Teaching and learning material
USER’S GUIDE TEACHER’S GUIDE
http://cenf.eu
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
Hi! Let me guide you! You have already gone through some examples and need further information on how to implement them in your teaching?You want to meet your adult learners‘ concrete needs and now you look for some inspiration for your classes?Or maybe you are just curious about the Numeracy in practice concept and want to know about the basics? Click the appropriate button below or read the whole text. Check the NIP platform:
http://cenf.eu
I want to benefit from the concept. Give me the basics!
I want to take action. Give me some inspiration for my classes!
I feel inspired by the examples. Give me some further information!
BASICS
ACTION
INSIGHTS
Part 1: ACTION
[Get into action - I]
80MATERIALS You can find 80 inspiring examples for teaching and learning situations on our website. All 80 examples can be found in English, some have been translated to different languages. The translations can be found in the respective language sections.
8UMBRELLA TOPICS The 80 examples are organised in different umbrella topics that we estimate relevant for adult learners, e.g.: “Enjoy eating and drinking with numeracy”“Stay safe and healthy with numeracy”“Numeracy within my family”“Be green with numeracy”.
1SOLUTION? A numeracy situation or problem never offers only one possible solution or consideration. Thus, the umbrella topics only serve as a kind of thematic guidance and the individual learning materials are not “ready to print and use” for all learners or situations.
∞POSSIBILITIES The exemplary material provided is just a starting point: feel free to use, adapt und think further. For more ideas you just need to go through the streets and your life with numeracy eyes, take photos of numeracy all around and listen to adult learners.
[Get into action - II]
The best way of teaching adults is: Don‘t start teaching Start with posing a „problem“ in a real context Ask questions to analyzeand give meaning to the math in the problem Challenge the participants to discuss,collaborate and solve the problem Discuss the math in it Evaluate the process
Source: Hoogland, Kees / Van Groenestijn (Ed.) (2021): Common European Numeracy Framework. Aspects and Levels. Available online: 2021 11 30 CENF Aspects and Levels IO3.pdf (europa.eu) [20.06.2024]
[Get into action - III
Setting the scene
Questioning
Exploration Research
Synthesis
Transfer
Feedback on the exploration stage Answer to the initial question What has been learned?
As far as possible Identify transfers and/or let learners imagine them
Choosing a numeracy situation Putting yourself in the learners' shoes Encourage immersion in the situation Identify practices and methods already in place
Trainer = mediator Leave time for research The important thing is not the result but the approach!
[Get into action - IV]
Navigating the exemplary material – Structure of an example Each material follows a certain structure:
- Numeric situation and overview
- Main information that summarizes the most important details of the overview (1) and the working plan (3)
- Working plan suggesting concrete learning activities and materials
- Suggestions for the teacher, in addition to the basic information here in the user’s guide
- Appendix with concrete or inspirational resources (videos, diagrams, articles, pictures, worksheets) corresponding to the working plan
The working plan shows an exemplary lesson structure with different learning activities and phases from activation to transfer. It also mentions possible material and resources to be used.
The grid with main information gives some details on content, target group, problem statement, materials and resources, problem statement, working questions and learning outcomes.
The description at the top opens the numeric learning situations. The overview refers to the parameters of the CENF and points out the main working question.
Part 2: BASICS
[Basic guide to NIP concept - I]
SUSTAINABLE SKILLS Mathematics and numeracy are inherently linked to real-life contexts and need to be functional. This principle serves as our didactic and pedagogical foundation when developing, adapting and implementing numeracy teaching and learning materials for the adult learners. We must know that adults use literacy, numeracy and digital skills to deal with problems and challenges in everyday life. By fostering sustainable skills, we ensure that learners can continuously apply, adapt, and refine their knowledge in a wide range of contexts. This sustainable approach not only enhances their confidence but also equips them for long-term success in both professional and personal realms, enabling them to navigate an ever-changing world with greater ease and competence.
