Mathematical literacy Definition and building blocks The investment is co-financed by the Republic of Slovenia and the European Union under the European Social Fund. Mathematical literacy | Definition and building blocks DEFINITION OF MATHEMATICAL LITERACY BUILDING BLOCKS OF MATHEMATICAL Mathematical literacy is a person's ability to employ mathematical thinking and mathematical LITERACY knowledge in order to: 1st BUILDING BLOCK • Use mathematical concepts, procedures and tools in differently structured environments; • Analyse, substantiate and effectively communicate his/her ideas and results when Mathematical thinking, understanding and use of mathematical concepts, formulating, solving and interpreting mathematical problems in differently structured procedures and strategies; communication as the basis of mathematical environments; literacy • Perceive and be aware of the role of mathematics in everyday and professional life; connect it with other areas and make responsible decisions based on mathematical knowledge; be 1.1. Understands messages with mathematical contents. willing to accept and co-create new mathematical findings 1.2. Knows and uses technical terminology and symbolism. 1.3. Presents, substantiates and evaluates his/her own thought processes. List of abbrevations 1.4. Recognizes, understands and uses mathematical concepts under different circumstances. MP – mathematical literacy NA-MA POTI – Scientific and Mathematical Literacy: 1.5. Knows and uses appropriate procedures and tools under different circumstances. The Development of Critical Thinking and Problem-solving 1.6. Predicts and assesses results, substantiates claims, procedures and decisions. 1.7. Uses different strategies when solving mathematical problems. 2nd BUILDING BLOCK Problem solving in diverse contexts (personal, social, professional, scientific) that allow a mathematical treatment 2.1. Discusses diverse real life problems (problems that do not require mathematical modelling). 2.2. Discusses situations using mathematical modelling: 2.2.1. Transfers a situation to the mathematical context; 2.2.2. Designs mathematical models for the given situation; 2.2.3. Uses mathematical models; 2.2.4. Evaluates mathematical models. 2.3. Understands mathematical practices in different contexts. | 2 Mathematical literacy | Definition and building blocks 1st BUILDING BLOCK: Mathematical thinking, understanding and use of mathematical concepts, procedures and strategies; communication as the basis of mathematical literacy 1.1. Understands messages1 with mathematical contents BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) (Receives) Understands simple a) (Receives) Understands simple a) (Receives) Understands simple a) (Receives) Understands simple, a) (Receives) Understands simple, oral, graphic messages with and structured messages with and structured messages with structured and complex structured and complex mathematical contents; mathematical contents; mathematical contents; messages with mathematical messages with mathematical b) Sums up a message with b) Uses simple reading strategies b) Uses simple and complex contents; contents; mathematical contents and during comprehensive reading reading strategies during b) Uses appropriate reading b) Uses appropriate answers questions; of mathematical texts and when comprehensive reading of strategies during comprehensive reading strategies during c) Independently obtains solving word problems; mathematical texts and when reading of mathematical comprehensive reading of information from oral sources. c) Sums up a message with solving word problems; texts and when solving word mathematical texts and when mathematical contents, extracts c) Sums up messages with problems; solving word problems; the essence and the required mathematical contents, extracts c) Sums up messages with c) Sums up messages with information; the essence and the required mathematical contents, extracts mathematical contents, extracts d) Independently obtains information, and creates a new the essence and the required the essence and the required information from oral and message; information, and creates a new information, and creates a new written sources. d) Independently obtains message; message; information from oral and d) Independently obtains d) Independently obtains written sources. information from credible information from credible sources. sources. 