Junior Cycle Mathematics - Curriculum
Junior CycleMathematics
ContentsPage3Introduction to junior cyclePage4RationalePage5AimPage6Overview: LinksPage9Overview: CoursePage13Expectations for StudentsLearning outcomesUnifying strandNumber strandGeometry and trigonometry strandAlgebra and functions strandStatistics and probability strandPage21Assessment and ReportingAssessment for the Junior Cycle Profile of AchievementRationale for the Classroom-Based Assessments in mathematicsPage25Appendix APage27Appendix B
3Junior CycleMathematicsIntroduction tojunior cycleIntroduction tojunior cycleJunior cycle education places students at the centre of the educational experience, enabling themto actively participate in their communities and in society and to be resourceful and confidentlearners in all aspects and stages of their lives. Junior cycle is inclusive of all students andcontributes to equality of opportunity, participation and outcome for all.The junior cycle allows students to make a greater connection with learning by focusing on thequality of learning that takes place and by offering experiences that are engaging and enjoyablefor them, and relevant to their lives. These experiences are of a high quality, contribute directlyto the physical, mental and social wellbeing of learners, and where possible, provide opportunitiesfor them to develop their abilities and talents in the areas of creativity, innovation and enterprise.The learner’s junior cycle programme builds on their learning to date and actively supports theirprogress in learning and in addition, supports them in developing the learning skills that willassist them in meeting the challenges of life beyond school.
4Junior CycleMathematicsRationaleRationaleThis mathematics specification provides students with access to important mathematical ideasto develop the mathematical knowledge and skills that they will draw on in their personal andwork lives. This specification also provides students, as lifelong learners, with the basis on whichfurther study and research in mathematics and many other fields are built.Mathematical ideas have evolved across societies and cultures over thousands of years, and areconstantly developing. Digital technologies are facilitating this expansion of ideas and providenew tools for mathematical exploration and invention. While the usefulness of mathematics forproblem solving is well known, mathematics also has a fundamental role in both enabling andsustaining cultural, social, economic and technological advances and empowering individuals tobecome critical citizens.The specification is underpinned by the conception of mathematics as an interconnected body ofideas and reasoning processes that students negotiate collaboratively with teachers and their peersand as independent learners. Number, measurement and geometry, statistics and probability arecommon aspects of most people’s mathematical experiences in everyday personal, study and worksituations. Equally important are the essential roles that algebra, functions and relations, logic,mathematical structure and working mathematically play in people’s understanding of the naturaland social worlds, and the interaction between them.The mathematics specification builds on students’ prior learning and focuses on developingincreasingly sophisticated and refined mathematical understanding, fluency, reasoning,computational thinking and problem solving. These capabilities enable students to respond tofamiliar and unfamiliar situations by employing mathematics to make informed decisions andsolve problems efficiently.The specification supports student learning across the whole educational system by ensuringthat the links between the various components of mathematics, as well as the relationshipbetween mathematics and other subjects, are emphasised. Mathematics is composed of multiplebut interrelated and interdependent concepts and structures which students can apply beyondthe mathematics classroom. For example, in science, understanding sources of error and theirimpact on the confidence of conclusions is vital; in geography, interpretation of data underpinsthe study of human populations and their physical environments; in history, students need to beable to imagine timelines and time frames to reconcile related events; and in English, derivingquantitative, logical and spatial information is an important aspect of making meaning of texts.Thus the understanding of mathematics developed through study at junior cycle can inform andsupport students’ learning across the whole educational system.
5Junior CycleMathematicsAimAimThe aim of junior cycle mathematics is to provide relevant and challenging opportunities forall students to become mathematically proficient so that they can cope with the mathematicalchallenges of daily life and enable them to continue their study of mathematics in senior cycle andbeyond. In this specification, mathematical proficiency is conceptualised not as a one-dimensionaltrait but as having five interconnected and interwoven components: conceptual understanding—comprehension of mathematical concepts, operations, and relations procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, andappropriately strategic competence—ability to formulate, represent, and solve mathematical problems in bothfamiliar and unfamiliar contexts adaptive reasoning—capacity for logical thought, reflection, explanation, justification andcommunication productive disposition—habitual inclination to see mathematics as sensible, useful, andworthwhile, coupled with a belief in diligence, perseverance and one’s own efficacy.