SKILLS FOR SOCIAL SURVIVAL Too many European citizens lack the necessary numeracy competences to participate autonomously and effectively in our technologized and number-drenched society and consequently are overlooked for certain jobs and have problems in their daily life, dealing with the abundance of number-related issues. Numeracy, literacy and digital skills are the pillars of basic skills for adults in the 21st century skills. In dealing with daily life situations, adults use a mixture of these abilities and skills. Numeracy is a social practice and necessary to participate in our digital and numeric world. A social practice view of numeracy not only considers the different contexts in which numeracy is practiced, but also how people’s lives and histories, goals, values and attitudes will influence the way they carry out numeracy.
SKILLS FOR DAILY LIFE Numeracy has a great significance in our everyday life. The ability of using mathematics and numbers in our personal and working life is essential each and every day and at all levels and stations of our life. Numeracy helps us to think critically, to bring logic into our life, to succeed with our tasks and to make decisions. There is no hot question or issue in our life that comes and goes without any numeracy aspect. In our examples we have a close look at some very urgent, contemporary, practical, and omnipresent topics we all have to face nearly every day. Those topics catch us when doing our shopping and preparing dinner, when using the bus instead of the car or buying a train ticket, when running five kilometers through the park, when planning our appointments, …
SKILLS FOR DAILY LIFE
SKILLS FOR SOCIAL SURVIVAL
SUSTAINABLE SKILLS
read more...
read more...
read more...
[Basic guide to NIP concept - II]
NUMERACYto encourageadult learners
NUMERACYfor adultsmust address adults
OURNUMERACY APPROACH
NUMERACY isfunctional
NUMERACYto involveadult learners
Part 3: INSIGHTS
[Insights - I]
Every learner and every teacher have their specific needs, requirements, dispositions and preferences. This is what we need to accept and make possible by offering inspirational material with basic model examples open for individual use and adaption. Thus, the examples of learning resources should be considered and used as exemplary and inspirational material presenting a guideline with a high range of possibilities of adapting those suggestions to a specific group of learners or an individual learner with their very personal requirements. Those examples are not designed for immediate print and use but require active adaption to the needs of the learners. Most of the examples come with specific suggestions for the user/teacher to guide a possible adaption.
The mentioned possibility of adapting and reshaping the materials is valid for different aspects of the exemplary material, e.g.:
- INDIVIDUALIZATION: The suggested characteristics of the tasks can and should be varied in accordance with the needs of the learners.
- TIME/DURATION: The respective indications are only rough guide-lines and can be varied by rein-forcing or skipping details, intro-ductory exercises, and reflections.
- DISPOSITIONS: The dispositions taken into account can be varied by putting special (other) emphasis on the learners’ needs.
- MATERIAL: It may be necessary to supplement, adapt or even replace materials with others.
- LEARNING SETTING: We need to be aware that everyday situations that require numeracy skills (e.g. finances) might be sensitive for some learners and therefore we need to ensure a harmonious and safe learning environment.
Our educational activities aim at numeracy skills being not only memorized, but first of all being practiced and functionally used by the learners in daily life or/and vocational situations. It is therefore recommended to implement the idea of HITS (higher impacts of teaching skills) as far and often as possible. In this context, it is helpful to consider the following key elements when teaching numeracy:
- Work with concrete and authentic material that learners will recognize from everyday life situations.
- Ask the learners questions and let them raise questions themselves. It can be crucial to discuss numeracy themes, contexts and numbers.
- Think of possible ways of transfer for your learners.
- Help learners to develop habits of collaborative learning.
learn more on HITS…
The HITS (High Impact Teaching Strategies) serve as a starting point for the teaching approaches presented in the examples. These are ten teaching practices which enrich and improve the learning of numeracy, mathematical ideas, concepts and contexts.
[Insights - V]
NUMERACYis context based
NUMERACYhas a useful content
HOW TO TEACH NUMERACY?
NUMERACYneeds time foractivation and discussion
NUMERACY is interactiveand dialogical
This material was produced in the Erasmusplus project Numeracy in Practice, projectnumber 2021-1-NL01-KA220-ADU-000 026 292. In this project, 11 partners in 11 countries worked together in designing, evaluating and improving the materials. All materials can be found on the website (www.cenf.eu)
This work is licensed under CC BY-SA 4.0. To view a copy of this license, visit https://creativecommons.org/licenses/by-sa/4.0/
NUMERACYis context based
It is a fact that adults need to manage situations and solve problems that deal with numbers. A development of numeracy competences with adult learners needs authentic lived-in situations of the learners – as this helps learners to understand the usefulness of numbers for their very personal and individual needs. This also means that some of the provided materials might not be applicable for some countries, cultures or target groups
NUMERACYhas a USEFUL CONTENT
Successful educational numeracy activities for adults can’t be found in schoolbooks for kids or in abstract worksheets, but must meet the adults’ realities, needs and challenges. Our teaching and learning activities must therefore be connected to learners’ individual realities, follow a holistic approach (literacy, numeracy and digital skills), aim for an improved numerate behaviour and must therefore be learner-centric.
