Dear Colleague,

Much ado has been made about importance of numeracy and the challenges faced by those who struggle with it. Health numeracy, which is of particular concern to our community at GBC/McMaster and beyond, is only now emerging as an area of concern for higher education and the public at large. Furthermore, there is very little available for a person who has been away from the educational system to do in order to get back on the numeracy track, or ways to self-assess. Questions like: Do I have enough grounding in numeracy to be able to thrive in a health care educational setting, or to manage my own health care information? cannot be answered simply by googling. The only approach readily available is to redo work from a high school curriculum. Unfortunately, much of that material is not targeted to helping individuals improve their numeracy in general/nor their health numeracy in particular.

Starting in the Fall of 2016, our team has been reviewing literature and building an understanding of both numeracy and its cousin, health numeracy, from health care and mathematics education perspectives as well as from first and second hand accounts of lived experiences of individuals working in the health care field.

We have done our best in converting what we learned from listening to these voices and are in the midst of constructing learning content for Health Numeracy we think will stand up to scrutiny.

#### What is Numeracy About?

First of all, we’d like to make the case that numeracy is often used as a term that captures a wide array of research in math education but its primacy is not supported by the fact that there are so many other terms used (Quantitative Literacy, Quantitative Reasoning and Mathematical Literacy + a series of research on word problem solving that is closely related). Thus when we use numeracy we are not saying it is the better term or the more correct one, just the one we chose for this work, while attempting to learn about this area of research.

Our current (and I believe final) approach to conceptualizing numeracy has come from a shift in perspective. Instead of asking ‘What is numeracy?’, we asked ‘What is numeracy about?’ and then contrasted numeracy’s aboutness with the aboutness of mathematics.

From there we developed a core mandate for numeracy (and its family members)

*Numeracy’s core mandate is an investigation into how our educational institutions and teachers within and outside of those formal systems can improve citizen (and student) use of mathematical abstractions (usually limited to arithmetic and perhaps basic algebra and geometry) to help make sense of the concrete world that they/we live in and to interpret the abstractions of others.*

The core mandate is a bit different from a definition and we believe it captures the many strands of research undertaken by math education researchers in this area. The core gave us a fresh perspective when analysing the myriad of definitions of numeracy and mathematics. We were struck by the following contrast which implicitly uses the aboutness perspective to distinguish between the two: It comes from the wonderful book edited by Lynn Steen and which the MAA makes available on their site as a .pdf file so that you can flip through it as well. In the essay which begins on page 67 Albert Manaster writes the following:

*In quantitative literacy, numbers describe features of concrete situations that enhance our understanding.*

*In mathematics, numbers are themselves the object of study and lead to the discovery and exploration of even more abstract objects. *

But Steen (2001) went a bit further and gave us a bit of help by looking at the aboutness of mathematics and numeracy in order to help disentangle the two:

Mathematics is abstract and Platonic, offering absolute truths **about** relations among ideal objects.

Numeracy is concrete and contextual, offering contingent solutions to problems **about** real situations.

The beauty of the above conceptualization is that it is useful in the any edicational context as it separates out activities which focus on strengthening ones understanding of mathematical objects as distinct from using those ‘mathematical objects’ to better understand concrete situations.

To often our students get a mixture of the two, and really have little chance to practice numeracy as described above as an activity on it own. To do so, we articulated a distinction between numeracy and mathematical tasks that can help teachers prepare exercises, assignments and assessments for their students.

**numeracy tasks:** are about concrete objects and their relations; (mathematical objects and relations are used as tools to help make sense of concrete phenomena).

**mathematics tasks:** are about mathematical ideas and objects and their relations (they live in abstract world and may use concrete contexts to strengthen student understanding of that world).

Our next focus was on tackling just what kinds of thinking a numeracy task would aim to expect from a student. Verschaffel et al (2000) Burkhardt (2008) and OECD (2016) produced good thinking process models, but we chose to go with Conrad Wolfram’s computational thinking process which involves 4 actions: Define, Abstract, Compute and Interpret.

From here we began to tighten up our understanding of numeracy task distinctness and to develop a numeracy task rubric which you can check out here.

The rubric is based on a few characteristics we developed based on the foundation we described above:

Suggested characteristics of a good Numeracy Task as rough foundation of rubric development.

