Unit 1 MFM32EF PDF

MFM32E Unit 1 Patterns, Functions and algebra. Content focus and assessment.  Learning Outcomes After completing this unit you should be able to:  Recognise the role of patterns in learning  Develop a broad understanding of the structure of mathematics and...

MFM32E Unit 1 Patterns, Functions and algebra. Content focus and assessment.  Learning Outcomes After completing this unit you should be able to:  Recognise the role of patterns in learning  Develop a broad understanding of the structure of mathematics and the impact this has on early mathematics learning and teaching  Recognise the pedagogical practices that support the exploration of patterns and structure in classroom learning  Understand the general and content focus of patterns, algebra, and mathematics  Understand why patterns and structure are important 2  Content Unit 1 Resources Teaching Mathematics: Foundation to Intermediate Phase. Siemon et al. 2012 Chapter 14 pages 226-241 Numeracy Handbook for Foundation Phase Teachers Grade R-3. Department of Basic Education RSA pages. 99- 111 CAPS English Mathematics Foundation Phase Grade 1-3 pages 9 - 10 3  Patterns Function and Algebra CAPS p. 9-10 General content focus  Algebra – the language for investigating and communicating of Mathematics  Can be extended to study of functions and other relationships between variables  Central part of this content area – learner achieve efficient manipulative skills in use of algebra  Also focuses on:  description of patterns and relationships using symbolic expressions, graphs and tables 4  Identification and analysis of regularities and change in patterns and  Foundation Phase Specific Content Focus CAPS p. 9-10 Learners work with both:  Number patterns ( e.g. skip counting ) and  Geometric patterns (e.g. pictures) Learners will use physical objects, drawings and symbolic forms to copy, extend, describe and create patterns Copying the pattern – help learners to see logic of how pattern is made Extending pattern – help learners to check that they have properly understood logic of the patterns Describing patterns – helps learners to develop language skills 5  Foundation Phase Specific Content Focus CAPS p. 9-10 Focusing on logic patterns – lays basis for developing algebraic thinking skills Number patterns support number concept development and operational sense built in Numbers, Operations and Relationships Geometric patterns include sequence of lines, shapes and objects – also patterns in the world. In geometric patterns learners apply their knowledge of space and shape 6  Foundation Phase overview CAPS English Mathematics Foundation Phase Grade 1-3. page 24 In Patterns, Functions and Algebra learners get the opportunities to:  complete and extend patterns represented in different forms  Identify and describe patterns Describing patterns lays the basis for learners in the Intermediate Phase to describe rules for patterns. This in turn becomes more formalized in algebraic work in the Senior Phase. 7 Foundation Phase overview CAPS English Mathematics Foundation Phase Grade 1-3. page 24 8  Patterns Numeracy Handbook for Foundation Phase Teachers Grade R-3. Department of Basic Education RSA pages. 99  A pattern – recurrence/repetition of events or objects. Pattern recognition enables us to predict:  The power of patterns lies in the predictions - allow us to make  What will happen under  Expectation of repletion enables us to plan certain circumstances the future  What must happen for a  Children have natural tendency to look for desired outcome to occur patterns Patterns in mathematics enable us to see structure:  In numbers  In mathematical operations  In geometric shapes and objects  Mathematics often defined as Pattern and structure science of patterns Teaching Mathematics: Foundation to Intermediate Phase. Mathematics teaching is about Siemon et al. 2012 Chapter 14 pages 226-233 searching for, describing, generalizing and justifying these Growing patterns – patterns patterns which each section Discovering pattern and structure – experiences consistent powerful way of thinking about growth. mathematics learning It is the visual link to Repeating patterns – patterns that number patterns occur in many classrooms – learners Lead to functional thinking are asked to copy, create and extend The challenge with repeating patterns. growing patterns – not to  May use a variety of materials – extend them – but to including materials such as leaves, predict down the line to buttons, paperclips, straws. find the missing term.  Lead to multiplicative thinking – 10 This approach commonly including proportional  Different kinds of patterns Numeracy Handbook for Foundation Phase Teachers Grade R-3. Department of Basic Education RSA pages. 99 The study of patterns lays the foundation for study of algebra. It is NB learners are exposed to range of different patterns form an early age - learn to look for patterns within patterns In classroom - early algebraic Early Algebraic thinking entails: thinking Teaching Mathematics: Foundation to Intermediate Phase. Siemon et al. 2012  Making explicit the mathematics Chapter 14 pages 234-235 of pattern (particularly repeating and growing patterns) – Functional thinking – focuses on extending these patterns to our number system relationship between two (or more) varying quantities  Studying early functional thinking – focus on the relationship  In early years – involve following between addition and rules for consistent changes and subtraction, commutative law for addition and the identities reversing this change.  Studying the structure of number  Functions involve consistent system and operations, - the change. 12 meaning of equal and meaningful  Each pattern leads to a generalization Patterns, Function and algebra Teaching Focus should be on encouraging learners Mathematics: Foundation to Intermediate Phase. to express their generalization verbally – Siemon et al. 2012 ensuring that the description is Chapter 14 pages 240 mathematically correct and justified Identifying patterns and structure in mathematics is the heart of learning Involves looking across a number of cases and teaching mathematics and identifying the common structure It not only changes the way we think It involves “awakening and sharpening about mathematics but also the way we “both learners’ and teachers' sensitivity to teach the structure of mathematics and to ways of exploiting situations that have the Our role as teachers – understand key potential of algebraic thinking to occur. ideas of mathematics – choose materials and pedagogical approaches The process of algebrafying and innovating that allow learners to explore patterns of the mathematics curriculum in all strands of mathematics, patterns that illuminate its structure 13 This approach – highly motivating –  Patterns and Conceptual knowledge conceptual  The recognition of patterns in and knowledge between situations Numeracy Handbook for Foundation Phase Teachers Grade R- 3. Department of Basic Education RSA.  