1 Message: people communicate with one another by conveying messages using various symbols (e.g. spoken language, gestures, body language, images, audio and light signals, written texts, etc.). In the communication process all the participants receive, send/create and interpret messages which are connected for a specific purpose; communication is always a two-way process as it involves the simultaneous detection and exchange of messages on both sides. | 3 Mathematical literacy | Definition and building blocks 1st BUILDING BLOCK: Mathematical thinking, understanding and use of mathematical concepts, procedures and strategies; communication as the basis of mathematical literacy 1.2. Knows and uses professional terminology and symbolism BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) Recognizes professional a) Recognizes professional a) Recognizes professional a) Recognizes professional a) Recognizes professional terminology in a message and terminology and symbolism in a terminology and symbolism in a terminology and symbolism in a terminology and symbolism in a understands its meaning; message and understands their message and understands their message and understands their message and understands their b) During activities and concrete meaning; meaning; meaning; meaning; presentations of mathematical b) Names and describes b) Writes a verbalized (simple) b) Writes a verbalized b) Writes a verbalized concepts, the learner names mathematical concepts using mathematical message using mathematical message using mathematical message using and describes concrete or mathematical terminology and mathematical symbols and mathematical symbols and mathematical symbols and graphic representations symbolism; vice versa (reads/verbalizes a vice versa (reads/verbalizes a vice versa (reads/verbalizes a (shapes, solids, numbers, c) Uses mathematical language2 text containing mathematical text containing mathematical text containing mathematical quantities, relations, colours, to describe a mathematical symbolism); symbolism); symbolism); position). situation. c) Uses appropriate terminology c) Uses appropriate terminology c) Uses appropriate terminology and symbolism to describe and symbolism to describe and symbolism to describe mathematical objects and mathematical objects and mathematical objects and structures, and their properties; structures, and their properties; structures, and their properties; d) Uses mathematical language to d) Formulates definitions in simple d) Formulates definitions in describe a situation; mathematical situations and mathematical situations, knows e) Understands the different uses them; their purpose, and uses them; meanings of individual e) Sensibly uses mathematical e) Sensibly uses mathematical mathematical terms and language in other contexts as language in other contexts as symbols. well; well; f) Understands the different f) Understands the different meanings of individual meanings of individual mathematical terms and mathematical terms and symbols, and uses them flexibly. symbols, and uses them flexibly. 2 Mathematical language: we use it to name or put into words mathematical concepts, objects, structures, etc. using technical (mathematical) terminology and symbols. | 4 Mathematical literacy | Definition and building blocks 1st BUILDING BLOCK: Mathematical thinking, understanding and use of mathematical concepts, procedures and strategies; communication as the basis of mathematical literacy 1.3. Presents, substantiates and evaluates his/her own thought processes3 BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) Orally presents the process of a) Appropriately presents the a) Appropriately presents and a) Appropriately presents, explains a) Appropriately presents, solving tasks, and talks about process of solving tasks and explains the process of solving and sums up the process of explains, substantiates and his/her findings and thought problems, and talks about tasks and problems, and solving tasks and problems, and sums up the process of solving process; his/her findings and thought mathematical thinking; mathematical thinking; tasks and problems, and b) Gets involved in a conversation process; b) Participates in a mathematical b) Participates in a mathematical mathematical thinking; about mathematical situations; b) Participates in a mathematical discussion; discussion; b) Participates in a mathematical c) Assesses his/her own work discussion; c) Assesses his/her own work c) Assesses his/her own work discussion; according to the set guidelines. c) Assesses his/her own work according to the set criteria. according to the set criteria. c) Assesses his/her own work according to the set criteria4. according to the set criteria. 3 Thought process: it is triggered by situations and we are aware of it only to an extent; through practice or reflection we try to become aware of our own thoughts when solving tasks; our emotions also trigger thoughts and are reflected through our behaviour, affecting our perseverance, our view of a task as a challenge, etc. 4 Criterion: is a “measure of success” that helps us to assess and be aware of our own knowledge and the fulfilment of learning intentions; we use it to define the important aspects of knowledge, understanding, abilities, skills. | 5 Mathematical literacy | Definition and building blocks 1st BUILDING BLOCK: Mathematical thinking, understanding and use of mathematical concepts, procedures and strategies; communication as the basis of mathematical literacy 1.4. Recognizes, understands and uses mathematical concepts5 under different circumstances BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) Recognizes a concrete