The Numeracy Progressions which were basically finalized in February 2008 are supposed to be part of the staple diet in adult numeracy learning in Aotearoa New Zealand.
The key task set before the country's adult educators was to see these progression "embedded" with a range of contexts, especially those of the "workplace".
The progessions were based on two primary sources: The New Zealand Numeracy Project in schools and an American Document Equipped for the Future.
Noticably lacking from the Numeracy Progressions is any mention of Algebra (apart from a quote in Bacground to the progressions). I wonder why this is so. It was mentioned in this 2004 document (see p. 4) where the early development of the numeracy progressions is discussed.
SABES the system for adult basic education supports offers a Framework for Adult Numeracy Standards. The website suggests that:
"Algebra includes more than formal methods of equation solving, age problems, and lots of X's and Y's. Conceptual understanding, algebra as a means of representation, and algebraic methods are all problem solving tools. Algebraic reasoning allows us to think about and express patterns, relations, and functions which ultimately give us access to technology."
I could not agree more. Yet, I notice that in New Zealand, Algebra is almost a dirty word when it comes to Adult Numeracy. However, the word occasionally appears - as in this NZQA unit for the Adult Literacy Educator.
I suspect the lack of algebra in the progression has much to do with its lack of presence in the Adult Numeracy Core Curriculum of 2001 in England which, like the progressions, sets forth perfomance continuums. However, it has made a presence in the 2007 review of the Core Curriculum.
So why is algebra overlooked?
* a concern with the everyday and the practical may mean algebra is seen as irrelevant.
* a lack of basic maths knowledge by many numeracy tutors may mean that algebra has been "avoided".
* similarly, anxiety over algebra on the part of tutors may mean algebra has been avoided.
* a conceptualisation of what algebra is and what it does is seriously lacking among numeracy educators.
In this short article, Donovan makes a case for the value of algebra for adults: The importance of algebra for everyone. Some of her early arguments in the piece are a bit suspect.
But she does hit upon some big things
• Seeing and formalizing patterns
• Generalization
• Using symbolic notation to express relationships
• An understanding of the relational meaning of the equals sign.
For more on the importance of algebra fro a productive economy click on this link.
Numeracy Pedagogy in Practice
The approach offered in this book is from a social and holistic perspective. It is called Beyond Worksheets. However, if you are looking for specific examples of this approach, they are not here. What the book does do is reflect on various theoretical approaches to teaching and learning numeracy, with various slants on constructivism at the forefront. In then suggests the instructional strategies that reflect a social and holistic approach. If you are in a hurry, then go straight to pages 46 and 48 for the priniciples, strategies and methods that reflect this approach.
Here's a short Article by Jon Swain: What makes a good numeracy teacher?
Here's a short Article by Jon Swain: What makes a good numeracy teacher?
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Models and approaches to adult numeracy "development".
I am cautious about the word "development". It implies that adult numeracy competence might be placed on a continuum - something I am not particularly sanguine about. However, I will leave it for the meantime.
Hoogland in this paper elaborates on a model of Adult numeracy development taken from Maguire and O'Donoghue (2002). Here the model tries relate learning to domains of increasingly rich contexts. It refers to formative, mathematical and integrative phases. I am not sure that the second of these is an entirely useful description. Perhaps another word could replace "mathematical"?
Hoogland in this paper elaborates on a model of Adult numeracy development taken from Maguire and O'Donoghue (2002). Here the model tries relate learning to domains of increasingly rich contexts. It refers to formative, mathematical and integrative phases. I am not sure that the second of these is an entirely useful description. Perhaps another word could replace "mathematical"?
Quantitative Reasoning
Bernard Madison talks about the need for college graduates and indeed all adults to become "critical consumers of numbers". He spoke at the Mathematics-Across-the-Curriculum/Quantitative Reasoning Conference at the Borough of Manhattan Community College. You can find a video of his address at the previous link.
One thing that he said stood out to me and I paraphrase: It is not so much the level of mathematics, but the difficulty of the context that determines how well people do.
This is no only the case with the transference of maths/numeracy "skills" from academic to everyday/work contexts. It is also very much the case with the transference of "skills" among the various academic disciplines.
For example, students who have had a throrough grounding in graphical work in formal mathematics are still often unable to critically analyse and interpret graphs in other academic or everyday contexts.