NUMERACYis INTERACTIVE and DIALOGICAL
An interactive and dialogical learning setting enables adults to activate their prior knowledge and skills and helps them to find ways to solve a mathematical problem and therefore manage a situation.Within a (mathematical) discussion, adult learners are invited to locate the situation as a mathematical one. They need to identify the mathematics in it and furthermore, analyse, structure and interpret the information to find possible procedures to solve the problem.
NUMERACYis functional
Numeracy involves the practical application of mathematical skills in everyday life. It must enable individuals to make informed decisions, solve real-world problems, and perform essential tasks. Thus, we must teach skills for practical use. If they are only learned and practiced, but not applied in real situations, they will fade quickly, and math anxiety will increase. Learning and practice must be followed by a functional use with concrete material in authentic situations such as daily life, vocational situations, or social media.
NUMERACY for adults must address adults
Successful educational numeracy activities for adults can’t be found in schoolbooks for kids or in abstract worksheets, but must meet the adults’ realities, needs and challenges. Our teaching and learning activities must therefore be connected to learners’ realities, follow a holistic approach (literacy, numeracy and digital skills), aim for an improved numerate behaviour and must therefore be learner-centric.
NUMERACY to involve adult learners
Adults often struggle with numeracy due to math anxiety, bad experiences during their school careers and a lack of practical application in their daily lives. We must accompany adults within their numeric worlds by enabling numeracy conversations, counteracting math anxiety, exploring the quantitative world around, working on awareness of successful numeracy behaviour, discussing numeracy themes like health or finances and by supporting a critical and sensible use of tools.
NUMERACYneeds time for activation and discussion
It is crucial that learners are given enough room and time for identifying (numeracy) problems in a authentic situation as well as for problem solving procedures. Having time for being an active part in the learning process helps adults to develop key competences they need to succeed in our modern society, just as critical thinking, communication, collaboration, creativity and flexibility.
NUMERACY to encourage adult learners
One important fact to remember is that individual with developing numeracy skills often underestimate and undermine their existing skills and abilities. Therefore, teaching and learning activities should also aim to help learners recognize their skills and become aware of successful numeracy decisions they already make in their everyday lives, in a private and professional context.
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Transcript
Teaching and learning material
USER’S GUIDE TEACHER’S GUIDE
http://cenf.eu
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
Hi! Let me guide you! You have already gone through some examples and need further information on how to implement them in your teaching?You want to meet your adult learners‘ concrete needs and now you look for some inspiration for your classes?Or maybe you are just curious about the Numeracy in practice concept and want to know about the basics? Click the appropriate button below or read the whole text. Check the NIP platform:
http://cenf.eu
I want to benefit from the concept. Give me the basics!
I want to take action. Give me some inspiration for my classes!
I feel inspired by the examples. Give me some further information!
BASICS
ACTION
INSIGHTS
Part 1: ACTION
[Get into action - I]
80MATERIALS You can find 80 inspiring examples for teaching and learning situations on our website. All 80 examples can be found in English, some have been translated to different languages. The translations can be found in the respective language sections.
8UMBRELLA TOPICS The 80 examples are organised in different umbrella topics that we estimate relevant for adult learners, e.g.: “Enjoy eating and drinking with numeracy”“Stay safe and healthy with numeracy”“Numeracy within my family”“Be green with numeracy”.
1SOLUTION? A numeracy situation or problem never offers only one possible solution or consideration. Thus, the umbrella topics only serve as a kind of thematic guidance and the individual learning materials are not “ready to print and use” for all learners or situations.
∞POSSIBILITIES The exemplary material provided is just a starting point: feel free to use, adapt und think further. For more ideas you just need to go through the streets and your life with numeracy eyes, take photos of numeracy all around and listen to adult learners.