object, a) Recognizes the mathematical a) Recognizes the mathematical a) Recognizes the mathematical a) Recognizes the mathematical an image of an object for concepts represented6 in concepts represented in concepts represented in concepts represented in presenting a mathematical different ways (concretely, different ways (concretely, different ways (concretely, different ways (concretely, concept; graphically, symbolically) in graphically, symbolically) also in graphically, symbolically) in graphically, symbolically) in b) Recognizes the mathematical known situations; less known situations; different situations; different situations; concepts represented in b) Uses different representations b) Uses sensible representations b) Uses sensible representations b) Uses sensible representations different ways (verbally, of mathematical concepts and of mathematical concepts and of mathematical concepts and of mathematical concepts and concretely, graphically) in switches between them; switches between them; switches between them; switches between them; known situations; c) Finds common properties and c) Uses examples to confirm c) Uses examples to confirm c) Uses examples or counter c) Illustrates a mathematical differences between individual or reject claims about the or reject claims about the examples to confirm or reject concept with a chosen representations of a chosen properties of mathematical properties of mathematical claims about the properties of representation; mathematical concept; concepts; concepts; mathematical concepts; d) Finds common properties and d) Can visualize sizes7 and d) Can visualize sizes and d) Can visualize sizes and d) Can visualize sizes and differences between concrete quantities. quantities; quantities; quantities; and graphical representations of e) Differentiates between e) Differentiates between e) Differentiates between a mathematical concept. mathematical concepts based mathematical concepts based mathematical concepts based on their properties and the on their properties, and on their properties, and relations between them; recognizes similar concepts and recognizes similar concepts and f) Interprets different (similar) the relations between them; the relations between them; situations using mathematical f) Interprets different situations f) Interprets different situations concepts. (including new ones) using (including new ones) using mathematical concepts. mathematical concepts. 5 Mathematical concept: a mental representation of a mathematical object (e.g. number, set, function, geometric solid and shape, plain, straight line, etc.), which reflects the main properties and relations. 6 Representation: presentation of a mathematical concept e.g. using concrete aids, graphic material, symbols, tables, computer simulations, etc. 7 Size: the result of measurement, which is expressed with a number and unit of measurement (e.g. | AB| = 7.5 cm; p = 54 cm2, etc.) | 6 Mathematical literacy | Definition and building blocks 1st BUILDING BLOCK: Mathematical thinking, understanding and use of mathematical concepts, procedures and strategies; communication as the basis of mathematical literacy 1.5. Knows and uses appropriate procedures8 and tools9 under different circumstances BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) Uses successful procedures a) Learns about and researches10 a) Knows and uses different a) Knows and uses different a) Knows and uses different during play and when solving various mathematical situations mathematical procedures when mathematical procedures when mathematical procedures when simple mathematical tasks; by: observing, one-to-one- researching mathematical researching unknown situations researching unknown situations b) Learns about and researches corresponding, comparing, situations and solving tasks; and solving tasks; and solving tasks; various mathematical situations sorting and organizing elements. b) Chooses appropriate procedures b) Chooses appropriate procedures b) Chooses appropriate by: observing, one-to-one- b) Solves mathematical tasks which lead to a solution; which lead to a solution; procedures which lead to a corresponding, comparing, and problems by counting, c) Uses his/her own procedures c) Uses his/her own procedures solution; sorting, organizing, counting measuring, collecting and when solving; when solving; c) Uses new (his/her own) elements, etc. presenting data; by drawing; d) Checks if the results of the d) Checks if the results of the procedures when solving; by properly expressing sizes implemented procedures are implemented procedures are d) Checks if the results of the and quantities; by carrying out correct; correct; implemented procedures are arithmetic procedures, taking correct; into account the properties of e) Chooses and uses appropriate e) Chooses and uses appropriate arithmetic operations; tools for solving, expressing and tools for solving, expressing and e) When carrying out various communicating. communicating. activities, the learner effectively c) Uses his/her own procedures uses different tools or aids when solving; and takes their limitations into d) Checks if the results of the account. implemented procedures are correct; e) Uses various aids and instruments. 