The realization of the value of these Page 101 patterns in explaining and or predicting – developed through the reflection and recognition of patterns and the realization of the value of these patterns in explaining and/or predicting Patterns in Foundation Phase – support for development of strong sense of number and conceptual knowledge  Patterns in FP should be used to develop advanced counting schemes Numeracy Handbook for Foundation Phase Teachers Grade R-3. Department of Basic Education RSA. Page 101  Develop advanced counting schemes – skip counting and counting on  Reveal properties of numbers – completing tens, bridging tens, adding and subtracting multiples of ten  Reveal properties of operations – addition and subtraction are inverse operations - multiplication and division are inverse operations - addition and multiplication are commutative - addition and multiplication are associative - multiplication is distributive over addition  Identify common properties in shapes and objects as well as distinguishing between shapes and objects  Patterns in Foundation Phase Numeracy Handbook for Foundation Phase Teachers Grade R-3. Department of Basic Education RSA. Page 104  Children must be given the opportunity to make patterns using physical objects – help them develop – physical knowledge of patterns  It will help learners to reflect on what it takes to extend/ make the next element in the pattern – develop their logico-mathematical / conceptual knowledge of patterns  Patterns involving physical objects/drawings provide a natural transition introduction to patterns involving numbers  Through recognizing patterns learners will develop: Their pattern skills, Numeracy Handbook for Foundation Phase Teachers Grade R-3. Department of Basic Education RSA. Their numbers sense Page 106 Their conceptual knowledge From Grade R – Grade 3 patterns and patterning play a critical role in revealing structure in:  Numbers  Mathematical operations  Geometric shapes and objects  Data  Assessment CAPS English Mathematics Grades 1-3 Continuous planned process of identifying, gathering and interpreting information about performance of learners, using various forms of assessment It involves four steps (GERU): Generating and collecting evidence of achievement Evaluating this evidence Recording the findings Using this information to understand and thereby assist learner’s development in order to improve the process of learning and teaching Assessment should be informal and formal. In the Foundation Phase – main techniques of formal and informal assessment are (WOOP):  observation by the teacher,  Oral discussions  Practical demonstrations  Assessment CAPS English Mathematics Grades 1-3 Informal or daily assessment  Process of continuously collecting information on learner’s achievement  Daily monitoring of learners’ progress  Done through observations, discussions, practical demonstrations, informal classroom interactions.  Enables the teacher to monitor learner’s progress to make daily instructional decisions Informal assessment is used: To provide feedback to the learners To inform planning for teaching The teacher may:  Keep a checklist  Use observation schedule  Mark an exercise Informal daily assessment tasks are not taken into account for promotion and  Assessment CAPS English Mathematics Grades 1-3 Formal assessment  Make up a formal programme of assessment for the year  Marked and formally recorded by teacher for progression and certification purposes  Provides teacher with a systematic way of evaluating how well learners are progressing in a grade and in a subject  Formal assessment tasks will happen mainly in small group focused sessions  Will take a few days to assess the whole class  All materials and apparatus that learners normally use should be available as usual (counters, number charts, etc.)  Forms of assessment used should be age and developmental level appropriate  Must cater for a range of cognitive levels and abilities of learners  Design of tasks should cover the content of the subject in a variety of ways  Variety of forms of assessment should be used ( observation, oral, practical and written)  To give learners opportunity to demonstrate what he or she can do  Assessment tasks in Mathematics need to include activities and exercises that are not language based – not dependent on reading – to reflect real abilities of  Assessment CAPS English Mathematics Grades 1-3 Programme for formal assessment o Teachers are encouraged to conduct a baseline assessment in first term o Formal assessment tasks include more than one topic in Mathematics o Assessment tasks over the year need to cover all content areas and topics o Numbers, Operations and relationships make up 60% of Mathematics in Grade 1-3. 60% of formal assessment each term should be focused on numbers, operations and relationships Recording and Reporting  Recording – process in which teacher documents the level of a learner’s performance in specific assessment task  Indicates learner progress towards achievement of knowledge prescribed in the Curriculum  Records of learner performance should provide evidence of the learner’s conceptual progression with a grade  Reporting - process of communicating learner performance to learners, parents, schools, and other stakeholders.  Reporting include report cards, parents’ meetings, school visitation days, parent-teacher conferences, phone calls, letters, class or school newsletters, Assessment CAPS English Mathematics Grades 1-3 Exemplar Assessment Tasks for Grades 1 to 3 CAPS English Mathematics Grades 1-3 Exemplar Assessme nt Tasks for Grades 1 to 3 CAPS English Mathematics Grades 1-3 Exemplar Assessme nt Tasks for Grades 1 to 3 CAPS English Mathematics Grades 1-3 psges 490 - 510 Weighting per term – Mathematics Annexure A Foundation Phase Department of Education Western Cape