Much of what Madison discusses in this video has great bearing on our understanding of adult numeracy performance in real-life contexts.
It also, once again, puts a question mark over the numeracy progressions and how they might be implemented. There is no doubt the as the progression are used by tutors, it must be in rich meaningful contexts.
However, there may be problems in trying to teach numeracy in rich contexts within classroom or institutional settings. Students, including adults, have certain expectations of what mathematics should "look like" and may well resist attempts to teach maths in highly contextualised ways.
Here is a 2006 paper by Ginsberg, Manly and Schmitt that addresses some of these issues.
One thing that he said stood out to me and I paraphrase: It is not so much the level of mathematics, but the difficulty of the context that determines how well people do.
This is no only the case with the transference of maths/numeracy "skills" from academic to everyday/work contexts. It is also very much the case with the transference of "skills" among the various academic disciplines.
For example, students who have had a throrough grounding in graphical work in formal mathematics are still often unable to critically analyse and interpret graphs in other academic or everyday contexts.
Much of what Madison discusses in this video has great bearing on our understanding of adult numeracy performance in real-life contexts.
It also, once again, puts a question mark over the numeracy progressions and how they might be implemented. There is no doubt the as the progression are used by tutors, it must be in rich meaningful contexts.
However, there may be problems in trying to teach numeracy in rich contexts within classroom or institutional settings. Students, including adults, have certain expectations of what mathematics should "look like" and may well resist attempts to teach maths in highly contextualised ways.
Here is a 2006 paper by Ginsberg, Manly and Schmitt that addresses some of these issues.
Research
In the field of adult numeracy there are a plethora of reports, some of which claim a research base. However, most of these tend to be both dry and jargon laden. These reports circulate, no unlike a car spinning it wheel trying to get of of the mud and yet digging only deeper in into murkiness.
The purpose of this section is to only present clear cut empirical research into adult numeracy.
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This first piece of research takes a look into the fascinating world of probabilistic numeracy.
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Here is an excellent study by Gail FitzSimons which looks at situated numeracy practices in a workplace - aptly titled "Learning numeracy on the job'.
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This is a comprehensive piece of research by Jon Swain, Elizabeth Baker, Deborah Holder, Barbara Newmarch and Diana Coben in 2005. It employs a number of methods including ethnographical approaches, case studies, interviews, diaries, photographs and the like. It also looks at some of the theoretical orientations that informed the research.
The findings include the very important area of adult numeracy practices outside the classroom.
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This recent article by FitzSimons and Coben (2009) looks at the implications of recent research for the teaching of adult numeracy for work and life. It is certainly a very worhtwhile read and does not skirt around the hard theoretical questions.
***************
The purpose of this section is to only present clear cut empirical research into adult numeracy.
***************
This first piece of research takes a look into the fascinating world of probabilistic numeracy.
***************
Here is an excellent study by Gail FitzSimons which looks at situated numeracy practices in a workplace - aptly titled "Learning numeracy on the job'.
***************
This is a comprehensive piece of research by Jon Swain, Elizabeth Baker, Deborah Holder, Barbara Newmarch and Diana Coben in 2005. It employs a number of methods including ethnographical approaches, case studies, interviews, diaries, photographs and the like. It also looks at some of the theoretical orientations that informed the research.
The findings include the very important area of adult numeracy practices outside the classroom.
***************
This recent article by FitzSimons and Coben (2009) looks at the implications of recent research for the teaching of adult numeracy for work and life. It is certainly a very worhtwhile read and does not skirt around the hard theoretical questions.
***************
Review of "Numeracy for adults: Latest findings from teaching and learning research
This is a report published by the Ministry of Education and written by Gill Thomas and Jenny Ward. It is intended to be one of a series on "Literacy Language and Numeracy Research".
It is one of the very first publications in New Zealand (aside from the adult numeracy progressions) that actually removes numeracy from its usually coupling with literacy and language (as LNL and then later LLN) and looks at it on it own terms (more or less). The LLN bond still , however, appears quite often throughout the report.
The report was published in July, 2009 and to a considerable degree recapitulates information in a TEC (Tertiary education Commission) report of February, 2009 called Strengthening literacy and numeracy: Theoretical framework , which does not specify particular authorship. A key difference between the two reports is that where the February report use the expression literacy and numeracy, the July report simply uses Numeracy.