[Get into action - II]
The best way of teaching adults is: Don‘t start teaching Start with posing a „problem“ in a real context Ask questions to analyzeand give meaning to the math in the problem Challenge the participants to discuss,collaborate and solve the problem Discuss the math in it Evaluate the process
Source: Hoogland, Kees / Van Groenestijn (Ed.) (2021): Common European Numeracy Framework. Aspects and Levels. Available online: 2021 11 30 CENF Aspects and Levels IO3.pdf (europa.eu) [20.06.2024]
[Get into action - III
Setting the scene
Questioning
Exploration Research
Synthesis
Transfer
Feedback on the exploration stage Answer to the initial question What has been learned?
As far as possible Identify transfers and/or let learners imagine them
Choosing a numeracy situation Putting yourself in the learners' shoes Encourage immersion in the situation Identify practices and methods already in place
Trainer = mediator Leave time for research The important thing is not the result but the approach!
[Get into action - IV]
Navigating the exemplary material – Structure of an example Each material follows a certain structure:
The working plan shows an exemplary lesson structure with different learning activities and phases from activation to transfer. It also mentions possible material and resources to be used.
The grid with main information gives some details on content, target group, problem statement, materials and resources, problem statement, working questions and learning outcomes.
The description at the top opens the numeric learning situations. The overview refers to the parameters of the CENF and points out the main working question.
Part 2: BASICS
[Basic guide to NIP concept - I]
SUSTAINABLE SKILLS Mathematics and numeracy are inherently linked to real-life contexts and need to be functional. This principle serves as our didactic and pedagogical foundation when developing, adapting and implementing numeracy teaching and learning materials for the adult learners. We must know that adults use literacy, numeracy and digital skills to deal with problems and challenges in everyday life. By fostering sustainable skills, we ensure that learners can continuously apply, adapt, and refine their knowledge in a wide range of contexts. This sustainable approach not only enhances their confidence but also equips them for long-term success in both professional and personal realms, enabling them to navigate an ever-changing world with greater ease and competence.
SKILLS FOR SOCIAL SURVIVAL Too many European citizens lack the necessary numeracy competences to participate autonomously and effectively in our technologized and number-drenched society and consequently are overlooked for certain jobs and have problems in their daily life, dealing with the abundance of number-related issues. Numeracy, literacy and digital skills are the pillars of basic skills for adults in the 21st century skills. In dealing with daily life situations, adults use a mixture of these abilities and skills. Numeracy is a social practice and necessary to participate in our digital and numeric world. A social practice view of numeracy not only considers the different contexts in which numeracy is practiced, but also how people’s lives and histories, goals, values and attitudes will influence the way they carry out numeracy.
SKILLS FOR DAILY LIFE Numeracy has a great significance in our everyday life. The ability of using mathematics and numbers in our personal and working life is essential each and every day and at all levels and stations of our life. Numeracy helps us to think critically, to bring logic into our life, to succeed with our tasks and to make decisions. There is no hot question or issue in our life that comes and goes without any numeracy aspect. In our examples we have a close look at some very urgent, contemporary, practical, and omnipresent topics we all have to face nearly every day. Those topics catch us when doing our shopping and preparing dinner, when using the bus instead of the car or buying a train ticket, when running five kilometers through the park, when planning our appointments, …
SKILLS FOR DAILY LIFE
SKILLS FOR SOCIAL SURVIVAL
SUSTAINABLE SKILLS
read more...
read more...
read more...
[Basic guide to NIP concept - II]
NUMERACYto encourageadult learners
NUMERACYfor adultsmust address adults
OURNUMERACY APPROACH
NUMERACY isfunctional
NUMERACYto involveadult learners
Part 3: INSIGHTS
[Insights - I]
Every learner and every teacher have their specific needs, requirements, dispositions and preferences. This is what we need to accept and make possible by offering inspirational material with basic model examples open for individual use and adaption. Thus, the examples of learning resources should be considered and used as exemplary and inspirational material presenting a guideline with a high range of possibilities of adapting those suggestions to a specific group of learners or an individual learner with their very personal requirements. Those examples are not designed for immediate print and use but require active adaption to the needs of the learners. Most of the examples come with specific suggestions for the user/teacher to guide a possible adaption.