8 Procedure: a form of systematic and prudent work, action or thinking to achieve a goal (e.g. an arithmetic procedure or algorithm; cognitive procedures: observing, comparing, organizing, sorting, etc.; mathematical procedures: counting, measuring, presenting data, solving equations, etc.). 9 Tool: a geometric tool, measuring aids and instruments, computer programs, etc. 10 Research: in this context it is meant as creative work or activity with which we wish to broaden and improve our knowledge. We use it to establish or confirm facts; to determine and test the results of past work; to solve new or existing problems; to develop new theories, etc. | 7 Mathematical literacy | Definition and building blocks 1st BUILDING BLOCK: Mathematical thinking, understanding and use of mathematical concepts, procedures and strategies; communication as the basis of mathematical literacy 1.6. Predicts and assesses results, substantiates claims, procedures and decisions BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) Assesses which data are a) Assesses which data are a) Assesses which data are a) Assesses which data are a) Assesses which data are necessary; necessary and sufficient in a necessary and sufficient in a necessary and sufficient in a necessary and sufficient in a b) Predicts what will happen based mathematical situation or task; mathematical situation or task; mathematical situation or task; mathematical situation or task; on his/her own experience; b) Predicts solutions based on his/ b) Predicts solutions based on his/ b) Predicts solutions based on his/ b) Predicts solutions based on his/ c) Checks whether the solutions her own experience; her mathematical knowledge her mathematical knowledge her mathematical knowledge are correct, recognizes wrong c) Assesses the suitability of and experience; and experience and the data and experience and the data solutions, and corrects them. implemented procedures when c) Assesses the suitability of obtained; obtained; solving tasks; the chosen and implemented c) Assesses the suitability of the c) Assesses the suitability of the d) Checks whether the solutions procedures when solving tasks; choice and implementations choice and implementations are correct, recognizes wrong d) Evaluates the solutions procedures when solving tasks; procedures when solving tasks; solutions, and corrects them. obtained, suggesting corrections d) Evaluates the solutions d) Evaluates the solutions obtained and improvements; obtained, assesses their and assesses whether they are e) Finds an example for his/her suitability, and suggests correct, sensible or suitable; claim. corrections and improvements; corrects inappropriate solutions e) Formulates his/her own and suggests improvements; mathematical claims, tests and e) Formulates mathematical claims substantiates them. and hypotheses, and tests them (proves or refutes them); f) Substantiates mathematical claims at an appropriate level of strictness. | 8 Mathematical literacy | Definition and building blocks 1st BUILDING BLOCK: Mathematical thinking, understanding and use of mathematical concepts, procedures and strategies; communication as the basis of mathematical literacy 1.7. Uses different strategies when solving mathematical problems11 BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) Uses known strategies to a) Uses known strategies a) Uses known strategies a) Uses different strategies (e.g. a) Uses sensible strategies (e.g. solve challenges (e.g. trial and (appropriate for the (appropriate for the trial and error, systematic trial and error, backward error, finding the odd one out, development stage) to solve development stage) to solve testing, special cases) to solve thinking, systematic testing, classification – appropriate for (routine) mathematical mathematical problems; mathematical problems; special cases, analogy) to solve the development stage); problems; b) Uses procedural knowledge b) Uses procedural knowledge mathematical problems; b) Uses procedural knowledge b) Uses procedural knowledge to solve diverse mathematical when solving diverse b) Uses procedural knowledge to solve challenges, finding to solve diverse (routine) problems (closed, open, with mathematical problems (closed, (e.g. inductive reasoning, different paths to the solutions mathematical problems (closed, too much data, insufficient data, open, with too much data, generalization, deductive and multiple solutions to the open, with too much data, inconsistent data, with multiple insufficient data, inconsistent reasoning) when solving diverse problem; insufficient data, inconsistent solutions, without solutions, data, with multiple solutions, mathematical problems (closed, c) Forms various questions based data, with multiple solutions, with an absurd solution); without solutions, with open, with too much data, on the given challenges; without