The situation then with these two reports is trying to figure which comes first (and thus which relies on which). The publication dates are not necessarily indicative of actual precedence in writing. Comparing the the two is not unlike comparing the synoptic gospels Matthew, Mark, and Luke. This is known as the synoptic problem.
Anyhow on to the review.
The report looks at 3 main issues:
1. How adults develop their numeracy expertise.
2. The features of effective embedded numeracy provision.
3. Managing and sustaining change to achieve effective long-term embedding of numeracy.
It tackles these 3 in terms of a quick over view. It then looks at the three in turn in greater detail.
The claim that it offers the latest findings from research is somewhat overstated. Indeed, much of the material covered has been mainstay stuff in adult maths education for the last 20 years. One only has to be vaguely familiar with areas like situtated cognition and learning (Lave and Wenger), constructivist orientations, Piagetian theory and the socio-cultural work of Vygotsky to realise this.
The report offered no clear understanding of what is really meant by "embedding". It is a term, I fear, that has gained currency recently, but has yet to be defined and clarified.
It was important to see the issue of maths anxiety covered and the references to research on short term memory
*****************************************************************
It is one of the very first publications in New Zealand (aside from the adult numeracy progressions) that actually removes numeracy from its usually coupling with literacy and language (as LNL and then later LLN) and looks at it on it own terms (more or less). The LLN bond still , however, appears quite often throughout the report.
The report was published in July, 2009 and to a considerable degree recapitulates information in a TEC (Tertiary education Commission) report of February, 2009 called Strengthening literacy and numeracy: Theoretical framework , which does not specify particular authorship. A key difference between the two reports is that where the February report use the expression literacy and numeracy, the July report simply uses Numeracy.
The situation then with these two reports is trying to figure which comes first (and thus which relies on which). The publication dates are not necessarily indicative of actual precedence in writing. Comparing the the two is not unlike comparing the synoptic gospels Matthew, Mark, and Luke. This is known as the synoptic problem.
Anyhow on to the review.
The report looks at 3 main issues:
1. How adults develop their numeracy expertise.
2. The features of effective embedded numeracy provision.
3. Managing and sustaining change to achieve effective long-term embedding of numeracy.
It tackles these 3 in terms of a quick over view. It then looks at the three in turn in greater detail.
The claim that it offers the latest findings from research is somewhat overstated. Indeed, much of the material covered has been mainstay stuff in adult maths education for the last 20 years. One only has to be vaguely familiar with areas like situtated cognition and learning (Lave and Wenger), constructivist orientations, Piagetian theory and the socio-cultural work of Vygotsky to realise this.
The report offered no clear understanding of what is really meant by "embedding". It is a term, I fear, that has gained currency recently, but has yet to be defined and clarified.
It was important to see the issue of maths anxiety covered and the references to research on short term memory
*****************************************************************
Assessing adult numeracy learning/performance
At present an assessment tool is being deveopled by the NZCER.
Here is a link to a trial of the tool.
The challenge that faces those who develop the tool is enormous, when one considers even the most fundamental definitions of numeracy. It is one thing to seek out a "context" for an assessment item. It is entirely another that that so-called "context" is suffciently de-institutionalized to offer the kinds of real everyday affordances that enable the adult to perform numeracy.
One seriously doubts, for example that multi-choice type questions even remotely approach that goal.
The issue of course is one of 'validity'. What does the test measure? How well does it measure? Here is an article that discusses the issues around numeracy assessment in some detail.
Here is a link to a trial of the tool.
The challenge that faces those who develop the tool is enormous, when one considers even the most fundamental definitions of numeracy. It is one thing to seek out a "context" for an assessment item. It is entirely another that that so-called "context" is suffciently de-institutionalized to offer the kinds of real everyday affordances that enable the adult to perform numeracy.
One seriously doubts, for example that multi-choice type questions even remotely approach that goal.
The issue of course is one of 'validity'. What does the test measure? How well does it measure? Here is an article that discusses the issues around numeracy assessment in some detail.
Transfer of skills/learning
Consider for a moment the varied terrains of adult numeracy learning and/or performance.