6Junior CycleMathematicsOverview: LinksOverview: LinksMathematics supports a broad range of learning experiences at junior cycle. Table 1 shows howjunior cycle mathematics is linked to central features of learning and teaching in junior cycle.Table 1: Links between junior cycle mathematics and the statements of learningSTATEMENTS OF LEARNINGThe statementExamples of possible relevant learningSOL 1: The studentcommunicates effectively usinga variety of means in a range ofcontexts in L1.Students organise, consolidate and communicate numericaland mathematical thinking clearly and coherently to peers,teachers and others verbally, and in written form usingdiagrams, graphs, tables and mathematical symbols.SOL 14: The student makesStudents learn to develop their critical thinking and reasoninginformed financial decisions and skills by making value-for-money calculations and judgementsdevelops good consumer skills.which will enable them to make informed financial decisions.SOL 15: The student recognisesthe potential uses ofmathematical knowledge, skillsand understanding in all areasof learning.Students apply their mathematical knowledge and skillsto a wide variety of problems across different subjects,including gathering, analysing, and presenting data, and usingmathematics to model real-world situations.SOL 16: The student describes,illustrates, interprets, predictsand explains patterns andrelationships.Students develop techniques to explore and understandpatterns and relationships in both mathematical and nonmathematical contexts.SOL 17: The student devisesand evaluates strategies forinvestigating and solvingproblems using mathematicalknowledge, reasoning and skills.Students develop problem-solving strategies through engagingin tasks for which the solution is not immediately obvious.They reflect on their own solution strategies to such tasksand compare them to those of others as part of a collaborativelearning cycle.SOL 18: The student observesand evaluates empirical eventsand processes and draws validdeductions and conclusions.Students generate and summarise data, select appropriategraphical or numerical methods to describe it, and drawconclusions from graphical and numerical summaries of thedata. As part of their understanding of mathematical proofthey come to appreciate the distinction between contingentdeductions from particular cases, and deductions which can beproved to be universally true.SOL 24: The student usestechnology and digital mediatools to learn, communicate,work and think collaborativelyand creatively in a responsibleand ethical manner.Students engage with digital technology to analyse and displaydata numerically and graphically; to display and explorealgebraic functions and their graphs; to explore shapes andsolids; to investigate geometric results in a dynamic way; andto communicate and collaborate with others.
7Junior CycleMathematicsOverview: LinksKey SkillsIn addition to their specific content and knowledge, the subjects and short courses of junior cycleprovide students with opportunities to develop a range of key skills. There are opportunities tosupport all key skills in this course but some are particularly significant.The junior cycle curriculum focuses on eight key skills:Key Skills of Junior CycleFigure 1: Key skills of junior cycle Developing my understanding andenjoyment of words and language Reading for enjoyment and withcritical understanding Knowing myself Writing for different purposes Making considered decisions Expressing ideas clearly andaccurately Setting and achievingpersonal goals Developing my spoken language Being able to reflect on my own learning Exploring and creating a variety oftexts, including multi-modal texts Using digital technology to managemyself and my learning Using language Using numbers Listening and expressing myself Performing and presentingBEINGLITERATE Discussing and debating Using digital technologyto communicateCOMMUNICATINGMANAGINGMYSELF Being healthy andphysically active Being social Being safe Being spiritual Developing goodrelationships and dealingwith conflictWORKINGWITHOTHERS Co-operating Respecting differenceKEYSKILLS Being confident Being positive aboutlearningSTAYINGWELL Being responsible, safeand ethical in usingdigital technology Contributing to makingthe world a better place Learning with others Working with othersthrough digitaltechnologyBEINGCREATIVEMANAGINGINFORMATION& THINKINGBEINGNUMERATE Being curious Gathering, recording,organising and evaluatinginformation and data Thinking creatively and critically Reflecting on and evaluatingmy learning Imagining Exploring options and alternatives Implementing ideas and taking action Learning creatively Stimulating creativity using digitaltechnology Expressing ideas mathematically Using digital technologyto access, manage and sharecontent Estimating, predicting and calculating Developing a positive dispositiontowards investigating, reasoningand problem-solving Seeing patterns, trends and relationships Gathering, interpreting and representing data Using digital technology to developnumeracy skills and understandingwww.juniorcycle.ie12914 NCCA Jr Cycle Key Skills Poster v2.indd 110/06/2016 12:58