solutions, with an c) Forms different questions and an absurd solution), when insufficient data, inconsistent d) Experiences solving challenges absurd solution); similar problems based on the investigating12 and discovering13; data, with multiple solutions, as a creative activity. c) Forms different questions and given mathematical situations c) Forms different questions and without solutions, with similar tasks based on the given or problems; similar problems based on the an absurd solution), when mathematical situations; d) Assesses the suitability of the given mathematical situations investigating and discovering; d) Assesses the suitability of the chosen strategies when solving or problems; c) Forms different questions and implemented strategies when problems; d) Assesses the suitability of the new problems based on the solving problems; e) Experiences solving chosen strategies when solving given mathematical situations e) Experiences solving mathematical problems as problems; or problems; mathematical problems as a challenge and a creative e) Experiences solving d) Assesses the suitability of the a challenge and a creative activity. mathematical problems as chosen strategies when solving activity. a challenge and a creative problems; activity. e) Experiences solving mathematical problems as a challenge and a creative activity. 11 Problem: is an initiative or challenge (task, situation, question) that requires an original solution, but the path to the solution is not given/known to the learner and he/she must look for it using his/her own thought processes. 12 Investigation: a primary and secondary school discussion of problem situations with unclear goals (we investigate tasks or challenges that do not specify what exactly we have to determine and how we can reach the solutions). 13 (Learning by) discovery: it is a more or less independent approach to solving and researching a problem, where the teacher maintains the learners’ interest in solving it, provides them with appropriate support, and guides them. | 9 Mathematical literacy | Definition and building blocks 2nd building block of mathematical literacy: Problem solving in diverse contexts (personal, social, professional, scientific) that allow a mathematical treatment 2.1. Discusses diverse real life problems14 (problems that do not require mathematical modelling) BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) Detects and defines a a) Detects and defines a a) Recognizes a mathematical a) Recognizes a mathematical a) Recognizes a mathematical mathematical problem in a life mathematical problem in a life problem in a life situation and problem in a life situation and problem in a life situation and situation; situation; expresses it using mathematical expresses it using mathematical expresses it using mathematical b) Illustrates the situation using b) Illustrates the situation using language; language; language; concrete material and describes concrete material and describes b) Designs his/her own problem- b) Designs his/her own problem- b) Designs his/her own problem- it using everyday language; it using mathematical language; solving plan and presents it; solving plan and presents it; solving plan and presents it; c) Participates in designing a c) Guided by the teacher, the c) Designs and uses a sensible c) Designs and uses sensible c) Designs and uses sensible problem-solving plan; learner designs his/her own mathematical strategy to solve mathematical strategies to solve mathematical strategies to solve d) Designs and uses an appropriate problem-solving plan and the problem and solves the the problem and solves the the problem and solves the mathematical strategy to solve presents it; problem; problem; problem; the problem; d) Designs and uses an appropriate d) Presents, interprets and d) Presents, interprets and d) Presents, interprets and e) Describes (partial and final) mathematical strategy to solve evaluates the (partial and final) evaluates the (partial and final) evaluates the (partial and final) solutions in context. the problem and solves the solutions in context. solutions in context. solutions in context. problem; e) Presents and thinks about how sensible the (partial and final) solutions are in context. 14 Life problem: is a challenge (task, question, situation) that requires an original solution and a different way of solving it using one’s thought processes. The context of a life problem stems from life or the everyday (e.g. a part of a newspaper article, the results of a study or a scientific paper, a news item, advertisement, etc.) and the data have not been didactically adapted to the learners’ prior knowledge or development stage). | 10 Mathematical literacy | Definition and building blocks 2nd building block of mathematical literacy: Problem solving in diverse contexts (personal, social, professional, scientific) that allow a mathematical treatment 2.2. Discusses situations using mathematical modelling15 2.2.1. Transfers a situation to the mathematical context BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) Participates in describing a a) Participates in describing a a) Recognizes that he/she will be a) Recognizes that he/she will be (personal) life problem in the (personal, social) life problem in able to mathematically model able to mathematically model mathematical language; the mathematical language; the given situation; the given situation; b) Participates in presenting the b) Presents the situation using b) Describes a (personal, social, b) Describes a (personal, social, situation using mathematical mathematical means and forms technical) problem in the technical, scientific) problem in means and in forming the the problem question. mathematical language; the mathematical language; problem question. c) Recognizes the quantities, c) Recognizes the quantities, mathematical concepts and mathematical concepts and relationships in the situation relationships in the situation being discussed, and decides on being discussed, and decides on their relevance; their relevance; d) Simplifies the situation to d) Simplifies the situation to enable a mathematical enable a mathematical treatment; treatment; e) Presents the situation using e) Presents the situation mathematical means and mathematically (with concepts forms problem questions in a represented in different ways; mathematical context. with procedures, figures, etc.) and forms problem questions in a mathematical context. 15 Mathematical modelling: is a form of solving a life problem through research, which involves an in-depth understanding of the context and the derivation of hypotheses which are important for finding a solution and which lead to generalized conceptual solutions or a model. The problem contains a great deal of data, which are often incomplete and must be organized; we must also decide which of them we will apply. | 11 Mathematical literacy | Definition and building blocks 2nd building block of mathematical literacy: Problem solving in diverse contexts (personal, social, professional, scientific) that allow a mathematical treatment 2.2. Discusses situations using mathematical modelling15 2.2.2. Designs mathematical models16 for the given situation BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) Participates in designing a a) When designing the model, the a) When designing the model, the model, defining the variables, learner defines the variables, learner defines the variables, and formulating the hypotheses; formulates the hypotheses, and formulates the hypotheses, and b) Participates in making the states the model's limitations; states the model's limitations; model by using appropriate b) Chooses a suitable type of b) Decides on the type of mathematical and technological model (empirical, simulation, model (empirical, simulation, tools. theoretical, algorithmic, etc.) theoretical, algorithmic, etc.) according to the given situation; and chooses a suitable one; c) Recognizes and writes down c) Recognizes and writes down the relationships between the the relationships between the selected variables or suggests a selected variables or suggests a mathematical structure for the mathematical structure for the given situation (e.g. a function given situation (e.g. a function rule, graph, linear equation, rule, graph, linear equation, system of linear equations, system of linear equations, diagram, table, geometric diagram, table, geometric object, image, description or the object, conic section, image, like); description or the like); d) Uses appropriate mathematical d) Uses appropriate mathematical and technological tools to make and technological tools to make the model. the model. 16 Mathematical model: is a special way of mathematically presenting the discussed non-mathematical object or phenomenon using mathematical language (e.g. we use direct proportion as a model when shopping; a geometric sphere as a model when discussing a ball). A mathematical model is not the illustration of mathematical concepts with other concepts (e.g. illustrating a line segment with a thin stick). | 12 Mathematical literacy | Definition and building blocks 2nd building block of mathematical literacy: Problem solving in diverse contexts (personal, social, professional, scientific) that allow a mathematical treatment 2.2. Discusses situations using mathematical modelling15 2.2.3. Uses mathematical models BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) Participates in describing the a) Describes the given model and a) Describes the given models a) Describes the given models given model; presents it; and his/her own models and his/her own models b) Follows the problem-solving b) Uses the given models; using different mathematical using different mathematical procedure according to the c) Takes into account the representations; representations; given model and carries out characteristics of the context b) Uses the given models and his/ b) Uses the given models and his/ individual steps; (appropriate units, accuracy, her own models; her own models; c) Describes mathematical rounding); c) Explains