Perhaps the most pressing issues in adult numeracy education is that of the domains in which adult numeracy learning and/or performance take place. They range from the highly monomorphic, institutionalised settings where adults to some extent recapitulate the learning of school mathematics, to the highly polymorphic terrains of everyday life or the workplace.
The relationship between these (if we construct them on a continuum) is highly problematic in terms of the so-called transfer of “skills”. Part of the discourse (in New Zealand) which addresses the disjunctures among them involves the equally problematic term “embedding”.
These varied terrains also raise critical issues with regard to how the numeracy performance of adults is assessed.
Related continuums might be those of:
formal learning/performance <<>> informal learning/performance
institutionalized learning/performance <<>> de-institutionalized learning/performance
exchange value <<>> use value (see Coben, 2002).
In 2010, Tine Wedege put out an important paper which problematizes the relationship between school mathematics and work mathematics.
Coben, D. (2002). Use value and exchange value in discursive domains of adult numeracy teaching. Literacy and Numeracy Studies, 11(2), 25-35.
Perhaps the most pressing issues in adult numeracy education is that of the domains in which adult numeracy learning and/or performance take place. They range from the highly monomorphic, institutionalised settings where adults to some extent recapitulate the learning of school mathematics, to the highly polymorphic terrains of everyday life or the workplace.
The relationship between these (if we construct them on a continuum) is highly problematic in terms of the so-called transfer of “skills”. Part of the discourse (in New Zealand) which addresses the disjunctures among them involves the equally problematic term “embedding”.
These varied terrains also raise critical issues with regard to how the numeracy performance of adults is assessed.
Related continuums might be those of:
formal learning/performance <<>> informal learning/performance
institutionalized learning/performance <<>> de-institutionalized learning/performance
exchange value <<>> use value (see Coben, 2002).
In 2010, Tine Wedege put out an important paper which problematizes the relationship between school mathematics and work mathematics.
Coben, D. (2002). Use value and exchange value in discursive domains of adult numeracy teaching. Literacy and Numeracy Studies, 11(2), 25-35.
Mathematics and Philosophy
Fundamental to an epistemology and ontology of mathematics and hence a pedagogy of mathematics lies a philosophy of mathematics.
One key writer in this area was Imre lakatos. Here is a review if his position.
Here is an examination of the relationship of mathematics to theology by Philip Davis
The essentials of, and for, mathematics.
The meaning of mathematical objects.
Syntax and meaning in mathematics - Luis Radford
One key writer in this area was Imre lakatos. Here is a review if his position.
Here is an examination of the relationship of mathematics to theology by Philip Davis
The essentials of, and for, mathematics.
The meaning of mathematical objects.
Syntax and meaning in mathematics - Luis Radford
Statistical literacy
Statistical literacy
International statistical literacy project
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International statistical literacy project
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Numeracy in the workplace
In New Zealand, there is increasingly a shift away from general adult numeracy education to situated contexts of adult numeracy, especially the workplace. So there is much talking about the embedding of numeracy.
NCVER numeracy in the workplace
Developing numeracy in the workplace (FitzSimons and Wedege)
A checklist for workplace numeracy training
Teaching and learning numeracy in the workplace
Handling chemicals and spraying (summary)
Handling chemical and spraying – fuller version
Learning numeracy for the future workplace
Learning numeracy for the future workplace - support document
The numeracies of boat builders
Example of a concrete workplace numeracy task sheet (what do you think of it?)
Overview of adult learning in the workplace
Functional skills in numeracy What might it mean in different domains?
Workplace LLN case studies
Math in the workplace
Numeracy in the future workplace (Beth Marr & Jan Hagston)
NCVER numeracy in the workplace
Developing numeracy in the workplace (FitzSimons and Wedege)
A checklist for workplace numeracy training
Teaching and learning numeracy in the workplace
Handling chemicals and spraying (summary)
Handling chemical and spraying – fuller version
Learning numeracy for the future workplace
Learning numeracy for the future workplace - support document
The numeracies of boat builders
Example of a concrete workplace numeracy task sheet (what do you think of it?)
Overview of adult learning in the workplace
Functional skills in numeracy What might it mean in different domains?
Workplace LLN case studies
Math in the workplace
Numeracy in the future workplace (Beth Marr & Jan Hagston)
Maths anxiety
Perhaps more than any other subject, mathematics seem to strike very into the heart of many adults. Maths anxiety is a very real phenomenon for many and has been put increasingly under the research spotlight.