- are about concrete situations involving concrete objects and their relations, not about predetermined mathematical structures.
- must (as much as possible) take the student away from their ‘in class’ setting and place them in a context that is concrete ‘real world’ in nature.
- are presented as close as possible to the way they would be in the concrete context they are about.
- are set in a context that is relevant and accessible to the student/program of study.
- require shifting from concrete to abstract (abstract to computable form… or mathematize/quantify concrete situation) or from abstract to concrete (interpret results)
- may involve computations. The computations/calculations are an important element of numeracy task completion, but can be done by computer or other means. The actual method used is not what the task is about.

References:

Burkhardt, H. (2008) Quantitative Literacy for All: How Can We Make it Happen. In Steen, L. ed. Calculation vs. Context, 137-162.

OECD (2016), “PISA 2015 Mathematics Framework”, in PISA 2015 Assessment and Analytical Framework: Science, Reading, Mathematic and Financial Literacy, OECD Publishing, Paris.

Steen, L.A., (2001) ‘Mathematics and numeracy: Two literacies, one language.’ *The mathematics educator*, *6*(1), pp.10-16. available: https://math.nie.edu.sg/ame/matheduc/tme/tmeV6_1/Doc%20p2.pdf

Verschaffel, L., Greer, B. and De Corte, E. eds. (2000) Making sense of word problems. CRC Press.

Wolfram, C. (n.d.) *Computational Thinking Process* downloaded from https://www.computationalthinking.org/ April, 2023.

**The Health Numeracy App: Instructional Design. (bit.ly/henupr)**

** Form:** We organized practice material in a format that allows the user control of their experience, a sense of privacy and safety, explanations of concepts and procedures, and scaffolded multi dimensional challenges in a fully online setting.

** Content: ** We have found that health numeracy develops through 3 (and a half?) levels that we are calling: Intuition, Conversion, Connection + an overlapping level called ‘Numbers in the World’. At each level there are units that need to be mastered, and in the units there are topics/lessons. The units and topics that were developed are designed based on numeracy needs for Health Science students and professionals, and citizens and patients.

**Intuition About Numbers and Their Relations:** The focus is on number sense skills necessary for health care contexts. The goal is to build intuition about numbers and number relations/operations from the simple to more complex. As such we start from the basic operations, and present questions that do not require electronic calculators, nor paper and pencil to solve. Our favourites are questions in which we believe calculators and procedural approaches would be a hindrance.

**Conversions:** Starting from some of the automatic skills that we hopefully strengthened in the Intuitive level, we move to switching between multiple representations of numbers and units and most importantly strengthening the users understanding of thinking about breaking numbers into parts (e.g. % of) strictly in the number world (i.e. without applying to actual quantities of objects).

**Measurements and Units:** Here we review many of the measurements commonly used in the health care system with a focus on prefixes and suffixes of the metric system and their connections to the intuitive number sense of previous levels.

**Breaking the code: Thinking With Numbers:** pulling numbers from stories, from charts and graphs is a skill that can be practiced. The goal is to design an increasingly challenging experience which reasonably numerate patient/citizen/health care professional, should be able to understand even if they are not an expert in the field. Finally, we explore some of the basics of summarizing data.

**Breaking the Code – Uncertainty, Chance and Probability:** One does not need sophisticated mathematics to be able to understand scenarious in which there is uncertainty and yet a decision needs to be made. Our goal is here is to help individuals understand the basic ideas of thinking about scenarios in which numbers and counting can help bring clarity. Key aspects of probabilistic thinking are experienced through a Thinking With Numbers Lens. The goal is to help users develop their ability to connect to situations in which they may need to critically understand risk in order to make the best decision for them and their families.

**Breaking the Code – Health:** In this level individuals apply their knowledge of numbers and their relations in order to make sense of information in a variety of contexts including nutrition, fitness and lifestyle, and social and environmental determinants of health.

**Breaking the code: Patient Perspective:** In this level individuals apply their knowledge of numbers and their relations in order to make sense of information in a variety of contexts related to results of screening tests, diagnoses, and treatment regimens from the patient perspective.

**Breaking the code: Practitioner Perspective:** In this level individuals apply their knowledge of numbers and their relations in order to make sense of information that may come to them as medical professionals.