8Junior CycleMathematicsOverview: LinksKEY SKILL ELEMENTS RELATING TO MATHEMATICSThe examples below identify some of the elements that are related to learning activities inmathematics. Teachers can also build many of the other elements of key skills into their classroomplanning. The eight key skills are set out in detail in Key Skills of Junior Cycle.Table 2: Links between junior cycle mathematics and key skillsKey skillKey skill elementExamples of possible student learning activitiesBeing creativeExploring options andalternativesAs students engage in a task for which thesolution is not immediately obvious, they askquestions, explore ideas and alternatives, evaluateideas and actions and take more responsibility fortheir learning.Being literateExpressing ideas clearlyand accuratelyStudents explain their thinking and justify theirreasoning, using mathematical terminologyappropriately and accurately.Being numerateUsing digital technologyStudents use digital technology to analyse andto develop numeracy skills display data numerically and graphically; toand understandingdisplay and explore algebraic functions and theirgraphs; to explore shapes and solids; to investigategeometric results in a dynamic way; and tocommunicate and collaborate with others.CommunicatingUsing numbersThinking creatively andManaginginformation and criticallythinkingStudents use numbers to describe or summarisea situation; to support their reasoning andconclusions; and to convey and explain patternsand relationships.Students engage in rich tasks which require themto use their mathematical knowledge and skills innovel ways.They reflect on their own approaches to suchtasks and compare them to those of others,evaluating the strengths and weaknesses ofdifferent possible approaches.ManagingmyselfBeing able to reflect on my Students reflect on which learning activities theyown learningfind most effective, using this knowledge to helpfurther their learning in mathematics.Staying wellBeing confidentStudents enjoy frequent opportunities toexperience success in mathematics. Theyexperience a positive approach to learning inwhich different approaches are valued and theyare encouraged to learn from mistakes.Working withothersLearning with othersStudents work on collaborative tasks with peers inwhich they develop both their mathematical andtheir interpersonal skills, offering mutual supportand feedback throughout the process.
9Junior CycleMathematicsOverview: CourseOverview: CourseThe specification for junior cycle mathematics focuses on developing students’ ability to thinklogically, strategically, critically, and creatively through the Unifying strand and the fourcontextual strands: Number; Geometry and trigonometry; Algebra and functions; and Statisticsand probability.The specification has been designed for a minimum of 240 hours timetabled student engagementacross the three years of junior cycle. This is a minimum and schools should be aware that thereare students who would benefit from an engagement of more than 240 hours to realise thenational improvement targets set out in the Literacy and Numeracy strategy (DES,2011).Figure 2: The structure of the specification for junior cycle mathematicsUnifying StrandNumberGeometry &trigonometryAlgebra &functionsElement: Building blocksElement: RepresentationElement: ConnectionsElement: Problem solvingElement: Generalisation and proofElement: CommunicationStatistics &probability
10Junior CycleMathematicsOverview: CourseUnifying strandThis strand permeates all of the contextual strands and is composed of the six elements of thespecification, which are shown below.There is no specific content linked to this strand; rather, its learning outcomes underpin the restof the specification. Each learning outcome in this strand is applicable to all of the activities andcontent of the other four strands—for example, students should be able to draw on all of theirmathematical knowledge and skills to solve a problem or to communicate mathematics.Furthermore, the elements of this strand are interdependent, so that students should develop thedifferent skills associated with each element in tandem rather than in isolation – for example,engaging in problem-solving can help students improve their understanding of building blocksand their ability to make connections within mathematics.The elementsElementsBuilding blocksStudents should understand and recall the concepts that underpin eachstrand, and be able to carry out the resulting procedures accurately,effectively, and appropriately.RepresentationStudents should be able to represent a mathematical situation in a varietyof different ways and translate flexibly between them.ConnectionsStudents should be able to make connections within strands and betweenstrands, as well as connections between mathematics and the real world.Problem solvingStudents should be able to investigate patterns, formulate conjectures,and engage in tasks in which the solution is not immediately obvious, infamiliar and unfamiliar contexts.Generalisation andproofStudents should be able to move from specific instances to generalmathematical statements, and to present and evaluate mathematicalarguments and proofs.CommunicationStudents should be able to communicate mathematics effectively in verbaland written form.