Maths anxiety: Impediment to success.
Maths anxiety: Impediment to success.
Reports
Here is a particularly useful report on the future of numeracy in the work place
A report by Diana Coben on adult numeracy in Scotland
Here is a report that has just come out (July 2009) entitled: Numeracy for adults - latest findings from teaching and learning research.
Unfortunately, the citation practices in the report are somewhat frustrating and when some fundamental claims are made, the reader is uncertain exactly where the theoretical or research basis lies.
The above report has a great deal in common (some 80%) with this one put out by TEC in February 09 entitled Strengthening literacy and numeracy: Theoretical framework.
The title of the July o9 document centres around research findings; whereas the February 09 document claims a theoretical basis.
The main difference between the documents is that the February 09 document consistently uses the phrase "literacy and Numeracy"; whereas the July document changes this to just "numeracy". i.e. literacy and numeracy >>>> numeracy.
Here is a report by FitzSimons and Coben (which I have also placed in the research section of this blog). It is a must read and covers key theoretical and research territory in a succinct and yet comprehensive way.
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A report by Diana Coben on adult numeracy in Scotland
Here is a report that has just come out (July 2009) entitled: Numeracy for adults - latest findings from teaching and learning research.
Unfortunately, the citation practices in the report are somewhat frustrating and when some fundamental claims are made, the reader is uncertain exactly where the theoretical or research basis lies.
The above report has a great deal in common (some 80%) with this one put out by TEC in February 09 entitled Strengthening literacy and numeracy: Theoretical framework.
The title of the July o9 document centres around research findings; whereas the February 09 document claims a theoretical basis.
The main difference between the documents is that the February 09 document consistently uses the phrase "literacy and Numeracy"; whereas the July document changes this to just "numeracy". i.e. literacy and numeracy >>>> numeracy.
Here is a report by FitzSimons and Coben (which I have also placed in the research section of this blog). It is a must read and covers key theoretical and research territory in a succinct and yet comprehensive way.
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Language issues and bilingualism
Here is a thesis I wrote on code-switching on weblogs.
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Assessment issues - IALS and ALLS
There is ongoing debate as too how reliably the earlier IALS (International Adult Literacy Survey) and the more recent ALLS (Adult Literacy and Life Skills Survey) have captured the "true" situation with respect to adult literacy and numeracy capabilities.
Thomas G. Sticht reflects on this question in a paper entitled:
The International Adult Literacy Survey: How well does it represent the literacy abilities of adults?
Another discussion on how earlier IALS results might be interpreted is:
International Adult Literacy Survey (IALS): an analysis of international comparisons of adult literacy
Here is the 1996 report by the MoE on how New Zeanders fared in the survey.
Adult Literacy in New Zealand: Results from the International Adult Literacy Survey
Detailed material on ALLS from Statistics Canada
Statistics Canada have made available a great deal of detailed information about the ALLs survey conducted there in 2003 (upon which the New Zealand survey was based)
Here is a guide to the survey questions respondents answered.
There is a good deal more information on this site.
The user manual for the Canadian ALLS survey
The master codebook for the survey.
More stuff here for serious satisticians !!!
Thomas G. Sticht reflects on this question in a paper entitled:
The International Adult Literacy Survey: How well does it represent the literacy abilities of adults?
Another discussion on how earlier IALS results might be interpreted is:
International Adult Literacy Survey (IALS): an analysis of international comparisons of adult literacy
Here is the 1996 report by the MoE on how New Zeanders fared in the survey.
Adult Literacy in New Zealand: Results from the International Adult Literacy Survey
Detailed material on ALLS from Statistics Canada
Statistics Canada have made available a great deal of detailed information about the ALLs survey conducted there in 2003 (upon which the New Zealand survey was based)
Here is a guide to the survey questions respondents answered.
There is a good deal more information on this site.
The user manual for the Canadian ALLS survey
The master codebook for the survey.
More stuff here for serious satisticians !!!
Policy Issues
In New Zealand, some would argue that much of the neo-liberal discourse around skills driving productivity focuses heavily on human capital. There is no doubt that this discourse in New Zealand follows that of many OECD countries, especially The UK, Canada, the US and Australia.