the model17 (discerns c) Explains the model (discerns solutions in context. d) Interprets the mathematical the variables, the functional the variables, the functional solutions (calculations obtained relations, the result from the relations, the result from the with the model) in context. given model) and takes into given model) and takes into account the characteristics of account the characteristics of the context (appropriate units, the context (appropriate units, accuracy, rounding); accuracy, rounding); d) Makes use of technological d) Makes use of technological tools (calculator, computer tools (measuring aids, tables, various programs, web calculation and graphical applications) when using the representation aids, etc.) when model; using the model; e) Knows and uses model e) Knows and uses model simulation techniques (e.g. simulation techniques (e.g. computer tables, programming, computer tables, programming, programs for working with programs for working with functions, dynamic geometry functions, dynamic geometry programs); programs); f) Interprets the mathematical f) Interprets the mathematical solutions (calculations obtained solutions (calculations obtained with the model) in context. with the model) in context. | 13 Mathematical literacy | Definition and building blocks 2nd building block of mathematical literacy: Problem solving in diverse contexts (personal, social, professional, scientific) that allow a mathematical treatment 2.2. Discusses situations using mathematical modelling15 2.2.4. Evaluates mathematical models BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) Describes the suitability of a) Discusses the suitability a) Discusses the suitability the model under different (reasonableness, correctness, (reasonableness, correctness, circumstances; accuracy) of the model under accuracy) of the model under b) Tests the model's usability different circumstances (e.g. different circumstances (e.g. based on new data and discussion of boundaries, discussion of boundaries, circumstances. discussion of hypotheses, discussion of hypotheses, neglected quantities); neglected quantities); b) Tests the model's usability b) Tests the model's usability based on new data, examples based on new data, examples and situations; and situations; c) Makes a more suitable model c) Makes a more suitable model after determining the flaws of after determining the flaws of the given model; the given model; d) Compares different models d) Compares different models (e.g. according to accuracy, (e.g. according to accuracy, scope of application, ease of scope of application, ease of use). use). | 14 Mathematical literacy | Definition and building blocks 2nd building block of mathematical literacy: Problem solving in diverse contexts (personal, social, professional, scientific) that allow a mathematical treatment 2.3. Understands mathematical practices17 in different contexts BASIC EDUCATION PRE-SCHOOL EDUCATION UPPER SECONDARY SCHOOL ages 1-6 FIRST EDUCATIONAL CYCLE SECOND EDUCATIONAL CYCLE THIRD EDUCATIONAL CYCLE ages 15-19 ages 6-9 ages 9-12 ages 12-15 a) Recognizes non-formal a) Recognizes non-formal a) Recognizes non-formal mathematical practices mathematical practices mathematical practices and describes them using and describes them using and describes them using mathematical language. mathematical language. mathematical language; b) Interprets mathematical practices within the context of the mathematical model; c) Recognizes and understands the importance of “non- mathematical factors” in mathematical practices (e.g. the importance of tools, tradition, a user's mathematical knowledge, the broader context of activities). 17 Mathematical practices: use of mathematics in professional situations/work processes, where we use different procedures than in school mathematics (e.g. joiner, tiler, salesperson, etc.). | 15 Collection NA-MA POTI ISSN 2820-4182 Collection editor: Jerneja Bone Mathematical literacy Definition and building blocks Original title: Matematična pismenost; Opredelitev in gradniki Authors: mag. Mateja Sirnik, Vesna Vršič, dr. Zlatan Magajna, dr. Tatjana Hodnik, dr. Nik Stopar, mag. Simona Pustavrh, Simona Vreš, Ana Kretič Mamič, Viktorija Ternar, Kristina Angelov Troha, Veronika Zadel, dr. Alenka Lipovec, dr. Amalija Žakelj, Eva Klemenčič, Fanika Fras Berro, Tina Klun, Marjanca Komar, Petra Krmelj, Anja Klavs Translation: Ensitra prevajanje, Brigita Vogrinec Škraba, s. p. Design: Simon Kajtna Layout: ABO grafika, d. o. o., Igor Kogelnik Published by: Zavod RS za šolstvo Representative: dr. Vinko Logaj On-line edition Ljubljana, 2022 Available: https://www.zrss.si/pdf/Matematicna_pismenost_gradniki_ANG.pdf The investment is co-financed by the Republic of Slovenia and the European Union under the European Social Fund. Publication was created in a project NA-MA POTI, 2016–2022, project leader: Jerneja Bone. Kataložni zapis o publikaciji (CIP) pripravili v Narodni in univerzitetni knjižnici v Ljubljani COBISS.SI-ID 121293571 ISBN 978-961-03-0722-8 (PDF) | 16 | 17