11Junior CycleMathematicsOverview: CourseNumberThis strand focuses on different aspects of number, laying the groundwork for the transition fromarithmetic to algebra. Learners explore different representations of numbers and the connectionsbetween them, as well as the properties and relationships of binary operations. They investigatenumber patterns, and use ratio and proportionality to solve a variety of problems in numerouscontexts. Learners are expected to be able to use calculators appropriately and accurately, as wellas to carry out calculations by hand and mentally. They appreciate when it is appropriate to useestimation and approximation, including to check the reasonableness of results.Geometry and trigonometryThis strand focuses on analysing characteristics and properties of two- and three-dimensionalgeometric shapes. Learners use geometry and trigonometry to model and solve problems involvingarea, length, volume, and angle measure. They develop mathematical arguments about geometricrelationships and explore the concept of formal proof, using deduction to establish the validity ofcertain geometric conjectures and critiquing the arguments of others.Algebra and functionsThis strand focuses on representing and analysing patterns and relationships found in numbers.Building on their work in the Number strand, learners generalise their observations, expressing,interpreting, and justifying general mathematical statements in words and in symbolic notation.They use the idea of equality to form and interpret equations, and the syntactic rules of algebrato transform expressions and solve equations. Learners explore and analyse the relationshipsbetween tables, diagrams, graphs, words, and algebraic expressions as representations offunctions.Statistics and probabilityThis strand focuses on determining probability from random events and generating andinvestigating data. Students explore the relationship between experimental and theoreticalprobability as well as completing a data investigation; from formulating a question and designingthe investigation through to interpreting their results in context and communicating theirfindings. Learners use graphical and numerical tools, including summary statistics and theconcepts and processes of probability, to explore and analyse patterns in data. Through theseactivities, learners gain an understanding of data anaysis as a tool for learning about the world.
12Junior CycleMathematicsOverview: CourseProgression from early childhood to senior cycleEARLY CHILDHOODAistear, the early childhood curriculum framework, celebrates early childhood as a time ofwellbeing and enjoyment where children learn from experiences as they unfold. Children’sinterests and play should be the source of their first mathematical experiences. These experiencescan become mathematical as they are represented and explored. Young children representtheir ideas by talking, but also through models and graphics. From the motoric and singsong beginnings of rhymes and geometric patterns built from unit blocks stem the gradualgeneralisation and abstraction of patterns throughout the child’s day.PRIMARY SCHOOLThe mathematics curriculum at primary school aims to provide children with a language and asystem through which to analyse, describe, illustrate and explain a wide range of experiences,make predictions, and solve problems. Mathematics education seeks to enable learners to thinkand communicate quantitatively and spatially, solve problems, recognise situations wheremathematics can be applied, and use appropriate technology to support such applications. Thejunior cycle mathematics specification consolidates and develops students’ learning from primaryschool and as such experience of the
Table 1 shows how junior cycle mathematics is linked to central features of learning and teaching in junior cycle. Table 1: Links between junior cycle mathematics and the statements of learning STATEMENTS OF LEARNING The statement Examples of possible relevant learning SOL 1: The student c
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Junior Cycle Wood Technology Overview: Links 6 Overview: Links Wood Technology supports a broad range of learning objectives at junior cycle. Tables 1 and 2 on the following pages show how junior cycle
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