gattegno School

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Development


Use Download file "SafariJSDatabaseGuide.pdf" with the Developer menu in safari to inspect the local database and create brix diagrams programmatically. Users can toggle between a database view (shown with the yellow sticky notes below and in the listing of the content of the selected database) and the presentation view (shown using the colored brix, here black (k), brown and red (nr) and orange (o).

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Evidence Creation

The tizard project announces the launch of the latest release of algebraLab for schools. Designed to support whole school adoption of the Cui programme. For more information email ian dot benson at cs.stanford.edu


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Evidence Collection

Prepare to collect your brix evidence by installing coda notes (double click on the extension downloaded from Coda to install it the toolbar of Safari), then visit sociality.stanford.edu/myEvidence.html and add a cursor position and a sticky note to the front of the postcard. Click Send Notes and complete the send to and sent from email addresses as shown on the back of the postcard below.



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Evidence Collection

Get ready for the new academic year by installing Safari (free download from Apple) and Coda Notes (free download from Panic). Brix(tm) is a trademark of Ian Benson and Partners Ltd, all other trademarks are property of the respective companies.


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don't panic (coda)

Just a few moments ago, Apple introduced Safari 5 here at Apple WWDC in San Francisco. This is the next major version of our favorite web browser. And with Safari 5 Safari Extensions, there is a new way for our young mathematicians to add



functionality to Safari. Follow this thread to monitor the building of SoMa - sociality's open media architecture.


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Caleb Gattegno Lesson


Click to play
In this Grade 1 lesson, recorded in Canada in 1964, Caleb Gattegno asks the children to solve a fractional division problem. Copyright in this transcript is held by the Canadian Film Board, and we are reproducing this extract for educational research purposes under the Fair Use Provision of the US Copyright Act.

Caleb Gattegno: `` I have ...

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Math Age: An Education Process Vendor's Perspective

Click to play
We visit an international trade show to learn about education process software, said to run in over 150 UK primary schools, that seeks to address an anomaly: many children appear to have widely different ``maths ages'' for related aspects of the math curriculum that have been grouped to be at the same ``standard level.''

This clip describes how math software is designed by an education process vendor.
Copyright Sociality MMIX. All Rights Reserved.

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Welcome to British Congress of Math Educators

TUESDAY, 6TH APRIL 2010 Session A19 Ian Benson Co-presenter Tom Kilsby
Aimed at: Early Years - Lower Primary – Upper Primary – Lower Secondary

Session Code A16.15-17.45

``for our purposes, the commutative squares in the pullback and pushout diagrams pertain to statements about cognitive (sub)systems'' what do transitive inference etc, Philips et al, 12/2009, plos (pdf below)

Download file "PLoS Computational Biology_ What Do Transitive Inference and Class Inclusion Have in Common.pdf"

``I believe that the biggest flaw in education is to assume that young people cannot grapple with abstraction at an early age. The whole world is an category of abstractions to children. The problem with teaching children the neat mathematical stuff that is there in the world is that there are far too few educated adults to re-enforce the ideas.''Scott Carter, 12/19/09 n-category cafe, page 6

Download file "n-category cafe.pdf"

Title: The role of conceptual mathematics in primary school reform
For the last five years, at the request of the Secretary of State for Education, the Tizard Programme, managed bysociality, has supported the mathematics education of a cohort of 250 young people, born this century, in 10 English schools. The programme is revisiting the mathematics curriculum pioneered by Dr Caleb Gattegno, that teaches algebra before arithmetic. Tizard has successfully reproduced the findings of a 20,000 student-year study led by teachers unions in Canada and Scotland between 1955 and 65. This presentation will discuss the UK pupils use of conceptual mathematics to overcome the market and public policy failure that led to Gattegno's math reforms in Leicestershire reverting to ``counting first.''


About the presenters:

Dr Ian Benson is a Cambridge mathematician and Stanford computer scientist, presently Principal Researcher for the trans-atlantic Tizard programme, and Visiting Professor at Kingston University (UK).

Tom Kilsby is Year 6 teacher and Mathematics Coordinator at Tizard primary school, West London


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Welcome to tizard



Tizard is a seven year old transatlantic research and development partnership for math reform: joining parents, schools, teachers and pupils in primary schools in UK, US and France. I am the principal investigator. Copies of my peer-reviewed books and research papers can be read via academia.org. Accounts on our work have been published in Aspect, the magazine of the UK organization for school improvement professionals, the Cambridge Computer Laboratory Ring Magazine, the magazine of Churchill College Cambridge and Prospect Magazine:

Download file "TizardAnnualReport2009-10.pdf"

Download file "Open minds. Open systems. A report on Year 1- 4..pdf"

Download file "Open Systems Open Minds. Technology and School Reform.pdf"

The Tizard Schools are re-evaluating a curriculum developed by Dr Caleb Gattegno, and known to the US and UK Departments of Education in the 1950s and 1960s as the Cui programme. William Brownell, Dean of the Education School at UC Berkeley and math educator evaluated the Scottish and English Cui programmes for the US government in 1966:

Download file "Brownell.pdf"

Brownell was described in Shulman (1974) as a leader in the study of the psychology of school subjects. Shulman observed that Brownell's ``brilliant experimental work on the teaching of arithmetic reads as well today as it did forty years ago.'' (Lee Shulman, the psychology of school subjects: a premature obituary, Journal of Research in Science Teaching, 1974, vol 11, pp319-339). Brownell challenged the whole concept of mental age as a criterion of readiness in learning mathematics. (W. A. Brownell. Readiness and the arithmetic curriculum, Elementary School Journal, v38, 1938, pp 344-354)

Gattegno wrote in 1955 ``the historic development of culture, if it has something to bring to our understanding of the (then) present moment, can be entirely foreign to what a mind stimulated in a new way can or could do, unforeseen in the former experience of the group. Too rigid a determinism, coupled with a slightly sentimental historicism, risk making us ignore whole continents potentially present in the mental universe.''

Brownell and Gattegno's voices remain in a minority. A substantial majority of mathematicians and educators continue to follow Maxwell's Genetic Principle: that ``the best way to guide to the mental development of the individual is to let him retrace the mental development of the race.''

Download file "62Mathematicians.pdf"

Standardisation based on 19th Century curriculum unfoldings has its critics, but as Christopher H. Tienken, Editor AASA Journal of Scholarship and Practice argues it remains the main determinant of state policy in US (Common Core CCSSI) and UK (National Curriculum).

Download file "Tienken.pdf"

Download file "CCSSI_Math Standards.pdf"

We spelt out the opportunity that is being missed in this Prospect magazine blog. You can read about our part in the campaign to revise the UK National Curriculum in Mathematics to remove extraneous content from Year 6, to make room for algebraic thinking and more time to work on fractions in the attached article from Prospect Magazine:

Download file "Prospect.pdf"

Tizard is part funded by the UK Department for Education (DfES), Department for Business, Innovation and Skills (DTI), Shuttleworth Foundation, Apple Inc, Devon, Leicestershire and London schools and the Rita and Rowland Benson Trust. It is hosted at Stanford Computer Science.






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