The following article suggests that other benefits of adult numeracy education may be marginalised in this discourse in Australia. Perhaps with keener theoretical understandings of adult numeracy learning and experience we might more fully engage with the real meaning of numeracy in the lives of ordinary people. Here is the article by Yasukawa, Widin and Chodkiewicz.
Do you think the same critique might be valid in the New Zealand context?
The following article suggests that other benefits of adult numeracy education may be marginalised in this discourse in Australia. Perhaps with keener theoretical understandings of adult numeracy learning and experience we might more fully engage with the real meaning of numeracy in the lives of ordinary people. Here is the article by Yasukawa, Widin and Chodkiewicz.
Do you think the same critique might be valid in the New Zealand context?
Relationship of Adult Numeracy to Numeracy Strategy in Schools
In New Zealand, the Adult Numeracy Initiative grew out of the Numeracy Project in schools. Indeed, some of the same people were involved in both. A similar situation exists in England.
This relationship in England is critiqued in this article by Coben, Swain and Tomlin. Might some of the conclusions be applicable to the New Zealand scene?
New Zealand Numeracy project
article 1
The Numeracy Project in Secondary Schools.
A critique of the numeracy project in schools
This relationship in England is critiqued in this article by Coben, Swain and Tomlin. Might some of the conclusions be applicable to the New Zealand scene?
New Zealand Numeracy project
article 1
The Numeracy Project in Secondary Schools.
A critique of the numeracy project in schools
Situated Learning
The work of Lave and Wenger (1991) is almost synonymous with the concept of Situated Learning which emphasises the affordances of authentic contexts in the learning process.
Lave, J., & Wenger, E. (1991). Situated Learning: Legitimate Periperal Participation. Cambridge, UK: Cambridge University Press.
Lave, J., & Wenger, E. (1991). Situated Learning: Legitimate Periperal Participation. Cambridge, UK: Cambridge University Press.
Ethnomathematics
In most the the formal discourse of adult numeracy education in New Zealand, it is fair to say the the relevance of ethnomathematics to the teaching of numeracy has fallen well below the radar screen.
Some articles
Ethnomathematics - A rich Cultural diversity
Peace, social justice and ethnomathematics
Ethnomathematics and philosophy
D’Ambrosio on ethnomathematics
Ethnomathematics: Concept Definition and Research Perspectives
Paulo Freire’s Contribution to an Epistemology of Ethnomathematics
Ethnomathematics and Mathematics Education (this is quite a big file 2mb and has some things relevant to adult education) It is the proceedings of the 10th International Congress of Mathematics Education held in Copenhagen back 2004
A critique of Ethnomathematics. Ethnomathematics is not without its critics. Here is one critique from back in 1997 looking at what ethnomathematics might mean in the South African context.
Bill Barton's 1996 thesis: Ethnomathematics: Exploring Cultural Diversity in Mathematics
Mathematics in Mäori Education.
Some discussion on ethnomathemtics tends to rule out of court the possibility of the mathematics classroom being viewed through an ethnomathematical lens. This piece of research from 2006, however, recognises the sociocultural contexts of an adult mathematics classroom and explores adults learning mathematics in the classroom from a "phenomenological, ethnographical, constructivist" point or view looking at a case study.
Literacy and numeracy issues for maori adult learners.
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Some articles
Ethnomathematics - A rich Cultural diversity
Peace, social justice and ethnomathematics
Ethnomathematics and philosophy
D’Ambrosio on ethnomathematics
Ethnomathematics: Concept Definition and Research Perspectives
Paulo Freire’s Contribution to an Epistemology of Ethnomathematics
Ethnomathematics and Mathematics Education (this is quite a big file 2mb and has some things relevant to adult education) It is the proceedings of the 10th International Congress of Mathematics Education held in Copenhagen back 2004
A critique of Ethnomathematics. Ethnomathematics is not without its critics. Here is one critique from back in 1997 looking at what ethnomathematics might mean in the South African context.
Bill Barton's 1996 thesis: Ethnomathematics: Exploring Cultural Diversity in Mathematics
Mathematics in Mäori Education.
Some discussion on ethnomathemtics tends to rule out of court the possibility of the mathematics classroom being viewed through an ethnomathematical lens. This piece of research from 2006, however, recognises the sociocultural contexts of an adult mathematics classroom and explores adults learning mathematics in the classroom from a "phenomenological, ethnographical, constructivist" point or view looking at a case study.