The mentioned possibility of adapting and reshaping the materials is valid for different aspects of the exemplary material, e.g.:
Our educational activities aim at numeracy skills being not only memorized, but first of all being practiced and functionally used by the learners in daily life or/and vocational situations. It is therefore recommended to implement the idea of HITS (higher impacts of teaching skills) as far and often as possible. In this context, it is helpful to consider the following key elements when teaching numeracy:
learn more on HITS…
The HITS (High Impact Teaching Strategies) serve as a starting point for the teaching approaches presented in the examples. These are ten teaching practices which enrich and improve the learning of numeracy, mathematical ideas, concepts and contexts.
[Insights - V]
NUMERACYis context based
NUMERACYhas a useful content
HOW TO TEACH NUMERACY?
NUMERACYneeds time foractivation and discussion
NUMERACY is interactiveand dialogical
This material was produced in the Erasmusplus project Numeracy in Practice, projectnumber 2021-1-NL01-KA220-ADU-000 026 292. In this project, 11 partners in 11 countries worked together in designing, evaluating and improving the materials. All materials can be found on the website (www.cenf.eu)
This work is licensed under CC BY-SA 4.0. To view a copy of this license, visit https://creativecommons.org/licenses/by-sa/4.0/
NUMERACYis context based
It is a fact that adults need to manage situations and solve problems that deal with numbers. A development of numeracy competences with adult learners needs authentic lived-in situations of the learners – as this helps learners to understand the usefulness of numbers for their very personal and individual needs. This also means that some of the provided materials might not be applicable for some countries, cultures or target groups
NUMERACYhas a USEFUL CONTENT
Successful educational numeracy activities for adults can’t be found in schoolbooks for kids or in abstract worksheets, but must meet the adults’ realities, needs and challenges. Our teaching and learning activities must therefore be connected to learners’ individual realities, follow a holistic approach (literacy, numeracy and digital skills), aim for an improved numerate behaviour and must therefore be learner-centric.
NUMERACYis INTERACTIVE and DIALOGICAL
An interactive and dialogical learning setting enables adults to activate their prior knowledge and skills and helps them to find ways to solve a mathematical problem and therefore manage a situation.Within a (mathematical) discussion, adult learners are invited to locate the situation as a mathematical one. They need to identify the mathematics in it and furthermore, analyse, structure and interpret the information to find possible procedures to solve the problem.
NUMERACYis functional
Numeracy involves the practical application of mathematical skills in everyday life. It must enable individuals to make informed decisions, solve real-world problems, and perform essential tasks. Thus, we must teach skills for practical use. If they are only learned and practiced, but not applied in real situations, they will fade quickly, and math anxiety will increase. Learning and practice must be followed by a functional use with concrete material in authentic situations such as daily life, vocational situations, or social media.
NUMERACY for adults must address adults
Successful educational numeracy activities for adults can’t be found in schoolbooks for kids or in abstract worksheets, but must meet the adults’ realities, needs and challenges. Our teaching and learning activities must therefore be connected to learners’ realities, follow a holistic approach (literacy, numeracy and digital skills), aim for an improved numerate behaviour and must therefore be learner-centric.
NUMERACY to involve adult learners
Adults often struggle with numeracy due to math anxiety, bad experiences during their school careers and a lack of practical application in their daily lives. We must accompany adults within their numeric worlds by enabling numeracy conversations, counteracting math anxiety, exploring the quantitative world around, working on awareness of successful numeracy behaviour, discussing numeracy themes like health or finances and by supporting a critical and sensible use of tools.
NUMERACYneeds time for activation and discussion
It is crucial that learners are given enough room and time for identifying (numeracy) problems in a authentic situation as well as for problem solving procedures. Having time for being an active part in the learning process helps adults to develop key competences they need to succeed in our modern society, just as critical thinking, communication, collaboration, creativity and flexibility.
NUMERACY to encourage adult learners
One important fact to remember is that individual with developing numeracy skills often underestimate and undermine their existing skills and abilities. Therefore, teaching and learning activities should also aim to help learners recognize their skills and become aware of successful numeracy decisions they already make in their everyday lives, in a private and professional context.