**Numbers in the World level:** this is our favourite as it stems from an aha!! moment from informal interactions with health science students in which it became clear that numerical facts that we took for granted (e.g. scale difference in population USA vs Canada) were not as well known as expected. We present you with a series of challenges about Health Science related number facts that will challenge every person no matter how ‘numerate’ they think they are.

If you would like to try a prototype of the application please click here.

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In the above design of the learning content the first 3 levels aim to review all of the mathematics a person would need for a basic ability in health numeracy. The rest of the units help strengthen some aspects of health literacy and get the participant to practice using numbers (and other mathematical objects) to help understand the presented concrete situations better.

#### We also considered other conceptualizations of numeracy, some of which are described below

*“Numeracy is, in summary, the ability and the confidence to use mathematical knowledge and skills in concrete real-world situations.” (Orpwood and Brown 2015)* www.numeracygap.ca/assets/img/Closing_the_numeracy_gap_V4.pdf

Such definitions are excellent, but only somewhat useful in helping guide teachers decide what topics need to be covered in a setting in which improvement in numeracy is the goal. The relation of numeracy to mathematics and to literacy have been a source of consternation for those who are working to tighten up conceptualizations of numeracy.

The key challenge is staying true to the teaching/learning context within which we are working, while acknowledging the complexity and flexibility of the term itself.

A useful conceptualization? {from Coben, D. (2006). What Is Specific about Research in Adult Numeracy and Mathematics Education?. *Adults Learning Mathematics*, *2*(1), 18-32.}

Coben sees two domains of numeracy is adapted from a schema developed for adult literacy by Kell (2001) in South Africa.

Adult numeracy in **Domain One** is characterized by formalisation and standardization of the curriculum, and technologisation, unitisation and commodification of learning and learning materials. It is competency-based and outcomes-focussed, with certification being the desired outcome, and explicit equivalence with educational levels in schools. It supports normative claims about the beneficial effects of numeracy for the individual and for society. Adult numeracy education in Skills for Life is located in Domain One because, as Kell puts it, speaking of literacy in Domain One, it is “created through the standardising processes of fixing levels, writing unit standards and setting performance criteria” (Kell, 2001, p.100).

By contrast, numeracy in **Domain Two** is “about informal and non-standard mathematics practices and processes in adults’ lives, which may bear little relation to formal, taught mathematics”. Domain One numeracy may have low use value but high exchange value “it is ‘hard currency’, yielding certificates tradeable on the labour market. Domain Two is the opposite: it has high use value but no exchange value beyond the community of practice in which it occurs…; it is ‘soft currency’… [and] situated in Jean Lave’s sense”; it is often ‘invisible’ or unregarded by those directly concerned; and it is often elided with ‘common sense’ (Coben, 2006).

Our work as teachers, especially in foundations ‘math’ teaching and upgrading, is primarily in Domain One as described by Coben, based on Kell above, but many of the struggling students may be working in Domain Two. The application we are designing must be able to help individuals acclimatize themselves to the abstracted methods of the dominant number system (whether they are numerate in domain 2 or not). If this is done well, the person can function in both Domain One and Two translating when needed, just as there are individuals who can speak in various local dialects, and communicate in the formalized literary languages of the states they are living in.

__A useful Definition of Health Numeracy:__

“Individual-level skills needed to understand and use quantitative health information, including basic computation skills, ability to use information in documents and non-text formats such as graphs, and ability to communicate orally.” and later… “The degree to which individuals have the capacity to access, process, interpret, communicate, and act on numerical, quantitative, graphical, biostatistical, and probabilistic health information needed to make effective health decisions.”

[Ancker JS & Kaufman D. (2007). Rethinking Health Numeracy: A Multidisciplinary Literature Review. *Journal of the American Medical Informatics Association,* 14(6), 713-721. ]

Along with a more focused context comes a conceptualization that is less theoretical, providing a more practical guide the practitioner who, like us, wishes to develop learning content for those who wish to improve this sub-type of numeracy.

We hope that the above tid bits of information have whetted your appetite for more and that you will provide us with your contact information and comments in the form below.

Thanks for visiting,

This project has been approved by the George Brown College Research Ethics Board, Approval No. [6004309]

Taras and Miroslav