Literacy and numeracy issues for maori adult learners.
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Adult Numeracy as a Social Practice
Related to the concept of situated learning is that of Communities of Practice. Here the emphasis moves a way from numeracy ad merely some individualistic skill or set of skills that a person processes to numeracy as a social practice that involves participation with others in authentic social contexts. This has very important implications for conceptualising how numeracy is taught, learnt and assessed.
Beyond worksheets - a social and holistic approach to numeracy (Ciancone, Hood, and Lehmann).
Adult Teachers as Researchers: Ethnographic approaches to numeracy and literacy as social practices in South Asia. (Street, Rogers, and Baker).
Beyond worksheets - a social and holistic approach to numeracy (Ciancone, Hood, and Lehmann).
Adult Teachers as Researchers: Ethnographic approaches to numeracy and literacy as social practices in South Asia. (Street, Rogers, and Baker).
Constructivist Orientations
This article by Hein (1991) lays out some broad constructivist principles from the point of view of a museum educator. It says nothing about numeracy. However, many of the principles espoused can be applied to adult numeracy education.
Definitional Issues
The ALL (Adult Literacy and Life Skills) survey gives the following "definition".
How might this "definition" link to the diagram above?
How might it link to the theoretical orientations to be discussed in this blog?
The ALL "Definition"
Numerate behaviour involves
managing a situation of solving a problem in a real context
everyday life
work
societal
further learning
by responding
identifying or locating
acting upon
interpreting
communicating about
to information about mathematical ideas
quantity and numbers
dimension and shape
patterns and relationships
data and chance
change
that is represented in a range of ways
objects and pictures
numbers and symbols
formulae
diagrams and maps
graphs
tables
texts
and requires activation of a range of enabling knowledge, behaviours and processes
mathematical knowledge and understanding
mathematical problem solving skills
literacy skills
beliefs and attitudes
managing a situation of solving a problem in a real context
everyday life
work
societal
further learning
by responding
identifying or locating
acting upon
interpreting
communicating about
to information about mathematical ideas
quantity and numbers
dimension and shape
patterns and relationships
data and chance
change
that is represented in a range of ways
objects and pictures
numbers and symbols
formulae
diagrams and maps
graphs
tables
texts
and requires activation of a range of enabling knowledge, behaviours and processes
mathematical knowledge and understanding
mathematical problem solving skills
literacy skills
beliefs and attitudes
A useful summary of definitions can be found on pages 5 to 10 of this document. Look in particular for the identification of formative, mathematical and integrative phases in numeracy development.
In this 2003 research review, Diana Coben reviews some of the key definitions and conceptulizations around adult numeracy. In particular focus on pages 9 through 21.
Five dimensions of numeracy are offered in this paper. They are foundational, psychological, affective, socio-cultural and critical.
This paper gives some historical background to the relationship of numeracy to mathematics.
Here are four reports on Maori adult literacy. Numeracy appears in most of the under the banner of LLN (Literacy, Language and Numeracy). However the last report does give some discussion on numeracy (see page 23).
Report 1
Report 2
Report 3
Report 4
None of the above reports refer to the broader theoretical and research framework of ethnomathematics.
These following papers do.
This discussion by Barton and Fairhall does.
Some research by Glenys Holt which makes the link between maori mathematics education and ethnomathematics. (Just click okay and you will get the document - you do not have to sign in.)
Acquiring the Mathematics Register in Te Reo Maori
Màori and Mathematics: “Nà te mea he pai mò tò roro!” (Because it’s good for your brain!)
The role of language in mathematics (discussion drawn from the maori experience)
Report 1
Report 2
Report 3
Report 4
None of the above reports refer to the broader theoretical and research framework of ethnomathematics.
These following papers do.
This discussion by Barton and Fairhall does.
Some research by Glenys Holt which makes the link between maori mathematics education and ethnomathematics. (Just click okay and you will get the document - you do not have to sign in.)
Acquiring the Mathematics Register in Te Reo Maori
Màori and Mathematics: “Nà te mea he pai mò tò roro!” (Because it’s good for your brain!)
The role of language in mathematics (discussion drawn from the maori experience)
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